Dissertations / Theses on the topic 'High-Order finite element methods'
To see the other types of publications on this topic, follow the link: High-Order finite element methods.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'High-Order finite element methods.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Marais, Neilen. "Efficient high-order time domain finite element methods in electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1499.
Abstract:
Thesis (DEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009.The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact that it is both explicit (i.e. no matrices need to be solved) and second order accurate in both time and space. The FDTD has limitations when dealing with certain geometrical shapes and when electrically large structures are analysed. The former limitation is caused by stair-casing in the geometrical modelling, the latter by accumulated dispersion error throughout the mesh. The FEM can be seen as a general mathematical framework describing families of concrete numerical method implementations; in fact the FDTD can be described as a particular FETD (Finite Element Time Domain) method. To date the most commonly described FETD CEM methods make use of unstructured, conforming meshes and implicit time stepping schemes. Such meshes deal well with complex geometries while implicit time stepping is required for practical numerical stability. Compared to the FDTD, these methods have the advantages of computational efficiency when dealing with complex geometries and the conceptually straight forward extension to higher orders of accuracy. On the downside, they are much more complicated to implement and less computationally efficient when dealing with regular geometries. The FDTD and implicit FETD have been combined in an implicit/explicit hybrid. By using the implicit FETD in regions of complex geometry and the FDTD elsewhere the advantages of both are combined. However, previous work only addressed mixed first order (i.e. second order accurate) methods. For electrically large problems or when very accurate solutions are required, higher order methods are attractive. In this thesis a novel higher order implicit/explicit FETD method of arbitrary order in space is presented. A higher order explicit FETD method is implemented using Gauss-Lobatto lumping on regular Cartesian hexahedra with central differencing in time applied to a coupled Maxwell’s equation FEM formulation. This can be seen as a spatially higher order generalisation of the FDTD. A convolution-free perfectly matched layer (PML) method is adapted from the FDTD literature to provide mesh termination. A curl conforming hybrid mesh allowing the interconnection of arbitrary order tetrahedra and hexahedra without using intermediate pyramidal or prismatic elements is presented. An unconditionally stable implicit FETD method is implemented using Newmark-Beta time integration and the standard curl-curl FEM formulation. The implicit/explicit hybrid is constructed on the hybrid hexahedral/tetrahedral mesh using the equivalence between the coupled Maxwell’s formulation with central differences and the Newmark-Beta method with Beta = 0 and the element-wise implicitness method. The accuracy and efficiency of this hybrid is numerically demonstrated using several test-problems.
2
Franke, David [Verfasser]. "Investigation of mechanical contact problems with high-order Finite Element Methods / David Franke." Aachen : Shaker, 2012. http://d-nb.info/1067734902/34.
3
Al-Shanfari, Fatima. "High-order in time discontinuous Galerkin finite element methods for linear wave equations." Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/15332.
Abstract:
In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract approximation analysis is a generalisation of the approach introduced by Claes Johnson (in Comput. Methods Appl. Mech. Engrg., 107:117-129, 1993), writing the second order problem as a system of fi rst order problems. We consider abstract spatial (time independent) operators, highorder in time basis functions when discretising in time; we also prove approximation results in case of linear constraints, e.g. non-homogeneous boundary data. We take the two steps approximation approach i.e. using high-order in time DGFEM; the discretisation approach in time introduced by D Schötzau (PhD thesis, Swiss Federal institute of technology, Zürich, 1999) to fi rst obtain the semidiscrete scheme and then conformal spatial discretisation to obtain the fully-discrete formulation. We have shown solvability, unconditional stability and conditional a priori error estimates within our abstract framework for the fully discretized problem. The skew-symmetric spatial forms arising in our abstract framework for the semi- and fully-discrete schemes do not full ll the underlying assumptions in D. Schötzau's work. But the semi-discrete and fully discrete forms satisfy an Inf-sup condition, essential for our proofs; in this sense our approach is also a generalisation of D. Schötzau's work. All estimates are given in a norm in space and time which is weaker than the Hilbert norm belonging to our abstract function spaces, a typical complication in evolution problems. To the best of the author's knowledge, with the approximation approach we used, these stability and a priori error estimates with their abstract structure have not been shown before for the abstract variational formulation used in this thesis. Finally we apply our abstract framework to the acoustic and an elasto-dynamic linear equations with non-homogeneous Dirichlet boundary data.
4
Marrett, Sean 1960. "A high-order finite element method for Tokamak plasma equilibria /." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56809.
Abstract:
A numerical method for the solution of the axisymmetric, free-boundary, Tokamak equilibrium problem is described. The method uses high-order polynomials defined over a mesh of triangular finite elements to solve the magnetohydrodynamic equilibrium (Grad-Shafranov) equation. Arbitrary coil and plasma current configurations can be specified. The formulation incorporates a nonlinear procedure for computing the coil currents required to place the plasma in a desired position. The solution to the nonlinear Grad-Shafranov equation is computed using a modified Newton's method. The inner-most system of sparse, linear equations is solved using a preconditioned, conjugate gradient algorithm. A computer program, PLEQUI (PLasma EQUIlibrium), was written in a portable FORTRAN dialect to implement the method. The method was tested using both fixed-boundary and free-boundary plasma problems. The program was validated by comparing the results to analytic solutions, by examining the flux plots, or by comparing the solution to the output of another finite-element code.
5
Moura, Rodrigo Costa. "A high-order unstructured discontinuous galerkin finite element method for aerodynamics." Instituto Tecnológico de Aeronáutica, 2012. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2158.
Abstract:
The present thesis discuss in a didactic and detailed way the high-order scheme known as the Discontinuous Galerkin (DG) method, with special focus on applications in aerodynamics. The theoretical formulation of the method is presented in one and two dimensions with great depth, being properly discussed issues of convergence, basis functions, interelement communication, boundary conditions, shock treatment, as well as inviscid and viscous numerical fluxes. As part of this effort, a parallel computer code was developed to simulate the Euler equations of gas dynamics in two dimensions with general boundary conditions over unstructured meshes of triangles. Numerical simulations are addressed in order to demonstrate the characteristics of the Discontinuous Galerkin scheme, as well as to validate the developed solver. It is worth mentioning that the present work can be regarded as new within the Brazilian scientific community and, as such, may be of great importance concerning the introduction of the DG method for Brazilian CFD researchers and practitioners.
6
Guo, Ruchi. "Design, Analysis, and Application of Immersed Finite Element Methods." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90374.
Abstract:
This dissertation consists of three studies of immersed finite element (IFE) methods for inter- face problems related to partial differential equations (PDEs) with discontinuous coefficients. These three topics together form a continuation of the research in IFE method including the extension to elasticity systems, new breakthroughs to higher degree IFE methods, and its application to inverse problems.
First, we extend the current construction and analysis approach of IFE methods in the literature for scalar elliptic equations to elasticity systems in the vector format. In particular, we construct a group of low-degree IFE functions formed by linear, bilinear, and rotated Q1 polynomials to weakly satisfy the jump conditions of elasticity interface problems. Then we analyze the trace inequalities of these IFE functions and the approximation capabilities of the resulted IFE spaces. Based on these preparations, we develop a partially penalized IFE (PPIFE) scheme and prove its optimal convergence rates.
Secondly, we discuss the limitations of the current approaches of IFE methods when we try to extend them to higher degree IFE methods. Then we develop a new framework to construct and analyze arbitrary p-th degree IFE methods. In this framework, each IFE function is the extension of a p-th degree polynomial from one subelement to the whole interface element by solving a local Cauchy problem on interface elements in which the jump conditions across the interface are employed as the boundary conditions. All the components in the analysis, including existence of IFE functions, the optimal approximation capabilities and the trace inequalities, are all reduced to key properties of the related discrete extension operator. We employ these results to show the optimal convergence of a discontinuous Galerkin IFE (DGIFE) method.
In the last part, we apply the linear IFE methods in the literature together with the shape optimization technique to solve a group of interface inverse problems. In this algorithm, both the governing PDEs and the objective functional for interface inverse problems are discretized optimally by the IFE method regardless of the location of the interface in a chosen mesh. We derive the formulas for the gradients of the objective function in the optimization problem which can be implemented efficiently in the IFE framework through a discrete adjoint method. We demonstrate the properties of the proposed algorithm by applying it to three representative applications.Doctor of Philosophy
Interface problems arise from many science and engineering applications modeling the transmission of some physical quantities between multiple materials. Mathematically, these multiple materials in general are modeled by partial differential equations (PDEs) with discontinuous parameters, which poses challenges to developing efficient and reliable numerical methods and the related theoretical error analysis. The main contributions of this dissertation is on the development of a special finite element method, the so called immersed finite element (IFE) method, to solve the interface problems on a mesh independent of the interface geometry which can be advantageous especially when the interface is moving. Specifically, this dissertation consists of three projects of IFE methods: elasticity interface problems, higher-order IFE methods and interface inverse problems, including their design, analysis, and application.
7
Chuang, Shih-Chang. "Parallel methods for high-performance finite element methods based on sparsity." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/18177.
8
Zhou, Dong. "High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/295839.
Abstract:
MathematicsPh.D.
Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time.
Temple University--Theses
9
Couchman, Benjamin Luke Streatfield. "On the convergence of higher-order finite element methods to weak solutions." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115685.
Abstract:
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 77-79).
The ability to handle discontinuities appropriately is essential when solving nonlinear hyperbolic partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a discretely conservative scheme. However, discrete conservation is not a strict requirement for convergence to a weak solution. This suggests a hierarchy of discretizations, where discretely conservative schemes are a subset of the larger class of methods that converge to the weak solution. We show here that a range of finite element methods converge to the weak solution without using discrete conservation arguments. The effect of using quadrature rules to approximate integrals is also considered. In addition, we show that solutions using non-conservation working variables also converge to weak solutions.
by Benjamin Luke Streatfield Couchman.
S.M.
10
Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.
Abstract:
Aquesta tesi proposa una millora del clàssic mètode dels elements finits (finite element method, FEM) per a un tractament eficient de dominis amb contorns corbs: el denominat NURBS-enhanced finite element method (NEFEM). Aquesta millora permet descriure de manera exacta la geometría mitjançant la seva representació del contorn CAD amb non-uniform rational B-splines (NURBS), mentre que la solució s'aproxima amb la interpolació polinòmica estàndard. Per tant, en la major part del domini, la interpolació i la integració numèrica són estàndard, retenint les propietats de convergència clàssiques del FEM i facilitant l'acoblament amb els elements interiors. Només es requereixen estratègies específiques per realitzar la interpolació i la integració numèrica en elements afectats per la descripció del contorn mitjançant NURBS.La implementació i aplicació de NEFEM a problemes que requereixen una descripció acurada del contorn són, també, objectius prioritaris d'aquesta tesi. Per exemple, la solució numèrica de les equacions de Maxwell és molt sensible a la descripció geomètrica. Es presenta l'aplicació de NEFEM a problemes d'scattering d'ones electromagnètiques amb una formulació de Galerkin discontinu. S'investiga l'habilitat de NEFEM per obtenir solucions precises amb malles grolleres i aproximacions d'alt ordre, i s'exploren les possibilitats de les anomenades malles NEFEM, amb elements que contenen singularitats dintre d'una cara o aresta d'un element. Utilitzant NEFEM, la mida de la malla no està controlada per la complexitat de la geometria. Això implica una dràstica diferència en la mida dels elements i, per tant, suposa un gran estalvi tant des del punt de vista de requeriments de memòria com de cost computacional. Per tant, NEFEM és una eina poderosa per la simulació de problemes tridimensionals a gran escala amb geometries complexes. D'altra banda, la simulació de problemes d'scattering d'ones electromagnètiques requereix mecanismes per aconseguir una absorció eficient de les ones scattered. En aquesta tesi es discuteixen, optimitzen i comparen dues tècniques en el context de mètodes de Galerkin discontinu amb aproximacions d'alt ordre.
La resolució numèrica de les equacions d'Euler de la dinàmica de gasos és també molt sensible a la representació geomètrica. Quan es considera una formulació de Galerkin discontinu i elements isoparamètrics lineals, una producció espúria d'entropia pot evitar la convergència cap a la solució correcta. Amb NEFEM, l'acurada imposició de la condició de contorn en contorns impenetrables proporciona resultats precisos inclús amb una aproximació lineal de la solució. A més, la representació exacta del contorn permet una imposició adequada de les condicions de contorn amb malles grolleres i graus d'interpolació alts. Una propietat atractiva de la implementació proposada és que moltes de les rutines usuals en un codi d'elements finits poden ser aprofitades, per exemple rutines per realitzar el càlcul de les matrius elementals, assemblatge, etc. Només és necessari implementar noves rutines per calcular les quadratures numèriques en elements corbs i emmagatzemar el valor de les funciones de forma en els punts d'integració. S'han proposat vàries tècniques d'elements finits corbs a la literatura. En aquesta tesi, es compara NEFEM amb altres tècniques populars d'elements finits corbs (isoparamètics, cartesians i p-FEM), des de tres punts de vista diferents: aspectes teòrics, implementació i eficiència numèrica. En els exemples numèrics, NEFEM és, com a mínim, un ordre de magnitud més precís comparat amb altres tècniques. A més, per una precisió desitjada NEFEM és també més eficient: necessita un 50% dels graus de llibertat que fan servir els elements isoparamètrics o p-FEM per aconseguir la mateixa precisió. Per tant, l'ús de NEFEM és altament recomanable en presència de contorns corbs i/o quan el contorn té detalls geomètrics complexes.
This thesis proposes an improvement of the classical finite element method (FEM) for an efficient treatment of curved boundaries: the NURBSenhanced FEM (NEFEM). It is able to exactly represent the geometry by means of the usual CAD boundary representation with non-uniform rational Bsplines (NURBS), while the solution is approximated with a standard piecewise polynomial interpolation. Therefore, in the vast majority of the domain, interpolation and numerical integration are standard, preserving the classical finite element (FE) convergence properties, and allowing a seamless coupling with standard FEs on the domain interior. Specifically designed polynomial interpolation and numerical integration are designed only for those elements affected by the NURBS boundary representation.
The implementation and application of NEFEM to problems demanding an accurate boundary representation are also primary goals of this thesis. For instance, the numerical solution of Maxwell's equations is highly sensitive to geometry description. The application of NEFEM to electromagnetic scattering problems using a discontinuous Galerkin formulation is presented. The ability of NEFEM to compute an accurate solution with coarse meshes and high-order approximations is investigated, and the possibilities of NEFEM meshes, with elements containing edge or corner singularities, are explored. With NEFEM, the mesh size is no longer subsidiary to geometry complexity, and depends only on the accuracy requirements on the solution, whereas standard FEs require mesh refinement to properly capture the geometry. This implies a drastic difference in mesh size that results in drastic memory savings, and also important savings in computational cost. Thus, NEFEM is a powerful tool for large-scale scattering simulations with complex geometries in three dimensions. Another key issue in the numerical solution of electromagnetic scattering problems is using a mechanism to perform the absorption of outgoing waves. Two perfectly matched layers are discussed, optimized and compared in a high-order discontinuous Galerkin framework.
The numerical solution of Euler equations of gas dynamics is also very sensitive to geometry description. Using a discontinuous Galerkin formulation and linear isoparametric elements, a spurious entropy production may prevent convergence to the correct solution. With NEFEM, the exact imposition of the solid wall boundary condition provides accurate results even with a linear approximation of the solution. Furthermore, the exact boundary representation allows using coarse meshes, but ensuring the proper implementation of the solid wall boundary condition. An attractive feature of the proposed implementation is that the usual routines of a standard FE code can be directly used, namely routines for the computation of elemental matrices and vectors, assembly, etc. It is only necessary to implement new routines for the computation of numerical quadratures in curved elements and to store the value of shape functions at integration points.
Several curved FE techniques have been proposed in the literature. In this thesis, NEFEM is compared with some popular curved FE techniques (namely isoparametric FEs, cartesian FEs and p-FEM), from three different perspectives: theoretical aspects, implementation and performance. In every example shown, NEFEM is at least one order of magnitude more accurate compared to other techniques. Moreover, for a desired accuracy NEFEM is also computationally more efficient. In some examples, NEFEM needs only 50% of the number of degrees of freedom required by isoparametric FEs or p-FEM. Thus, the use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details.
11
Jansson, Niclas. "High performance adaptive finite element methods for turbulent fluid flow." Licentiate thesis, KTH, Numerisk analys, NA, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-30277.
Abstract:
Understanding the mechanics of turbulent fluid flow is of key importance for industry and society as for example in aerodynamics and aero-acoustics. The massive computational cost for resolving all turbulent scales in a realistic problem makes direct numerical simulation of the underlying Navier-Stokes equations impossible. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized where the mesh is adaptively resolved, based on a posteriori error control. These adaptive methods have been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method for modern parallel computer architectures. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallellization of local mesh refinement methods such as recursive longest edge bisection. We also address the load balance problem with the development of an a priori predictive dynamic load balancing method. Current results are encouraging with almost linear strong scaling to thousands of cores on several modern architectures.QC 20110223
12
Jansson, Niclas. "High Performance Adaptive Finite Element Methods : With Applications in Aerodynamics." Doctoral thesis, KTH, High Performance Computing and Visualization (HPCViz), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-125742.
Abstract:
The massive computational cost for resolving all scales in a turbulent flow makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized by adaptively resolution of the mesh, based on a posteriori error estimation. Such adaptive methods have previously been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method that enables efficient computation of time resolved approximations of turbulent flow for complex geometries with a posteriori error control. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallelization of local mesh refinement methods such as recursive longest edge bisection, and the development of an a priori predictive dynamic load balancing method, based on a weighted dual graph. We also address the challenges of emerging supercomputer architectures with the development of new hybrid parallel programming models, combining traditional message passing with lightweight one-sided communication. Our implementation has proven to be both general and efficient, scaling up to more than twelve thousands cores.Den höga beräkningskostnaden för att lösa upp alla turbulenta skalor för ett realistiskt problem gör en direkt numerisk simulering av Navier-Stokes ekvationer omöjlig. De senaste framstegen inom adaptiva finita element metoder ger ett nytt kraftfullt verktyg inom Computational Fluid Dynamics (CFD). Beräkningskostnaden för en simulering av turbulent flöde kan minimeras genom att beräkningsnätet adaptivt förfinas baserat på en a posteriori feluppskattning. Dessa adaptiva metoder har tidigare implementerats för seriella beräkningar, medan en effektiv parallellisering av metoden inte är trivial. I denna avhandling presenterar vi vår utveckling av en adaptiv finita element lösare, anpassad för att effektivt beräkna tidsupplösta approximationer i komplicerade geometrier med a posteriori felkontroll. Effektiva datastrukturer och metoder för ostrukturerade beräkningsnät av tetrahedrar presenteras. Avhandlingen behandlar även effektiv parallellisering av lokala nätförfiningsmetoder, exempelvis recursive longest edge bisection. Även lastbalanseringsproblematiken behandlas, där problemet lösts genom utvecklandet av en prediktiv dynamisk lastbalanseringsmetod, baserad på en viktad dualgraf av beräkningsnätet. Slutligen avhandlas även problematiken med att effektivt utnyttja nytillkomna superdatorarkitekturer, genom utvecklandet av en hybrid parallelliserings modell som kombinerar traditionell meddelande baserad parallellisering med envägskommunikation. Detta har resulterat i en generell samt effektiv implementation med god skalning upp till fler än tolv tusen processorkärnor.
QC 20130816
13
Hulett, Cameron. "Design procedures for high temperature components using finite element methods." Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/14306.
Abstract:
Bibliography: leaves 109-114.A procedure for design and redesign of high temperature components is developed. The thesis begins with a description of an engineering problem, namely the failure of a steel plant pre-reduction kiln, which incorporates a number of commonly occurring design problems. A redesign procedure, which follows a more prescriptive rather than a descriptive method, is established for the case study. An investigation of the material properties, loading conditions and component failure is undertaken. Each investigation begins with an overall view of the topic, which is then narrowed to suit the case study. The procedure developed during the investigations begins by using conventional theoretical techniques to determine the material properties and loadings involved. Simple and then more detailed finite element modelling establishes more accurate results for so.me complicated problems. In particular the thermal loading of the kiln is found to be considerably larger than the self weight loading. Failure analysis techniques together with a sophisticated non-destructive testing technique, Holographic Interferometry, are employed to investigate flaws and failure modes. The technique developed enables the qualification and quantification of material properties and flaws for in situ components. The dominant failure mode for the kiln is stress corrosion which can be prevented by avoiding corrosion and lowering the thermal stresses. However the existence of flaws enables fatigue failure to occur. The procedure continues with a life assessment due to fatigue, however in the kiln case study, the validity of this is uncertain due to insufficient test data. Recommendations for redesign are then given. The design procedure enables an ordered and effective means of solving in situ component failure and redesign problems.
14
Nazarov, Murtazo. "Adaptive Algorithms and High Order Stabilization for Finite Element Computation of Turbulent Compressible Flow." Doctoral thesis, KTH, Numerisk analys, NA, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-34532.
Abstract:
This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows. The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D. To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity. The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation.QC 20110627
15
Dubcová, Lenka. "Novel self-adaptive higher-order finite elements methods for Maxwell's equations of electromagnetics." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2008. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
16
Franke, David Christian [Verfasser], Ernst [Akademischer Betreuer] Rank, and Karl [Akademischer Betreuer] Schweizerhof. "Investigation of mechanical contact problems with high-order Finite Element Methods / David Franke. Gutachter: Karl Schweizerhof. Betreuer: Ernst Rank." München : Universitätsbibliothek der TU München, 2011. http://d-nb.info/1019590068/34.
17
Arthurs, Christopher J. "Efficient simulation of cardiac electrical propagation using adaptive high-order finite elements." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:ad31f06f-c4ed-4c48-b978-1ef3b12fe7a1.
Abstract:
This thesis investigates the high-order hierarchical finite element method, also known as the finite element p-version, as a computationally-efficient technique for generating numerical solutions to the cardiac monodomain equation. We first present it as a uniform-order method, and through an a priori error bound we explain why the associated cardiac cell model must be thought of as a PDE and approximated to high-order in order to obtain the accuracy that the p-version is capable of. We perform simulations demonstrating that the achieved error agrees very well with the a priori error bound. Further, in terms of solution accuracy for time taken to solve the linear system that arises in the finite element discretisation, it is more efficient that the state-of-the-art piecewise linear finite element method. We show that piecewise linear FEM actually introduces quite significant amounts of error into the numerical approximations, particularly in the direction perpendicular to the cardiac fibres with physiological conductivity values, and that without resorting to extremely fine meshes with elements considerably smaller than 70 micrometres, we can not use it to obtain high-accuracy solutions. In contrast, the p-version can produce extremely high accuracy solutions on meshes with elements around 300 micrometres in diameter with these conductivities. Noting that most of the numerical error is due to under-resolving the wave-front in the transmembrane potential, we also construct an adaptive high-order scheme which controls the error locally in each element by adjusting the finite element polynomial basis degree using an analytically-derived a posteriori error estimation procedure. This naturally tracks the location of the wave-front, concentrating computational effort where it is needed most and increasing computational efficiency. The scheme can be controlled by a user-defined error tolerance parameter, which sets the target error within each element as a proportion of the local magnitude of the solution as measured in the H^1 norm. This numerical scheme is tested on a variety of problems in one, two and three dimensions, and is shown to provide excellent error control properties and to be likely capable of boosting efficiency in cardiac simulation by an order of magnitude. The thesis amounts to a proof-of-concept of the increased efficiency in solving the linear system using adaptive high-order finite elements when performing single-thread cardiac simulation, and indicates that the performance of the method should be investigated in parallel, where it can also be expected to provide considerable improvement. In general, the selection of a suitable preconditioner is key to ensuring efficiency; we make use of a variety of different possibilities, including one which can be expected to scale very well in parallel, meaning that this is an excellent candidate method for increasing the efficiency of cardiac simulation using high-performance computing facilities.
18
Fallas, Chinchilla Juan Carlos. "Modelling of high pressure instruments and experiments using finite element methods." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31250.
Abstract:
The study of matter at extreme conditions has been of great importance for modern society. A correct understanding of materials and environments subject to high pressures and temperatures enabled the development of car and jet engines, manufacture of goods, energy production and space travels among other human milestones. Discoveries in magnetism, geology, chemistry, and crystallography have been reported in literature as well, illustrating relevant contributions of this research area. Science at extreme conditions constantly requires to innovate instruments and characterisation methods. Sophisticated proficiencies are needed to explore and reproduce conditions of interest for this field. Since the 1990s, high pressure instruments for neutron scattering have boosted the study of compressed matter. The design and subsequent improvement of the Paris-Edinburgh (PE) press and toroidal anvils successfully impacted this area, currently being the most extensively used instrument for high pressure neutron scattering, commonly used for pressures of the order of 10 GPa. Recent incorporation of toroidal anvils made of Zirconia Toughened Alumina (ZTA) has opened new experimental possibilities. Neutron transparency and mechanical resistance are key properties of this ceramic material. At this point it is essential to understand ZTA anvils design and working conditions in order to increase experimental capabilities and access new frontiers in compressed matter. Computer-based modelling technique Finite Element Analysis (FEA) has been a recent ally for instrumentation design and optimisation. Phenomena such as mechanical stress, deformations, and thermal distributions can be modelled in an object, gathering information regarding its mechanical stability, behaviour and failure. Although this method is popular in industrial and engineering design and applications, it has not been widely employed in high pressure research due to scarce information in material properties under extreme conditions, as well as in innovative ceramics and metallic alloys introduced in these types of scientific devices.
19
Pipilis, Konstantinos Georgiou. "Higher order moving finite element methods for systems described by partial differential-algebraic equations." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/7510.
20
LOMBARDI, Guido. "Singular high-order complete vector functions for the analysis and design of electromagnetic structures with Finite Methods." Doctoral thesis, Politecnico di Torino, 2004. http://hdl.handle.net/11583/2504599.
Abstract:
This dissertation presents new singular curl- and divergence- conforming vector bases that incorporate the edge conditions.
Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester–Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems.
21
Quint, Karsten [Verfasser]. "Thermomechanically coupled processes for functionally graded materials : experiments, modelling, and finite element analysis using high-order DIRK-methods / Karsten Quint." Clausthal-Zellerfeld : Universitätsbibliothek Clausthal, 2012. http://d-nb.info/1024717844/34.
22
Koch, Marcel [Verfasser], and Christian [Akademischer Betreuer] Engwer. "Generating block-structured kernels for low order finite element methods : a high-performance oriented view / Marcel Koch ; Betreuer: Christian Engwer." Münster : Universitäts- und Landesbibliothek Münster, 2021. http://d-nb.info/123663246X/34.
23
Rieben, Robert N. "A novel high order time domain vector finite element method for the simulation of electromagnetic devices /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2004. http://uclibs.org/PID/11984.
24
Oliver, Todd A. 1980. "A high-order, adaptive, discontinuous Galerkin finite element method for the Reynolds-Averaged Navier-Stokes equations." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/46818.
Abstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 175-182).
This thesis presents high-order, discontinuous Galerkin (DG) discretizations of the Reynolds-Averaged Navier-Stokes (RANS) equations and an output-based error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the Spalart-Allmaras (SA) turbulence model are examined. The dual consistency of multiple DG discretizations of the RANS-SA system is analyzed. The approach of simply weighting gradient dependent source terms by a test function and integrating is shown to be dual inconsistent. A dual consistency correction for this discretization is derived. The analysis also demonstrates that discretizations based on the popular mixed formulation, where dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis. The output error estimation and output-based adaptation algorithms used here are extensions of methods previously developed in the finite volume and finite element communities. In particular, the methods are extended for application on the curved, highly anisotropic meshes required for boundary conforming, high-order RANS simulations. Two methods for generating such curved meshes are demonstrated. One relies on a user-defined global mapping of the physical domain to a straight meshing domain. The other uses a linear elasticity node movement scheme to add curvature to an initially linear mesh. Finally, to improve the robustness of the adaptation process, an "unsteady" algorithm, where the mesh is adapted at each time step, is presented. The goal of the unsteady procedure is to allow mesh adaptation prior to converging a steady state solution, not to obtain a time-accurate solution of an unsteady problem. Thus, an estimate of the error due to spatial discretization in the output of interest averaged over the current time step is developed. This error estimate is then used to drive an h-adaptation algorithm. Adaptation results demonstrate that the high-order discretizations are more efficient than the second-order method in terms of degrees of freedom required to achieve a desired error tolerance. Furthermore, using the unsteady adaptation process, adaptive RANS simulations may be started from extremely coarse meshes, significantly decreasing the mesh generation burden to the user.
by Todd A. Oliver.
Ph.D.
25
Oliver, Todd A. "A High-Order, Adaptive, Discontinuous Galerkin Finite Element Method for the Reynolds-Averaged Navier-Stokes Equations." Ft. Belvoir : Defense Technical Information Center, 2008. http://handle.dtic.mil/100.2/ADA488912.
26
Santos, Caio Fernando Rodrigues dos 1986. "Orthogonal and minimum energy high-order bases for the finite element method = Bases ortogonais de alta ordem e de mínima energia para o método de elementos finitos." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265837.
Abstract:
Orientador: Marco Lúcio BittencourtTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
Made available in DSpace on 2018-08-26T18:11:15Z (GMT). No. of bitstreams: 1 Santos_CaioFernandoRodriguesdos_D.pdf: 60307032 bytes, checksum: 4e05fc37f22f1d9206fa3c5665d9bc34 (MD5) Previous issue date: 2015
Resumo: Nesse trabalho apresentamos os procedimentos de construção de bases para o Método de Elementos Finitos (MEF) de alta ordem considerando o procedimento de diagonalização simultânea dos modos internos da matriz de massa e rigidez unidimensionais e a ortogonalização dos modos de contorno usando procedimentos de mínima energia. Nesse caso, os conceitos de ortogonalização de mínima energia são usados como uma maneira eficiente de se construir modos de contorno ortogonais aos modos internos das funções de forma $1D$. Novas funções de forma unidimensionais para o MEF de alta ordem são apresentadas para a construção de bases simultaneamente diagonais de mínima energia para o operador de Helmholtz. Além disso, um procedimento para o cálculo das matrizes de massa e rigidez $2D$ e $3D$, como combinação dos coeficientes unidimensionais das matrizes de massa, rigidez e mista é apresentado para elementos quadrilaterais e hexaédricos distorcidos em problemas de projeção, Poisson, estado plano e estado geral em problemas de elasticidade linear. O uso de procedimentos via matrizes unidimensionais permite obter um speedup significativo em comparação com o procedimento padrão, para malhas distorcidas e não distorcidas. Com esse procedimento, é possível armazenar apenas as funções de forma unidimensionais e suas derivadas calculadas nos pontos de integração unidimensionais gerando uma redução no consumo de memória. O desempenho das bases propostas foi verificado através de testes numéricos e os resultados comparados com aqueles usando a base padrão com polinômios de Jacobi. Características como esparsidade, condicionamento numérico e número de iterações usando o método dos gradientes conjugados com precondicionador diagonal também são investigados. Além disso, investigamos o uso da matriz de massa local, utilizando bases simultaneamente diagonais de mínima energia, como pré-condicionador. Os resultados foram comparados com o uso do precondicionador diagonal e SSOR (Symmetric Successive Over Relaxation)
Abstract: In this work we present construction procedures of bases for the high-order finite element method (FEM) considering a procedures for the simultaneous diagonalization of the internal modes of the one-dimensional mass and stiffness matrices and orthogonalization of the boundary modes using minimum energy procedure. The concepts of minimum energy orthogonalization are used efficiently to construct one-dimensional boundary modes orthogonal to the internal modes of the shape functions. New one-dimensional bases for the high-order FEM are presented for the construction of the simultaneously diagonal and minimum energy basis for the Helmholtz norm. Furthermore, we present a calculation procedure for the $2D$ and $3D$ mass and stiffness matrices, as the combination of one-dimensional coefficients of the mass, stiffness and Jacobian matrices. This procedure is presented for quadrilateral and hexahedral distorted elements in projection, Poisson, plane state and general linear elasticity problems. The use of the one-dimensional matrices procedure allows a significant speedup compared to the standard procedure for distorted and undistorted meshes. Also, this procedure stores only one-dimensional shape functions and their derivatives calculated using one-dimensional integration points, which generates a reduction in memory consumption. The performance of the proposed bases was verified by numerical tests and the results are compared with those using the standard basis using Jacobi polynomials. Sparsity patterns, condition numbers and number of iterations using the conjugate gradient methods with diagonal preconditioner are also investigated. Furthermore, we investigated the use of the local mass matrix using simultaneously diagonal and minimum energy bases as preconditioner to solve the system of equations. The results are compared with the diagonal preconditioner and Symmetric Successive Over Relaxation (SSOR)
Doutorado
Mecanica dos Sólidos e Projeto Mecanico
Doutor em Engenharia Mecânica
27
Jimack, Peter K. "Finite element methods using high degree piecewise polynomials on continuously deforming grids." Thesis, University of Bristol, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330300.
28
Kolchuzhin, Vladimir. "Methods and Tools for Parametric Modeling and Simulation of Microsystems based on Finite Element Methods and Order Reduction Technologies." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000550.
Abstract:
In der vorliegenden Arbeit wird die Entwicklung eines effizienten Verfahrens zur parametrischen Finite Elemente Simulation von Mikrosystemen und zum Export dieser Modelle in Elektronik- und Systemsimulationswerkzeuge vorgestellt. Parametrische FE-Modelle beschreiben den Einfluss von geometrischen Abmessungen, Schwankungen von Materialeigenschaften und veränderten Umgebungsbedingungen auf das Funktionsverhalten von Sensoren und Aktuatoren. Parametrische FE-Modelle werden für die Auswahl geeigneter Formelemente und deren Dimensionierung während des Entwurfsprozesses in der Mikrosystemtechnik benötigt. Weiterhin ermöglichen parametrische Modelle Sensitivitätsanalysen zur Bewertung des Einflusses von Toleranzen und Prozessschwankungen auf die Qualität von Fertigungsprozessen. In Gegensatz zu üblichen Sample- und Fitverfahren wird in dieser Arbeit eine Methode entwickelt, welche die Taylorkoeffizienten höherer Ordnung zur Beschreibung des Einflusses von Designparametern direkt aus der Finite-Elemente- Formulierung, durch Ableitungen der Systemmatrizen, ermittelt. Durch Ordnungsreduktionsverfahren werden die parametrischen FE-Modelle in verschiedene Beschreibungssprachen für einen nachfolgenden Elektronik- und Schaltungsentwurf überführt. Dadurch wird es möglich, neben dem Sensor- und Aktuatorentwurf auch das Zusammenwirken von Mikrosystemen mit elektronischen Schaltungen in einer einheitlichen Simulationsumgebung zu analysieren und zu optimierenThe thesis deals with advanced parametric modeling technologies based on differentiation of the finite element equations which account for parameter variations in a single FE run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also high order partial derivatives with regard to design parameters by means of automatic differentiation. As result, Taylor vectors of the system’s response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. A novel approaches for the parametric MEMS simulation have been investigated for mechanical, electrostatic and fluidic domains in order to improve the computational efficiency. Objective of reduced order modeling is to construct a simplified model which approximates the original system with reasonable accuracy for system level design of MEMS. The modal superposition technique is most suitable for system with flexible mechanical components because the deformation state of any flexible system can be accurately described by a linear combination of its lowest eigenvectors. The developed simulation approach using parametric FE analyses to extract basis functions have been applied for parametric reduced order modeling. The successful implementation of a derivatives based technique for parameterization of macromodel by the example of microbeam and for exporting this macromodel into MATLAB/Similink to simulate dynamical behavior has been reported
29
Rawat, Vineet. "Finite Element Domain Decomposition with Second Order Transmission Conditions for Time-Harmonic Electromagnetic Problems." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1243360543.
30
Chiocchetti, Simone. "High order numerical methods for a unified theory of fluid and solid mechanics." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346999.
Abstract:
This dissertation is a contribution to the development of a unified model of
continuum mechanics, describing both fluids and elastic solids as a general
continua, with a simple material parameter choice being the distinction
between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic
media. Additional physical effects such as surface tension, rate-dependent
material failure and fatigue can be, and have been, included in the same
formalism.
The model extends a hyperelastic formulation of solid mechanics in
Eulerian coordinates to fluid flows by means of stiff algebraic relaxation
source terms. The governing equations are then solved by means of high
order ADER Discontinuous Galerkin and Finite Volume schemes on fixed
Cartesian meshes and on moving unstructured polygonal meshes with
adaptive connectivity, the latter constructed and moved by means of a in-
house Fortran library for the generation of high quality Delaunay and Voronoi
meshes.
Further, the thesis introduces a new family of exponential-type and semi-
analytical time-integration methods for the stiff source terms governing
friction and pressure relaxation in Baer-Nunziato compressible multiphase
flows, as well as for relaxation in the unified model of continuum mechanics,
associated with viscosity and plasticity, and heat conduction effects.
Theoretical consideration about the model are also given, from the
solution of weak hyperbolicity issues affecting some special cases of the
governing equations, to the computation of accurate eigenvalue estimates, to
the discussion of the geometrical structure of the equations and involution
constraints of curl type, then enforced both via a GLM curl cleaning method,
and by means of special involution-preserving discrete differential operators,
implemented in a semi-implicit framework.
Concerning applications to real-world problems, this thesis includes
simulation ranging from low-Mach viscous two-phase flow, to shockwaves in
compressible viscous flow on unstructured moving grids, to diffuse interface
crack formation in solids.
31
Gersbacher, Christoph [Verfasser], and Dietmar [Akademischer Betreuer] Kröner. "Higher-order discontinuous finite element methods and dynamic model adaptation for hyperbolic systems of conservation laws." Freiburg : Universität, 2017. http://d-nb.info/1136263853/34.
32
Hendriana, Dena. "On finite element and control volume upwinding methods for high Peclet number flows." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/37735.
33
Pacheco, Roman Oscar. "Evaluation of Finite Element simulation methods for High Cycle Fatigue on engine components." Thesis, Linköpings universitet, Mekanik och hållfasthetslära, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-148779.
Abstract:
This document reflects the results of evaluating three computational methods to analyse the fatigue life of components mounted on the cylinder block; two currently in use at Scania and one that has been further developed from its previous state. Due to the cost of testing and the exponential increase in computational power throughout the years, the cheaper computational analyses have gained in popularity. When a component is mounted in a fairly complex assembly such as an engine, simplifications need to be made in order to make the analysis as less expensive as possible while keeping a high degree of accuracy. The methods of Virtual Vibrations, VROM and VFEM have been evaluated and compared in terms of accuracy, computational cost, user friendliness and general capacities. Additionally, the method VFEM has been further developed and improved from its previous state. A in-depth investigation regarding the differences of the methods has been conducted and improvements to make them more efficient are suggested herein. The reader can also find a decision matrix and recommendations regarding which method to use depending on the general characteristics of the component of interest and other factors. Two components, which differ in complexity and mounting nature, have been used to do the research.
34
Qin, Shanlin. "Fractional order models: Numerical simulation and application to medical imaging." Thesis, Queensland University of Technology, 2017. https://eprints.qut.edu.au/115108/1/115108_9066888_shanlin_qin_thesis.pdf.
Abstract:
This thesis is primarily concerned with developing new models and numerical methods based on the fractional generalisation of the Bloch and Bloch-Torrey equations to account for anomalous MRI signal attenuation. The two main contributions of the research are to investigate the anomalous evolution of MRI signals via the fractionalised Bloch equations, and to develop new effective numerical methods with supporting analysis to solve the time-space fractional Bloch-Torrey equations.
35
Aghabarati, Ali. "Multilevel and algebraic multigrid methods for the higher order finite element analysis of time harmonic Maxwell's equations." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=121485.
Abstract:
The Finite Element Method (FEM) applied to wave scattering and quasi-static vector field problems in the frequency domain leads to sparse, complex-symmetric, linear systems of equations. For large problems with complicated geometries, most of the computer time and memory used by FEM goes to solving the matrix equation. Krylov subspace methods are widely used iterative methods for solving large sparse systems. They depend heavily on preconditioning to accelerate convergence. However, application of conventional preconditioners to the "curl-curl" operator which arises in vector electromagnetics does not result in a satisfactory performance and specialized preconditioning techniques are required. This thesis presents effective Multilevel and Algebraic Multigrid (AMG) preconditioning techniques for p-adaptive FEM analysis. In p-adaption, finite elements of different polynomial orders are present in the mesh and the system matrix can be structured into blocks corresponding to the orders of the basis functions. The new preconditioners are based on a p-type multilevel Schwarz (pMUS) approximate inversion of the block structured system. A V-cycle multilevel correction starts by applying Gauss-Seidel to the highest block level, then the next level down, and so on. On the other side of the V, Gauss-Seidel iterations are applied in the reverse order. At the bottom of the cycle is the lowest order system, which is usually solved exactly with a direct solver. The proposed alternative is to use Auxiliary Space Preconditioning (ASP) at the lowest level and continue the V-cycle downwards, first into a set of auxiliary, node-based spaces, then through a series of progressively smaller matrices generated by an Algebraic Multigrid (AMG). The algebraic coarsening approach is especially useful for problems with fine geometric details, requiring a very large mesh in which the bulk of the elements remain at low order. In addition, for wave problems, a "shifted Laplace" technique is applied, in which part of the ASP/AMG algorithm uses a perturbed, complex frequency. A significant convergence acceleration is achieved. The performance of Krylov algorithms is further enhanced during p-adaption by incorporation of a deflation technique. This projects out from the preconditioned system the eigenvectors corresponding to the smallest eigenvalues. The construction of the deflation subspace is based on efficient estimation of the eigenvectors from information obtained when solving the first problem in a p-adaptive sequence. Extensive numerical experiments have been performed and results are presented for both wave and quasi-static problems. The test cases considered are complicated to solve and the numerical results show the robustness and efficiency of the new preconditioners. Deflated Krylov methods preconditioned with the current Multilevel/ASP/AMG approach are always considerably faster than the reference methods and speedups of up to 10 are achieved for some test problems.La méthode des éléments finis (FEM) appliquée à la dispersion des ondes et aux problèmes de champ de vecteurs quasi-statique dans le domaine fréquentiel mène à des systèmes d'équations linéaires rares, symétriques-complexes. Pour de grands problèmes ayant des géométries complexes, la plupart du temps et de la mémoire d'ordinateur utilisé par FEM va à la résolution de l'équation de la matrice. Les méthodes itératives de Krylov sont celles largement utilisées dans la résolution de grands systèmes creux. Elles dépendent fortement des préconditionnement qui accélèrent la convergence. Toutefois, l'application de préconditionnements conventionnels à l'opérateur "rot-rot" qui surgit en électromagnétisme vectoriel n'aboutit pas à des résultats satisfaisants et des techniques de préconditionnement spécialisés sont exigées.Cette thèse présente des techniques de préconditionnement efficaces multiniveau et multigrilles algébrique (AMG) pour l'analyse p-adaptative FEM. Dans la p-adaptation, des éléments finis de différents ordres polynomiaux sont présents dans le maillage et la matrice du système peut être structurée en blocs correspondant aux ordres des fonctions de base. Les nouveaux préconditionneurs sont basés sur un type d'inversion approximative à multiniveau p Schwarz (pMUS) du système structuré de bloc. Une correction à niveaux multiples en cycle V débute par l'application de Gauss-Seidel au niveau du bloc le plus élevé, suivi par le niveau inférieur, et ainsi de suite. De l'autre côté du V, des itérations de Gauss-Seidel sont appliquées en ordre inverse. Au bas du cycle se trouve le système d'ordre le plus bas, qui est habituellement résolu exactement avec un solveur direct. L'alternative proposée est d'utiliser l'espace auxiliaire de préconditionnement (ASP) au niveau le plus bas et de poursuivre le cycle en V vers le bas, d'abord en un ensemble d'auxiliaires, basé sur les espacements de nœuds, à travers une série de plus en plus petites de matrices générées par un multigrille algébrique (AMG). L'approche de grossissement algébrique est particulièrement utile aux problèmes ayant de fins détails géométriques, nécessitant une très grande maille dans laquelle la majeure partie des éléments restent à un niveau plus bas.En outre, pour des problèmes d'onde, la technique "décalé Laplace" est appliquée, dans laquelle une partie de l'algorithme ASP/AMG utilise une fréquence complexe perturbée. Une accélération de la convergence significative est atteinte. La performance des algorithmes de Krylov est davantage renforcée au cours du p-adaptation par l'incorporation d'une technique de déflation. Cette saillie fait dépasser hors du système préconditionné, les vecteurs propres correspondants aux plus petites valeurs propres. La construction du sous-espace de déflation est basée sur une estimation efficace des vecteurs propres à partir d'informations obtenues lors de la résolution du premier problème dans une séquence p-adaptatif. Des expériences numériques approfondies ont été effectuées et les résultats sont présentés à la fois aux problèmes d'onde et quasi-statiques. Les cas de test sont considérés comme compliqués à résoudre et les résultats numériques montrent la robustesse et l'efficacité des nouveaux préconditionnements. Les méthodes de Krylov de déflation préconditionnés par l'approche multiniveaux/ASP/AMG actuelle sont toujours considérablement plus rapides que les méthodes de référence et des accélérations allant jusqu'à 10 sont atteintes pour certains problèmes de test.
36
Vikas, Sharma. "Development of Space-Time Finite Element Method for Seismic Analysis of Hydraulic Structures." Kyoto University, 2018. http://hdl.handle.net/2433/235094.
Abstract:
Kyoto University (京都大学)0048
新制・課程博士
博士(農学)
甲第21374号
農博第2298号
新制||農||1066(附属図書館)
学位論文||H30||N5147(農学部図書室)
京都大学大学院農学研究科地域環境科学専攻
(主査)教授 村上 章, 教授 藤原 正幸, 教授 渦岡 良介
学位規則第4条第1項該当
37
Stenius, Ivan. "Finite element modelling of hydroelasticity in hull-water impacts." Licentiate thesis, KTH, Aeronautical and Vehicle Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4304.
Abstract:
The work in this thesis focuses on the use of explicit finite element analysis (FEA) in the modelling of fluid-structure interaction of panel-water impacts. Paper A, considers modelling of a two-dimensional rigid wedge impacting a calm water surface. From analytical methods and results of a systematic parameter study a generalised approach for determination of fluid discretization and contact parameters in the modelling of arbitrary hull-water impact situations is developed and presented. In paper B the finite element modelling methodology suggested in paper A is evaluated for elastic structures by a convergence study of structural response and hydrodynamic load. The structural hydroelastic response is systematically studied by a number of FE-simulations of different impact situations concerning panel deadrise, impact velocity and boundary conditions. In paper B a tentative method for dynamic characterization is also derived. The results are compared with other published results concerning hydroelasticity in panel water impacts. The long-term goal of this work is to develop design criteria, by which it can be determined whether the loading situation of a certain vessel type should be regarded as quasi-static or dynamic, and which consequence on the design a dynamic loading has.
38
Fjellstedt, Christoffer. "Methods for including stiffness parameters from reduced finite element models in simulations of multibody systems." Thesis, Uppsala universitet, Fasta tillståndets elektronik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-387499.
Abstract:
Two methods using lumped element (lumped parameter) methods to model flexible bodies have been presented. The methods are based on the concept of using a Guyan reduced stiffness matrix to describe the elasticity of a body. The component to be modeled has been divided into two parts using FE software and the mass and inertia tensor for the respective part of the component have been retrieved. The first method has been based on including the elements from the stiffness matrix in compliant constraints. The compliant constraints have been derived and a prototype has been implemented in MATLAB. It has been shown that using compliant constraints and stiffness parameters from a Guyan reduced stiffness matrix it is possible, with highly accurate results, to describe the deformation of a flexible body in multibody simulations. The second method is based on springs and dampers and has been implemented in the simulation environment Dymola. The springs and dampers have been constructed to include coupling elements from a Guyan reduced stiffness matrix. It has been shown that using the proposed method it is possible, with highly accurate results, to describe the static deformation of a flexible body. Further, using dynamic simulations of a full robot manipulator model, it has been shown that it is possible to use the spring-damper model to capture the deformation of the links of a manipulator in dynamic simulations with large translations and rotations.
39
FERRERO, ANDREA. "Computational fluid dynamics for aerospace propulsion systems: an approach based on discontinuous finite elements." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2598559.
Abstract:
The purpose of this work is the development of a numerical tool devoted to the
study of the flow field in the components of aerospace propulsion systems. The
goal is to obtain a code which can efficiently deal with both steady and unsteady
problems, even in the presence of complex geometries.
Several physical models have been implemented and tested, starting from Euler
equations up to a three equations RANS model. Numerical results have been compared
with experimental data for several real life applications in order to understand
the range of applicability of the code. Performance optimization has been
considered with particular care thanks to the participation to two international
Workshops in which the results were compared with other groups from all over the
world.
As far as the numerical aspect is concerned, state-of-art algorithms have been implemented
in order to make the tool competitive with respect to existing softwares.
The features of the chosen discretization have been exploited to develop adaptive
algorithms (p, h and hp adaptivity) which can automatically refine the discretization.
Furthermore, two new algorithms have been developed during the research
activity. In particular, a new technique (Feedback filtering [1]) for shock capturing
in the framework of Discontinuous Galerkin methods has been introduced. It is
based on an adaptive filter and can be efficiently used with explicit time integration
schemes. Furthermore, a new method (Enhance Stability Recovery [2]) for
the computation of diffusive fluxes in Discontinuous Galerkin discretizations has
been developed. It derives from the original recovery approach proposed by van
Leer and Nomura [3] in 2005 but it uses a different recovery basis and a different
approach for the imposition of Dirichlet boundary conditions. The performed numerical
comparisons showed that the ESR method has a larger stability limit in
explicit time integration with respect to other existing methods (BR2 [4] and original
recovery [3]). In conclusion, several well known test cases were studied in order
to evaluate the behavior of the implemented physical models and the performance
of the developed numerical schemes.
40
Bargos, Fabiano Fernandes 1984. "Implementação de elementos finitos de alta ordem baseado em produto tensorial." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263502.
Abstract:
Orientador: Marco Lucio BittencourtDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
Made available in DSpace on 2018-08-13T18:20:59Z (GMT). No. of bitstreams: 1 Bargos_FabianoFernandes_M.pdf: 7838730 bytes, checksum: fc693b4a6996fada9f50dfaa2a0a102b (MD5) Previous issue date: 2009
Resumo: Esse trabalho apresenta uma implementação, em ambiente MatLab, de códigos para o Método dos Elementos Finitos de Alta Ordem em malhas estruturadas e não estruturadas para aplicação em problemas 2D e 3D. Apresenta-se um resumo dos procedimentos para construção das bases de funções para quadrados, triângulos, hexaedros e tetraedros através do produto tensorial. Faz-se um estudo detalhado da continuidade C0 da aproximação para expansões modais em quadrados e mostra-se que com uma numeração adequada das funções de aresta a continuidade é automaticamente obtida. Por fim, através da imposição de uma solução analítica, analisam-se os problemas de projeção e Poisson, 2D e 3D, em malhas de quadrados, triângulos e hexaedros, para refinamentos h e p
Abstract: An implementation in MatLab environment of a code for the High Order Finite Element Method on structured and non-structured mesh for 2D and 3D application problems is showed. The construction of basis functions for squares, triangles, hexahedral and tetrahedral, based on tensorial product, is briefly presented. It is showed that the approximation continuity in modal expansions for squares can be reached with a suitable functions numbering. Finally, through a analytical solution, the 2D and 3D projection and Poisson problems are investigates in squares, triangles and hexahedrons meshes with h and p refinements
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
41
Li, Boning. "Extending the scaled boundary finite-element method to wave diffraction problems." University of Western Australia. School of Civil and Resource Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0173.
Abstract:
[Truncated abstract] The study reported in this thesis extends the scaled boundary finite-element method to firstorder and second-order wave diffraction problems. The scaled boundary finite-element method is a newly developed semi-analytical technique to solve systems of partial differential equations. It works by employing a special local coordinate system, called scaled boundary coordinate system, to define the computational field, and then weakening the partial differential equation in the circumferential direction with the standard finite elements whilst keeping the equation strong in the radial direction, finally analytically solving the resulting system of equations, termed the scaled boundary finite-element equation. This unique feature of the scaled boundary finite-element method enables it to combine many of advantages of the finite-element method and the boundaryelement method with the features of its own. ... In this thesis, both first-order and second-order solutions of wave diffraction problems are presented in the context of scaled boundary finite-element analysis. In the first-order wave diffraction analysis, the boundary-value problems governed by the Laplace equation or by the Helmholtz equation are considered. The solution methods for bounded domains and unbounded domains are described in detail. The solution process is implemented and validated by practical numerical examples. The numerical examples examined include well benchmarked problems such as wave reflection and transmission by a single horizontal structure and by two structures with a small gap, wave radiation induced by oscillating bodies in heave, sway and roll motions, wave diffraction by vertical structures with circular, elliptical, rectangular cross sections and harbour oscillation problems. The numerical results are compared with the available analytical solutions, numerical solutions with other conventional numerical methods and experimental results to demonstrate the accuracy and efficiency of the scaled boundary finite-element method. The computed results show that the scaled boundary finite-element method is able to accurately model the singularity of velocity field near sharp corners and to satisfy the radiation condition with ease. It is worth nothing that the scaled boundary finite-element method is completely free of irregular frequency problem that the Green's function methods often suffer from. For the second-order wave diffraction problem, this thesis develops solution schemes for both monochromatic wave and bichromatic wave cases, based on the analytical expression of first-order solution in the radial direction. It is found that the scaled boundary finiteelement method can produce accurate results of second-order wave loads, due to its high accuracy in calculating the first-order velocity field.
42
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1205350171405-81971.
Abstract:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this workIn der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben
43
Simon, Kristin [Verfasser]. "Higher order stabilized surface finite element methods for diffusion-convection-reaction equations on surfaces with and without boundary / Kristin Simon." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1147834520/34.
44
Nadukandi, Prashanth. "Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/109155.
Abstract:
We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction
(CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a
consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was
ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory
numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to
convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution
Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent
approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of
he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi:
10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is
used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good
shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the
Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to
ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the
problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi
dimensional extension of the HRPG method using multi-linear block finite elements is also presented.
Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz
equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method
(FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation
method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover
he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045-
7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the
analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi:
10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion
accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an
expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin
ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the
error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small.Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion
45
Tarar, Wasim Akram. "A New Finite Element Procedure for Fatigue Life Prediction and High Strain Rate Assessment of Cold Worked Advanced High Strength Steel." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1204575243.
46
Jirathearanat, Suwat. "Advanced methods for finite element simulation for part and process design in tube hydroforming." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1071878178.
Abstract:
Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains xxv, 222 p.; also includes graphics (some color). Includes bibliographical references (p. 185-191).
47
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.
Abstract:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work.In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.
48
Nguyen, Van-Dang. "High-Performance Finite Element Methods : with Application to Simulation of Diffusion MRI and Vertical Axis Wind Turbines." Licentiate thesis, KTH, Beräkningsvetenskap och beräkningsteknik (CST), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-225952.
Abstract:
The finite element methods (FEM) have been developed over decades, and together with the growth of computer engineering, they become more and more important in solving large-scale problems in science and industry. The objective of this thesis is to develop high-performance finite element methods (HP-FEM), with two main applications in mind: computational diffusion magnetic resonance imaging (MRI), and simulation of the turbulent flow past a vertical axis wind turbine (VAWT). In the first application, we develop an efficient high-performance finite element framework HP-PUFEM based on a partition of unity finite element method to solve the Bloch-Torrey equation in heterogeneous domains. The proposed framework overcomes the difficulties that the standard approaches have when imposing the microscopic heterogeneity of the biological tissues. We also propose artificial jump conditions at the external boundaries to approximate the pseudo-periodic boundary conditions which allows for the water exchange at the external boundaries for non-periodic meshes. The framework is of a high level simplicity and efficiency that well facilitates parallelization. It can be straightforwardly implemented in different FEM software packages and it is implemented in FEniCS for moderate-scale simulations and in FEniCS-HPC for the large-scale simulations. The framework is validated against reference solutions, and implementation shows a strong parallel scalability. Since such a high-performance simulation framework is still missing in the field, it can become a powerful tool to uncover diffusion in complex biological tissues. In the second application, we develop an ALE-DFS method which combines advanced techniques developed in recent years to simulate turbulence. We apply a General Galerkin (G2) method which is continuous piecewise linear in both time and space, to solve the Navier-Stokes equations for a rotating turbine in an Arbitrary Lagrangian-Eulerian (ALE) framework. This method is enhanced with dual-based a posterior error control and automated mesh adaptation. Turbulent boundary layers are modeled by a slip boundary condition to avoid a full resolution which is impossible even with the most powerful computers available today. The method is validated against experimental data of parked turbines with good agreements. The thesis presents contributions in the form of both numerical methods for high-performance computing frameworks and efficient, tested software, published open source as part of the FEniCS-HPC platform.QC 20180411
49
Mashmool, Mojtaba [Verfasser], and Stefanos [Akademischer Betreuer] Fasoulas. "Application of finite element methods to the simulation of high temperature superconductors / Mojtaba Mashmool ; Betreuer: Stefanos Fasoulas." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2018. http://d-nb.info/1153403625/34.
50
Schroeder, Philipp W. [Verfasser], Gert [Akademischer Betreuer] Lube, Gert [Gutachter] Lube, Andreas [Gutachter] Dillmann, and Leo G. [Gutachter] Rebholz. "Robustness of High-Order Divergence-Free Finite Element Methods for Incompressible Computational Fluid Dynamics / Philipp W. Schroeder ; Gutachter: Gert, Lube; Andreas, Dillmann; Leo G., Rebholz ; Betreuer: Gert, Lube." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2019. http://d-nb.info/1180026489/34.