Bibliografie tematiche / High-Order finite element methods

Letteratura scientifica selezionata sul tema "High-Order finite element methods"

Autore: Grafiati

Pubblicato: 8 giugno 2024

Cita una fonte nei formati APA, MLA, Chicago, Harvard e in molti altri stili

Scegli il tipo di fonte:

Consulta la lista di attuali articoli, libri, tesi, atti di convegni e altre fonti scientifiche attinenti al tema "High-Order finite element methods".

Accanto a ogni fonte nell'elenco di riferimenti c'è un pulsante "Aggiungi alla bibliografia". Premilo e genereremo automaticamente la citazione bibliografica dell'opera scelta nello stile citazionale di cui hai bisogno: APA, MLA, Harvard, Chicago, Vancouver ecc.

Puoi anche scaricare il testo completo della pubblicazione scientifica nel formato .pdf e leggere online l'abstract (il sommario) dell'opera se è presente nei metadati.

Articoli di riviste sul tema "High-Order finite element methods":

Abreu, Eduardo, Ciro Díaz, Juan Galvis e Marcus Sarkis. "On high-order conservative finite element methods". Computers & Mathematics with Applications 75, n. 6 (marzo 2018): 1852–67. http://dx.doi.org/10.1016/j.camwa.2017.10.020.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Harari, Isaac, e Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems". Journal of Computational Acoustics 05, n. 01 (marzo 1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

The goal of this work is to design and analyze quadratic finite elements for problems of time-harmonic acoustics, and to compare the computational efficiency of quadratic elements to that of lower-order elements. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solutions to exterior problems. Galerkin/least-squares technology is utilized to develop robust methods in which stability properties are enhanced while maintaining higher-order accuracy. The design of Galerkin/least-squares methods depends on the order of interpolation employed, and in this case quadratic elements are designed to yield dispersion-free solutions to model problems. The accuracy of Galerkin/least-squares and traditional Galerkin elements is compared, as well as the accuracy of quadratic versus standard linear interpolation, incorporating the effects of representing the radiation condition in exterior problems. The efficiency of the various methods is measured in terms of the cost of computation, rather than resolution requirements. In this manner, clear guidelines for selecting the order of interpolation are derived. Numerical testing validates the superior performance of the proposed methods. This work is a first step to gaining a thorough analytical understanding of the performance of p refinement as a basis for the development of h-p finite element methods for large-scale computation of solutions to acoustic problems.

Bagheri, Babak, L. Ridgway Scott e Shangyou Zhang. "Implementing and using high-order finite element methods". Finite Elements in Analysis and Design 16, n. 3-4 (giugno 1994): 175–89. http://dx.doi.org/10.1016/0168-874x(94)90063-9.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Lin, Qun, e Junming Zhou. "Superconvergence in high-order Galerkin finite element methods". Computer Methods in Applied Mechanics and Engineering 196, n. 37-40 (agosto 2007): 3779–84. http://dx.doi.org/10.1016/j.cma.2006.10.027.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Larson, Mats G., e Sara Zahedi. "Stabilization of high order cut finite element methods on surfaces". IMA Journal of Numerical Analysis 40, n. 3 (25 aprile 2019): 1702–45. http://dx.doi.org/10.1093/imanum/drz021.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

Abstract We develop and analyse a stabilization term for cut finite element approximations of an elliptic second-order partial differential equation on a surface embedded in ${\mathbb{R}}^d$. The new stabilization term combines properly scaled normal derivatives at the surface together with control of the jump in the normal derivatives across faces, and provides control of the variation of the finite element solution on the active three-dimensional elements that intersect the surface. We show that the condition number of the stiffness matrix is $O(h^{-2})$, where $h$ is the mesh parameter. The stabilization term works for linear as well as for higher-order elements and the derivation of its stabilizing properties is quite straightforward, which we illustrate by discussing the extension of the analysis to general $n$-dimensional smooth manifolds embedded in ${\mathbb{R}}^d$, with codimension $d-n$. We also state the properties of a general stabilization term that are sufficient to prove optimal scaling of the condition number and optimal error estimates in energy- and $L^2$-norm. We finally present numerical studies confirming our theoretical results.

Winther, Kaibo Hu &. Ragnar. "Well-Conditioned Frames for High Order Finite Element Methods". Journal of Computational Mathematics 39, n. 3 (giugno 2021): 333–57. http://dx.doi.org/10.4208/jcm.2001-m2018-0078.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Dobrev, Veselin A., Tzanio V. Kolev e Robert N. Rieben. "High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics". SIAM Journal on Scientific Computing 34, n. 5 (gennaio 2012): B606—B641. http://dx.doi.org/10.1137/120864672.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Yurun, Fan, e M. J. Crochet. "High-order finite element methods for steady viscoelastic flows". Journal of Non-Newtonian Fluid Mechanics 57, n. 2-3 (maggio 1995): 283–311. http://dx.doi.org/10.1016/0377-0257(94)01338-i.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Opschoor, Joost A. A., Philipp C. Petersen e Christoph Schwab. "Deep ReLU networks and high-order finite element methods". Analysis and Applications 18, n. 05 (21 febbraio 2020): 715–70. http://dx.doi.org/10.1142/s0219530519410136.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

Approximation rate bounds for emulations of real-valued functions on intervals by deep neural networks (DNNs) are established. The approximation results are given for DNNs based on ReLU activation functions. The approximation error is measured with respect to Sobolev norms. It is shown that ReLU DNNs allow for essentially the same approximation rates as nonlinear, variable-order, free-knot (or so-called “[Formula: see text]-adaptive”) spline approximations and spectral approximations, for a wide range of Sobolev and Besov spaces. In particular, exponential convergence rates in terms of the DNN size for univariate, piecewise Gevrey functions with point singularities are established. Combined with recent results on ReLU DNN approximation of rational, oscillatory, and high-dimensional functions, this corroborates that continuous, piecewise affine ReLU DNNs afford algebraic and exponential convergence rate bounds which are comparable to “best in class” schemes for several important function classes of high and infinite smoothness. Using composition of DNNs, we also prove that radial-like functions obtained as compositions of the above with the Euclidean norm and, possibly, anisotropic affine changes of co-ordinates can be emulated at exponential rate in terms of the DNN size and depth without the curse of dimensionality.

Jund, Sébastien, e Stéphanie Salmon. "Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping". International Journal of Applied Mathematics and Computer Science 17, n. 3 (1 ottobre 2007): 375–93. http://dx.doi.org/10.2478/v10006-007-0031-2.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

Arbitrary High-Order Finite Element Schemes and High-Order Mass LumpingComputers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of orderkand show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up toP5elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

Più fonti

Tesi sul tema "High-Order finite element methods":

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

Guo, Ruchi. "Design, Analysis, and Application of Immersed Finite Element Methods". Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90374.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

Mathematics
Ph.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

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.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)". Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

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.

Più fonti

Libri sul tema "High-Order finite element methods":

S̆olin, Pavel. Higher-order finite element methods. Boca Raton, Fla: Chapman & Hall/CRC, 2004.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Vandandoo, Ulziibayar, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky e Galmandakh Chuluunbaatar. High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-44784-6.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

University of Wales. Institute for Numerical Methods in Engineering. e Langley Research Center. Aerothermal Loads Branch., a cura di. Finite element methods of analysis for high speed viscous flows. Hampton, Va: Aerothermal Loads Branch, Loads and Aeroelasticity Division, NASA Langley Research Center, 1987.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

George C. Marshall Space Flight Center., a cura di. Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows. Marshall Space Flight Center, Ala: NASA-Marshall Space Flight Center, 1988.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Zhang, Yong-Tao. High order WENO schemes for Hamilton-Jacobi equations on triangular meshes. Hampton, Va: ICASE, NASA Langley Research Center, 2001.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Yan, Jue. Local discontinuous Galerkin methods for partial differential equations with higher order derivates. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Hsing-jen, Chang, e Langley Research Center, a cura di. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Xingren, Zhang, e Langley Research Center, a cura di. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Cerca il testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Più fonti

Capitoli di libri sul tema "High-Order finite element methods":

Lyu, Yongtao. "High Order Lagrange Element". In Finite Element Method, 171–94. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_8.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Khursheed, Anjam. "High-Order Elements". In The Finite Element Method in Charged Particle Optics, 99–110. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5201-7_5.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Duczek, S., C. Willberg e U. Gabbert. "Higher Order Finite Element Methods". In Lamb-Wave Based Structural Health Monitoring in Polymer Composites, 117–59. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49715-0_6.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Lin, Qun. "High Performance Finite Element Methods". In Recent Progress in Computational and Applied PDES, 269–88. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0113-8_20.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Schöberl, Joachim, e Christoph Lehrenfeld. "Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes". In Advanced Finite Element Methods and Applications, 27–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_2.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

St.-Cyr, Amik, e Stephen J. Thomas. "High-Order Finite Element Methods for Parallel Atmospheric Modeling". In Lecture Notes in Computer Science, 256–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11428831_32.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Sabonnadière, Jean-Claude, e Jean-Louis Coulomb. "General theory of second order isoparametric elements". In Finite Element Methods in CAD, 91–103. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4684-8739-8_5.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Sabonnadière, Jean-Claude, e Jean-Louis Coulomb. "General theory of second order isoparametric elements". In Finite Element Methods in CAD, 91–103. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4615-9879-4_5.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Cuvelier, C., A. Segal e A. A. van Steenhoven. "Second Order Elliptic PDEs". In Finite Element Methods and Navier-Stokes Equations, 352–75. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_11.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Kyriakoudi, Konstantina C., e Michail A. Xenos. "Finite Element Methods with Higher Order Polynomials". In Exploring Mathematical Analysis, Approximation Theory, and Optimization, 161–76. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-46487-4_10.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Atti di convegni sul tema "High-Order finite element methods":

D'Aquila, Luke, Brian Helenbrook e Alireza Mazaheri. "High-Order Shock Fitting with Finite Element Methods". In AIAA AVIATION 2020 FORUM. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-3047.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Woopen, Michael, Aravind Balan e Georg May. "A Unifying Computational Framework for Adaptive High-Order Finite Element Methods". In 22nd AIAA Computational Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2015. http://dx.doi.org/10.2514/6.2015-2601.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Kollmannsberger, Stefan, Alexander Du¨ster e Ernst Rank. "Force Transfer for High Order Finite Element Methods Using Intersected Meshes". In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26539.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

High order Finite Element Methods have been shown to be an efficient approach for computing the behavior of fluids and structures alike. However the coupling of such methods in a framework for a partitioned fluid-structure interaction is still in its early stages. A difficulty hereby is a conservative transfer of the loads from the fluid to the solid and an appropriate transfer of the structural displacements back to the boundary of the fluid. This contribution describes the coupling of a high order finite element structural code to the commercial finite volume fluid solver CFX and focuses on the transfer of the loads. For this purpose, the fluid mesh and the structural mesh are intersected. The force acting on the solid is then computed by a composed integration scheme performed on the intersected mesh. The approach can be interpreted as a projection method taking into account the discretization on both sides, i.e. fluid and solid. Numerical examples will demonstrate the basic properties of this new type of data transfer.

Shumlak, U., R. Lilly, S. Miller, N. Reddell e E. Sousa. "High-order finite element method for plasma modeling". In 2013 IEEE 40th International Conference on Plasma Sciences (ICOPS). IEEE, 2013. http://dx.doi.org/10.1109/plasma.2013.6634927.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Shumlak, U., R. Lilly, S. Miller, N. Reddell e E. Sousa. "High-order finite element method for plasma modeling". In 2013 IEEE Pulsed Power and Plasma Science Conference (PPPS 2013). IEEE, 2013. http://dx.doi.org/10.1109/ppc.2013.6627593.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Sheshadri, Abhishek, e Antony Jameson. "Shock detection and capturing methods for high order Discontinuous-Galerkin Finite Element Methods". In 32nd AIAA Applied Aerodynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-2688.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Shumlak, U., J. B. Coughlin, D. W. Crews, I. A. M. Datta, A. Ho, A. R. Johansen, E. T. Meier, Y. Takagaki e W. R. Thomas. "High-Order Finite Element Method for High-Fidelity Plasma Modeling". In 2020 IEEE International Conference on Plasma Science (ICOPS). IEEE, 2020. http://dx.doi.org/10.1109/icops37625.2020.9717941.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Troutman, Roy, e Nelson L. Max. "Radiosity algorithms using higher order finite element methods". In the 20th annual conference. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/166117.166144.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Wang, Li, W. Kyle Anderson e Lafayette K. Taylor. "Multiscale Large Eddy Simulation of Turbulence Using High-Order Finite Element Methods". In 7th AIAA Theoretical Fluid Mechanics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-3211.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Taggar, Karanvir, Emad Gad e Derek McNamara. "High-order unconditionally stable time-domain finite element method". In 2018 18th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM). IEEE, 2018. http://dx.doi.org/10.1109/antem.2018.8572958.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Rapporti di organizzazioni sul tema "High-Order finite element methods":

Kirby, Robert M., e Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, agosto 2008. http://dx.doi.org/10.21236/ada500484.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Kirby, Robert M., e Robert Haimes. Visualization of High-Order Finite Element Methods. Fort Belvoir, VA: Defense Technical Information Center, marzo 2013. http://dx.doi.org/10.21236/ada578239.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Gao, Kai. Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation. Office of Scientific and Technical Information (OSTI), novembre 2018. http://dx.doi.org/10.2172/1481964.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Adjerid, Slimane, Mohammed Aiffa e Joseph E. Flaherty. High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems. Fort Belvoir, VA: Defense Technical Information Center, dicembre 1993. http://dx.doi.org/10.21236/ada290410.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

White, D., M. Stowell, J. Koning, R. Rieben, A. Fisher, N. Champagne e N. Madsen. Higher-Order Mixed Finite Element Methods for Time Domain Electromagnetics. Office of Scientific and Technical Information (OSTI), febbraio 2004. http://dx.doi.org/10.2172/15014733.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Dobrev, V. A., F. C. Grogan, T. V. Kolev, R. Rieben e V. Z. Tomov. Level set methods for detonation shock dynamics using high-order finite elements. Office of Scientific and Technical Information (OSTI), maggio 2017. http://dx.doi.org/10.2172/1361591.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Rieben, Robert N. A Novel High Order Time Domain Vector Finite Element Method for the Simulation of Electromagnetic Devices. Office of Scientific and Technical Information (OSTI), gennaio 2004. http://dx.doi.org/10.2172/15014486.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Graville. L51764 Hydrogen Cracking in the Heat-Affected Zone of High-Strength Steels-Year 2. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), marzo 1997. http://dx.doi.org/10.55274/r0010170.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

During year 1 of this project a test to evaluate the sensitivity of the heat affected zone (HAZ) to hydrogen cracking was developed. This was in response to a need for a test which provided unambiguous results in contrast to existing test methods which often led to difficulties in interpretation. For example, WIC tests usually cracked in the weld metal rather than the HAZ and therefore did not produce a clear indication of the sensistivity of the HAZ. The new test involves a machined notch which can be placed in the HAZ thus forcing crack initiation to occur in the desired region. A further advantage of the new test is that it is quantitative with each test specimen providing a measure of the sensitivity of the HAZ in that test. Existing tests are usually of the crack/no-crack type requiring a series of tests at different preheats to be carried out in order to establish a critical value. This is an expensive, time-consuming approach. The new test measures the deflection to first load drop (normally the onset of significant cracking) when the welded specimen is loaded in bending. It was also shown during the first year of the project that the simple geometry of the test lends itself to easy analysis enabling the stress/strain distribution to be calculated by finite element analysis. The quantitative measurement of susceptibility in the test enabled the cracking of more complex welds to be predicted on the basis of a local critical hydrogen model. The objective of the work was to extend the notched bend test to the evaluation of weld metal sensitivity to hydrogen cracking. The experiments were designed to determine whether the test could discriminate between two different weld metals and to study the effects of reducing hydrogen content. In addition, finite element analysis of the weld metal test was carried out and finite difference analysis used to predict the local hydrogen concentration. This work modifies the notched bend test, developed for evaluating the sensitivity of the heat affected zone (HAZ), to allow the evaluation of weld metal. The results showed that weld metal could readily be evaluated, with the test discriminating among weld metals of different composition and hydrogen contact. Finite element analysis was undertaken and showed that for the two weld metals tested, cracking occurred at the same local stress when the hydrogen content was the same, despite differences in strength. A finite model was used to calculate the distribution of hydrogen as a function of aging time. Although the general trends were confirmed by the experimental measurements of hydrogen content, there was considerable scatter attributed to the small hydrogen volumes measured.

Jiang, W., e Benjamin W. Spencer. Modeling 3D PCMI using the Extended Finite Element Method with higher order elements. Office of Scientific and Technical Information (OSTI), marzo 2017. http://dx.doi.org/10.2172/1409274.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Chauhan. L52134 Development of Methods For Assessing Corrosion Metal Loss Defects In Casing Strings. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), luglio 2003. http://dx.doi.org/10.55274/r0010892.

Testo completo

Gli stili APA, Harvard, Vancouver, ISO e altri

Abstract (sommario):

An industry survey, dominated by PRCI member companies, was undertaken to gather key information regarding the design, operation and inspection of well bore casing strings. The aim of the survey was to gather information regarding the design standards, fields, gas composition, completion configuration, operational details, inspection methods and type of damage found. Survey results representing 67 storage facilities with a total of 4724 wells were received. This represents approximately 16% of US gas storage facilities. Facilities with initial completion dates between 1920 and 1990 were represented within the survey. The date of conversion from production to gas storage of the responding facilities ranged from the 1920�s to 2000. Non-linear finite element analysis has been used to determine the significance of an isolated pit corrosion metal loss defect in tubing/casing strings subject to the bounding load cases. Pit defects of depths up to 80% of the wall thickness (t) and diameter 2t were investigated to determine the failure behavior under the nineteen bounding load cases. Nine full-scale burst tests were undertaken in order to determine whether existing assessment methods could be used to predict failure of casing and tubing. Failure loci of 2t diameter and 80% deep defects have been derived for casing subject to combined loading. Full scale testing has only been undertaken with internal pressure loading to validate the approach taken to predict failure.