Дисертації з теми "Higher order finite element"
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Oskooei, Saeid G. "A higher order finite element for sandwich plate analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0014/MQ34105.pdf.
Повний текст джерелаEl-Esber, Lina. "Hierarchal higher order finite element modeling of periodic structures." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82483.
Повний текст джерелаWagner, Carlee F. "Improving shock-capturing robustness for higher-order finite element solvers." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101498.
Повний текст джерелаCataloged from PDF version of thesis.
Includes bibliographical references (pages 81-91).
Simulation of high speed flows where shock waves play a significant role is still an area of development in computational fluid dynamics. Numerical simulation of discontinuities such as shock waves often suffer from nonphysical oscillations which can pollute the solution accuracy. Grid adaptation, along with shock-capturing methods such as artificial viscosity, can be used to resolve the shock by targeting the key flow features for grid refinement. This is a powerful tool, but cannot proceed without first converging on an initially coarse, unrefined mesh. These coarse meshes suffer the most from nonphysical oscillations, and many algorithms abort the solve process when detecting nonphysical values. In order to improve the robustness of grid adaptation on initially coarse meshes, this thesis presents methods to converge solutions in the presence of nonphysical oscillations. A high order discontinuous Galerkin (DG) framework is used to discretize Burgers' equation and the Euler equations. Dissipation-based globalization methods are investigated using both a pre-defined continuation schedule and a variable continuation schedule based on homotopy methods, and Burgers' equation is used as a test bed for comparing these continuation methods. For the Euler equations, a set of surrogate variables based on the primitive variables (density, velocity, and temperature) are developed to allow the convergence of solutions with nonphysical oscillations. The surrogate variables are applied to a flow with a strong shock feature, with and without continuation methods, to demonstrate their robustness in comparison to the primitive variables using physicality checks and pseudo-time continuation.
by Carlee F. Wagner.
S.M.
Li, Ming-Sang. "Higher order laminated composite plate analysis by hybrid finite element method." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/40145.
Повний текст джерелаBonhaus, Daryl Lawrence. "A Higher Order Accurate Finite Element Method for Viscous Compressible Flows." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/29458.
Повний текст джерелаPh. D.
Garbin, Turpaud Fernando, and Pachas Ángel Alfredo Lévano. "Higher-order non-local finite element bending analysis of functionally graded." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2019. http://hdl.handle.net/10757/626024.
Повний текст джерелаTimoshenko Beam Theory (TBT) and an Improved First Shear Deformation Theory (IFSDT) are reformulated using Eringen’s non-local constitutive equations. The use of 3D constitutive equation is presented in IFSDT. A material variation is made by the introduction of FGM power law in the elasticity modulus through the height of a rectangular section beam. The virtual work statement and numerical results are presented in order to compare both beam theories.
Tesis
鍾偉昌 and Wai-cheong Chung. "Geometrically nonlinear analysis of plates using higher order finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207601.
Повний текст джерелаChung, Wai-cheong. "Geometrically nonlinear analysis of plates using higher order finite elements /." [Hong Kong : University of Hong Kong], 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12225022.
Повний текст джерелаMarais, Neilen. "Higher order hierarchal curvilinear triangular vector elements for the finite element method in computational electromagnetics." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53447.
Повний текст джерелаENGLISH ABSTRACT: The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can be used to solve a large class of Electromagnetics problems with high accuracy, and good computational efficiency. Computational efficiency can be improved by using element basis functions of higher order. If, however, the chosen element type is not able to accurately discretise the computational domain, the converse might be true. This paper investigates the application of elements with curved sides, and higher order basis functions, to computational domains with curved boundaries. It is shown that these elements greatly improve the computational efficiency of the FEM applied to such domains, as compared to using elements with straight sides, and/or low order bases.
AFRIKAANSE OPSOMMING: Die Eindige Element Metode (EEM) kan breedvoerig op Numeriese Elektromagnetika toegepas word, met uitstekende akkuraatheid en 'n hoë doeltreffendheids vlak. Numeriese doeltreffendheid kan verbeter word deur van hoër orde element basisfunksies gebruik te maak. Indien die element egter nie die numeriese domein effektief kan diskretiseer nie, mag die omgekeerde geld. Hierdie tesis ondersoek die toepassing van elemente met geboë sye, en hoër orde basisfunksies, op numeriese domeine met geboë grense. Daar word getoon dat sulke elemente 'n noemenswaardinge verbetering in die numeriese doeltreffendheid van die EEM meebring, vergeleke met reguit- en/of laer-orde elemente.
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.
Повний текст джерелаCataloged 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.
Alon, Yair. "Analysis of thick composite plates using higher order three dimensional finite elements." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA243188.
Повний текст джерелаThesis Advisor(s): Kolar, Ramesh. Second Reader: Lindsey, G. H. "December 1990." Description based on title screen as viewed on March 30, 2010. DTIC Descriptor(s): Thickness, stability, composite materials, laminates, theory, elastic properties, orientation(direction), composite structures, three dimensional, solutions(general), integration, plates, anisotropy, isotropism, convergence, thinness, behavior, nonlinear analysis, static tests, formulas(mathematics), lagrangian functions, fibers DTIC Identifier(s): Laminates, plates, structural response, composite structures, finite element analysis, nonlinear analysis, stress strain relations, theses, displacement, buckling, interpolation. Author(s) subject terms: Finite element, nonlinear analysis, plate bending thick plates, laminated composites, buckling, constant arc length three dimensional element Includes bibliographical references (p. 87-88). Also available in print.
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.
Повний текст джерелаLamichhane, Bishnu P. "Higher order mortar finite elements with dual Lagrange multiplier spaces and applications." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-26215.
Повний текст джерелаBucalém, Miguel Luiz. "On higher-order mixed-interpolated general shell finite elements." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/60125.
Повний текст джерелаPipilis, 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.
Повний текст джерелаHamiche, Karim. "A high-order finite element model for acoustic propagation." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/400677/.
Повний текст джерелаLu, Hongqiang. "High order finite element solution of elastohydrodynamic lubrication problems." Thesis, University of Leeds, 2006. http://etheses.whiterose.ac.uk/1341/.
Повний текст джерелаQuattrochi, Douglas J. (Douglas John). "Hypersonic heat transfer and anisotropic visualization with a higher order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35567.
Повний текст джерелаIncludes bibliographical references (leaves 83-89).
Higher order discretizations of the Navier-Stokes equations promise greater accuracy than conventional computational aerodynamics methods. In particular, the discontinuous Galerkin (DG) finite element method has O(hP+l) design accuracy and allows for subcell resolution of shocks. This work furthers the DG finite element method in two ways. First, it demonstrates the results of DG when used to predict heat transfer to a cylinder in a hypersonic flow. The strong shock is captured with a Laplacian artificial viscosity term. On average, the results are in agreement with an existing hypersonic benchmark. Second, this work improves the visualization of the higher order polynomial solutions generated by DG with an adaptive display algorithm. The new algorithm results in more efficient displays of higher order solutions, including the hypersonic flow solutions generated here.
by Douglas J. Quattrochi.
S.M.
Sticko, Simon. "Towards higher order immersed finite elements for the wave equation." Licentiate thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-301937.
Повний текст джерелаeSSENCE
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.
Повний текст джерелаMarais, Neilen. "Efficient high-order time domain finite element methods in electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1499.
Повний текст джерелаThe 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.
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.
Повний текст джерелаBen, Romdhane Mohamed. "Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/39258.
Повний текст джерелаPh. D.
Barrera, Cruz Jorge Luis. "A Hierarchical Interface-enriched Finite Element Method for the Simulation of Problems with Complex Morphologies." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430838711.
Повний текст джерелаAghabarati, 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.
Повний текст джерелаLa 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.
Barter, Garrett E. (Garrett Ehud) 1979. "Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44931.
Повний текст джерелаThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 135-143).
The accurate simulation of supersonic and hypersonic flows is well suited to higher-order (p > 1), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary. Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a nonsmooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficulties, this work proposes a new, higher-order, state based artificial viscosity with an associated governing partial differential equation (PDE). In the governing PDE, the shock sensor acts as a forcing term, driving the artificial viscosity to a non-zero value where it is necessary. The decay rate of the higher-order solution modes and edge-based jumps are both shown to be reliable shock indicators. This new approach leads to a smooth, higher-order representation of the artificial viscosity that evolves in time with the solution. For applications involving the Navier-Stokes equations, an artificial dissipation operator that preserves total enthalpy is introduced. The combination of higher-order, PDE-based artificial viscosity and enthalpy-preserving dissipation operator is shown to overcome the disadvantages of the non-smooth artificial viscosity. The PDE-based artificial viscosity can be used in conjunction with an automated grid adaptation framework that minimizes the error of an output functional. Higher-order solutions are shown to reach strict engineering tolerances with fewer degrees of freedom.
(cont.) The benefit in computational efficiency for higher-order solutions is less dramatic in the vicinity of the shock where errors scale with O(h/p). This includes the near-field pressure signals necessary for sonic boom prediction. When applied to heat transfer prediction on unstructured meshes in hypersonic flows, the PDE-based artificial viscosity is less susceptible to errors introduced by poor shock-grid alignment. Surface heating can also drive the output-based grid adaptation framework to arrive at the same heat transfer distribution as a well-designed structured mesh.
by Garrett Ehud Barter.
Ph.D.
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.
Повний текст джерелаRogers, Craig A. "An axisymmetric linear/high-order finite element for filament wound composite structures." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/52316.
Повний текст джерелаPh. D.
Ellis, Truman Everett. "High Order Finite Elements for Lagrangian Computational Fluid Dynamics." DigitalCommons@CalPoly, 2010. https://digitalcommons.calpoly.edu/theses/282.
Повний текст джерелаSantos, 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.
Повний текст джерелаTese (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
McIvor, James David Colin. "The analysis of dynamically loaded flexible journal bearings using higher-order finite elements." Thesis, King's College London (University of London), 1988. https://kclpure.kcl.ac.uk/portal/en/theses/the-analysis-of-dynamically-loaded-flexible-journal-bearings-using-higherorder-finite-elements(8cb1e4bc-41a7-4a66-bf72-5b5e93668509).html.
Повний текст джерелаJin, Si. "Structural damage detection using higher-order finite elements and a scanning laser vibrometer /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9974641.
Повний текст джерелаFranke, David [Verfasser]. "Investigation of mechanical contact problems with high-order Finite Element Methods / David Franke." Aachen : Shaker, 2012. http://d-nb.info/1067734902/34.
Повний текст джерелаAl-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.
Повний текст джерелаBagwell, Scott G. "A high order finite element coupled multi-physics approach to MRI scanner design." Thesis, Swansea University, 2018. https://cronfa.swan.ac.uk/Record/cronfa40797.
Повний текст джерелаSevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.
Повний текст джерелаLa 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.
Sato, Fernando Massami. "Numerical experiments with stable versions of the Generalized Finite Element Method." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-16102017-101710/.
Повний текст джерелаO Método dos Elementos Finitos Generalizados (MEFG) é essencialmente baseado no método da partição da unidade, que explora o conceito de partição da unidade para compatibilizar um conjunto de funções escolhidas para localmente aproximar de forma eficiente a solução. Apesar de suas vantagens bem conhecidas, o método pode apresentar algumas desvantagens. Por exemplo, o aumento do espaço de aproximação por meio das funções de enriquecimento pode introduzir dependências lineares no sistema de equações resolvente, assim como o aparecimento de elementos de mistura. Para contornar as desvantagens apontadas acima, algumas versões aprimoradas do MEFG foram desenvolvidas. O MEFG Estável é uma primeira versão aqui considerada na qual as funções de enriquecimento do MEFG são modificadas. O MEFG Estável de ordem superior propõe uma modificação adicional para a geração das funções de forma atreladas ao espaço enriquecido. Esta pesquisa visa apresentar e testar numericamente essas novas versões do MEFG recentemente propostas. Além de destacar suas principais características, alguns aspectos sobre a integração numérica quando usado o MEFG Estável de ordem superior, em particular, são também abordados. Por exemplo, detalha-se uma regra de divisão da área do elemento quadrilateral, guiada pela própria definição de sua partição da unidade. Os exemplos escolhidos para os experimentos numéricos consistem em chapas com geometrias favoráveis para explorar as vantagens de cada método. Essencialmente, examinam-se funções singulares com boas propriedades de aproximar a solução nas vizinhanças de vértices de cantos, bem como funções polinomiais para aproximar soluções suaves. Ademais, uma comparação entre o MEF convencional e os métodos aqui descritos é feita levando-se em consideração o número de condição do sistema escalonado e as razões de convergência do erro relativo em deslocamento. Finalmente, os experimentos numéricos mostram que o MEFG Estável de ordem superior é a mais robusta e confiável entre as versões do MEFG testadas.
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.
Повний текст джерелаStöcker, 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.
Повний текст джерелаIn 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
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.
Повний текст джерелаIn 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.
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.
Повний текст джерелаQC 20110627
Bangemann, Tim Richard. "Nonlinear finite element treatment of bifurcation in the post-buckling analysis of thin elastic plates and shells." Thesis, Brunel University, 1995. http://bura.brunel.ac.uk/handle/2438/6362.
Повний текст джерелаHauck, Andreas [Verfasser], and Manfred [Gutachter] Kaltenbacher. "Higher Order Finite Elements for Coupled and Anisotropic Field Problems / Andreas Hauck. Gutachter: Manfred Kaltenbacher." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2016. http://d-nb.info/1102529192/34.
Повний текст джерелаRawat, 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.
Повний текст джерелаGuo, Ruchi. "Design, Analysis, and Application of Immersed Finite Element Methods." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90374.
Повний текст джерелаDoctor 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.
Lee, Seung-Cheol. "Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1394730392.
Повний текст джерелаArthurs, 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.
Повний текст джерелаWang, Yaqi. "hp-mesh adaptation for 1-D multigroup neutron diffusion problems." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4707.
Повний текст джерелаRieben, 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.
Повний текст джерелаOliver, 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.
Повний текст джерелаThis 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.