Готові списки джерел за темами / Multilevel Finite Element Method

Добірка наукової літератури з теми "Multilevel Finite Element Method"

Автор: Grafiati
Опубліковано: 14 березня 2023

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Статті в журналах з теми "Multilevel Finite Element Method"

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Niekamp, R., and E. Stein. "The hierarchically graded multilevel finite element method." Computational Mechanics 27, no. 4 (April 7, 2001): 302–4. http://dx.doi.org/10.1007/s004660100242.

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2

Han, Xiaole, Yu Li, and Hehu Xie. "A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods." Numerical Mathematics: Theory, Methods and Applications 8, no. 3 (August 2015): 383–405. http://dx.doi.org/10.4208/nmtma.2015.m1334.

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AbstractIn this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconforming finite element methods, this multilevel correction method can also produce the lower-bound approximations of the eigenvalues.
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3

Zhang, Yamiao, Biwu Huang, Jiazhong Zhang, and Zexia Zhang. "A Multilevel Finite Element Variational Multiscale Method for Incompressible Navier-Stokes Equations Based on Two Local Gauss Integrations." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/4917054.

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A multilevel finite element variational multiscale method is proposed and applied to the numerical simulation of incompressible Navier-Stokes equations. This method combines the finite element variational multiscale method based on two local Gauss integrations with the multilevel discretization using Newton correction on each step. The main idea of the multilevel finite element variational multiscale method is that the equations are first solved on a single coarse grid by finite element variational multiscale method; then finite element variational multiscale approximations are generated on a succession of refined grids by solving a linearized problem. Moreover, the stability analysis and error estimate of the multilevel finite element variational multiscale method are given. Finally, some numerical examples are presented to support the theoretical analysis and to check the efficiency of the proposed method. The results show that the multilevel finite element variational multiscale method is more efficient than the one-level finite element variational multiscale method, and for an appropriate choice of meshes, the multilevel finite element variational multiscale method is not only time-saving but also highly accurate.
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4

Hoppe, Ronald H. W., and Barbara Wohlmuth. "Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods." Applications of Mathematics 40, no. 3 (1995): 227–48. http://dx.doi.org/10.21136/am.1995.134292.

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5

Huang Junlong, 黄俊龙, and 余景景 Yu Jingjing. "Bioluminescence Tomography Based on Multilevel Adaptive Finite Element Method." Chinese Journal of Lasers 45, no. 6 (2018): 0607003. http://dx.doi.org/10.3788/cjl201845.0607003.

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6

Axelsson, O., and M. Larin. "An algebraic multilevel iteration method for finite element matrices." Journal of Computational and Applied Mathematics 89, no. 1 (March 1998): 135–53. http://dx.doi.org/10.1016/s0377-0427(97)00241-0.

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7

Akimov, Pavel A., Alexandr M. Belostosky, Marina L. Mozgaleva, Mojtaba Aslami, and Oleg A. Negrozov. "Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis." Advanced Materials Research 1040 (September 2014): 664–69. http://dx.doi.org/10.4028/www.scientific.net/amr.1040.664.

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The distinctive paper is devoted to correct multilevel discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.
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8

Aslami, Mojtaba, and Pavel A. Akimov. "Wavelet-based finite element method for multilevel local plate analysis." Thin-Walled Structures 98 (January 2016): 392–402. http://dx.doi.org/10.1016/j.tws.2015.10.011.

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Xie, Hehu, and Tao Zhou. "A multilevel finite element method for Fredholm integral eigenvalue problems." Journal of Computational Physics 303 (December 2015): 173–84. http://dx.doi.org/10.1016/j.jcp.2015.09.043.

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10

Lin, Qun, Hehu Xie, and Fei Xu. "Multilevel correction adaptive finite element method for semilinear elliptic equation." Applications of Mathematics 60, no. 5 (September 15, 2015): 527–50. http://dx.doi.org/10.1007/s10492-015-0110-x.

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Дисертації з теми "Multilevel Finite Element Method"

1

Jung, M., and U. Rüde. "Implicit extrapolation methods for multilevel finite element computations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800516.

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Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as \034 -extrapolation. For finite element systems this algorithm can be shown to be equivalent to higher order finite elements. The analysis is local and does not use global expansions, so that the implicit extrapolation technique may be used on unstructured meshes and in cases where the solution fails to be globally smooth. Furthermore, the natural multilevel structure can be used to construct efficient multigrid and multilevel preconditioning techniques. The effectivity of the method is demonstrated for heat conduction problems and problems from elasticity theory.
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2

Nepomnyaschikh, Sergey V. "Optimal Multilevel Extension Operators." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500971.

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In the present paper we suggest the norm-preserving explicit operator for the extension of finite-element functions from boundaries of domains into the inside. The construction of this operator is based on the multilevel decomposition of functions on the boundaries and on the equivalent norm for this decomposition. The cost of the action of this operator is proportional to the number of nodes.
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3

Green, Seth. "Multilevel, subdivision-based, thin shell finite elements : development and an application to red blood cell modeling /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/7110.

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4

Unwin, Helena Juliette Thomasin. "Uncertainty quantification of engineering systems using the multilevel Monte Carlo method." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277877.

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This thesis examines the quantification of uncertainty in real-world engineering systems using the multilevel Monte Carlo method. It is often infeasible to use the traditional Monte Carlo method to investigate the impact of uncertainty because computationally it can be prohibitively expensive for complex systems. Therefore, the newer multilevel method is investigated and the cost of this method is analysed in the finite element framework. The Monte Carlo and multilevel Monte Carlo methods are compared for two prototypical examples: structural vibrations and buoyancy driven flows through porous media. In the first example, the impact of random mass density is quantified for structural vibration problems in several dimensions using the multilevel Monte Carlo method. Comparable eigenvalues and energy density approximations are found for the traditional Monte Carlo method and the multilevel Monte Carlo method, but for certain problems the expectation and variance of the quantities of interest can be computed over 100 times faster using the multilevel Monte Carlo method. It is also tractable to use the multilevel method for three dimensional structures, where the traditional Monte Carlo method is often prohibitively expensive. In the second example, the impact of uncertainty in buoyancy driven flows through porous media is quantified using the multilevel Monte Carlo method. Again, comparable results are obtained from the two methods for diffusion dominated flows and the multilevel method is orders of magnitude cheaper. The finite element models for this investigation are formulated carefully to ensure that spurious numerical artefacts are not added to the solution and are compared to an analytical model describing the long term sequestration of CO2 in the presence of a background flow. Additional cost reductions are achieved by solving the individual independent samples in parallel using the new podS library. This library schedules the Monte Carlo and multilevel Monte Carlo methods in parallel across different computer architectures for the two examples considered in this thesis. Nearly linear cost reductions are obtained as the number of processes is increased.
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Bängtsson, Erik. "Robust Preconditioners Based on the Finite Element Framework." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7828.

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Robust preconditioners on block-triangular and block-factorized form for three types of linear systems of two-by-two block form are studied in this thesis. The first type of linear systems, which are dense, arise from a boundary element type of discretization of crack propagation problems. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems, which are sparse, indefinite and nonsymmetric, arise from a finite element (FE) discretization of the partial differential equations (PDE) that describe (visco)elastic glacial isostatic adjustment (GIA). The Schur complement approximation in the block preconditioners is constructed by assembly of local, exactly computed Schur matrices. The quality of the approximation is verified in numerical experiments. When the block preconditioners for the indefinite problem are combined with an inner iterative scheme preconditioned by a (nearly) optimal multilevel preconditioner, the resulting preconditioner is (nearly) optimal and robust with respect to problem size, material parameters, number of space dimensions, and coefficient jumps. Two approaches to mathematically formulate the PDEs for GIA are compared. In the first approach the equations are formulated in their full complexity, whereas in the second their formulation is confined to the features and restrictions of the employed FE package. Different solution methods for the algebraic problem are used in the two approaches. Analysis and numerical experiments reveal that the first strategy is more accurate and efficient than the latter. The block structure in the third type of algebraic systems is due to a fine-coarse splitting of the unknowns. The inverse of the pivot block is approximated by a sparse matrix which is assembled from local, exactly inverted matrices. Numerical experiments and analysis of the approximation show that it is robust with respect to problem size and coefficient jumps.
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6

Karlsson, Christian. "A comparison of two multilevel Schur preconditioners for adaptive FEM." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-219939.

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There are several algorithms for solving the linear system of equations that arise from the finite element method with linear or near-linear computational complexity. One way is to find an approximation of the stiffness matrix that is such that it can be used in a preconditioned conjugate residual method, that is, a preconditioner to the stiffness matrix. We have studied two preconditioners for the conjugate residual method, both based on writing the stiffness matrix in block form, factorising it and then approximating the Schur complement block to get a preconditioner. We have studied the stationary reaction-diffusion-advection equation in two dimensions. The mesh is refined adaptively, giving a hierarchy of meshes. In the first method the Schur complement is approximated by the stiffness matrix at one coarser level of the mesh, in the second method it is approximated as the assembly of local Schur complements corresponding to macro triangles. For two levels the theoretical bound of the condition number is 1/(1-C²) for either method, where C is the Cauchy-Bunyakovsky-Schwarz constant. For multiple levels there is less theory. For the first method it is known that the condition number of the preconditioned stiffness matrix is O(l²), where l is the number of levels of the preconditioner, or, equivalently, the number mesh refinements. For the second method the asymptotic behaviour is not known theoretically. In neither case is the dependency of the condition number of C known. We have tested both methods on several problems and found the first method to always give a better condition number, except for very few levels. For all tested problems, using the first method it seems that the condition number is O(l), in fact it is typically not larger than Cl. For the second method the growth seems to be superlinear.
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Aghabarati, Ali. "Multilevel and algebraic multigrid methods for the higher order finite element analysis of time harmonic Maxwell's equations." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=121485.

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The Finite Element Method (FEM) applied to wave scattering and quasi-static vector field problems in the frequency domain leads to sparse, complex-symmetric, linear systems of equations. For large problems with complicated geometries, most of the computer time and memory used by FEM goes to solving the matrix equation. Krylov subspace methods are widely used iterative methods for solving large sparse systems. They depend heavily on preconditioning to accelerate convergence. However, application of conventional preconditioners to the "curl-curl" operator which arises in vector electromagnetics does not result in a satisfactory performance and specialized preconditioning techniques are required. This thesis presents effective Multilevel and Algebraic Multigrid (AMG) preconditioning techniques for p-adaptive FEM analysis. In p-adaption, finite elements of different polynomial orders are present in the mesh and the system matrix can be structured into blocks corresponding to the orders of the basis functions. The new preconditioners are based on a p-type multilevel Schwarz (pMUS) approximate inversion of the block structured system. A V-cycle multilevel correction starts by applying Gauss-Seidel to the highest block level, then the next level down, and so on. On the other side of the V, Gauss-Seidel iterations are applied in the reverse order. At the bottom of the cycle is the lowest order system, which is usually solved exactly with a direct solver. The proposed alternative is to use Auxiliary Space Preconditioning (ASP) at the lowest level and continue the V-cycle downwards, first into a set of auxiliary, node-based spaces, then through a series of progressively smaller matrices generated by an Algebraic Multigrid (AMG). The algebraic coarsening approach is especially useful for problems with fine geometric details, requiring a very large mesh in which the bulk of the elements remain at low order. In addition, for wave problems, a "shifted Laplace" technique is applied, in which part of the ASP/AMG algorithm uses a perturbed, complex frequency. A significant convergence acceleration is achieved. The performance of Krylov algorithms is further enhanced during p-adaption by incorporation of a deflation technique. This projects out from the preconditioned system the eigenvectors corresponding to the smallest eigenvalues. The construction of the deflation subspace is based on efficient estimation of the eigenvectors from information obtained when solving the first problem in a p-adaptive sequence. Extensive numerical experiments have been performed and results are presented for both wave and quasi-static problems. The test cases considered are complicated to solve and the numerical results show the robustness and efficiency of the new preconditioners. Deflated Krylov methods preconditioned with the current Multilevel/ASP/AMG approach are always considerably faster than the reference methods and speedups of up to 10 are achieved for some test problems.
La méthode des éléments finis (FEM) appliquée à la dispersion des ondes et aux problèmes de champ de vecteurs quasi-statique dans le domaine fréquentiel mène à des systèmes d'équations linéaires rares, symétriques-complexes. Pour de grands problèmes ayant des géométries complexes, la plupart du temps et de la mémoire d'ordinateur utilisé par FEM va à la résolution de l'équation de la matrice. Les méthodes itératives de Krylov sont celles largement utilisées dans la résolution de grands systèmes creux. Elles dépendent fortement des préconditionnement qui accélèrent la convergence. Toutefois, l'application de préconditionnements conventionnels à l'opérateur "rot-rot" qui surgit en électromagnétisme vectoriel n'aboutit pas à des résultats satisfaisants et des techniques de préconditionnement spécialisés sont exigées.Cette thèse présente des techniques de préconditionnement efficaces multiniveau et multigrilles algébrique (AMG) pour l'analyse p-adaptative FEM. Dans la p-adaptation, des éléments finis de différents ordres polynomiaux sont présents dans le maillage et la matrice du système peut être structurée en blocs correspondant aux ordres des fonctions de base. Les nouveaux préconditionneurs sont basés sur un type d'inversion approximative à multiniveau p Schwarz (pMUS) du système structuré de bloc. Une correction à niveaux multiples en cycle V débute par l'application de Gauss-Seidel au niveau du bloc le plus élevé, suivi par le niveau inférieur, et ainsi de suite. De l'autre côté du V, des itérations de Gauss-Seidel sont appliquées en ordre inverse. Au bas du cycle se trouve le système d'ordre le plus bas, qui est habituellement résolu exactement avec un solveur direct. L'alternative proposée est d'utiliser l'espace auxiliaire de préconditionnement (ASP) au niveau le plus bas et de poursuivre le cycle en V vers le bas, d'abord en un ensemble d'auxiliaires, basé sur les espacements de nœuds, à travers une série de plus en plus petites de matrices générées par un multigrille algébrique (AMG). L'approche de grossissement algébrique est particulièrement utile aux problèmes ayant de fins détails géométriques, nécessitant une très grande maille dans laquelle la majeure partie des éléments restent à un niveau plus bas.En outre, pour des problèmes d'onde, la technique "décalé Laplace" est appliquée, dans laquelle une partie de l'algorithme ASP/AMG utilise une fréquence complexe perturbée. Une accélération de la convergence significative est atteinte. La performance des algorithmes de Krylov est davantage renforcée au cours du p-adaptation par l'incorporation d'une technique de déflation. Cette saillie fait dépasser hors du système préconditionné, les vecteurs propres correspondants aux plus petites valeurs propres. La construction du sous-espace de déflation est basée sur une estimation efficace des vecteurs propres à partir d'informations obtenues lors de la résolution du premier problème dans une séquence p-adaptatif. Des expériences numériques approfondies ont été effectuées et les résultats sont présentés à la fois aux problèmes d'onde et quasi-statiques. Les cas de test sont considérés comme compliqués à résoudre et les résultats numériques montrent la robustesse et l'efficacité des nouveaux préconditionnements. Les méthodes de Krylov de déflation préconditionnés par l'approche multiniveaux/ASP/AMG actuelle sont toujours considérablement plus rapides que les méthodes de référence et des accélérations allant jusqu'à 10 sont atteintes pour certains problèmes de test.
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8

Marquez, Damian Jose Ignacio. "Multilevel acceleration of neutron transport calculations." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19731.

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Thesis (M.S.)--Nuclear and Radiological Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Stacey, Weston M.; Committee Co-Chair: de Oliveira, Cassiano R.E.; Committee Member: Hertel, Nolan; Committee Member: van Rooijen, Wilfred F.G.
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9

Thess, M. "Parallel Multilevel Preconditioners for Problems of Thin Smooth Shells." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801416.

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In the last years multilevel preconditioners like BPX became more and more popular for solving second-order elliptic finite element discretizations by iterative methods. P. Oswald has adapted these methods for discretizations of the fourth order biharmonic problem by rectangular conforming Bogner-Fox-Schmidt elements and nonconforming Adini elements and has derived optimal estimates for the condition numbers of the preconditioned linear systems. In this paper we generalize the results from Oswald to the construction of BPX and Multilevel Diagonal Scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells of arbitrary forms where we use Koiter's equations of equilibrium for an homogeneous and isotropic thin shell, clamped on a part of its boundary and loaded by a resultant on its middle surface. We use the two discretizations mentioned above and the preconditioned conjugate gradient method as iterative method. The parallelization concept is based on a non-overlapping domain decomposition data structure. We describe the implementations of the multilevel preconditioners. Finally, we show numerical results for some classes of shells like plates, cylinders, and hyperboloids.
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10

Elfverson, Daniel. "Multiscale Methods and Uncertainty Quantification." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262354.

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In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements. We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. We prove that the error in the solution produced by the multiscale method decays independently of the fine scale variation in the data or the computational domain. We consider the following aspects of multiscale methods: continuous and discontinuous underlying numerical methods, adaptivity, convection-diffusion problems, Petrov-Galerkin formulation, and complex geometries. For uncertainty quantification problems we consider the estimation of p-quantiles and failure probability. We use spatial a posteriori error estimates to develop and improve variance reduction techniques for Monte Carlo methods. We improve standard Monte Carlo methods for computing p-quantiles and multilevel Monte Carlo methods for computing failure probability.
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Книги з теми "Multilevel Finite Element Method"

1

Oswald, Peter. Multilevel finite element approximation: Theory and applications. Stuttgart: Teubner, 1994.

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2

Dryja, Maksymilian. Multilevel additive methods for elliptic finite element problems. New York: Courant Institute of Mathematical Sciences, New York University, 1990.

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3

Mitchell, William F. Unified multilevel adaptive finite element methods for elliptic problems. Urbana, Ill: Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1988.

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4

B, James B., Riley Michael F, and Langley Research Center, eds. Structural optimization by generalized, multilevel decomposition. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1985.

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5

Multilevel block factorization preconditioners: Matrix-based analysis and algorithms for solving finite element equations. New York: Springer, 2008.

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6

Oswald, Peter. Multilevel Finite Element Approximation. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-91215-2.

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7

Lyu, Yongtao. Finite Element Method. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9.

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Dhatt, Gouri, Gilbert Touzot, and Emmanuel Lefrançois. Finite Element Method. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2012. http://dx.doi.org/10.1002/9781118569764.

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9

Lawrence, Taylor Richard, Nithiarasu Perumal, and Zhu J. Z, eds. The finite element method. 6th ed. Oxford: Elsevier/Butterworth-Heinemann, 2005.

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10

Poceski, A. Mixed finite element method. Berlin: Springer-Verlag, 1991.

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Частини книг з теми "Multilevel Finite Element Method"

1

Thess, Michael. "Multilevel Preconditioners for Temporal-Difference Learning Methods Related to Recommendation Engines." In Advanced Finite Element Methods and Applications, 175–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_8.

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2

Aslam, M. Nauman, Jiazhong Zhang, Nannan Dang, and Riaz Ahmad. "Model Reduction on Approximate Inertial Manifolds for NS Equations through Multilevel Finite Element Method and Hierarchical Basis." In Nonlinear Systems and Complexity, 249–70. Cham: Springer International Publishing, 2012. http://dx.doi.org/10.1007/978-3-030-94301-1_11.

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3

Lazarov, R. D., P. S. Vassilevski, and S. D. Margenov. "Solving elliptic problems by the domain decomposition method using preconditioning matrices derived by multilevel splittings of the finite element matrix." In Lecture Notes in Computer Science, 826–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/3-540-18991-2_47.

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4

Bramble, James H. "Multilevel Methods in Finite Elements." In Multiscale Problems and Methods in Numerical Simulations, 97–151. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-39810-3_3.

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Lyu, Yongtao. "Finite Element Analysis Using Triangular Element." In Finite Element Method, 93–118. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_5.

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Lyu, Yongtao. "Finite Element Analysis Using Rectangular Element." In Finite Element Method, 119–57. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_6.

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Lyu, Yongtao. "Finite Element Analysis Using Beam Element." In Finite Element Method, 65–92. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_4.

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Lyu, Yongtao. "Finite Element Analysis Using Bar Element." In Finite Element Method, 45–63. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_3.

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Otsuru, Toru, Takeshi Okuzono, Noriko Okamoto, and Yusuke Naka. "Finite Element Method." In Computational Simulation in Architectural and Environmental Acoustics, 53–78. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54454-8_3.

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Kuna, Meinhard. "Finite Element Method." In Solid Mechanics and Its Applications, 153–92. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6680-8_4.

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Тези доповідей конференцій з теми "Multilevel Finite Element Method"

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Akimov, Pavel A., Alexandr M. Belostoskiy, Vladimir N. Sidorov, Marina L. Mozgaleva, and Oleg A. Negrozov. "Application of discrete-continual finite element method for global and local analysis of multilevel systems." In INTERNATIONAL CONFERENCE ON PHYSICAL MESOMECHANICS OF MULTILEVEL SYSTEMS 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4901473.

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Kolchuzhin, Vladimir A., and Jan E. Mehner. "A parametric multilevel MEMS simulation methodology using finite element method and mesh morphing." In 2012 13th Intl. Conf. on Thermal, Mechanical & Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE). IEEE, 2012. http://dx.doi.org/10.1109/esime.2012.6191776.

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Yin, F., and X. Q. Sheng. "Application of multilevel inverse-based ILU preconditioning to implicit time domain finite element method." In Computational Electromagnetics (ICMTCE). IEEE, 2011. http://dx.doi.org/10.1109/icmtce.2011.5915540.

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Akimov, P. A., M. L. Mozgaleva, M. Aslami, and O. A. Negrozov. "Advanced Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Three-Dimensional Local Structural Analysis." In International Conference on Computer Information Systems and Industrial Applications. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/cisia-15.2015.194.

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Malhotra, Manish, and Peter M. Pinsky. "Matrix-Free Iterative Methods for Parallel Finite Element Computations in Acoustics." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0396.

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Анотація:
Abstract In this paper we consider the iterative solution of non-Hermitian, indefinite and complex-valued matrix problems arising from finite element discretization of time-harmonic acoustics problems in exterior domains. The computational model is based on using Galerkin least squares finite element methods for the acoustic fluid, combined with the non-local Dirichlet-to-Neumann map as the radiation boundary condition. The emphasis here is to develop efficient computational procedures that are suitable for parallel iterative solution of large-scale problems. In this context, we develop a low-storage implementation of the non-local DtN map which allows the use of this exact boundary condition without any storage penalties related to its non-local nature. In order to accelerate iterative convergence, we consider a multilevel preconditioning approach based on the h-version of the hierarchical finite element method. Finite element formulations that employ hierarchical shape functions yield better conditioned matrices than formulations based on the usual Lagrange functions. This improved conditioning translates into a faster rate of convergence if projections between nodal and hierarchical basis functions are used to construct the preconditioning operator. We present numerical results for the solution of two-dimensional scattering problems to examine convergence rates that are realized on practical discretizations.
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Tzoulis, A., and T. F. Eibert. "Antenna Modeling with the Hybrid Finite Element - Boundary Integral - Multilevel Fast Multipole - Uniform Geometrical Theory of Diffraction Method." In 2007 2nd International ITG Conference on Antennas. IEEE, 2007. http://dx.doi.org/10.1109/inica.2007.4353939.

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Ozgun, Ozlem, Raj Mittra, and Mustafa Kuzuoglu. "Solution of large scattering problems using a multilevel scheme in the context of Characteristic Basis Finite Element Method." In 2010 IEEE International Symposium Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting. IEEE, 2010. http://dx.doi.org/10.1109/aps.2010.5561875.

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Schobert, Dennis T., and Thomas F. Eibert. "Fast solution of finite element/boundary integral problems employing hierarchical Green's function interpolation combined with multilevel fast multipole method." In 2012 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2012. http://dx.doi.org/10.1109/iceaa.2012.6328717.

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Blondeel, Philippe, Pieterjan Robbe, Stijn François, Geert Lombaert, and Stefan Vandewalle. "An overview of p-refined Multilevel quasi-Monte Carlo Applied to the Geotechnical Slope Stability Problem." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12236.

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Анотація:
Engineering problems are often characterized by significant uncertainty in their material parameters. Multilevel sampling methods are a straightforward manner to account for this uncertainty. The most well known multilevel method is the Multilevel Monte Carlo method (MLMC). First developed by Giles, see [1], this method relies on a hierarchy of successive refined Finite Element meshes of the considered engineering problem, in order to achieve a computational speedup. Most of the samples are taken on coarse and computationally cheap meshes, while a decreasing number of samples are taken on finer and computationally expensive meshes. Classically, the mesh hierarchy is constructed by selecting a coarse mesh discretization of the problem, and recursively applying an h-refinement approach to it, see [2]. This will be referred to as h-MLMC. However, in the h-MLMC mesh hierarchy, the number of degrees of freedom increases almost geometrical with increasing level, leading to a large computational cost. An efficient manner to reduce this computational cost, is by means of the novel sampling method called p-refined Multilevel Quasi-Monte Carlo (p-MLQMC), see [3]. The p-MLQMC method uses a hierarchy of p-refined Finite Element meshes, combined with a deterministic Quasi-Monte Carlo sampling rule. This combination significantly reduced the computational cost with respect to h-MLMC. However, the p-MLQMC method presents the practitioner with a challenge. This challenge consists in adequately incorporating the uncertainty, represented as a random field, in the Finite Element model. In previous work, see [4], we have tackled this challenge by investigating how the evaluation points, used to calculate point evaluations of the random field by means of the Karhunen-Loève (KL) expansion, need to be selected in order to achieve the lowest computational cost. We found that using sets of nested evaluation points across the mesh hierarchy, i.e., the Local Nested Approach (LNA), yields a speedup up to a factor 5 with respect to sets consisting of non-nested evaluation points, i.e., the Non-Nested Approach (NNA). Furthermore, we have shown that p-MLQMC-LNA yields a speedup up to a factor 70 with respected to h-MLMC. Currently, our research focus lies on implementing the use of higher order Quasi-Monte Carlo rules, and hierarchical shape functions in p-MLQMC. Both paths show promising results for further computational savings in the p-MLQMC method. All the aforementioned implementations are benchmarked on a slope stability problem, with spatially varying uncertainty in the ground. The chosen quantity of interest (QoI) consists of the vertical displacement of the top of the slope.[1] Michael B. Giles. Multilevel Monte Carlo path simulation. Oper. Res., 56(3):607–617, 2008. [2] K. A. Cliffe, M. B. Giles, R. Scheichl, and A. L. Teckentrup. Multilevel Monte Carlo methods and applications to elliptic pdes with random coefficients. Comput. Vis. Sci., 14(1):3, Aug 2011. [3] Philippe Blondeel, Pieterjan Robbe, Cédric Van hoorickx, Stijn François, Geert Lombaert, and Stefan Vandewalle. p-refined multilevel quasi-monte carlo for galerkin finite element methods with applications in civil engineering. Algorithms, 13(5), 2020. [4] Philippe Blondeel, Pieterjan Robbe, Stijn François, Geert Lombaert, and Stefan Vandewalle. On the selection of random field evaluation points in the p-mlqmc method. arXiv, 2020.
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Tzoulis, A., and T. F. Eibert. "Computations for various edge configurations with the hybrid Finite Element - Boundary Integral - Multilevel Fast Multipole - uniform geometrical theory of diffraction method including double diffraction." In 2006 First European Conference on Antennas and Propagation Conference. IEEE, 2006. http://dx.doi.org/10.1109/eucap.2006.4584800.

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Звіти організацій з теми "Multilevel Finite Element Method"

1

Babuska, Ivo, Uday Banerjee, and John E. Osborn. Superconvergence in the Generalized Finite Element Method. Fort Belvoir, VA: Defense Technical Information Center, January 2005. http://dx.doi.org/10.21236/ada440610.

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Coyle, J. M., and J. E. Flaherty. Adaptive Finite Element Method II: Error Estimation. Fort Belvoir, VA: Defense Technical Information Center, September 1994. http://dx.doi.org/10.21236/ada288358.

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Babuska, I., and J. M. Melenk. The Partition of Unity Finite Element Method. Fort Belvoir, VA: Defense Technical Information Center, June 1995. http://dx.doi.org/10.21236/ada301760.

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Duarte, Carlos A. A Generalized Finite Element Method for Multiscale Simulations. Fort Belvoir, VA: Defense Technical Information Center, May 2012. http://dx.doi.org/10.21236/ada577139.

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Manzini, Gianmarco, and Vitaliy Gyrya. Final Report of the Project "From the finite element method to the virtual element method". Office of Scientific and Technical Information (OSTI), December 2017. http://dx.doi.org/10.2172/1415356.

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Manzini, Gianmarco. The Mimetic Finite Element Method and the Virtual Element Method for elliptic problems with arbitrary regularity. Office of Scientific and Technical Information (OSTI), July 2012. http://dx.doi.org/10.2172/1046508.

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Babuska, I., B. Andersson, B. Guo, H. S. Oh, and J. M. Melenk. Finite Element Method for Solving Problems with Singular Solutions. Fort Belvoir, VA: Defense Technical Information Center, July 1995. http://dx.doi.org/10.21236/ada301749.

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Babuska, Ivo, and Manil Suri. On Locking and Robustness in the Finite Element Method. Fort Belvoir, VA: Defense Technical Information Center, May 1990. http://dx.doi.org/10.21236/ada232245.

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Gerken, Jobie M. An implicit finite element method for discrete dynamic fracture. Office of Scientific and Technical Information (OSTI), December 1999. http://dx.doi.org/10.2172/751964.

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Roach, Robert. Laser Spot Welding using an ALE Finite Element Method. Office of Scientific and Technical Information (OSTI), April 2018. http://dx.doi.org/10.2172/1762029.

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