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检索条件"丛书名=Lecture Notes in Computational Science and Engineering 37"

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Volume Locking Phenomena Arising in a Hybrid Symmetric Interior Penalty Method with Continuous Numerical Traces 23rd

Volume Locking Phenomena Arising in a Hybrid Symmetric Inter...

引用

23rd International Conference on Domain Decomposition Methods

作者： Koyama, Daisuke Kikuchi, Fumio Univ Electrocommun Chofugaoka 1-5-1 Chofu Tokyo Japan Univ Tokyo Meguro Ku Komaba 3-8-1 Tokyo Japan

A hybrid version of the symmetric interior penalty (HSIP) method is considered for linear elasticity problems for nearly incompressible materials. When the 1 conforming finite element method is applied to such problem... 详细信息

ISBN: (纸本)9783319523897;9783319523880

A hybrid version of the symmetric interior penalty (HSIP) method is considered for linear elasticity problems for nearly incompressible materials. When the ¹ conforming finite element method is applied to such problems, volume locking phenomena occur. Discontinuous Galerkin (DG) methods are known as a remedy for the locking. The HSIP method has two unknowns which are approximations for the displacement and its trace on the skeleton. The latter is often called the numerical trace. The HSIP method with the discontinuous numerical trace is free from locking. On the other hand, it is numerically observed that the HSIP method with the continuous numerical trace causes volume locking phenomena when the ¹ elements are employed for the two unknowns. The numerical fact is mathematically proved in this paper. © Springer International Publishing AG 2017.

关键词： Numerical methods

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Relaxing the Roles of Corners in BDDC by Perturbed Formulation 23rd

Relaxing the Roles of Corners in BDDC by Perturbed Formulati...

引用

23rd International Conference on Domain Decomposition Methods

作者： Badia, Santiago Hieu Nguyen Univ Politecn Cataluna Jordi Girona 1-3Edifici C1 ES-08034 Barcelona Spain UPC CIMNE Parc Mediterrani TecnolEsteve Terradas 5 Castelldefels 08860 Spain Duy Tan Univ Inst Res & Dev 3 Quang Trung Danang Vietnam

ISBN: (纸本)9783319523897;9783319523880

We present a perturbed formulation of the BDDC method where the invertibility of the global coarse matrix is automatically guaranteed and positive direct solvers can be used without corner constraints or a change of basis. The perturbed method has the same polylogarithmic bounds for the precondition number and is weakly scalable. It is suitable for large scale simulations as small coarse spaces associated with only edge or/and face constraints can be used. In addition, it offers extra robustness when there are disconnected subdomains or in other situations where constraints fails to fix a small number of rigid body modes. © Springer International Publishing AG 2017.

关键词： Artificial intelligence

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BDDC and FETI-DP Methods with Enriched Coarse Spaces for Elliptic Problems with Oscillatory and High Contrast Coefficients 23rd

BDDC and FETI-DP Methods with Enriched Coarse Spaces for Ell...

引用

23rd International Conference on Domain Decomposition Methods

作者： Kim, Hyea Hyun Chung, Eric T. Wang, Junxian Kyung Hee Univ Dept Appl Math Yongin South Korea Kyung Hee Univ Inst Nat Sci Yongin South Korea Chinese Univ Hong Kong Dept Math Sha Tin Hong Kong Peoples R China Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China

ISBN: (纸本)9783319523897;9783319523880

BDDC (Balancing Domain Decomposition by Constraints) and FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithms with adaptively enriched coarse spaces are developed and analyzed for second order elliptic problems with high contrast and random coefficients. Among many approaches to form adaptive coarse spaces, we consider an approach using eigenvectors of generalized eigenvalues problems defined on each subdomain interface, see Mandel and Sousedík (2007), Galvis and Efendiev (2010), Spillane et al. (2011), Spillane et al. (2013), Klawonn et al. (2015). © Springer International Publishing AG 2017.

关键词： Eigenvalues and eigenfunctions

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Evaluation of Local Multiscale Approximation Spaces for Partition of Unity Methods 1

引用

8th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Schweitzer, Marc Alexander Wu, Sa Rhein Friedrich Wilhelms Univ Bonn Inst Numer Simulat Wegelerstr 6 D-53115 Bonn Germany Fraunhofer Inst Algorithms & Sci Comp SCAI Sankt St Augustin Germany

ISBN: (数字)9783319519548

ISBN: (纸本)9783319519548;9783319519531

The simulation of the behavior of heterogeneous and composite materials poses a number of challenges to numerical methods e.g. due to the presence of discontinuous material coefficients. Moreover, the material properties of fibers and inclusions are significantly different from those of the surrounding matrix. Thus, the gradients of the solution feature a substantial discontinuity at the material interface between inclusions and matrix. Hence, materials with many fine scale inclusions need a very high resolution mesh in the context of traditional finite element (FE) analysis. However, many approaches within the context of numerical homogenization have been proposed to tackle and overcome this need for a large number of degrees of freedom. To this end, either discontinuous coefficients are replaced by smooth effective coefficients or, standard FE shape functions are replaced by more complex, numerically computed shape functions while the overall quality of the approximation is retained. In this paper we study two-dimensional examples of heat transfer and (linear) elasticity in composite materials using a number of different homogenization approaches with the overall goal of evaluating and comparing their performance when used for the construction of multiscale enrichment functions for a partition of unity method (PUM).

关键词： Composite materials

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Treatment of Singular Matrices in the Hybrid Total FETI Method 23rd

Treatment of Singular Matrices in the Hybrid Total FETI Meth...

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23rd International Conference on Domain Decomposition Methods

作者： Markopoulos, A. Riha, L. Brzobohaty, T. Jirutkova, P. Kucera, R. Meca, O. Kozubek, T. IT4Innovat Natl Supercomp Ctr 17 Listopadu15-2172 Ostrava Czech Republic

ISBN: (纸本)9783319523897;9783319523880

The goal is to show how to treat singular matrices via kernel detection so that any robust direct sparse solver for non-singular matrices may be used. This technique applied in the Hybrid total FETI method enables us to process large coarse problems, for which the classical FETI method fails. Efficiency of the algorithms is illustrated in our ESPRESO library for problems with billions of unknowns. © Springer International Publishing AG 2017.

关键词： Artificial intelligence

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Approximate Solutions to Poisson Equation Using Least Squares Support Vector Machines 1

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Wu, Ziku Liu, Zhenbin Li, Fule Yu, Jiaju Qingdao Agr Univ Sci & Informat Coll Qingdao 266109 Peoples R China Dalian Maritime Univ Sch Informat Sci & Technol Dalian 116026 Peoples R China

ISBN: (数字)9783319672021

ISBN: (纸本)9783319672021;9783319672014

This article deals with Poisson Equations with Dirichlet boundary conditions. A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solutions consist of two parts. The first part is a known function that satisfies boundary conditions. The other is two terms product. One term is known function which is zero on boundary, another term is unknown which is related to kernel functions. This method has been successfully tested on rectangle and disc domain and has yielded higher accuracy solutions.

关键词： Poisson equation

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.Preconditioning for Nonsymmetry and Time-Dependence 23rd

.Preconditioning for Nonsymmetry and Time-Dependence

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23rd International Conference on Domain Decomposition Methods

作者： McDonald, Eleanor Hon, Sean Pestana, Jennifer Wathen, Andy Univ Oxford Radcliffe Observ Quarter Math Inst Oxford OX2 6GG England Univ Strathclyde Dept Math & Stat Glasgow G1 1XH Lanark Scotland

ISBN: (纸本)9783319523897;9783319523880

For symmetric systems, rigorous convergence bounds can be obtained which depend only on the eigenvalues of the system. However for nonsymmetric systems, no generally descriptive convergence bounds are known and therefore the development of preconditioners for these problems is typically heuristic. In this paper, we describe one simple but frequently occurring example of nonsymmetric Toeplitz matrices, where we are able to guarantee rapid convergence of an appropriate iterative method. The method employs a simple trick of reordering the variables to rewrite the system as a symmetric one. A symmetric positive definite absolute value preconditioner is also proposed which is used within a standard symmetric solver such as minres. We also show how this can be applied to time-dependent linear ODEs which are inherently nonsymmetric. © Springer International Publishing AG 2017.

关键词： Iterative methods

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Domain Decomposition Methods in science and engineering XXIII 1st ed. 2017

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丛书名： lecture notes in computational science and engineering

2017年

作者： Chang-Ock Lee Xiao-Chuan Cai David E. Keyes Hyea Hyun Kim Axel Klawonn Eun-Jae Park Olof B. Widlund

ISBN: (数字)9783319523897

ISBN: (纸本)9783319523880

This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in science and engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.

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Deflated Krylov Iterations in Domain Decomposition Methods 23rd

Deflated Krylov Iterations in Domain Decomposition Methods

引用

23rd International Conference on Domain Decomposition Methods

作者： Gurieva, Y. L. Ilin, V. P. Perevozkin, D. V. RAS SB Inst Computat Math & Math Geophys Novosibirsk Russia Novosibirsk State Univ Novosibirsk Russia

ISBN: (纸本)9783319523897;9783319523880

The paper is dedicated to an experimental evaluation of some coarse grid techniques in the context of additive Schwarz method and Krylov subspace methods. Some theoretical aspects are considered and a few modifications of well-known methods are presented. The choice of a correction operator is also studied. The results indicate that a coarse grid correction approach may accelerate an iterative process if employed sensibly. The paper also presents a comparison of overlapping and coarse grid correction in terms of convergence speed and performance. © Springer International Publishing AG 2017.

关键词： Domain decomposition methods

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Meshless Multi-Point Flux Approximation 1

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8th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Lukyanov, Alexander A. Vuik, Cornelis Schlumberger Doll Res Ctr One Hampshire St Cambridge MA 02139 USA Delft Univ Technol Delft Inst Appl Math Fac Elect Engn Math & Comp Sci EEMCS NL-2628 CD Delft Netherlands

ISBN: (数字)9783319519548

ISBN: (纸本)9783319519548;9783319519531

The reservoir simulation of the complex reservoirs with anisotropic permeability, which includes faults and non-orthogonal grids, with a fully discontinuous permeability tensor in the discretization is a major challenge. Several methods have already been developed and implemented within industry standard reservoir simulators for non-orthogonal grids (e.g., Multi-Point Flux Approximation (MPFA) "O" method). However, it has been noticed that some of the numerical methods for elliptic/parabolic equations may violate the maximum principle (i.e., lead to spurious oscillations), especially when the anisotropy is particularly strong. It has been found that the oscillations are closely related to the poor approximation of the pressure gradient in the flux computation. Therefore, proposed methods must correctly approximate underlying operators, satisfy a discrete maximum principle and have coercivity properties. Furthermore, the method must be robust and efficient. This paper presents the meshless multi-point flux approximation of second order elliptic operators containing a tensor coefficient. The method is based on a pressure gradient approximation commonly used in meshless methods (or Smoothed Particle Hydrodynamics method-SPH method). The proposed discretization schemes can be written as a sum of sparse positive semidefinite matrix and perturbation matrix. We show that convergence rates are retained as for finite difference methods O(h(alpha));1 <= alpha <= 2, where h denotes the maximum particle spacing. The results are presented, discussed and future studies are outlined.

关键词： Pressure gradient

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