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Inexact Additive Schwarz Solvers for hp-FEM Discretizations in Three Dimensions

  • Sven Beuchler
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 66)

Abstract

In this paper, a boundary value problem of second order in three space dimensions is discretized by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned conjugate gradient method with an overlapping domain decomposition preconditioner with in-exact subproblem solvers. In addition to a global solver for the low order functions, the ingredients of this preconditioner are local solvers for the patches. Here, a solver is used which utilizes the tensor product structure of the patches. The efficiency in time and iteration numbers of the presented solver is shown in several numerical examples for diffusion like problems as well as for problems in linear elasticity.

Keywords

Bilinear Form Domain Decomposition Coarse Mesh Multigrid Method Spectral Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für Numerische SimulationRheinische Friedrich–Wilhelms–Universität BonnBonnGermany

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