Bookcover of Subspace Correction Methods for Linear Elasticity
Booktitle:

Subspace Correction Methods for Linear Elasticity

Algebraic Multigrid & Subspace Corrections for almost incompressible Materials

Südwestdeutscher Verlag für Hochschulschriften (2012-09-04 )

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ISBN-13:

978-3-8381-3103-0

ISBN-10:
3838131037
EAN:
9783838131030
Book language:
English
Blurb/Shorttext:
The monograph at hand deals with the numerical solution of the equations of linear elasticity. We focus on first order discretizations of those equations by means of linear finite elements. In order to solve the arising discrete problems efficiently we exploit the framework of subspace correction methods. First we present an overview of existing subspace correction methods. Later we introduce in detail a variant, namely „algebraic multigrid based on computational molecules“ (AMGm), being specifically suitable for standard discretizations of the equations of linear elasticity. Since the standard linear discretization suffers from locking if the material becomes incompressible, we consider a varational formulation based on „reduced integration“ using piecewise linear finite elements in a second part. This discretization can be shown to be stable in the incompressible limit. In order to solve the arising discrete problem efficiently we discuss a preconditioner based on subspace corrections. This preconditioner is based on a suitable splitting of the vector space. With proper numerical methods for the subproblems we are able to set up an efficient and robust preconditioner.
Publishing house:
Südwestdeutscher Verlag für Hochschulschriften
Website:
https://www.svh-verlag.de
By (author) :
Erwin Karer
Number of pages:
144
Published on:
2012-09-04
Stock:
Available
Category:
Mathematics
Price:
69.90 €
Keywords:
Linear Elasticity, Algebraic Multigrid, subspace correction methods, almost incompressible

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