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Published in:
Multi-Scale Methods in Simulation—A Path to a Better Understanding of the Behaviour of StructuresMulti-scalemethod Read chapter Read first chapter

2019 | OriginalPaper | Chapter

5. Fast Boundary Element Methods for Composite Materials

Authors : Richards Grzhibovskis, Christian Michel, Sergej Rjasanow

Published in: Multi-scale Simulation of Composite Materials

Publisher: Springer Berlin Heidelberg

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Abstract

In this chapter, we construct numerical solutions to the problems in the field of solid mechanics by combining the Boundary Element Method (BEM) with interpolation by means of radial basis functions. The main task is to find an approximation to a particular solution of the corresponding elliptic system of partial differential equations. To construct the approximation, the differential operator is applied to a vector of radial basis functions. The resulting vectors are linearly combined to interpolate the function on the right-hand side. The solvability of the interpolation problem is established. Additionally, stability and accuracy estimates for the method are given. A fast numerical method for the solution of the interpolation problem is proposed. These theoretical results are then illustrated on several numerical examples related to the Lamé system.

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previous chapter Parallel Inelastic Heterogeneous Multi-Scale Simulations
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Footnotes
1
One seeks for the solution u in the subspace \(\left\{ v\in ( H^{1}( \varOmega ))^{3}:\text {div }\sigma _d( v,x) \in ( L^{2}( \varOmega ))^{3}\right\} \) of the Sobolev space \(( H^{1}( \varOmega ))^{3}\).
 
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Metadata
Title
Fast Boundary Element Methods for Composite Materials
Authors
Richards Grzhibovskis
Christian Michel
Sergej Rjasanow
Copyright Year
2019
Publisher
Springer Berlin Heidelberg
Book
Multi-scale Simulation of Composite Materials

Print ISBN: 978-3-662-57956-5

Electronic ISBN: 978-3-662-57957-2

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-662-57957-2_5

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