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Erschienen in:
Multi-Scale Methods in Simulation—A Path to a Better Understanding of the Behaviour of StructuresMulti-scalemethod Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

5. Fast Boundary Element Methods for Composite Materials

verfasst von : Richards Grzhibovskis, Christian Michel, Sergej Rjasanow

Erschienen in: Multi-scale Simulation of Composite Materials

Verlag: 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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Vorheriges Kapitel Parallel Inelastic Heterogeneous Multi-Scale Simulations
Nächstes Kapitel Experimental Studies
Fußnoten
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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Metadaten
Titel
Fast Boundary Element Methods for Composite Materials
verfasst von
Richards Grzhibovskis
Christian Michel
Sergej Rjasanow
Copyright-Jahr
2019
Verlag
Springer Berlin Heidelberg
Buch
Multi-scale Simulation of Composite Materials

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

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

Copyright-Jahr: 2019

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

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