# Multi-scale Simulation of Composite MaterialsFast Boundary Element Methods for Composite Materials

Multi-scale Simulation of Composite Materials: Fast Boundary Element Methods for Composite Materials [In this chapter, we construct numerical solutions to the problems in the field of solid mechanics by combining theMethodBoundary Element Boundary Element Method (BEM) with interpolation by means ofRadial basis functions 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 theLamésystem Lamé system.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Multi-scale Simulation of Composite MaterialsFast Boundary Element Methods for Composite Materials

Part of the Mathematical Engineering Book Series
Editors: Diebels, Stefan; Rjasanow, Sergej
44 pages

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# References (49)

Publisher
Springer Berlin Heidelberg
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
ISBN
978-3-662-57956-5
Pages
97 –141
DOI
10.1007/978-3-662-57957-2_5
Publisher site
See Chapter on Publisher Site

### Abstract

[In this chapter, we construct numerical solutions to the problems in the field of solid mechanics by combining theMethodBoundary Element Boundary Element Method (BEM) with interpolation by means ofRadial basis functions 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 theLamésystem Lamé system.]

Published: Feb 2, 2019