Multilevel approximation of boundary integral operators

  • Authors:

  • Klaus Gibermann

  • Affiliations:

  • Ahead Software GmbH, Karlsbad, Germany

  • Venue:
  • Computing
  • Year:
  • 2001

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Abstract

In this paper we consider a multilevel approximation of boundaryelement matrices as they arise from the discretization of boundaryelement matrices as they arise from the discretization of boundaryintegral equations by Galerkins method. Our main emphasis lies inthe numerical treatment of boundary integral equations defined oncomplex detailed two-dimensional manifolds in the three dimensionalspace. Although we do not assume that the underlying discretizationhas any hierarchical structure we present a scheme which providesus with a suitable hierarchy. Under reasonable assumptions on thekernel of the integral operator our multilevel approximation leadsto a significant compression of the stiffness matrix withoutloosing the asymptotic approximation property of Galerkins method.An application of this approximation is the fast matrixmultiplication which is needed in an iterative solution process.