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Numerische Mathematik

, Volume 123, Issue 1, pp 145–176 | Cite as

A Galerkin method for retarded boundary integral equations with smooth and compactly supported temporal basis functions

  • S. SauterEmail author
  • A. Veit
Article

Abstract

We consider retarded boundary integral formulations of the three-dimensional wave equation in unbounded domains. Our goal is to apply a Galerkin method in space and time in order to solve these problems numerically. In this approach the computation of the system matrix entries is the major bottleneck. We will propose new types of finite-dimensional spaces for the time discretization. They allow variable time-stepping, variable order of approximation and simplify the quadrature problem arising in the generation of the system matrix substantially. The reason is that the basis functions of these spaces are globally smooth and compactly supported. In order to perform numerical tests concerning our new basis functions we consider the special case that the boundary of the scattering problem is the unit sphere. In this case explicit solutions of the problem are available which will serve as reference solutions for the numerical experiments.

Mathematics Subject Classification

35L05 65N38 65R20 

Notes

Acknowledgments

Thanks are due to Christoph Schwab for fruitful discussions concerning the use of the PUM for the time discretization.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZurichSwitzerland

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