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Fast Solvers of the Lippmann-Schwinger Equation

  • Gennadi Vainikko
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)

Abstract

The electromagnetic and acoustic scattering problems for the Helmholtz equation in two and three dimensions are equivalent to the Lippmann-Schwinger equation which is a weakly singular volume integral equation on the support of the scatterer. We propose for the Lippmann-Schwinger equation two discretizations of the optimal accuracy order, accompanied by fast solvers of corresponding systems of linear equations. The first method is of the second order and based on simplest cubatures; the scatterer is allowed to be only piecewise smooth. The second method is of arbitrary order and is based on a fully discrete version of the collocation method with trigonometric test functions; the scatterer is assumed to be smooth on whole space ℝn and of compact support.

Keywords

Arithmetical Operation Fourier Coefficient Collocation Method Helmholtz Equation Piecewise Smooth 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Gennadi Vainikko
    • 1
  1. 1.Institute of MathematicsHelsinki University of TechnologyFinland

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