Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods

  • Cristian Pérez
  • Reinhold Schneider
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Wavelet Galerkin methods for integral operators yield numerically sparse discretizations. This concept can be applied to develop fast and efficient methods for boundary integral equations and solving boundary-value problems for second-order elliptic partial differential equations. We apply these methods to the coupling of finite and boundary element methods to solve an exterior two-dimensional Laplacian. Adopting biorthogonal wavelet matrix compression for the boundary terms with N j degrees of freedom, we show that it fits the optimal convergence rate of the coupling Galerkin methods, while the number of nonzero entries in the corresponding stiffness matrices is considerably smaller than NJ 2.


Bilinear Form Boundary Element Method Boundary Integral Equation Wavelet Base Biorthogonal Wavelet 
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© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Cristian Pérez
  • Reinhold Schneider

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