20th GAMM-Seminar Leipzig on
Numerical Methods for Non-Local Operators

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
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  Wavlet-Galerkin solution of Partial differential equations
Patel Dhaneshkumar (University Baroda)

Discrete elliptic operators are used in the approximation of solution of a uniformly elliptic and possibly variable coefficient differential equations. In computations, the sparsity and small condition numbers of the discrete operators are the key to efficiency. Sparsity enhances the speed of iterations, while the small condition number guarantees rapid convergence of such iterations. The matrices that we obtain using finite difference methods are sparse. However, they have large condition numbers. Using the Galerkin method with Fourier system, we can obtain a bounded condition number but the matrix is no longer sparse. In the Galerkin method with a wavelet base, we obtain both the advantages. In the talk I will cover the following things: (1)Error estimates to show the advantage of wavelet-Galerkin method over finite difference method and Fourier-Galerkin method not only in terms of fast computation and rapid convergence but by obtaining better accuracy. (2)Use of different Wavelets to Solve PDE

References: [A] H.Resnikoff and R.Wells, Wavelet Analysis, Springer-Verlag, New York, 1998

[B] K.Amaratunga and Williams J., Wavelet-Galerkin solutions for one dimensional partial differential equations, International J. Num.Methods in Eng. 37(1994), pp.2703--2716.

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Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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