An accurate Fourier-spectral solver for variable coefficient elliptic equations

Authors:
Moshe Israeli;Alexander Sherman
Affiliations:
Computer Science Department, Technion-Israel Institute of Technology, Technion city, Haifa, Israel;Applied Mathematics Department, Technion-Israel Institute of Technology, Technion city, Haifa, Israel
Venue:
ISTASC'05 Proceedings of the 5th WSEAS/IASME International Conference on Systems Theory and Scientific Computation
Year:
2005

Citing 5
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Abstract

We develop a solver for nonseparable, self adjoint elliptic equations with a variable coefficient. If the coefficient is the square of a harmonic function, a transformation of the dependent variable, results in a constant coefficient Poisson equation. A highly accurate, fast, Fourier-spectral algorithm can solve this equation. When the square root of the coefficient is not harmonic, we approximate it by a harmonic function. A small number of correction steps are then required to achieve high accuracy. The procedure is particularly efficient when the approximation error is small. For a given function this error becomes smaller as the size of the domain decreases. A highly parallelizable, hierarchical procedure allows a decomposition into small sub-domains. Numerical experiments illustrate the accuracy of the approach even at very coarse resolutions.