Circulant Wavelet Preconditioners for Solving Elliptic Differential Equations and Boundary Integral Equations |
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Authors: | D Rostami Varnos Fadrani |
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Institution: | (1) Department of Mathematics and Computer Science, Faculty of Science, University of Tehran, P.O. Box 14155-6455, Tehran, Iran |
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Abstract: | In this paper is discussed solving an elliptic equation and a boundary integral equation of the second kind by representation of compactly supported wavelets. By using wavelet bases and the Galerkin method for these equations, we obtain a stiff sparse matrix that can be ill-conditioned. Therefore, we have to introduce an operator which maps every sparse matrix to a circulant sparse matrix. This class of circulant matrices is a class of preconditioners in a Banach space. Based on having some properties in the spectral theory for this class of matrices, we conclude that the circulant matrices are a good class of preconditioners for solving these equations. We called them circulant wavelet preconditioners (CWP). Therefore, a class of algorithms is introduced for rapid numerical application. |
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Keywords: | Wavelets preconditioning circulant operator boundary integral equations |
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