Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition |
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Authors: | Ying Jiang |
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Affiliation: | a Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, PR China b Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA |
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Abstract: | We develop a fast fully discrete Fourier-Galerkin method for solving a class of singular boundary integral equations. We prove that the number of multiplications used in generating the compressed matrix is O(nlog3n), and the solution of the proposed method preserves the optimal convergence order O(n−t), where n is the order of the Fourier basis functions used in the method and t denotes the degree of regularity of the exact solution. Moreover, we propose a preconditioning which ensures the numerical stability when solving the preconditioned linear system. Numerical examples are presented to confirm the theoretical estimates and to demonstrate the approximation accuracy and computational efficiency of the proposed algorithm. |
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Keywords: | 65R20 45E05 41A55 65F35 |
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