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Fast Fourier–Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition

✍ Scribed by Ying Jiang; Yuesheng Xu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
463 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

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(n log 3 n), 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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