کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4640623 | 1341281 | 2010 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Fast Fourier–Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition Fast Fourier–Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition](/preview/png/4640623.png)
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)O(nlog3n), and the solution of the proposed method preserves the optimal convergence order O(n−t)O(n−t), where nn is the order of the Fourier basis functions used in the method and tt 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.
Journal: Journal of Computational and Applied Mathematics - Volume 234, Issue 9, 1 September 2010, Pages 2792–2807