A fast Fourier-collocation method for second boundary integral equations

✍ Scribed by Haotao Cai

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 501 KB
• Volume: 234
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.12.012

✦ Synopsis

In this paper we develop a fast collocation method for second boundary integral equations by the trigonometric polynomials. We propose a convenient way to compress the dense matrix representation of a compact integral operator with a smooth kernel under the Fourier basis and the corresponding collocation functionals. The compression leads to a sparse matrix with only O(n log 2 n) number of nonzero entries, where 2n + 1 denotes the order of the matrix. Thus we develop a fast Fourier-collocation method. We prove that the fast Fourier-collocation method gives the optimal convergence order up to a logarithmic factor. Moreover, we design a fast scheme for solving the corresponding truncated linear system. We establish that this algorithm preserves the quasi-optimal convergence of the approximate solution with requiring a number of O(n log 3 n) multiplications.