{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:37Z","timestamp":1787329297333,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We propose in this paper a convenient way to compress the dense matrix representation of a compact integral operator with a smooth kernel under the Fourier basis. The compression leads to a sparse matrix with only ${\\cal O}(n\\log n)$ nonzero entries, where $2n$ or $2n+1$ denotes the order of the matrix. Based on this compression strategy, we develop a fast Fourier\u2013Galerkin method for solving a class of singular boundary integral equations. We prove that the fast Fourier\u2013Galerkin method gives the optimal convergence order ${\\cal O}(n^{-t})$, where t denotes the degree of regularity of the exact solution. Moreover, we design a fast scheme for solving the corresponding truncated linear system. We show that solving this system requires only an ${\\cal O}(n\\log^2 n)$ number of multiplications. We present numerical examples to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed algorithm.<\/jats:p>","DOI":"10.1137\/070703478","type":"journal-article","created":{"date-parts":[[2008,4,18]],"date-time":"2008-04-18T18:06:43Z","timestamp":1208542003000},"page":"1965-1984","source":"Crossref","is-referenced-by-count":28,"title":["A Fast Fourier\u2013Galerkin Method for Solving Singular Boundary Integral Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Haotao","family":"Cai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuesheng","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,18]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"K. E. 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