The numerical solution of the biharmonic equation by conformal mapping
Publication in refereed journal

香港中文大學研究人員

引用次數
替代計量分析
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其它資訊
摘要The solution to the biharmonic equation in a simply connected region Omega in the plane is computed in terms of the Goursat functions. The boundary conditions are conformally transplanted to the disk with a numerical conformal map. A linear system is obtained for the Taylor coefficients of the Goursat functions. The coefficient matrix of the linear system can be put in the form I + K, where K is the discretization of a compact operator. K can be thought of as the composition of a block Hankel matrix with a diagonal matrix. The compactness leads to clustering of eigenvalues, and the Hankel structure yields a matrix-vector multiplication cost of O(N log N). Thus, if the conjugate gradient method is applied to the system, then superlinear convergence will be obtained. Numerical results are given to illustrate the spectrum clustering and superlinear convergence.
著者Chan RH, Delillo TK, Horn MA
期刊名稱SIAM Journal on Scientific Computing
出版年份1997
月份11
日期1
卷號18
期次6
出版社SIAM PUBLICATIONS
頁次1571 - 1582
國際標準期刊號1064-8275
電子國際標準期刊號1095-7197
語言英式英語
關鍵詞biharmonic equation; Hankel matrices; numerical conformal mapping
Web of Science 學科類別Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED

上次更新時間 2020-20-11 於 01:59