標題: | Fast direct solver for the biharmonic equation on a disk and its application to incompressible flows |
作者: | Lai, MC Liu, HC 應用數學系 Department of Applied Mathematics |
關鍵字: | biharmonic equation;polar coordinates;Sherman-Morrison formula;FFT;vorticity stream function formulation |
公開日期: | 25-May-2005 |
摘要: | We develop a simple and efficient FFT-based fast direct solver for the biharmonic equation on a disk. The biharmonic equation is split into a coupled system of harmonic problems. We first use the truncated Fourier series expansion to derive a set of coupled singular ODEs, then we solve those singular equations by second-order finite difference discretizations. Using a radial grid with shifting a half mesh away from the origin, we can handle the coordinate singularity easily without pole conditions. The Sherman-Morrison formula is then applied to solve the resultant linear system in a cost-efficient way. The computational complexity of the method consists of O(MN log(2) N) arithmetic operations for M x N grid points. The numerical accuracy check and some applications to the incompressible Navier-Stokes flows inside a disk are conducted. (c) 2004 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.amc.2004.04.064 http://hdl.handle.net/11536/13699 |
ISSN: | 0096-3003 |
DOI: | 10.1016/j.amc.2004.04.064 |
期刊: | APPLIED MATHEMATICS AND COMPUTATION |
Volume: | 164 |
Issue: | 3 |
起始頁: | 679 |
結束頁: | 695 |
Appears in Collections: | Articles |
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