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


Files in This Item:

  1. 000228871500003.pdf

If it is a zip file, please download the file and unzip it, then open index.html in a browser to view the full text content.