標題: | A fast iterative solver for the variable coefficient diffusion equation on a disk |
作者: | Lai, MC Tseng, YH 應用數學系 Department of Applied Mathematics |
關鍵字: | variable diffusion equation;polar coordinates;iterative method;Ginzburg-Landau vortices |
公開日期: | 1-九月-2005 |
摘要: | We present an efficient iterative method for solving the variable coefficient diffusion equation on a unit disk. The equation is written in polar coordinates and is discretized by the standard centered difference approximation under the grid arrangement by shifting half radial mesh away from the origin so that the coordinate singularity can be handled naturally without pole conditions. The resultant matrix is symmetric positive definite so the preconditioned conjugate gradient (PCG) method can be applied. Different preconditioners have been tested for comparison, in particular, a fast direct solver derived from the equation and the semi-coarsening multigrid are shown to be almost scalable with the problem size and outperform other preconditioners significantly. The present elliptic solver has been applied to study the vortex dynamics of the Ginzburg-Landau equation with a variable diffusion coefficient. (c) 2005 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.jcp.2005.02.005 http://hdl.handle.net/11536/13383 |
ISSN: | 0021-9991 |
DOI: | 10.1016/j.jcp.2005.02.005 |
期刊: | JOURNAL OF COMPUTATIONAL PHYSICS |
Volume: | 208 |
Issue: | 1 |
起始頁: | 196 |
結束頁: | 205 |
顯示於類別: | 期刊論文 |