標題: | Fast direct solver for Poisson equation in a 2D elliptical domain |
作者: | Lai, MC 應用數學系 Department of Applied Mathematics |
關鍵字: | fast Poisson solver;elliptical coordinates;compact scheme;symmetry condition |
公開日期: | 1-一月-2004 |
摘要: | In this article, we extend our previous work (M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56-68, 2002) for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution as a truncated Fourier series, then solving the differential equations of Fourier coefficients by finite difference discretizations. Using a grid by shifting half mesh away from the pole and incorporating the derived numerical boundary value, the difficulty of coordinate singularity can be elevated easily. Unlike the case of 2D disk domain, the present difference equation for each Fourier mode is coupled with its conjugate mode through the numerical boundary value near the pole; thus, those two modes are solved simultaneously. Both second- and fourth-order accurate schemes for Dirichlet and Neumann problems are presented. In particular, the fourth-order accuracy can be achieved by a three-point compact stencil which is in contrast to a five-point long stencil for the disk case. (C) 2003 Wiley Periodicals, Inc. |
URI: | http://dx.doi.org/10.1002/num.10080 http://hdl.handle.net/11536/27301 |
ISSN: | 0749-159X |
DOI: | 10.1002/num.10080 |
期刊: | NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS |
Volume: | 20 |
Issue: | 1 |
起始頁: | 72 |
結束頁: | 81 |
顯示於類別: | 期刊論文 |