Symmetry Reductions and Multigrid-Finite Element Methods for Semilinear Elliptic Eigenvalue Problems

• Main Authors: Cheng Hsuan Li, 李政軒
• Other Authors: Cheng Sheng Chien
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/42942115681719457351

碩士 === 國立中興大學 === 應用數學系 === 91 === We discuss effcient numerical methods for solving semilinear elliptic eigenvalue problems. First, we use the ideal of symmetry reductions to discretize our problems in a symmetry cell by the finite element method. By doing this the size of the discretized matrix becomes relatively small. Then we incorporate the V -cycle scheme multigrid method in the context of continuation method to trace solution branches of the discrete problems, where the Lanczos method is used as the relaxation scheme. Finally, we report some numerical results to show the algorithms we propose are effcient and robust, which also can be easily implemented.