Error analysis of the Trefftz method for solving Laplace's eigenvalue problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:200

Article

Li, Zi-Cai

关键词: Trefftz method;    boundary approximation method;    eigenvalue problem;    Helmholtz equation;    interfaces;   

DOI  :  10.1016/j.cam.2005.12.017

来源: Elsevier

【 摘 要 】

For solving Laplace's eigenvalue problems we propose new algorithms using the Trefftz method (TM) (i.e., the boundary approximation method (BAM)), by means of degeneracy of numerical Helmholtz equations. Since piecewise particular solutions can be fully adopted, the new algorithms benefit high accuracy of eigenvalues and eigenfunctions, low cost in CPU time and computer storage. Also the algorithms can be applied to solve the problems with multiple interfaces and singularities. In this paper, error estimates are derived for the approximate eigenvalues and eigenfunctions obtained. Numerical experiments for smooth and singular solutions are reported in this paper to show significance of the algorithms proposed and to verify the theoretical results made. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free