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Analysis of Boundary Element Methods for Laplacian Eigenvalue Problems
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- Introduction
- + Formulations and properties of Laplacian eigenvalue problems
- + Eigenvalue problems of holomorphic Fredholm operator functions
- + Approximation of holomorphic eigenvalue problems
- + Galerkin approximation of boundary integral operator eigenvalue problems
- + Numerical methods for algebraic nonlinear eigenvalue problems
- Numerical Experiments
- References
This book provides an analysis of the boundary element method for the numerical solution of Laplacian eigenvalue problems. The representation of Laplacian eigenvalue problems in the form of boundary integral equations leads to nonlinear eigenvalue problems for related boundary integral operators. The concept of holomorphic Fredholm operator functions is used for the analysis of the boundary integral formulations of Laplacian eigenvalue problems. A convergence and error analysis for the Galerkin approximation of eigenvalue problems for holomorphic coercive operator functions is established. These results are applied to the Galerkin boundary element discretization of Laplacian eigenvalue problems. Different methods for the solution of algebraic nonlinear eigenvalue problems such as inverse iteration, Rayleigh functional iterations and Kummer's method are presented. For the latter method a numerical analysis for simple and multiple eigenvalues is given. In a numerical example, a boundary element and a finite element approximation of a Laplacian eigenvalue problem are compared. The theoretical results of the analysis of the boundary element method could be confirmed.
Book Details
Authors
Series
Monographic Series TU Graz: Computation in Engineering and Science
Publishers
Verlag der Technischen Universität Graz
Publication year : 2009
License: All rights reserved ©
Times read: 4
