A Boundary Element Algorithm for the Dirichlet Eigenvalue Problem of the Laplace Operator

O. Steinbach () and G. Unger ()
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O. Steinbach: Graz University of Technology, Institute of Computational Mathematics
G. Unger: Graz University of Technology, Institute of Computational Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 191-198 from Springer

Abstract: Abstract A novel boundary element method for the solution of the interior Dirichlet eigenvalue problem for the Laplace operator is presented and analyzed. Hereby, the linear eigenvalue problem for the partial differential operator is transformed into a nonlinear eigenvalue problem for an associated boundary integral operator. This nonlinear eigenvalue problem is solved by using a Newton scheme. We discuss the convergence and the boundary element discretization of this algorithm, and give some numerical results.

Keywords: Eigenvalue Problem; Boundary Element; Boundary Element Method; Partial Differential Operator; Simple Eigenvalue (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_22

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DOI: 10.1007/978-3-540-69777-0_22

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