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