Abstract
The solution of eigenvalue problems for partial differential operators by using boundary integral equation methods usually involves some Newton potentials which may be resolved by using a multiple reciprocity approach. Here we propose an alternative approach which is in some sense equivalent to the above. Instead of a linear eigenvalue problem for the partial differential operator we consider a nonlinear eigenvalue problem for an associated boundary integral operator. This nonlinear eigenvalue problem can be solved by using some appropriate iterative scheme, here we will consider a Newton scheme. We will discuss the convergence and the boundary element discretization of this algorithm, and give some numerical results.
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Steinbach, O., Unger, G. A boundary element method for the Dirichlet eigenvalue problem of the Laplace operator. Numer. Math. 113, 281–298 (2009). https://doi.org/10.1007/s00211-009-0239-1
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DOI: https://doi.org/10.1007/s00211-009-0239-1