Eigenvalue Characterization and Computation for the Laplacian on General 2-d Domains
نویسندگان
چکیده
In this paper we address the problem of determining and efficiently computing an approximation to the eigenvalues of the negative Laplacian −" on general domain Ω ⊂ R2 subject to homogeneous Dirichlet or Neumann boundary conditions. The basic idea is to look for eigenfunctions as the superposition of generalized eigenfunctions of the corresponding free space operator in the spirit of the classical Method of Particular Solutions. The main advantages of the proposed approach are the possibility of targeting each eigenvalue independently without need for extensive scanning of the positive real axis and the use of small matrices.
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