| Abstract: | Chebyshev collocation techniques are developed in this paper to compute the eigenvalues of the Laplacian based on a boundary integral formulation for two-dimensional domains with piecewise smooth boundaries. Unlike the traditional domain methods (for example, the finite element method) which discretizes the eigenfunctions on the two-dimensional domain, only a one-dimensional function defined on the boundary is discretized. Global expansions in terms of Chebyshev polynomials are used in each smooth piece of the boundary to solve the integral equation. Comparing with the boundary element method, this method obtains higher accuracy for a smaller discretized matrix. Finally, an efficient algorithm for generating the discretized matrix (say, n × n) is developed that requires only O(n2 log n) operations. |
