An algorithm to compute the eigenvalues/functions of the laplacian operator within a region containing a sharp corner

Abstract

An algorithm to compute the eigenvalues/functions of the Laplacian operator within a region with a sharp corner or line segment is given. Point matching is used around the boundary and the algorithm is based on the Dew and Scraton (1973) method. It is shown that the numerical solution is an exact solution of a perturbed form of the problem and error estimates are obtained. A transformed problem, which eliminates the zero eigenvalue, is used for the Neumann problem.

Keywords:

• Eigenvalues/functions
• Laplacian
• Reentrant region
• Point matching
• Chebyshev polynomials

C.R. Categories:

• 5.17