A fast wavelet collocation method with compression techniques for Steklov eigenvalue problems of Helmholtz equations

Abstract

A fast wavelet collocation method with compression techniques is proposed for solving the Steklov eigenvalue problem. Based on the potential theory, the Steklov eigenvalue problem is reformulated as a boundary integral equation with logarithmic singularity. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique leads to the algorithm faster. We show that the proposed method requires only linear computational complexity and has the optimal convergence order for the approximate eigenvalues and eigenfunctions. The numerical examples are provided and analyzed.