Acoustic eigenvalue analysis using a fast boundary element approach and a contour integral method

Abstract

In this paper, a contour integral method called the block Sakurai-Sugiura (SS) method is implemented to solve eigenvalue problems governed by the Helmholtz equation and formulated through the boundary element method. In the SS method, the nonlinear eigenvalue problem is converted into a standard linear eigenvalue problem, and eigenvalues whose multiplicity is larger than one can also be extracted by using the block version of the SS method. In order to solve the boundary element linear equations with multiple right-hand sides efficiently, a block IDR(s) solver and an adaptive cross approximation are employed to improve the overall computational efficiency. Numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.