Solving acoustic nonlinear eigenvalue problems with a contour integral method

In this paper, a contour integral method (especially the block Sakurai–Sugiura method) is used to solve the eigenvalue problems governed by the Helmholtz equation, and formulated through two meshless methods. Singular value decomposition is employed to filter out the irrelevant eigenvalues. The accuracy and the ease of use of the proposed approach is illustrated with some numerical examples, and the choice of the contour integral method parameters is discussed. In particular, an application of the method on a sphere with realistic impedance boundary condition is performed and validated by comparison with results issued from a finite element method software.