An eigenvalue search algorithm for the modal analysis of a resonator in free space

In this article we present an algorithm for the three-dimensional numerical simulation of the sound spectrum and the propagation of acoustic radiation inside and around long slender hollow objects. The fluid inside and close to the object is meshed by Lagrangian tetrahedral finite elements. To obtain results in the far field of the object, complex conjugated Astley-Leis infinite elements are used. To apply these infinite elements the finite element domain is meshed either in a spherical or an ellipsoidal shape. Advantages and disadvantages of both shapes regarding the form of the object are discussed in this article. The formulation leads to a quadratic eigenvalue problem with real, large and nonsymmetric matrices. An eigenvalue search algorithm is implemented to concentrate on the computation of the interior eigenmodes. This algorithm is based on a linearization of the quadratic problem in a state space formulation. The search algorithm uses a complex shift to efficiently extract the relevant eigenvalues only.