Iterative estimation of eigenmodes for acoustic cavities

In this paper, a stochastic estimation method of the number of eigenvalues of nonlinear eigenproblem (initially proposed by Maeda et al., JSIAM Letters 3, 61-64, (2011)) is employed iteratively in order to identify eigenvalues of acoustic cavities. Applied to several discretization formulations of the Helmholtz equation, the proposed approach handles complex acoustic cavities. Specific developments are carried out concerning the approximation of the stochastic estimator for the solved kernels. The method's accuracy is illustrated with academic nonlinear eigenproblems with various boundary conditions. In particular, a sphere problem with constant surface impedance is solved and validated by comparison with results issued from a finite element method software.