An efficient numerical method for determining trapped modes in acoustic waveguides

Abstract

An efficient numerical method for determining all trapped modes of the Helmholtz equation based on the finite element method and exact nonlocal boundary conditions is proposed. An infinite two-dimensional channel with parallel walls at infinity, which may contain obstacles of arbitrary shape, is considered. It is assumed that the frequencies of the trapped modes lie below a certain threshold value. The discrete problem is an algebraic eigenvalue problem for symmetric positive definite sparse matrices, one of which depends nonlinearly on the spectral parameter. A fast iterative method for solving such problems is introduced. The results of the numerical calculations are presented.

Keywords

• acoustic waveguide
• trapped mode
• discrete and continuous spectrum
• finite element method
• nonlinear spectral problem