Recent development of dual BEM in acoustic problems

Abstract

In this paper, recent development of the dual BEM in acoustic problem is presented. The role of hypersingular integral equation in the dual BEM for the problems with a degenerate boundary is examined. First, the dual integral formulation is proposed. Based on the formulation, we develop four methods – the complex-valued dual BEM, the real-part dual BEM, the real-valued dual MRM, and the complete complex-valued MRM. For the real-part dual BEM and the real-valued dual MRM, the spurious eigenvalues occur and can be filtered out by using residual technique or singular value decomposition method. It is also found that the complete MRM with infinite terms of series is equivalent to the complex-valued dual BEM if the constant potential in the zeroth-order fundamental solution is chosen to be an appropriate complex value. The dual formulation can be applied to solve acoustic problems with degenerate boundaries. An illustrative example for acoustic eigenfrequencies of a cavity with an incomplete partition is shown to verify the validity of the four methods. The results are compared with those of FEM and experiment. Good agreement is made.