RECENT DEVELOPMENT OF DUAL BEM IN ACOUSTIC PROBLEMS

Abstract

In this lecture, 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 degenerate boundary is examined. First, the dual integral formulation is proposed. Based on the formulation, we develop four methods — the dual complex-valued BEM, the real part of dual BEM, the dual real-valued MRM, and the complete complex-valued MRM. After constructing the dual MRM, spurious eigenvalues in the conventional MRM can be filtered out. It is also found that the complete MRM with infinite terms of series is equivalent to the dual complex-valued 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 of acoustic frequencies of a cavity with an incomplete partition are determined by the four methods. The results are compared with those of FEM and experiment. Good agreement is made.