Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using an efficient mixed-part dual BEM

Abstract

In this paper, we develop an efficient mixed-part dual BEM to solve the eigensolutions of a circular cavity analytically and numerically. The method is proposed by choosing a fewer number of equations from the dual BEM instead of all of the equations in the dual BEM developed by Chen and his coworkers. To solve this problem analytically, the spurious solution can be filtered out by adding constraints from the dual boundary integral equations. The proposed method is superior to the complex-valued BEM not only for half effort in constructing the influence matrix, but also for its fewer size of dimension. Also, numerical experiments are performed to compare with the analytical results and the true eigensolutions can be easily extracted out in conjunction with the singular value decomposition technique (SVD). The optimum number of collocation point and appropriate collocating positions for the additional constraints are discussed.