Improvement of the indirect BEM and the MFS for solving fictitious-frequency problems in 2D exterior acoustics

• Main Authors: Nien, Chi-Feng, 粘祺烽
• Other Authors: Chen, Jeng-Tzong
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/t8yamc

碩士 === 國立臺灣海洋大學 === 河海工程學系 === 106 === Regarding the treatment for the fictitious frequency as well as spurious resonance in using the indirect boundary element method (BEM) and the method of fundamental solutions (MFS), we propose an alternative approach in this thesis. The present approach is different from the mixed potential approach in the indirect method as well as the Burton and Miller approach in the direct BEM. In the proposed approach, we add some fundamental solutions with unknown source strength in the representation of the field to complete the base of solution space. From the viewpoint of adding source, the present idea is similar to the combined Helmholtz interior integral equation formulation (CHIEF) method in the direct BEM. The difference between the added source points and the null-field point of CHIEF method is their role. The added source points supply the deficient base due to the fictitious frequency while the null-field point of CHIEF provides the extra constraint equations. Therefore, we examine the CHIEF constraint by employing the self-regularization technique for the influence matrix in the direct BEM. Based on this idea, the constraint equation in the present approach may be found by adding the right unitary vectors of zero singular value. Then, a square bordered matrix is obtained. The bordered matrix is invertible for the fictitious frequency if the extra source points do not locate at the failure position. This is the reason why the property is analogous to the idea of the CHIEF method in the direct BEM. Therefore, the proposed approach can fill in the gap that there is no CHIEF method in the indirect BEM and the MFS. Since the proposed approach only needs to use the single-layer potential, it has an advantage over the existing formulations. To demonstrate the validity of the present idea, the problem of an infinite plane containing a circular and elliptic radiator or scatter is considered. In the real implementation, all fictitious frequencies in the certain range of the wavenumber are found first by the direct searching algorithm. Four circular and elliptical boundary cases with different boundary conditions and fictitious frequencies are considered, respectively. Finally, we also analytically derive the locations of possible failure source points by using the degenerate kernel.