伸缩虚拟边界元法解二维Helmholtz外问题

以位势理论为基础，提出了求解Helmholtz外问题的伸缩虚拟边界元法．给出了该方法在全波数域内获得唯一解的严格数学证明，其核心是通过伸缩虚拟边界使对偶内问题的特征频率(本征值)避开与波数重合，从而保证了解的唯一性，同以往前人提出的几种解法途径相比，该法简单得多；通过诸多边界曲线形状和不同边界量的声辐射算例，从计算精度、稳定性以及克服解的非唯一性等方面，对该方法进行了检验．计算结果表明：对远场或近场辐射声压，该方法都具有非常高的效率和精度．

THE EXPANDING-CONTRACTING VIRTUAL BOUNDARY ELEMENT METHOD FOR 2D-HELMHOLTZ EXTERIOR PROBLEMS

Based on potential theory, an expanding-contracting virtual boundary element method (ECVBEM) is presented for solving 2D-Helmholtz exterior problems in this paper. The strict mathematics proof for existence of a unique solution by this method in whole wave number range is given. Since the shape of virtual boundary may arbitrarily change in a certain extent, so the eigenfrequency (eigenvalue) of corresponding Helmholtz interior problem on virtual boundary may arbitrarily change too. The main advantage of the method is to keep the eigenfrequency of corresponding interior problem away from the given wave number of the original Helmholtz exterior problem. In this way, the unique solution can be ensured. As compared with other methods proposed before, the method presented by this paper is simpler. Tests of the ECVBEM are carried out to explore calculation precision and stability as well as ability to overcome the non-uniqueness of solution through several examples for two-dimension Helmholtz exterior problem. The calculated results of the different shapes of cavities under the various boundary conditions show that the sound pressures by the present effective method in both far and near fields are of high accuracy.