声散射问题的等几何双重互易边界元法

Isogeometric dual reciprocity boundary element method for acoustic scattering problems

提出了三维频域声散射问题的等几何双重互易边界元法。采用频域无关的基本解求解非齐次亥姆霍兹方程,无需如传统边界元法在求解频率声散射问题时重复计算系数矩阵。引入双重互易法将域积分转换为边界积分,得到三维无限域双重互易展开基函数,实现了双重互易法在无限域声场问题上将域积分转换为边界积分的应用,最大程度保留了边界元法降维的优点;同时,为提高域积分的求解精度,给出了变异系数的取值范围。数值结果表明,等几何双重互易边界元法在求解频域声散射问题时具有较好的精度和稳定性。

The isogeometric dual reciprocity boundary element method for frequency domain acoustic scattering problem is proposed.A frequency-independent fundamental solution is adopted to solve the nonhomogeneous Helmholtz equation,which avoids calculating the coefficient matrix repeatedly when solving the frequency acoustic scattering problem,such as the traditional boundary element method.By introducing the dual reciprocity method to transform the domain integral to the boundary integral,the basis function of three-dimensional infinite domain dual reciprocity expansion is obtained.The application of the dual reciprocity method when converting domain integral to boundary integral in the infinite domain sound field problem is realized,and the advantage of the boundary element method to reduce dimension is preserved to the greatest extent.Meanwhile,in order to improve the solving accuracy of the domain integral,the value range of the coefficient of variation is given.The numerical results show that the isogeometric dual reciprocity boundary element method has better accuracy and stability in solving the frequency domain acoustic scattering problem.