一种具有唯一解的边界元法计算三维声散射问题  

Computing Three-dimensional Acoustic Scattering Problems with Unique-solution Boundary Element Method

作　　者：高贵兵[1] 张道兵[1] 岳文辉[2] 李善德[3] 

机构地区：[1]湖南科技大学能源与安全工程学院,湘潭411201 [2]湖南科技大学湖南省机械设备健康维护重点实验室,湘潭411201 [3]华中科技大学数字制造与装备技术国家重点实验室,武汉430074

出　　处：《机械科学与技术》2013年第8期1172-1175,共4页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家高科技支撑计划项目(863)(2012BAF02B01);国家自然科学基金项目(51075142)资助

摘　　要：针对传统边界元法在求解外部声学问题时存在非唯一解的缺点,本文利用Burton-miller公式有效解决这一问题。对于Burton-miller公式引入的超奇异积分算子,采用奇异性减少技术进行弱奇异积分规划,有效避免了计算超奇异积分的困难,数值处理变得十分有效。此外,在算法中还采用有效的块对角预处理迭代求解器加速求解线性方程系统,全面提高算法的计算效率。数值算例验证了算法计算三维声散射问题的准确性、有效性及潜在的工程应用价值。We employ the Burton-Miller formula to overcome the non-unique problem of the conventional boundary element method for exterior acoustic scattering problems. We apply the effective singularity subtraction algorithm to implementing the hypersingular integral involved in the Burton-Miller formula, thus obtaining the improved weak form of the hypersingular integral, whose evaluation is no longer difficult. Furthermore, our algorithm adopts the ef- fective block diagonal pre-conditioner and the iterative solver to solve the matrix equation, thus improving its overall computational efficiency. Several numerical examples demonstrate the accuracy, efficiency and potential engineer- ing application of our algorithm.

关 键 词：边界元法 Burton—miller公式 声散射 前处理 算法 

分 类 号：TB529[理学—物理]