Bleszynski E, Bleszynski M, Jaroszewicz T
Monopole Research, Thousand Oaks, California 91360, USA.
J Acoust Soc Am. 2008 Dec;124(6):3684-93. doi: 10.1121/1.2998787.
An approach for solving volumetric integral equations in acoustics, applicable to problems involving large density contrasts, is described. While the conventional Lippmann-Schwinger integral equations become under such circumstances ill conditioned, the proposed approach reformulates them and casts them into an equivalent system of well-conditioned surface and volume integral equations. The corresponding fast solver [utilizing stiffness matrix compression based on fast Fourier transforms and characterized by O(N log N) solution complexity and storage requirements, where N is the number of unknowns] was enhanced to incorporate the proposed formulation. Features of the solution method and of the solver are illustrated on representative examples of numerically large problems.
本文描述了一种求解声学中体积积分方程的方法，该方法适用于涉及大密度对比度的问题。在这种情况下，传统的李普曼-施温格积分方程会变得病态，而所提出的方法对其进行了重新表述，并将其转化为一个等价的良态表面和体积积分方程组。相应的快速求解器[利用基于快速傅里叶变换的刚度矩阵压缩，其解的复杂度和存储需求为O(N log N)，其中N是未知数的数量]得到了改进，以纳入所提出的公式。通过数值上较大问题的代表性示例说明了求解方法和求解器的特点。
