Regularized Combined Field Integral Equations for Acoustic Transmission Problems
Regularized Combined Field Integral Equations for Acoustic Transmission Problems
复制标题
声传输问题的正则组合场积分方程
DOI：
10.1137/140964230
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Turc
中科院分区：
文献类型：
--
作者：
Y. Boubendir;V. Domínguez;D. Levadoux;C. Turc
本文给出了一类求解二维和三维均匀可穿透散射体散射问题的良好条件积分方程。我们的新边界积分方程是通过使用正则算子得到的，正则算子是将传输边界条件分别映射到介质界面上的外部和内部柯西数据的导纳算子的适当近似。我们把这些正则化边界积分方程称为广义组合源积分方程（GCSIE）。导纳算符可以用Dirichlet-to-Neumann算符及其逆表示。我们用复波数的简单边界层算子来构造正则化算子。正则算子定义中复数波数的选择保证了GCSIE的唯一可解性。证明了GCSIE是材料间断界面的第二类积分方程。
We present a new class of well-conditioned integral equations for the solution of two and three dimensional scattering problems by homogeneous penetrable scatterers. Our novel boundary integral equations result from using regularizing operators which are suitable approximations of the admittance operators that map the transmission boundary conditions to the exterior and, respectively, interior Cauchy data on the interface between the media. We refer to these regularized boundary integral equations as generalized combined source integral equations (GCSIE). The admittance operators can be expressed in terms of Dirichlet-to-Neumann operators and their inverses. We construct our regularizing operators in terms of simple boundary layer operators with complex wavenumbers. The choice of complex wavenumbers in the definition of the regularizing operators ensures the unique solvability of the GCSIE. The GCSIE are shown to be integral equations of the second kind for regular enough interfaces of material discontinu...