Numerical solution of high‐frequency acoustic scattering problems by integral equations preconditioned using pseudo‐differential impedance operators
Numerical solution of high‐frequency acoustic scattering problems by integral equations preconditioned using pseudo‐differential impedance operators
复制标题
使用伪微分阻抗算子预处理的积分方程数值求解高频声散射问题
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
P. Calamia
中科院分区：
文献类型：
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作者：
D. Calvo;P. Calamia
由于存在大量未知因素，目标或粗糙表面的高频散射的精确计算可能具有挑战性。然而，使用近似的Dirichlet - to - Neumann表面算子可以得到一种折衷方法，这种算子已知为伪微分形式，并且可以使用有理近似有效地实现。这些算子可用作预条件，得到求解亥姆霍兹积分方程的条件良好的迭代算法。利用这些算法，我们计算了二维和三维目标的散射，以及入射场靠近感兴趣的掠掠角的具有光滑凹或凸部分的粗糙表面。这种情况对水下声学特别重要，因为声场在浅水中掠过自由表面或底部。
Exact computations of high‐frequency scattering by targets or rough surfaces can be challenging because of the large number of unknowns. A compromise can be obtained, however, using approximate Dirichlet‐to‐Neumann surface operators that are known in pseudo‐differential form and efficiently implemented using rational approximations. These operators can be used as preconditioners to obtain well‐conditioned iterative algorithms to solve the Helmholtz integral equation. Using these algorithms, we compute scattering by two‐ and three‐dimensional targets, and rough surfaces with smooth concave or convex parts with incident fields near grazing angles of interest. This case is particularly important for underwater acoustics, where sounds field graze the free surface or bottom in shallow water.