Compressed Absorbing Boundary Conditions via Matrix Probing
Compressed Absorbing Boundary Conditions via Matrix Probing
复制标题
通过矩阵探测压缩吸收边界条件
DOI：
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发表时间：
2014
影响因子：
2.9
通讯作者：
L. Demanet
中科院分区：
文献类型：
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作者：
Rosalie Bélanger;L. Demanet
为了在非均质介质中提供亥姆霍兹方程的吸收边界条件的精确近似值，吸收层有时被要求厚得不切实际。通过层剥离消除外部未知数，总是可以将吸收层简化为边界处的算子，但所涉及的线性代数是昂贵的。我们建议绕过消去程序，直接用随机狄利克雷数据从几个外部亥姆霍兹解中拟合压缩形式的面对面算子。结果是对吸收边界条件的简明描述，其复杂性在频率参数中缓慢增长（通常是对数增长）。
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose bypassing the elimination procedure and directly fitting the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. The result is a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter.