Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities
Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities
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DOI：
10.1016/j.jmaa.2004.04.003
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发表时间：
2004-08
影响因子：
1.3
通讯作者：
H. Ammari;Hyeonbae Kang
中科院分区：
文献类型：
--
作者：
H. Ammari;Hyeonbae Kang
我们考虑二维和三维的亥姆霍兹方程的解。基于层位势技术，我们为此类解决方案提供了对扰动的完全渐近展开的严格系统推导，该扰动是由于存在具有与背景介质不同的本构参数的直径较小的不均匀性而引起的。预计我们的结果将在开发有效算法方面找到重要应用，以从边界测量中重建小的介电不均匀性。
We consider solutions to the Helmholtz equation in two and three dimensions. Based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium. It is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements.