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A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation
arXiv - CS - Numerical Analysis Pub Date : 2021-05-06 , DOI: arxiv-2105.02665
Pierre Marechal, Walter Simo Tao Lee, Faouzi Triki

The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be consistent, and the proposed numerical simulations are quite promising.

中文翻译:

Mollifier方法对非均质Helmholtz方程的Cauchy问题进行正则化

考虑了折射率不均匀的非均质亥姆霍兹方程的柯西问题。这个问题的不适性是通过变态化形式来解决的。这种方法被证明是一致的,并且所提出的数值模拟是很有前途的。
更新日期:2021-05-07
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