Year: 2022
Author: Hailong Guo, Xu Yang
Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1162–1179
Abstract
This paper proposes a deep unfitted Nitsche method for solving elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy minimization problem involving two weakly coupled components. This enables us to train two deep neural networks to represent two components of the solution in high-dimensional space. The curse of dimensionality is alleviated by using the Monte-Carlo method to discretize the unfitted Nitsche energy functional. We present several numerical examples to show the performance of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0201
Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1162–1179
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Deep learning unfitted Nitsche method interface problem deep neural network.
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