TY - JOUR
T1 - Deep Unfitted Nitsche Method for Elliptic Interface Problems
AU - Guo , Hailong
AU - Yang , Xu
JO - Communications in Computational Physics
VL - 4
SP - 1162
EP - 1179
PY - 2022
DA - 2022/03
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0201
UR - https://global-sci.org/intro/article_detail/cicp/20380.html
KW - Deep learning, unfitted Nitsche method, interface problem, deep neural network.
AB - <p style="text-align: justify;">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.</p>