Deep Unfitted Nitsche Method for Elliptic Interface Problems (Communications in Computational Physics, 2022)
This paper proposes a deep unfitted Nitsche method for solving elliptic interface problems with high contrasts in high dimensions. To capture discontinuitiesof the solution caused by interfaces, we reformulate the problem as an energy minimization problem involving two weakly coupled components. This enables us totrain 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-Carlomethod to discretize the unfitted Nitsche energy functional. We present several numerical examples to show the performance of the proposed method.