Deep unfitted Nitsche method for elliptic interface problems
Deep unfitted Nitsche method for elliptic interface problems
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DOI：
10.4208/cicp.oa-2021-0201
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Hailong Guo;Xu Yang
中科院分区：
文献类型：
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作者：
Hailong Guo;Xu Yang
本文提出了一种计算高维高对比度椭圆界面问题的深度非拟合Nitsche方法。为了捕捉界面引起的解的不连续性，我们将问题重新表述为涉及两个弱耦合组件的能量最小化。这使我们能够训练两个深度神经网络来表示高维解的两个分量。采用蒙特-卡罗方法对未拟合的Nitsche能量函数进行离散，从而减轻了维数灾难。我们提出了几个数值例子来显示所提出的方法的性能。
This paper proposes a deep unfitted Nitsche method for computing 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 involving two weakly coupled components. This enables us to train two deep neural networks to represent two components of the solution in high-dimensional. The curse of dimensionality is alleviated by using the Monte-Carlo method to discretize the unfitted Nitsche energy function. We present several numerical examples to show the performance of the proposed method.