A shallow Ritz method for elliptic problems with singular sources

DOI10.1016/j.jcp.2022.111547OpenAlexW3185981343MaRDI QIDQ2675616

Te-Sheng Lin, Wei-Fan Hu, Wei-Syuan Lin, Che-Chia Chang, Ming-Chih Lai

Publication date: 24 September 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.12013

zbMATH Keywords

elliptic problemsimmersed boundary methodlevel set functionsingular sourcedeep Ritz methodshallow neural network

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Related Items (5)

A discontinuity capturing shallow neural network for elliptic interface problems ⋮ A cusp-capturing PINN for elliptic interface problems ⋮ An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications ⋮ A shallow physics-informed neural network for solving partial differential equations on static and evolving surfaces ⋮ High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems

Uses Software

• Adam
• DGM

Cites Work

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