Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method-Reference-Cited by-同舟云学术

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Solving Elliptic Problems with Singular Sources Using Singularity Splitting Deep Ritz Method

Published:2023-08-08 Issue:4 Volume:45 Page:A2043-A2074
ISSN:1064-8275
Container-title:SIAM Journal on Scientific Computing
language:en
Short-container-title:SIAM J. Sci. Comput.

Author:

Hu Tianhao¹^ORCID,Jin Bangti²,Zhou Zhi³^ORCID

Affiliation:

1. School of Mathematics, Jilin University, Changchun 130012, People’s Republic of China.

2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, People’s Republic of China.

3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China.

Funder

Hong Kong Research Grants Council

Chinese University of Hong Kong

Hong Kong Polytechnic University

Engineering and Physical Sciences Research Council

Publisher

Society for Industrial & Applied Mathematics (SIAM)

Subject

Applied Mathematics,Computational Mathematics

Reference60 articles.

1. The Gap between Theory and Practice in Function Approximation with Deep Neural Networks

2. Introduction to Numerical Continuation Methods

3. Neural Network Learning

4. A Priori Mesh Grading for an Elliptic Problem with Dirac Right-Hand Side

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1. Phase field smoothing-PINN: A neural network solver for partial differential equations with discontinuous coefficients;Computers & Mathematics with Applications;2024-10

2. Solving Poisson Problems in Polygonal Domains with Singularity Enriched Physics Informed Neural Networks;SIAM Journal on Scientific Computing;2024-07-30

3. Generalization Error in the Deep Ritz Method with Smooth Activation Functions;Communications in Computational Physics;2024-06

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