Imperial College London
Alternate

ProfessorMatthewPiggott

Faculty of Engineering, Department of Earth Science & Engineering

Professor of Computational Geoscience and Engineering
 
 
 
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Contact

 

m.d.piggott Website

 
 
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Location

 

4.82Royal School of MinesSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Song:2022,
author = {Song, W and Zhang, M and Wallwork, JG and Gao, J and Tian, Z and Sun, F and Piggott, MD and Chen, J and Shi, Z and Chen, X and Wang, J},
title = {M2N: mesh movement networks for PDE solvers},
url = {http://arxiv.org/abs/2204.11188v1},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - Mainstream numerical Partial Differential Equation (PDE) solvers requirediscretizing the physical domain using a mesh. Mesh movement methods aim toimprove the accuracy of the numerical solution by increasing mesh resolutionwhere the solution is not well-resolved, whilst reducing unnecessary resolutionelsewhere. However, mesh movement methods, such as the Monge-Ampere method,require the solution of auxiliary equations, which can be extremely expensiveespecially when the mesh is adapted frequently. In this paper, we propose toour best knowledge the first learning-based end-to-end mesh movement frameworkfor PDE solvers. Key requirements of learning-based mesh movement methods arealleviating mesh tangling, boundary consistency, and generalization to meshwith different resolutions. To achieve these goals, we introduce the neuralspline model and the graph attention network (GAT) into our modelsrespectively. While the Neural-Spline based model provides more flexibility forlarge deformation, the GAT based model can handle domains with more complicatedshapes and is better at performing delicate local deformation. We validate ourmethods on stationary and time-dependent, linear and non-linear equations, aswell as regularly and irregularly shaped domains. Compared to the traditionalMonge-Ampere method, our approach can greatly accelerate the mesh adaptationprocess, whilst achieving comparable numerical error reduction.
AU  - Song,W
AU  - Zhang,M
AU  - Wallwork,JG
AU  - Gao,J
AU  - Tian,Z
AU  - Sun,F
AU  - Piggott,MD
AU  - Chen,J
AU  - Shi,Z
AU  - Chen,X
AU  - Wang,J
PY  - 2022///
TI  - M2N: mesh movement networks for PDE solvers
UR  - http://arxiv.org/abs/2204.11188v1
UR  - http://hdl.handle.net/10044/1/97946
ER  -
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