A new finite element level set reinitialization method based on the shifted boundary method

Recently, the development of deep learning (DL), which has accomplished unbelievable success in many fields, especially in scientific computational fields. And almost all computational problems and physical phenomena can be described by partial differential equations (PDEs). In this work, we proposed two potential high-order geometric flows. Motivation by the physicalinformation neural networks (PINNs) and the traditional level set method (LSM), we have integrated deep neural networks (DNNs) and LSM to make the proposed method more robust and efficient. Also, to test the sensitivity of the system to different input data, we set up three sets of initial conditions to test the model. Furthermore, numerical experiments on different input data are implemented to demonstrate the effectiveness and superiority of the proposed models compared to the state-of-the-art approach.

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Learning high-order geometric flow based on the level set method

Yang

Liang

et al. 2022

Nonlinear Dyn

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Optimization-based level-set re-initialization: A robust interface preserving approach in multiphase problems

Hashemi,

Ryzhakov

et al. 2024

Computer Methods in Applied Mechanics and Engineering

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Nonlinear elasticity with the Shifted Boundary Method

Atallah,

Scovazzi

2024

Computer Methods in Applied Mechanics and Engineering

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A new finite element level set reinitialization method based on the shifted boundary method

Cited by 4 publications

References 32 publications

Learning high-order geometric flow based on the level set method

Learning high-order geometric flow based on the level set method

Optimization-based level-set re-initialization: A robust interface preserving approach in multiphase problems

Nonlinear elasticity with the Shifted Boundary Method

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