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07/11/2022
Numerical Approximations of the Allen-Cahn-Ohta-Kawasaki (ACOK) Equation with Modified Physics Informed Neural Networks (PINNs)
The physics informed neural networks (PINNs) has been widely utilized to...
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11/25/2021
A Remark on the Invariant Energy Quadratization (IEQ) Method for Preserving the Original Energy Dissipation Laws
In this letter, we revisit the IEQ method and provide a new perspective ...
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04/14/2021
Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation
The scalar auxiliary variable (SAV) method was introduced by Shen et al....
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03/16/2021
A Revisit of The Energy Quadratization Method with A Relaxation Technique
This letter revisits the energy quadratization (EQ) method by introducin...
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03/03/2021
Second-order Decoupled Energy-stable Schemes for Cahn-Hilliard-Navier-Stokes equations
The Cahn-Hilliard-Navier-Stokes (CHNS) equations represent the fundament...
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03/03/2021
A General Framework to Derive Linear, Decoupled and Energy-stable Schemes for Reversible-Irreversible Thermodynamically Consistent Models: Part I Incompressible Hydrodynamic Mo
In this paper, we present a general numerical platform for designing acc...
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09/24/2020
Discovery of Governing Equations with Recursive Deep Neural Networks
Model discovery based on existing data has been one of the major focuses...
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07/09/2020
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard...
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07/09/2020
Discovering Phase Field Models from Image Data with the Pseudo-spectral Physics Informed Neural Networks
In this paper, we introduce a new deep learning framework for discoverin...
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06/03/2020
A Non-uniform Time-stepping Convex Splitting Scheme for the Time-fractional Cahn-Hilliard Equation
In this paper, a non-uniform time-stepping convex-splitting numerical al...
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10/16/2019
Arbitrarily High-order Linear Schemes for Gradient Flow Models
We present a paradigm for developing arbitrarily high order, linear, unc...
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07/11/2019
Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
We present a systematical approach to developing arbitrarily high order,...
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07/09/2019
Arbitrarily High-order Unconditionally Energy Stable Schemes for Gradient Flow Models Using the Scalar Auxiliary Variable Approach
In this paper, we propose a novel family of high-order numerical schemes...
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11/26/2018