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09/06/2023
Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals
In this paper, we propose two efficient fully-discrete schemes for Q-ten...
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07/14/2023
Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks
This paper proposes a novel approach to integrating partial differential...
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03/09/2023
Energy regularized models for logarithmic SPDEs and their numerical approximations
Understanding the properties of the stochastic phase field models is cru...
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11/02/2022
A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with general mobility
In this paper, we propose and analyze a linear second-order numerical me...
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10/21/2022
Energy stability and error estimates of a maximum bound principle preserving scheme for the dynamic Ginzburg-Landau equations of superconductivity
The paper proposes a decoupled numerical scheme of the time-dependent Gi...
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09/08/2022
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation
In this paper, we study a second-order accurate and linear numerical sch...
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06/15/2022
A linear adaptive BDF2 scheme for phase field crystal equation
In this paper, we present and analyze a linear fully discrete second ord...
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04/25/2022
Structure-preserving numerical method for Ampere-Nernst-Planck model
Charge dynamics play essential role in many practical applications such ...
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04/01/2022
An implicit–explicit second order BDF numerical scheme with variable steps for gradient flows
In this paper, we propose and analyze an efficient implicit–explicit (IM...
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03/27/2022
Multi-phase image segmentation by the Allen–Cahn Chan–Vese model
This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-ph...
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03/17/2022
An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation
In this paper, we propose an active contour model with a local variance ...
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03/14/2022
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations
It is well-known that the Allen-Cahn equation not only satisfies the ene...
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03/09/2022
Generalized SAV-exponential integrator schemes for Allen-Cahn type gradient flows
The energy dissipation law and the maximum bound principle (MBP) are two...
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09/23/2021
Two-phase segmentation for intensity inhomogeneous images by the Allen-Cahn Local Binary Fitting Model
This paper proposes a new variational model by integrating the Allen-Cah...
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04/19/2021
Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator
Based on a nonlocal Laplacian operator, a novel edge detection method of...
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10/23/2020
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
A large class of semilinear parabolic equations satisfy the maximum boun...
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05/23/2020
