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Multioutput FOSLS Deep Neural Network for Solving Allen–Cahn Equation
AbstractThis paper utilizes feed-forward neural networks to approximate solutions and their scaled gradients of the Allen–Cahn equation. A...
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Stability Analysis of Several Time Discrete Schemes for Allen–Cahn and Cahn–Hilliard Equations
AbstractIn this paper, the stability of several time discrete schemes for Allen–Cahn and Cahn–Hilliard equations and an error estimate for...
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Stability and Error Estimates of High Order BDF-LDG Discretizations for the Allen–Cahn Equation
AbstractWe construct high order local discontinuous Galerkin (LDG) discretizations coupled with third and fourth order backward differentiation...
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Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes
In this paper, we develop a polygonal mesh adaptation algorithm for a fully implicit scheme based on discontinuous Galerkin (DG) finite element...
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Unconditional energy stability and maximum principle preserving scheme for the Allen-Cahn equation
In this paper, we propose a novel fully implicit numerical scheme that satisfies both nonlinear energy stability and maximum principle for the space...
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Maximum bound principle preserving linear schemes for nonlocal Allen–Cahn equation based on the stabilized exponential-SAV approach
The nonlocal Allen–Cahn equation with nonlocal diffusion operator is important for simulating a series of physical and biological phenomena involving...
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Collocation-based numerical simulation of fractional order Allen–Cahn equation
This article looks for a reliable numerical technique to solve the Allen–Cahn equation using the Caputo time-fractional derivative. The fractional...
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An adaptive discontinuous finite volume element method for the Allen-Cahn equation
In this paper, the discontinuous finite volume element method (DFVEM) is considered to solve the Allen-Cahn equation which contains strong...
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Second-Order Error Analysis for Fractal Mobile/Immobile Allen–Cahn Equation on Graded Meshes
The fractal mobile/immobile model bridges between Fickian fluxes at early times and non-Gaussian behavior at late times. In this work, an averaged L1...
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An efficient and explicit local image inpainting method using the Allen–Cahn equation
Image inpainting is the process of restoring damaged areas in an image using information available from neighboring regions. In this paper, we...
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Mean Curvature Flow and Low Energy Solutions of the Parabolic Allen-Cahn Equation on the Three-Sphere
In this article, we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the...
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An efficient approximation to the stochastic Allen-Cahn equation with random diffusion coefficient field and multiplicative noise
This paper studies the stochastic Allen-Cahn equation involving random diffusion coefficient field and multiplicative force noise. A new...
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Analysis and approximations of an optimal control problem for the Allen–Cahn equation
The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen–Cahn equation. A tracking functional is...
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Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation
The convective Allen–Cahn (CAC) equation has been widely used for simulating multiphase flows of incompressible fluids, which contains an extra...
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Exact solutions for travelling waves using Tanh method for two dimensional stochastic Allen–Cahn equation with multiplicative noise
The research outlined here focuses on the hyperbolic tangent (tanh) method for deriving analytical solutions for travelling wave to the...
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A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint
The conservative Allen-Cahn equation satisfies three important physical properties, namely the mass conservation law, the energy dissipation law, and...
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A Splitting Method for the Allen-Cahn/Cahn-Hilliard System Coupled with Heat Equation Based on Maxwell-Cattaneo Law
We analyze here a finite element space semidiscretization of the Allen-Cahn/Cahn-Hilliard system coupled with heat equation and based on the...
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Energy stable and maximum bound principle preserving schemes for the Allen-Cahn equation based on the Saul’yev methods
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart...
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Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method
The matrix-valued Allen-Cahn (MAC) equation was first introduced as a model problem of finding the stationary points of an energy for orthogonal...
