An efficient and energy-stable scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential

AIMS Mathematics, Год журнала: 2025, Номер 10(3), С. 5568 - 5582

Опубликована: Янв. 1, 2025

Язык: Английский

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Benchmark problems for physics-informed neural networks: The Allen–Cahn equation

AIMS Mathematics, Год журнала: 2025, Номер 10(3), С. 7319 - 7338

Опубликована: Янв. 1, 2025

Язык: Английский

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Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method

Computers & Mathematics with Applications, Год журнала: 2025, Номер 189, С. 1 - 23

Опубликована: Апрель 2, 2025

Язык: Английский

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A Unified Algorithm Framework for Phase‐Field Based Multimaterial Topology Optimization With Various Graded Interfaces

International Journal for Numerical Methods in Engineering, Год журнала: 2025, Номер 126(10)

Опубликована: Май 20, 2025

ABSTRACT In this work, we present a unified algorithm framework for multimaterial topology optimization with various graded interfaces based on the phase field method. framework, problem is transformed into solving set of linear partial differential equations (PDEs). We then introduce scalar variable to grade material property, resulting in complex nonlinear interpolation operator effective elastic tensor. Following that, define an auxiliary substitute all transformations elliptic equation system. A second‐order accurate Crank–Nicolson scheme applied reformulated system, which high‐order terms are treated semi‐explicit fashion. prove that proposed unconditionally energy stable and demonstrate its stability as well accuracy by numerical examples. series benchmark problems different interfacial behaviors topological design investigated verify effectiveness our The sensitivity parameters model analyzed evaluate their effects structure.

Язык: Английский

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Phase field modeling of melting and solidification dynamics in metallic powders during the bed fusion process

Communications in Nonlinear Science and Numerical Simulation, Год журнала: 2025, Номер unknown, С. 108762 - 108762

Опубликована: Март 1, 2025

Язык: Английский

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Maximum Principle-Preserving Computational Algorithm for the 3D High-Order Allen–Cahn Equation

Mathematics, Год журнала: 2025, Номер 13(7), С. 1085 - 1085

Опубликована: Март 26, 2025

We propose an unconditionally stable computational algorithm that preserves the maximum principle for three-dimensional (3D) high-order Allen–Cahn (AC) equation. The presented applies operator-splitting technique decomposes original equation into nonlinear and linear diffusion equations. To guarantee unconditional stability of numerical solution, we solve using frozen coefficient technique, which simplifies computations by approximating variable coefficients constants within small regions. For equation, use implicit finite difference scheme under method. validate efficiency proposed algorithm, conducted several tests. results confirm achieves even large time step sizes polynomial potential. In addition, analyze motion mean curvature in space show solutions closely match analytical solutions. Finally, robustness method is evaluated noisy data conditions, its ability to accurately classify complex structures demonstrated. These reliability simulating phase-field models with a

Язык: Английский

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Highly efficient and accurate numerical schemes for the anisotropic phase field crystal models by using the improved scalar auxiliary variable (iSAV) approach

Communications in Nonlinear Science and Numerical Simulation, Год журнала: 2025, Номер unknown, С. 108875 - 108875

Опубликована: Апрель 1, 2025

Язык: Английский

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Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions

Applied Mathematics Letters, Год журнала: 2025, Номер 169, С. 109609 - 109609

Опубликована: Май 17, 2025

Язык: Английский

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