Unconditionally stable Monte Carlo simulation for solving the multi-dimensional Allen-Cahn equation

Monte Carlo methods (65C05) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Methods of ordinary differential equations applied to PDEs (35A24) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
A fast explicit operator splitting method for passive scalar advection
A second-order operator splitting Fourier spectral method for fractional-in-space reaction-diffusion equations
High-order energy stable schemes of incommensurate phase-field crystal model
A second order operator splitting method for Allen-Cahn type equations with nonlinear source terms
An explicit hybrid finite difference scheme for the Allen-Cahn equation
Quasi-Monte Carlo algorithms for diffusion equations in high dimensions
A finite element method for Allen-Cahn equation on deforming surface
On a Monte Carlo scheme for some linear stochastic partial differential equations
Stochastic heat equation: numerical positivity and almost surely exponential stability
Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme
The numerical solutions for the energy-dissipative and mass-conservative Allen-Cahn equation
Error estimates for second-order SAV finite element method to phase field crystal model
Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere
The curse of dimensionality of decision-making units: a simple approach to increase the discriminatory power of data envelopment analysis
Numerical solution of high dimensional stationary Fokker-Planck equations via tensor decomposition and Chebyshev spectral differentiation
Fast and stable explicit operator splitting methods for phase-field models
Nearest Neighbour Searches and the Curse of Dimensionality