A boundary integral method for the simulation of two-dimensional particle coarsening
Journal of Scientific Computing
A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation
SIAM Journal on Numerical Analysis
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
A Fourier-wavelet Monte Carlo method for fractal random fields
Journal of Computational Physics
Numerical simulation of randomly forced turbulent flows
Journal of Computational Physics
Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility
Mathematics of Computation
Mathematics of Computation
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
Spectral methods for mesoscopic models of pattern formation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems
Journal of Computational Physics
A Numerical Study on Large-Time Asymptotics of the Lifshitz–Slyozov System
Journal of Scientific Computing
A Guide to Monte Carlo Simulations in Statistical Physics
A Guide to Monte Carlo Simulations in Statistical Physics
Mesoscopic simulation for self-organization in surface processes
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Concentration effects in mesoscopic simulation of coarsening
Mathematics and Computers in Simulation
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The self-organization of particles in a two phase system in the coexistence region through a diffusive mechanism is known as Ostwald ripening. This phenomenon is an example of a multiscale problem in that the microscopic level interaction of the particles can greatly impact the macroscale or observable morphology of the system. Ostwald ripening is studied here through the use of a mesoscopic model which is a stochastic partial integrodifferential equation that is derived from a spin exchange Ising model. This model is studied through the use of recently developed and benchmarked spectral schemes for the simulation of solutions to stochastic partial differential equations. The typical cluster size is observed to grow like t1/3 over range of times with faster growth at later times. The results included here also demonstrate the effect of adjusting the interparticle interaction on the morphological evolution of the system at the macroscopic level.