A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation
SIAM Journal on Numerical Analysis
On the Cahn-Hilliard equation with degenerate mobility
SIAM Journal on Mathematical Analysis
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Parallel Multilevel Algorithms for Multi-constraint Graph Partitioning (Distinguished Paper)
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Computation of multiphase systems with phase field models
Journal of Computational Physics
A discontinuous Galerkin method for the Cahn-Hilliard equation
Journal of Computational Physics
On large time-stepping methods for the Cahn--Hilliard equation
Applied Numerical Mathematics
A nonstiff, adaptive mesh refinement-based method for the Cahn-Hilliard equation
Journal of Computational Physics
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations
Journal of Computational Physics
A numerical method for the ternary Cahn--Hilliard system with a degenerate mobility
Applied Numerical Mathematics
Adaptive time-stepping and computational stability
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Three-dimensional, fully adaptive simulations of phase-field fluid models
Journal of Computational Physics
A nonconforming finite element method for the Cahn-Hilliard equation
Journal of Computational Physics
Inpainting of Binary Images Using the Cahn–Hilliard Equation
IEEE Transactions on Image Processing
Journal of Computational Physics
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
Journal of Computational Physics
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We present an efficient numerical framework for analyzing spinodal decomposition described by the Cahn-Hilliard equation. We focus on the analysis of various implicit time schemes for two and three dimensional problems. We demonstrate that significant computational gains can be obtained by applying embedded, higher order Runge-Kutta methods in a time adaptive setting. This allows accessing time-scales that vary by five orders of magnitude. In addition, we also formulate a set of test problems that isolate each of the sub-processes involved in spinodal decomposition: interface creation and bulky phase coarsening. We analyze the error fluctuations using these test problems on the split form of the Cahn-Hilliard equation solved using the finite element method with basis functions of different orders. Any scheme that ensures at least four elements per interface satisfactorily captures both sub-processes. Our findings show that linear basis functions have superior error-to-cost properties. This strategy - coupled with a domain decomposition based parallel implementation - let us notably augment the efficiency of a numerical Cahn-Hillard solver, and open new venues for its practical applications, especially when three dimensional problems are considered. We use this framework to address the isoperimetric problem of identifying local solutions in the periodic cube in three dimensions. The framework is able to generate all five hypothesized candidates for the local solution of periodic isoperimetric problem in 3D - sphere, cylinder, lamella, doubly periodic surface with genus two (Lawson surface) and triply periodic minimal surface (P Schwarz surface).