A Robust Solver for a Mixed Finite Element Method for the Cahn-Hilliard Equation
arXiv:1709.04003
Originality Incremental advance
AI Analysis
Provides an efficient solver for phase-field simulations, addressing a key computational bottleneck in materials science.
Developed a robust solver for the Cahn-Hilliard equation using a preconditioned MINRES algorithm with multigrid, achieving performance independent of mesh size and time step, with mild dependence on interfacial width.
We develop a robust solver for a mixed finite element convex splitting scheme for the Cahn-Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spacial mesh size and the time step size for a given interfacial width parameter. The dependence on the interfacial width parameter is also mild.