SIAM Journal on Scientific Computing
A Two-Level Method for the Discretization of Nonlinear Boundary Value Problems
SIAM Journal on Numerical Analysis
Computation of multiphase systems with phase field models
Journal of Computational Physics
Error analysis of a mixed finite element method for the Cahn-Hilliard equation
Numerische Mathematik
Sharp interface tracking using the phase-field equation
Journal of Computational Physics
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Transactions on Mathematical Software (TOMS)
Numerical simulation of the three-dimensional Rayleigh-Taylor instability
Computers & Mathematics with Applications
Efficient numerical solution of discrete multi-component Cahn-Hilliard systems
Computers & Mathematics with Applications
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We consider two-phase flow problems, modelled by the Cahn-Hilliard equation. In this work, the nonlinear fourth-order equation is decomposed into a system of two coupled second-order equations for the concentration and the chemical potential. We analyse solution methods based on an approximate two-by-two block factorization of the Jacobian of the nonlinear discrete problem. We propose a preconditioning technique that reduces the problem of solving the non-symmetric discrete Cahn-Hilliard system to a problem of solving systems with symmetric positive definite matrices where off-the-shelf multilevel and multigrid algorithms are directly applicable. The resulting solution methods exhibit optimal convergence and computational complexity properties and are suitable for parallel implementation. We illustrate the efficiency of the proposed methods by various numerical experiments, including parallel results for large scale three dimensional problems.