Efficient Preconditioners for Large Scale Binary Cahn-Hilliard Models

Abstract

In this work we consider preconditioned iterative solution methods for numerical simulations of multiphase flow problems, modelled by the Cahn-Hilliard equation. We focus on diphasic flows and the construction and efficiency of a preconditioner for the algebraic systems arising from finite element discretizations in space and the -method in time. The preconditioner utilizes to a full extent the algebraic structure of the underlying matrices and exhibits optimal convergence and computational complexity properties. Large scale umerical experiments are included as well as performance comparisons with other solution methods.

Fluctuation assisted spreading of a fluid filled elastic blister

“…To describe the deformation and spreading of the blister we deploy a scaling analysis and perform numerical simulations of (2) in one and two dimensions by using the finite element method [38]. The deterministic parts of (2) are solved implicitly [31,39], while the noise-term η(x, t) is treated explicitly as in [40]. The numerical simulations are complemented by an initial condition for the blister height h(0, x) = + (1 − tanh(50(x 2 + y 2 ))), where is the pre-wetted layer and pinned boundary conditions imposed at the edge Γ i.e.…”

Simulation of thin film flows with a moving mesh mixed finite element method

“…Recently, different precondition strategies for solving fourth-order PDEs like (5) have been proposed. For example, the precondition strategies in [29,30,31] for Cahn-Hilliard equations.…”

Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements

“…A block preconditioning strategy is proposed by Neytcheva et al [12]. They consider the Cahn-Hilliard equation with a smooth potential coupled with the Navier-Stokes equation and apply two fully implicit schemes of the θ-method (backward Euler and Crank-Nicolson) for the discretization in time.…”