Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

Abstract

We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and thus offers the opportunity to study long time behaviour of materials with atomic details. This requires adaptive time stepping and efficient time discretization schemes, for which we use an embedded Rosenbrock scheme. To resolve spatial scales of practical relevance, parallel algorithms are also required, which scale to large numbers of processors. The developed preconditioner provides such a tool. It is based on an approximate factorization of the system matrix and can be implemented efficiently. The preconditioner is analyzed in detail and shown to speed up the computation drastically.

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• Classical dynamical density functional theory: from fundamentals to applications
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• Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview
• A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions
• Controlling grain boundaries by magnetic fields
• A microscopic field theoretical approach for binary mixtures of active and passive particles
• An efficient numerical framework for the amplitude expansion of the phase-field crystal model
• Magnetically induced/enhanced coarsening in thin films
• Parallel energy-stable phase field crystal simulations based on domain decomposition methods