An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal
model. The suggested method is proved to preserve a modified energy dissipation law at the …

Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn
equation has been an open problem in recent years. This work provides a positive answer …

The scalar auxiliary variable (SAV) approach [42] is a very popular and efficient method to
simulate various phase field models. To save the computational cost, a new SAV approach …

In the natural world, the phase field transition on the surface of a three-dimensional (3D)
object is common. The square phase-field crystal (SPFC) equation is an effective model for …

We present and evaluate several explicit, large time-stepping algorithms for the Allen-Cahn
equation. Our approach incorporates a stabilization technique and uses Taylor series …

In this paper, we present a second-order accurate and linear numerical scheme for the
phase field crystal equation and prove its convergence in the discrete sense. The key …

In this paper, we propose several novel numerical techniques to deal with nonlinear terms in
gradient flows. These step-by-step solving schemes, termed 3S-SAV and 3S-IEQ schemes …

An efficiently linear time-marching method is proposed for the incompressible fluid flows
coupled Ohta–Kawasaki model of diblock copolymer melt. Although this model satisfies the …

A unified framework of invariant-conserving explicit Runge-Kutta schemes for the nonlinear
Hamiltonian ODEs and PDEs are proposed by utilizing the invariant energy quadratization …

Over the years, energy-dissipation-preserving (EDP) numerical methods (EDP-NMs) for the
nonlinear system of energy dissipation have attracted considerable attention because they …