Stabilized Semi-implicit Spectral Deferred Correction Methods for Allen-cahn and Cahn-hilliard Equations
نویسندگان
چکیده
Stabilized semi-implicit spectral defect correction (SSISDC) methods are constructed for the time discretization of Allen-Cahn and Cahn-Hilliard equations. These methods are unconditionally stable, lead to simple linear system to solve at each iteration and can achieve high-order time accuracy with a few iterations in each time step. Ample numerical results are presented to demonstrate the effectiveness of the SSISDC methods for solving the Allen-Cahn and Cahn-Hilliard equations.
منابع مشابه
The existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0
متن کاملHigh Order Local Discontinuous Galerkin Methods for the Allen-cahn Equation: Analysis and Simulation
In this paper, we present a local discontinuous Galerkin (LDG) method for the AllenCahn equation. We prove the energy stability, analyze the optimal convergence rate of k + 1 in L norm and present the (2k + 1)-th order negative-norm estimate of the semidiscrete LDG method for the Allen-Cahn equation with smooth solution. To relax the severe time step restriction of explicit time marching method...
متن کاملOn large time-stepping methods for the Cahn–Hilliard equation
In this work, we will analyze a class of large time-stepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerica...
متن کاملNumerical Approximations of Allen-cahn and Cahn-hilliard Equations
Stability analyses and error estimates are carried out for a number of commonly used numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the schemes we considered are either unconditionally energy stable, or conditionally energy stable with reasonable stability conditions in the semi-discretized versions. Error estimates for selected schemes with a spectral-Ga...
متن کاملCoarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method.
An efficient semi-implicit Fourier spectral method is implemented to solve the Cahn-Hilliard equation with a variable mobility. The method is orders of magnitude more efficient than the conventional forward Euler finite-difference method, thus allowing us to simulate large systems for longer times. We studied the coarsening kinetics of interconnected two-phase mixtures using a Cahn-Hilliard equ...
متن کامل