Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
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 …
equation has been an open problem in recent years. This work provides a positive answer …
Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
We propose and analyze a class of temporal up to fourth-order unconditionally structure-
preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first …
preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first …
A conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier
We present a new numerical scheme for solving a conservative Allen–Cahn equation with a
space–time dependent Lagrange multiplier. Since the well-known classical Allen–Cahn …
space–time dependent Lagrange multiplier. Since the well-known classical Allen–Cahn …
Fast explicit integration factor methods for semilinear parabolic equations
In this paper, an explicit numerical method and its fast implementation are proposed and
discussed for the solution of a wide class of semilinear parabolic equations including the …
discussed for the solution of a wide class of semilinear parabolic equations including the …
An exponential time differencing Runge–Kutta method ETDRK32 for phase field models
W Cao, H Yang, W Chen - Journal of Scientific Computing, 2024 - Springer
The exponential time differencing Runge–Kutta method (ETDRK) developed by Cox and
Matthews has proven effective in computing nonlinear partial differential equation. However …
Matthews has proven effective in computing nonlinear partial differential equation. However …
Third-order accurate, large time-step** and maximum-principle-preserving schemes for the Allen-Cahn equation
We present and evaluate several explicit, large time-step** algorithms for the Allen-Cahn
equation. Our approach incorporates a stabilization technique and uses Taylor series …
equation. Our approach incorporates a stabilization technique and uses Taylor series …
Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions
H Zhang, X Qian, J ** explicit, high-order accurate, and stable algorithms for nonlinear differential
equations remains an exceedingly difficult task. In this work, a systematic approach is …
equations remains an exceedingly difficult task. In this work, a systematic approach is …
Stability and convergence of Strang splitting. Part I: scalar Allen-Cahn equation
We consider a class of second-order Strang splitting methods for Allen-Cahn equations with
polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the …
polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the …
A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systems
X **ao, X Feng - Mathematics and Computers in Simulation, 2022 - Elsevier
In this paper, a highly efficient space–time operator splitting finite element method is
presented to solve the two-and three-dimensional Allen–Cahn equations. The main …
presented to solve the two-and three-dimensional Allen–Cahn equations. The main …
[HTML][HTML] Multiphase image segmentation using a phase-field model
In this paper, we propose a new, fast, and stable hybrid numerical method for multiphase
image segmentation using a phase-field model. The proposed model is based on the Allen …
image segmentation using a phase-field model. The proposed model is based on the Allen …