相关论文: Maximum bound preservation of exponential integrat…
The Allen-Cahn equation (ACE) inherently possesses two crucial properties: the maximum principle and the energy dissipation law. Preserving these two properties at the discrete level is also necessary in the numerical methods for the ACE.…
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 nonlinear propagators are computed explicitly. We show that…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction…
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of the high-dimensional multi-particle…
A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
Limiters are nonlinear hybridization techniques that are used to preserve positivity and monotonicity when numerically solving hyperbolic conservation laws. Unfortunately, the original methods suffer from the truncation-error being…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We develop a numerical scheme for the Kepler problem that preserves exactly all first integrals: angular momentum, total energy, and the Laplace-Runge-Lenz vector. This property ensures that orbital trajectories retain their precise shape…
This work presents a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system, incorporating periodic, closed, and thermal boundary conditions. The system comprises the incompressible Navier-Stokes equations…
In this paper we present a novel approach for the prescription of high order boundary conditions when approximating the solution of the Euler equations for compressible gas dynamics on curved moving domains. When dealing with curved…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
We investigate low-regularity integrator (LRI) methods for the Q-tensor model governing nematic liquid-crystalline semilinear parabolic equation. First- and second-order temporal discretizations are developed using Duhamel's formula, and we…
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…