相关论文: High order conservative schemes for the generalize…

We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO)…

In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…

We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated…

We present a new method to propagate rotating Bose-Einstein condensates subject to explicitly time-dependent trapping potentials. Using algebraic techniques, we combine Magnus expansions and splitting methods to yield any order methods for…

We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

This article focuses on an energy-conservation Galerkin finite element method (FEM) for the generalized Klein-Gordon-Zakharov (KGZ) equations. This method combines the bilinear finite element method for spatial discretization with the…

Bayesian optimization is an effective method for solving expensive black-box optimization problems. Most existing methods use Gaussian processes (GP) as the surrogate model for approximating the black-box objective function, it is…

In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…

Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are considered to be first-order flows. This is a popular topic…

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…

In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schr\"odinger equation by combining the scalar auxiliary variable approach with the exponential…

This paper develops a family of fast, structure-preserving numerical algorithms for the nonlinear Maxwell-Ampere Nernst-Planck equations. For the first-order scheme, the Slotboom transformation rewrites the Nernst-Planck equation to enable…

In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…

We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…

Our work is about energy conserving fourth-order time discretizations of a three-field formulation of Maxwell's equations in conjunction with a spatial discretization using higher-order and compatible de Rham finite element spaces. Toward…

We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…

In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…