相关论文: Exponential Integrators for Phase-Field Equations …

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and…

We introduce a new class of arbitrary-order exponential time differencing methods based on spectral deferred correction (ETDSDC) and describe a simple procedure for initializing the requisite matrix functions. We compare the stability and…

The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…

Phase-field simulations are a practical but also expensive tool to calculate microstructural evolution. This work aims to compare explicit time integrators for a broad class of phase-field models involving coupling between the phase-field…

For reaction-diffusion equations in irregular domain with moving boundaries, the numerical stability constraints from the reaction and diffusion terms often require very restricted time step size, while complex geometries may lead to…

In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…

Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many such problems, the dominant…

In this paper, we present new types of exponential integrators for Stochastic Differential Equations (SDEs) that take the advantage of the exact solution of (generalised) geometric Brownian motion. We examine both Euler and Milstein…

In this paper, we propose a $\mu$-mode integrator for computing the solution of stiff evolution equations. The integrator is based on a $d$-dimensional splitting approach and uses exact (usually precomputed) one-dimensional matrix…

Phase field models are gradient flows with their energy naturally dissipating in time. In order to preserve this property, many numerical schemes have been well-studied. In this paper we consider a well-known method, namely the exponential…

We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…

Two types of second-order in time partial differential equations (PDEs), namely semilinear wave equations and semilinear beam equations are considered. To solve these equations with exponential integrators, we present an approach to compute…

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…

Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…

In this paper, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously satisfy discrete analogues of the energy dissipation laws and…

The goal of this project is to compare the performance of exponential time integrators with traditional methods such as diagonally implicit Runge-Kutta methods in the context of solving the system of reduced magnetohydrodynamics (RMHD). In…

We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…

This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…

We propose two new classes of time integrators for stiff DEs: the implicit-explicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational…

In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…