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Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…
Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By…
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained…
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,…
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…
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…
Recently, ParaExp was proposed for the time integration of hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a…
In this paper, we investigate the use of higher-order exponential Rosenbrock time integration methods on the shallow water equations on the sphere. This stiff, nonlinear model provides a testing ground for accurate and stable time…
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…
High-performance computing trends towards many-core systems are expected to continue over the next decade. As a result, parallel-in-time methods, mathematical formulations which exploit additional degrees of parallelism in the time…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes…
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 present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on…
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…
In this paper, we implement exponential integrators, specifically Integrating Factor (IF) and Exponential Time Differencing (ETD) methods, using pseudo-spectral techniques to solve phase-field equations within a Python framework. These…
The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation,…
This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaDiag based on first and second order accurate exponential…
Maxwell's equations for propagation of electromagnetic waves in dispersive and absorptive (passive) media are represented in the form of the Schr\"odinger equation $i\partial \Psi/\partial t = {H}\Psi$, where ${H}$ is a linear differential…