Related papers: Exponential integrators for large-scale stiff matr…
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…
Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in…
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…
A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially…
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…
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 is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
A stable approach for integrating the impedance matrix in cylindrical, radial inhomogeneous structures is developed and studied. A Stroh-like system using the time-harmonic displacement-traction state vector is used to derive the Riccati…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
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…
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…
This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
In this paper we propose a novel class of methods for high order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the…
Time integration of advection dominated advection-diffusion problems on refined meshes can be a challenging task, since local refinement can lead to a severe time step restriction, whereas standard implicit time stepping is usually hardly…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…
In this work we present a low-rank algorithm for computing low-rank approximations of large-scale Lyapunov operator $\varphi$-functions. These computations play a crucial role in implementing of matrix-valued exponential integrators for…
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…