Related papers: Should exponential integrators be used for advecti…
In this paper, we investigate the application of exponential integrators to advection-dominated problems. We focus on Krylov subspace and Leja interpolation methods to compute the action of exponential and related matrix functions.…
In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for…
We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…
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…
The solution of inverse problems in a variational setting finds best estimates of the model parameters by minimizing a cost function that penalizes the mismatch between model outputs and observations. The gradients required by the numerical…
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…
Exponential integrators that use Krylov approximations of matrix functions have turned out to be efficient for the time-integration of certain ordinary differential equations (ODEs). This holds in particular for linear homogeneous ODEs,…
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…
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 present a publicly available software for exponential integrators that computes the $\varphi_l(z)$ functions using polynomial interpolation. The interpolation method at Leja points have recently been shown to be competitive with the…
Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear…
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…
We present an open-source CUDA-based package that consists of a compilation of exponential integrators where the action of the matrix exponential or the $\varphi_l$ functions on a vector is approximated using the method of polynomial…
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…
We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study two new classes of exponential Runge-Kutta (ERK) integrators…
Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
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…