相关论文: On the performance of exponential integrators for …
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
We propose a fast integrator to a class of dynamical systems with several temporal scales. The proposed method is developed as an extension of the variable step size Heterogeneous Multiscale Method (VSHMM), which is a two-scale integrator…
An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The…
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…
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 introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…
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…
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…
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…
In this work we present a proof of concept of CUDA-capable, resistive, multi-fluid models of relativistic magnetohydrodynamics (RMHD). Resistive and multi-fluid codes for simulating models of RMHD suffer from stiff source terms, so it is…
We present a class of exponential integrators to compute solutions of the stochastic Schr\"odinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the…
In this paper, we propose and analyze ETD-Multistep-Pad\'{e} (ETD-MS-Pad\'{e}) and ETD Implicit Multistep-Pad\'{e} (ETD-IMS-Pad\'{e}) for semilinear parabolic delay differential equations with smooth solutions. In our previous work [15], we…
MHD turbulence is likely to play an important role in several astrophysical scenarios where the magnetic Reynolds is very large. Numerically, these cases can be studied efficiently by means of Large Eddy Simulations, in which the…
The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…
In this note we consider the ideal compressible magneto-hydrodynamics (MHD) equations in a special two dimensional setting. We show that there exist particular initial data for which one obtains infinitely many entropy-conserving weak…
Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty…
We present a new magnetohydrodynamic (MHD) simulation code with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements…
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…
In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context, we compare Leja and Krylov based methods to compute the…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…