Related papers: A new class of high-order methods for multirate di…
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…
Multirate time integration methods apply different step sizes to resolve different components of the system based on the local activity levels. This local selection of step sizes allows increased computational efficiency while achieving the…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed…
Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast and slow variables can be linearly separated using additive or…
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…
Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires…
Differential equations arising in many practical applications are characterized by multiple time scales. Multirate time integration seeks to solve them efficiently by discretizing each scale with a different, appropriate time step, while…
In this paper, two new families of fourth-order explicit exponential Runge--Kutta (ERK) methods with four stages are studied for solving first-order differential systems $y'(t)+My(t)=f(y(t))$. By comparing the Taylor series of the exact…
This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the computational costs to different activity levels of the system.…
In this paper, two novel classes of implicit exponential Runge-Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, we analyze the symplectic conditions of two kinds of exponential integrators, and present a…
This work focuses on the construction of a new class of fourth-order accurate methods for multirate time evolution of systems of ordinary differential equations. We base our work on the Recursive Flux Splitting Multirate (RFSMR) version of…
In this work we present two new families of multirate time step adaptivity controllers, that are designed to work with embedded multirate infinitesimal (MRI) time integration methods for adapting time steps when solving problems with…
This work considers multirate generalized-structure additively partitioned Runge-Kutta (MrGARK) methods for solving stiff systems of ordinary differential equations (ODEs) with multiple time scales. These methods treat different partitions…
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order ($p$-order polynomial) modal discontinuous Galerkin method. The core algorithm that based on a global…
Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper…
When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…
Implicit-Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is partitioned into stiff and nonstiff processes with the goal of lower computational costs than a purely…
Among the family of fourth-order time integration schemes, the two-stage Gauss--Legendre method, which is an implicit Runge--Kutta method based on collocation, is the only superconvergent. The computational cost of this implicit scheme for…