Parareal Algorithms Implemented with IMEX Runge-Kutta Methods

Wang Zhiyong; Wu Shulin

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Parareal Algorithms Implemented with IMEX Runge-Kutta Methods

机译：使用IMEX Runge-Kutta方法实现的超现实算法

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Parareal algorithm is a very powerful parallel computation method and has received much interest from many researchers over the past few years. The aim of this paper is to investigate the performance of parareal algorithm implemented with IMEX Runge-Kutta (RK) methods. A stability criterion of the parareal algorithm coupled with IMEX RK methods is established and the advantage (in the sense of stability) of implementing with this kind of RK methods is numerically investigated. Finally, numerical examples are given to illustrate the efficiency and performance of different parareal methods.

机译：超现实算法是一种非常强大的并行计算方法，并且在过去几年中引起了许多研究人员的关注。本文的目的是研究使用IMEX Runge-Kutta（RK）方法实现的超现实算法的性能。建立了结合IMEX RK方法的超现实算法的稳定性准则，并数值研究了使用这种RK方法实现的优势（从稳定性的角度）。最后，通过数值例子说明了不同的超现实方法的效率和性能。

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《Mathematical Problems in Engineering》 |2015年第4期|395340.1-395340.12|共12页
作者
Wang Zhiyong; Wu Shulin;
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Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610731, Sichuan, Peoples R China.;

Sichuan Univ Sci & Engn, Sch Sci, Zigong 643000, Sichuan, Peoples R China.;

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1. Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models [J] . Florian De?Vuyst Advanced Modeling and Simulation in Engineering Sciences . 2016,第1期

机译：求解时间相关问题的有效求解器：概述IMEX，LATIN，PARAEXP和PARAREAL算法，可解决热型问题，并可能使用近似指数积分器和降阶模型
2. On linearly implicit IMEX Runge-Kutta methods for degenerate convection-diffusion problems modeling polydisperse sedimentation [J] . Boscarino Sebastiano, Buerger Raimund, Mulet Pep, Bulletin of the Brazilian Mathematical Society . 2016,第1期

机译：线性隐式IMEX Runge-Kutta方法用于退化多对流沉降的简并对流扩散问题
3. LINEARLY IMPLICIT IMEX RUNGE-KUTTA METHODS FOR A CLASS OF DEGENERATE CONVECTION-DIFFUSION PROBLEMS [J] . Boscarino Sebastiano, Buerger Raimund, Mulet Pep, SIAM Journal on Scientific Computing . 2015,第2期

机译：一类退化对流扩散问题的线性隐式IMEX RUNGE-KUTTA方法
4. Construction of IMEX Methods with Inherent Runge-Kutta Stability [C] . Michal Bras, Giuseppe Izzo, Zdzislaw Jackiewicz International Conference of Numerical Analysis and Applied Mathematics . 2016

机译：具有固有跑步稳定性的IMEX方法的构建
5. Theory and implementation of numerical methods based on Runge-Kutta integration for solving optimal control problems [D] . Schwartz, Adam Lowell 1996

机译：基于Runge-Kutta积分求解最优控制问题的数值方法的理论与实现
6. A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM [O] . JEHANZEB HAMEED CHAUDHRY, DON ESTEP, SIMON TAVENER, -1

机译：两种阶段计算方法的后验误差分析及其在有效离散和稀疏算法中的应用。
7. Parareal Algorithms Implemented with IMEX Runge-Kutta Methods [O] . Zhiyong Wang, Shulin Wu 2015

机译：使用IMEX Runge-Kutta方法实现的宫算法
8. Overcoming Geometry-Induced Stiffness with IMplicit-Explicit (IMEX) Runge-Kutta Algorithms on Unstructured Grids with Applications to CEM, CFD, and CAA [R] . Kanevsky, Alex 2004

机译：用非显微网格上的显式显式（ImEX）Runge-Kutta算法克服几何诱导的刚度，并应用于CEm，CFD和Caa

Parareal Algorithms Implemented with IMEX Runge-Kutta Methods

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