Alternating directions implicit integration in a general linear method framework

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:387

Article; Proceedings Paper

Sarshar, Arash¹  Roberts, Steven¹  Sandu, Adrian¹ 

[1] Virginia Tech, Dept Comp Sci, Computat Sci Lab, Blacksburg, VA 24061 USA

关键词: Initial value problems;    Time integration;    IMEX methods;    Alternating directions;   

DOI  :  10.1016/j.cam.2019.112619

来源: Elsevier

【 摘 要 】

Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional equations. Classical ADI methods have order at most two, due to the splitting errors. Moreover, when the time discretization of stiff one-dimensional problems is based on Runge-Kutta schemes, additional order reduction may occur. This work proposes a new ADI approach based on the partitioned General Linear Methods framework. This approach allows the construction of high order ADI methods. Due to their high stage order, the proposed methods can alleviate the order reduction phenomenon seen with other schemes. Numerical experiments are shown to provide further insight into the accuracy, stability, and applicability of these new methods. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free