Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 387, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2019.112619
Keywords
Initial value problems; Time integration; IMEX methods; Alternating directions
Categories
Funding
- National Science Foundation [NSF CCF-1613905, NSF ACI-1709727]
- Air Force Office of Scientific Research grant AFOSR DDDAS [FA9550-17-1-0015]
- Computational Science Laboratory at Virginia Tech
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This paper presents a new ADI approach based on the partitioned General Linear Methods framework, which allows for the construction of high order ADI methods and alleviates the order reduction phenomenon seen with other schemes. Numerical experiments provide further insight into the accuracy, stability, and applicability of these new methods.
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.
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