TY - JOUR
T1 - Unconditional stability for multistep ImEx schemes
T2 - Practice
AU - Seibold, Benjamin
AU - Shirokoff, David
AU - Zhou, Dong
N1 - Funding Information:
The authors wish to acknowledge support by the National Science Foundation through grants DMS–1719640 (B. Seibold and D. Zhou) and DMS–1719693 (D. Shirokoff). D. Shirokoff was supported by a grant from the Simons Foundation (#359610).
Funding Information:
The authors wish to acknowledge support by the National Science Foundation through grants DMS–1719640 (B. Seibold and D. Zhou) and DMS–1719693 (D. Shirokoff). D. Shirokoff was supported by a grant from the Simons Foundation (# 359610 ).
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are allowed to be stiff. For a class of new ImEx multistep schemes that involve a free parameter, strategies are presented on how to choose the ImEx splitting and the time stepping parameter, so that unconditional stability is achieved under the smallest approximation errors. These strategies are based on recently developed stability concepts, which also provide novel insights into the limitations of existing semi-implicit backward differentiation formulas (SBDF). For instance, the new strategies enable higher order time stepping that is not otherwise possible with SBDF. With specific applications in nonlinear diffusion problems and incompressible channel flows, it is demonstrated how the unconditional stability property can be leveraged to efficiently solve stiff nonlinear or nonlocal problems without the need to solve nonlinear or nonlocal problems implicitly.
AB - This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are allowed to be stiff. For a class of new ImEx multistep schemes that involve a free parameter, strategies are presented on how to choose the ImEx splitting and the time stepping parameter, so that unconditional stability is achieved under the smallest approximation errors. These strategies are based on recently developed stability concepts, which also provide novel insights into the limitations of existing semi-implicit backward differentiation formulas (SBDF). For instance, the new strategies enable higher order time stepping that is not otherwise possible with SBDF. With specific applications in nonlinear diffusion problems and incompressible channel flows, it is demonstrated how the unconditional stability property can be leveraged to efficiently solve stiff nonlinear or nonlocal problems without the need to solve nonlinear or nonlocal problems implicitly.
KW - High order time stepping
KW - ImEx stability
KW - Linear multistep ImEx
KW - Semi-implicit backward differentiation
KW - Unconditional stability
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U2 - 10.1016/j.jcp.2018.09.044
DO - 10.1016/j.jcp.2018.09.044
M3 - Article
AN - SCOPUS:85054441636
SN - 0021-9991
VL - 376
SP - 295
EP - 321
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -