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Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods
Abstract
In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge–Kutta methods with Radau nodes and that possess high stage order. Here, we show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge–Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge–Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge–Kutta methods and/or achieve a given accuracy several times times faster in terms of computational runtime.
- Authors:
-
[2]
- Tulane Univ., New Orleans, LA (United States)
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 2315644
- Report Number(s):
- LA-UR-21-28709
Journal ID: ISSN 1064-8275
- Grant/Contract Number:
- 89233218CNA000001; DMS-2012875
- Resource Type:
- Accepted Manuscript
- Journal Name:
- SIAM Journal on Scientific Computing
- Additional Journal Information:
- Journal Volume: 45; Journal Issue: 6; Journal ID: ISSN 1064-8275
- Publisher:
- Society for Industrial and Applied Mathematics (SIAM)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; additive integrators; linearly implicit; implicit-explicit; fully implicit Runge–Kutta; general linear methods
Citation Formats
Buvoli, Tommaso, and Southworth, Benjamin Scott. Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods. United States: N. p., 2023.
Web. doi:10.1137/21m1446988.
Buvoli, Tommaso, & Southworth, Benjamin Scott. Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods. United States. https://doi.org/10.1137/21m1446988
Buvoli, Tommaso, and Southworth, Benjamin Scott. Wed .
"Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods". United States. https://doi.org/10.1137/21m1446988.
@article{osti_2315644,
title = {Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods},
author = {Buvoli, Tommaso and Southworth, Benjamin Scott},
abstractNote = {In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge–Kutta methods with Radau nodes and that possess high stage order. Here, we show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge–Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge–Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge–Kutta methods and/or achieve a given accuracy several times times faster in terms of computational runtime.},
doi = {10.1137/21m1446988},
journal = {SIAM Journal on Scientific Computing},
number = 6,
volume = 45,
place = {United States},
year = {Wed Nov 29 00:00:00 EST 2023},
month = {Wed Nov 29 00:00:00 EST 2023}
}
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