Implicit-Explicit Multirate Infinitesimal GARK Methods

Chinomona, Rujeko; Reynolds, Daniel R.

doi:10.1137/20m1354349

Title: Implicit-Explicit Multirate Infinitesimal GARK Methods

Journal Article · 09 September 2021 · SIAM Journal on Scientific Computing

DOI: https://doi.org/10.1137/20m1354349 · OSTI ID:1836556

Chinomona, Rujeko ^[1];

^[2]

Southern Methodist Univ., Dallas, TX (United States); Southern Methodist University
Southern Methodist Univ., Dallas, TX (United States)

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

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Research Organization:: Southern Methodist Univ., Dallas, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: SC0021354

OSTI ID:: 1836556

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 43; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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