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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 43-65, 2022/11/10
Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a partial differential equation, providing possibilities for accelerating the computation of its solution. While parallelisation in time has allowed remarkable speed-ups in applications involving parabolic equations, its effectiveness in the hyperbolic framework remains debatable: growth of instabilities and slow convergence are both strong issues in this case, which often negate most of the advantages from time-parallelisation. Here, we focus on the Multigrid Reduction in Time algorithm, investigating in detail its performance when applied to non-linear conservation laws with a variety of discretisation schemes. Specific attention is given to high-accuracy Weighted Essentially Non-Oscillatory reconstructions, coupled with Strong Stability Preserving integrators, which are often the discretisations of choice for such equations. A technique to improve the performance of MGRIT when applied to a low-order, more dissipative scheme is also outlined. This study aims at identifying the main causes for degradation in the convergence speed of the algorithm and finds the Courant-Friedrichs-Lewy limit to be the principal determining factor.
Keywords: parallel-in-time integration, multigrid, conservation laws, WENO, high-order methods