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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. 365-390, 2022/02/28
We consider monolithic algebraic multigrid (AMG) algorithms for the solution of block linear systems arising from multiphysics simulations. While the multigrid idea is applied directly to the entire linear system, AMG operators are constructed by leveraging the matrix block structure. In particular, each block corresponds to a set of physical unknowns and physical equations. Multigrid components are constructed by first applying existing AMG procedures to matrix sub-blocks. The resulting AMG sub-components are then composed together to define a monolithic AMG preconditioner. Given the problem-dependent nature of multiphysics systems, different blocking choices may work best in different situations, and so software flexibility is essential. We apply different blocking strategies to systems arising from resistive magnetohydrodynamics in order to demonstrate the associated trade-offs.
Keywords: multigrid, algebraic multigrid, multiphysics, magnetohydrodynamics