Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD

Phillips, Edward G.; Shadid, John N.; Cyr, Eric C.; Elman, Howard C.; Pawlowski, Roger P.

doi:10.1137/16M1074084

Title: Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD

Journal Article · Thu Nov 17 00:00:00 EST 2016 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/16M1074084· OSTI ID:1598347

Phillips, Edward G. ^[1]; Shadid, John N. ^[1]; Cyr, Eric C. ^[1]; Elman, Howard C. ^[2]; Pawlowski, Roger P. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of Maryland, College Park, MD (United States)

The scalable iterative solution of strongly coupled three-dimensional incompressible resistive magnetohydrodynamics (MHD) equations is quite challenging because disparate time scales arise from the electromagnetics, the hydrodynamics, as well as the coupling between these systems. This study considers a mixed finite element discretization of a dual saddle point formulation of the incompressible resistive MHD equations using a stable nodal (Q2/Q1) discretization for the hydrodynamics and a stable edge-node discretization of a reduced form of the Maxwell equations. This paper introduces new approximate block factorization preconditioners for this system which reduce the system to approximate Schur complement systems that can be solved using algebraic multilevel methods. These preconditioners include a new augmentation-based approximation for the magnetic induction saddle point system as well as efficient approximations of the Schur complements that arise from the complex coupling between the Navier--Stokes equations and the Maxwell equations.

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Research Organization:: Univ. of Maryland, College Park, MD (United States); Lockheed Martin Corporation, Littleton, CO (United States)

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

Grant/Contract Number:: SC0009301; AC04-94AL85000

OSTI ID:: 1598347

Journal Information:: SIAM Journal on Scientific Computing, Vol. 38, Issue 6; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 28 works

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Cited By (2)

A face‐based monolithic approach for the incompressible magnetohydrodynamics equations Ata, Kayhan; Sahin, Mehmet International Journal for Numerical Methods in Fluids, Vol. 92, Issue 5 https://doi.org/10.1002/fld.4786	journal	May 2020
Second order unconditionally convergent and energy stable linearized scheme for MHD equations Zhang, Guo-Dong; Yang, Jinjin; Bi, Chunjia Advances in Computational Mathematics, Vol. 44, Issue 2 https://doi.org/10.1007/s10444-017-9552-x	journal	August 2017

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mixed finite elements

Title: Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD

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