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

Abstract

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.

Authors:
 [1];  [1];  [1];  [2];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of Maryland, College Park, MD (United States)
Publication Date:
Research Org.:
Univ. of Maryland, College Park, MD (United States); Lockheed Martin Corpration, Litteton, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1598347
Grant/Contract Number:  
SC0009301; AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 6; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; magnetohydrodynamics; preconditioners; mixed finite elements

Citation Formats

Phillips, Edward G., Shadid, John N., Cyr, Eric C., Elman, Howard C., and Pawlowski, Roger P. Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD. United States: N. p., 2016. Web. doi:10.1137/16M1074084.
Phillips, Edward G., Shadid, John N., Cyr, Eric C., Elman, Howard C., & Pawlowski, Roger P. Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD. United States. doi:10.1137/16M1074084.
Phillips, Edward G., Shadid, John N., Cyr, Eric C., Elman, Howard C., and Pawlowski, Roger P. Thu . "Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD". United States. doi:10.1137/16M1074084. https://www.osti.gov/servlets/purl/1598347.
@article{osti_1598347,
title = {Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD},
author = {Phillips, Edward G. and Shadid, John N. and Cyr, Eric C. and Elman, Howard C. and Pawlowski, Roger P.},
abstractNote = {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.},
doi = {10.1137/16M1074084},
journal = {SIAM Journal on Scientific Computing},
number = 6,
volume = 38,
place = {United States},
year = {2016},
month = {11}
}

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