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Parallel Auxiliary Space AMG for H(Curl) Problems

Journal Article · · Journal of Computational Mathematics
 [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. In addition, we discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu (HX) auxiliary space decomposition. An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H(curl) problems.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1670552
Report Number(s):
LLNL-JRNL--237306; 356052
Journal Information:
Journal of Computational Mathematics, Journal Name: Journal of Computational Mathematics Journal Issue: 5 Vol. 27; ISSN 0254-9409
Publisher:
Global Science PressCopyright Statement
Country of Publication:
United States
Language:
English

Cited By (13)

An analysis of the TDNNS method using natural norms journal November 2017
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh journal October 2013
Convergence of HX Preconditioner for Maxwell's Equations with Jump Coefficients (ii): The Main Results preprint January 2017
Exploring basal sliding with a fluidity-based, ice-sheet model using FOSLS: Fluidity-Based Ice-Sheet Models journal March 2018
Right preconditioned MINRES for singular systems † journal January 2020
Parallel numerical solution of the time-harmonic Maxwell equations in mixed form: PARALLEL SOLUTION OF THE TIME-HARMONIC MAXWELL EQUATIONS journal April 2011
Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids book January 2009
Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method journal April 2014
Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method journal November 2015
Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems journal March 2019
Parallel Solution Methods and Preconditioners for Evolution Equations journal April 2018
Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method text January 2015
Robust and scalable 3D geo-electromagnetic modeling approach using the finite element method text January 2014

Figures / Tables (11)

Fig. 6.1(p. 15)figure Fig. 6.1
Table 6.1(p. 16)table Table 6.1
Fig. 6.2(p. 17)figure Fig. 6.2
Fig. 6.3(p. 17)figure Fig. 6.3
Table 6.2(p. 18)table Table 6.2
Fig. 6.4(p. 19)figure Fig. 6.4
Fig. 6.5(p. 19)figure Fig. 6.5
Table 6.3(p. 20)table Table 6.3
Table 6.4(p. 20)table Table 6.4
Fig. 6.6(p. 21)figure Fig. 6.6
Table 6.5(p. 21)table Table 6.5

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Related Subjects

97 MATHEMATICS AND COMPUTING