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Title: 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)
+ Show Author Affiliations

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, Vol. 27, Issue 5; ISSN 0254-9409
Publisher:
Global Science PressCopyright Statement
Country of Publication:
United States
Language:
English

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Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids book January 2009
An analysis of the TDNNS method using natural norms journal November 2017
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
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Convergence of HX Preconditioner for Maxwell's Equations with Jump Coefficients (ii): The Main Results preprint January 2017

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