Parallel auxiliary space AMG for definite Maxwell problems

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Motivated by the needs of large multi-physics simulation codes, we are interested in algebraic solvers for the linear systems arising in time-domain electromagnetic simulations. Our focus is on finite element discretization, and we are developing scalable parallel preconditioners which employ only fine-grid information, similar to algebraic multigrid (AMG) for diffusion problems. In the last few years, the search for efficient algebraic preconditioners for H(curl) bilinear forms has intensified. The attempts to directly construct AMG methods had some success, see [12, 1, 7]. Exploiting available multilevel methods on auxiliary mesh for the same bilinear form led to efficient auxiliary mesh preconditioners ... continued below

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Kolev, T V & Vassilevski, P S February 16, 2007.

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Motivated by the needs of large multi-physics simulation codes, we are interested in algebraic solvers for the linear systems arising in time-domain electromagnetic simulations. Our focus is on finite element discretization, and we are developing scalable parallel preconditioners which employ only fine-grid information, similar to algebraic multigrid (AMG) for diffusion problems. In the last few years, the search for efficient algebraic preconditioners for H(curl) bilinear forms has intensified. The attempts to directly construct AMG methods had some success, see [12, 1, 7]. Exploiting available multilevel methods on auxiliary mesh for the same bilinear form led to efficient auxiliary mesh preconditioners to unstructured problems as shown in [4, 8]. A computationally more attractive approach was recently proposed by Hiptmair and Xu [5]. In contrast to the auxiliary mesh idea, the method in [5] uses a nodal H{sup 1}-conforming auxiliary space on the same mesh. This significantly simplifies the computation of the corresponding interpolation operator. In the present talk, we consider several options for constructing unstructured mesh AMG preconditioners for H(curl) problems and report a summary of computational results from [10, 9]. Our approach is slightly different than the one from [5], since we apply AMG directly to variationally constructed coarse-grid operators, and therefore no additional Poisson matrices are needed on input. We also consider variable coefficient problems, including some that lead to a singular matrix. Both type of problems are of great practical importance and are not covered by the theory of [5].

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5 p. (0.3 MB)

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  • Presented at: Oberwolfach Institute workshop on "Computational Electromagnetism and Acoustics", Oberwolfach, Germany, Feb 03 - Feb 10, 2007

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  • Report No.: UCRL-PROC-228221
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 902302
  • Archival Resource Key: ark:/67531/metadc888551

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  • February 16, 2007

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  • Sept. 22, 2016, 2:13 a.m.

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  • April 13, 2017, 6:16 p.m.

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Kolev, T V & Vassilevski, P S. Parallel auxiliary space AMG for definite Maxwell problems, article, February 16, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc888551/: accessed May 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.