A multilevel approach for trace system in HDG discretizations

Muralikrishnan, Sriramkrishnan; Bui-Thanh, Tan; Shadid, John N.

doi:10.1016/j.jcp.2020.109240

A multilevel approach for trace system in HDG discretizations

Journal Article · 09 January 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109240· OSTI ID:1595938

^[1]; ^[1]; Shadid, John N. ^[2]

Univ. of Texas, Austin, TX (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations. Specifically, we first create a coarse solver by eliminating and/or limiting the front growth in nested dissection. This is accomplished by projecting the trace data into a sequence of same or high-order polynomials on a set of increasingly h-coarser edges/faces. We then combine the coarse solver with a block-Jacobi fine scale solver to form a two-level solver/preconditioner. Numerical experiments indicate that the performance of the resulting two-level solver/preconditioner depends on the smoothness of the solution and can offer significant speedups and memory savings compared to the nested dissection direct solver. While the proposed algorithms are developed within the HDG framework, they are applicable to other hybrid(ized) high-order finite element methods. Moreover, we show that our multilevel algorithms can be interpreted as a multigrid method with specific intergrid transfer and smoothing operators. With several numerical examples from Poisson, pure transport, and convection-diffusion equations we demonstrate the robustness and scalability of the algorithms with respect to solution order. Here, while scalability with mesh size in general is not guaranteed and depends on the smoothness of the solution and the type of equation, improving it is a part of future work.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000; NA0003525; SC0018147; NSF-DMS1620352

OSTI ID:: 1595938

Alternate ID(s):: OSTI ID: 1592819

Report Number(s):: SAND-2019-3380J; 673812; TRN: US2100896

Journal Information:: Journal of Computational Physics, Vol. 407, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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A multilevel approach for trace system in HDG discretizations

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