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Title: Final Report - Subcontract B6183769

Abstract

During my visit to LLNL during July 5{15, 2016, we worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear system arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12 [1]. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly inde nite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of numerical quadrature formulae. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in [2]. Like traditional geometric multilevel methods, this scheme relies on extensive knowledge of the underlying finite element space in order to construct both the smoother and the coarse grid correction components.

Authors:
 [1]
  1. Univ. of California, San Diego, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1366936
Report Number(s):
LLNL-SR-733142
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Bank, R. Final Report - Subcontract B6183769. United States: N. p., 2017. Web. doi:10.2172/1366936.
Bank, R. Final Report - Subcontract B6183769. United States. doi:10.2172/1366936.
Bank, R. Mon . "Final Report - Subcontract B6183769". United States. doi:10.2172/1366936. https://www.osti.gov/servlets/purl/1366936.
@article{osti_1366936,
title = {Final Report - Subcontract B6183769},
author = {Bank, R.},
abstractNote = {During my visit to LLNL during July 5{15, 2016, we worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear system arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12 [1]. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly inde nite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of numerical quadrature formulae. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in [2]. Like traditional geometric multilevel methods, this scheme relies on extensive knowledge of the underlying finite element space in order to construct both the smoother and the coarse grid correction components.},
doi = {10.2172/1366936},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jun 12 00:00:00 EDT 2017},
month = {Mon Jun 12 00:00:00 EDT 2017}
}

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