skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Final Report - Subcontract B623760

Abstract

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. 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 de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite 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 the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.

Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1410786
Report Number(s):
LLNL-SR-742143
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 B623760. United States: N. p., 2017. Web. doi:10.2172/1410786.
Bank, R. Final Report - Subcontract B623760. United States. doi:10.2172/1410786.
Bank, R. Fri . "Final Report - Subcontract B623760". United States. doi:10.2172/1410786. https://www.osti.gov/servlets/purl/1410786.
@article{osti_1410786,
title = {Final Report - Subcontract B623760},
author = {Bank, R.},
abstractNote = {During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. 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 de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite 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 the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.},
doi = {10.2172/1410786},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Nov 17 00:00:00 EST 2017},
month = {Fri Nov 17 00:00:00 EST 2017}
}

Technical Report:

Save / Share: