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

Title: A geometric multigrid preconditioning strategy for DPG system matrices

Abstract

Here, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan (2010, 2011) guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general – though there are some results for Poisson, e.g.– is how best to precondition the DPG system matrix, so that iterative solvers may be used to allow solution of large-scale problems.

Authors:
 [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Rice Univ., Houston, TX (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); Argonne National Laboratory - Argonne Leadership Computing Facility
OSTI Identifier:
1399559
Alternate Identifier(s):
OSTI ID: 1429686
Report Number(s):
SAND-2017-7727J
Journal ID: ISSN 0898-1221; PII: S0898122117304133
Grant/Contract Number:
AC04-94AL85000; AC02-06CH11357; NA0003525
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 74; Journal Issue: 8; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Discontinuous Petrov–Galerkin; Adaptive finite elements; Iterative solvers; Geometric multigrid; Discontinuous Petrov Galerkin; adaptive finite elements; geometric multigrid; iterative solvers

Citation Formats

Roberts, Nathan V., and Chan, Jesse. A geometric multigrid preconditioning strategy for DPG system matrices. United States: N. p., 2017. Web. doi:10.1016/j.camwa.2017.06.055.
Roberts, Nathan V., & Chan, Jesse. A geometric multigrid preconditioning strategy for DPG system matrices. United States. doi:10.1016/j.camwa.2017.06.055.
Roberts, Nathan V., and Chan, Jesse. Wed . "A geometric multigrid preconditioning strategy for DPG system matrices". United States. doi:10.1016/j.camwa.2017.06.055.
@article{osti_1399559,
title = {A geometric multigrid preconditioning strategy for DPG system matrices},
author = {Roberts, Nathan V. and Chan, Jesse},
abstractNote = {Here, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan (2010, 2011) guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general – though there are some results for Poisson, e.g.– is how best to precondition the DPG system matrix, so that iterative solvers may be used to allow solution of large-scale problems.},
doi = {10.1016/j.camwa.2017.06.055},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 8,
volume = 74,
place = {United States},
year = {Wed Aug 23 00:00:00 EDT 2017},
month = {Wed Aug 23 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on August 23, 2018
Publisher's Version of Record

Save / Share: