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 largescale problems.
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Rice Univ., Houston, TX (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), 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; OSTI ID: 1549891
 Report Number(s):
 SAND20177727J
Journal ID: ISSN 08981221; PII: S0898122117304133
 Grant/Contract Number:
 AC0494AL85000; AC0206CH11357; NA0003525
 Resource Type:
 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 08981221
 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. https://www.osti.gov/servlets/purl/1399559.
@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 largescale problems.},
doi = {10.1016/j.camwa.2017.06.055},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 8,
volume = 74,
place = {United States},
year = {2017},
month = {8}
}
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