@String{j-INF-TECH = "Informations-technik"}
@String{j-NUM-MATH = "Num. Math"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM J. Sci.~Stat.~Comput."}
@String{pub-AMS = "Amer. Math. Soc."}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-ANL = "Argonne National Laboratory"}
@String{pub-ANL:adr = "Argonne, IL, USA"}
@String{pub-IEEE = "IEEE"}
@String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver
Spring, MD 20910, USA"}
@String{pub-SIAM = "SIAM"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@Article{Douglas:1988:INM,
author = "Craig C. Douglas and Michael E. Henderson and Susumu
Horiguchi and Willard L. Miranker and Barry F. Smith
and Andrew Winkler",
title = "The interaction of numerics and machines",
journal = j-INF-TECH,
volume = "30",
pages = "83--98",
year = "1988",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
}
@Article{Douglas:1989:USA,
author = "Craig C. Douglas and Barry F. Smith",
title = "Using symmetries and antisymmetries to analyze a
parallel multigrid algorithm: the elliptic boundary
value problem case",
journal = j-SIAM-J-NUMER-ANAL,
volume = "26",
number = "6",
pages = "1439--1461",
month = dec,
year = "1989",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
MRclass = "65N55 (65Y05)",
MRnumber = "91d:65187",
MRreviewer = "Murli M. Gupta",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "JSTOR database;
ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
acknowledgement = ack-nhfb,
keyword = "multigrid, parallel, robust multigrid",
}
@Article{Widlund:1990:DDA,
author = "Olof B. Widlund and Barry F. Smith",
title = "A domain decomposition algorithm using a hierarchical
basis",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "11",
pages = "1212--1220",
year = "1990",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "hierarchical basis, Schur complement, domain
decomposition",
}
@Article{Smith:1991:DDA,
author = "Barry F. Smith",
title = "A domain decomposition algorithm for elliptic problems
in three dimensions",
journal = j-NUM-MATH,
volume = "60",
pages = "219--234",
year = "1991",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "domain decomposition, wirebasket methods, iterative
substructuring",
}
@InProceedings{Gropp:1992:EDD,
author = "William D. Gropp and Barry F. Smith",
booktitle = "Domain Decomposition Methods in Science and
Engineering",
title = "Experiences with Domain Decomposition in Three
Dimensions: Overlapping {S}chwarz Methods",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "323--333",
year = "1992",
ISBN = "0-8218-5158-6",
ISBN-13 = "978-0-8218-5158-6",
bibdate = "Mon Jul 11 14:09:33 MDT 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "Schwarz methods, parallel computing",
}
@InProceedings{Smith:1992:ISA,
author = "Barry F. Smith",
editor = "Tony F. Chan and David E. Keyes and G{\'e}rard A.
Meurant and Jeffrey S. Scroggs and Robert G. Voigt",
booktitle = "Fifth International Symposium on Domain Decomposition
Methods for Partial Differential Equations",
title = "An iterative substructuring algorithm for problems in
three dimensions",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "91--98 (of xiii + 623)",
year = "1992",
ISBN = "0-89871-288-2",
ISBN-13 = "978-0-89871-288-9",
LCCN = "QA402.2 .I57 1991",
bibdate = "Mon Jul 11 14:09:33 MDT 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "domain decomposition, iterative substructuring",
}
@Article{Smith:1992:ODD,
author = "Barry F. Smith",
title = "An optimal domain decomposition preconditioner for
elasticity problems",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "13",
pages = "364--378",
year = "1992",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "Schwarz methods, domain decomposition, Schur
complements, iterative substructuring",
}
@TechReport{Chan:1993:MDD,
author = "Tony F. Chan and Barry F. Smith",
title = "Multigrid and Domain Decomposition on Unstructured
Grids",
number = "93-42",
institution = "UCLA, Dept. of Mathematics",
year = "1993",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
note = "To appear in the Proceedings of 1993 International
Conference on Domain Decomposition",
abstract = "Multigrid and domain decomposition methods have proven
to be versatile methods for the iterative solution of
linear and nonlinear systems of equations arising from
the discretization of PDEs. The efficiency of these
methods derives from the use of a grid hierarchy. In
some applications to problems on unstructured grids,
however, no natural multilevel structure of the grid is
available and thus must be generated as part of the
solution procedure. In this paper, we consider the
problem of generating a multilevel grid hierarchy when
only a fine, unstructured grid is given. We restrict
attention to problems in two dimensions. Our techniques
generate a sequence of coarser grids by first forming a
maximal independent set of the graph of the grid or its
dual and then applying a Cavendish type algorithm to
form the coarser triangulation. Iterates on the
different levels are combined using standard
interpolation and restriction operators. Numerical
tests indicate that convergence using this approach can
be as fast as standard multigrid and domain
decomposition methods on a structured mesh.",
keyword = "unstructured meshes, domain decomposition, multilevel
methods, multigrid",
}
@TechReport{Dryja:1993:SAI,
author = "Maksymilian Dryja and Barry F. Smith and Olof B.
Widlund",
title = "{Schwarz} analysis of iterative substructuring
algorithms for problems in three dimensions",
number = "MCS-P250-0791",
institution = pub-ANL,
address = pub-ANL:adr,
year = "1993",
bibdate = "Mon Jul 11 14:09:33 MDT 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
note = "Published in \cite{Dryja:1994:SAI}.",
keyword = "domain decomposition, iterative substructuring,
Schwarz methods, wirebasket methods, Neumann--Neumann
methods",
}
@TechReport{Gropp:1993:DDS,
author = "William D. Gropp and Barry F. Smith",
title = "The design of data-structure-neutral libraries for the
iterative solution of sparse linear systems",
number = "MCS-P356-0393",
institution = pub-ANL,
address = pub-ANL:adr,
year = "1993",
bibdate = "Mon Jul 11 14:09:33 MDT 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "Krylov space methods, software libraries, sparse
linear systems, numerical libraries, parallel
computing",
}
@Article{Smith:1993:PII,
author = "Barry F. Smith",
title = "A parallel implementation of an iterative
substructuring algorithm for problems in three
dimensions",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "14",
pages = "406--423",
year = "1993",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "domain decomposition, iterative substructuring,
parallel computing",
}
@TechReport{Chan:1994:OSM,
author = "Tony F. Chan and Barry F. Smith and Jun Zou",
title = "Overlapping {Schwarz} Methods on Unstructured Meshes
using Non-matching Coarse Grids",
number = "94-8",
institution = "UCLA, Dept. of Mathematics",
year = "1994",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
abstract = "We consider two level overlapping Schwarz domain
decomposition methods for solving the finite element
problems that arise from discretizations of elliptic
problems on general unstructured meshes in two and
three dimensions. Standard finite element interpolation
from the coarse to the fine grid may be used. Our
theory requires no assumption on the substructures
which constitute the whole domain, so each substructure
can be of arbitrary shape and of different size. The
global coarse mesh is allowed to be non-nested to the
fine grid on which the discrete problem is to be solved
and both the coarse meshes and the fine meshes need not
be quasi-uniform. In addition, the domains defined by
the fine and coarse grid need not be identical. The one
important constraint is that the closure of the coarse
grid must cover any portion of the fine grid boundary
for which Neumann boundary conditions are given. In
this general setting, our algorithms have the same
optimal convergence rate of the usual two level
overlapping domain decomposition methods on structured
meshes. The condition number of the preconditioned
system depends only on the (possibly small) overlap of
the substructures and the size of the coarse grid, but
is independent of the sizes of the subdomains.",
keyword = "unstructured meshes, non-nested coarse meshes, Schwarz
methods",
}
@Article{Dryja:1994:SAI,
author = "Maksymilian Dryja and Barry F. Smith and Olof B.
Widlund",
title = "{Schwarz} Analysis of Iterative Substructuring
Algorithms for Elliptic Problems in Three Dimensions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "31",
number = "6",
pages = "1662--1694",
month = dec,
year = "1994",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
MRclass = "65N55 (65N22 65N30)",
MRnumber = "95m:65211",
MRreviewer = "B. Kellogg",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gropp:1994:SEP,
author = "William D. Gropp and Barry F. Smith",
booktitle = "Proceedings of Scalable Parallel Libraries
Conference",
title = "Scalable, Extensible, and Portable Numerical
Libraries",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "87--93",
year = "1994",
bibdate = "Mon Jul 11 14:09:33 MDT 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/s/smith-barry-francis.bib",
keyword = "numerical libraries, scientific computing, parallel
computing",
}
