My list of technical reports and preprints.
This is a list of my technical reports and preprints that you may look at:
Table of Contents:
Petter E. Bj{\o}rstad and Maksymilian Dryja
April 1998.
This paper studies a variant of the Additive Average
Schwarz algorithm \cite{Bjorstad:1997:ASM} where the coarse space
consists of two subspaces. This approach
results in a simpler and more parallel algorithm
while we retain the essential convergence properties
of the original method.
Our theory is confirmed by numerical experiments showing that
the new algorithm is often superior to the original variant.
BIBTEX reference:
@ARTICLE{Bjorstad:1998:CSF,
author="Petter E. Bj{\o}rstad and Maksymilian Dryja ",
title="A Coarse Space Formulation with good parallel
properties for an Additive Schwarz Domain Decomposition Algorithm",
journal="Submitted to Numerische Mathematik",
year="1999",
URL="http://www.ii.uib.no/~petter/reports/pbmax_olof98.ps.gz"
}
Petter E. Bj{\o}rstad and Bj{\o}rn Peter Tj{\o}stheim
May 1998.
We solve the biharmonic eigenvalue problem $\Delta^2u = \lambda u$ and
the buckling plate problem ${\Delta}^2u = - {\lambda}\Delta u$ on the unit
square using a highly accurate spectral Legendre-Galerkin method. We study
the nodal lines for the first eigenfunction near a corner for the two
problems. Five sign changes are computed and the results show
that the eigenfunction exhibits a self similar pattern as one
approaches the corner. The amplitudes of the extremal values and
the coordinates of their location as measured from the corner are
reduced by constant factors. These results are compared with
the known asymptotic expansion of the solution near a corner.
This comparison shows that the asymptotic expansion is highly accurate
already from the first sign change as we have complete agreement
between the numerical and the analytical results.
Thus, we have an accurate description of
the eigenfunction in the entire domain.
BIBTEX reference:
@ARTICLE{Bjorstad:1998:ANH,
AUTHOR="Petter E. Bj{\o}rstad and Bj{\o}rn Peter Tj{\o}stheim",
Title="A note on high precision solutions of two fourth order eigenvalue problems",
Year="1999",
Journal="Submitted to Computing",
URL="http://www.ii.uib.no/~petter/reports/hump.ps.gz"
}
Petter E. Bj{\o}rstad
November 1997.
This article, written for the science student paper at the University
of Bergen in Norwegian (sorry!), gives a brief overview of computer
evolution and the use of high performance computers to advance
scientific research. The entire text is written in nontechnical
style for a general audience.
BIBTEX reference:
@ARTICLE{Bjorstad:1997:CST,
AUTHOR="Petter E. Bj{\o}rstad",
Title="Computational Science, en tredje vei for forskning",
Month="November",
Year="1997",
Note="In UiB student paper QED "
Journal="QED",
URL="http://www.ii.uib.no/~petter/reports/qed97.pdf.gz"
}
Jeremy Cook, Petter E. Bj{\o}rstad, Jon Br{\ae}khus
April 1996.
We discuss the use of high performance computing equipment in
large, commercial structural analysis programs. In particular, we consider
the strategy for modifying a standard industrial code from a pure F77 version
to a form suitable for a range of parallel computers. The code is parallelized
using the PVM message passing library for communication between
processes and the ScaLAPACK and BLACS libraries for parallel linear algebra
operations. The parallel code is suitable for a range of parallel computers,
however for the purposes of verification and benchmarking, two specific hardware
architectures were targeted in this work. These are an 8-node
DEC Alpha cluster with 233MHz EV45 processors and FDDI/GIGASwitch interconnect,
and a 32-node Parsytec GC/PowerPlus with 64 PowerPC-601 processors and a
Transputer interconnect.
BIBTEX reference:
@INPROCEEDINGS{Cook:1996:MPS,
AUTHOR="Jeremy Cook and Petter Bj{\o}rstad and Jon Br{\ae}khus",
Title="Multilevel Parallel Solution of Large, Sparse Finite Element
Equations from Structural Analysis",
BOOKTITLE="High-Performance Computing and Networking",
Month="April",
Year="1996",
Note="Lecture Notes in Computer Science"
Volume="1067",
Pages="404---412",
Editor = "H. Liddel and A. Colbrook and B Hertzberger and P. Sloot",
Publisher="Springer",
URL="http://www.ii.uib.no/~petter/reports/hpcn96.ps.gz"
}
Petter E. Bj{\o}rstad
November 1996
This paper will highlight, by way of examples, a few
seemingly very different mathematical problems and
show how they have direct relevance to the construction
of efficient computational procedures for the simulation
of oil reservoirs on parallel computers.
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1997:MPC,
AUTHOR="Petter E. Bj{\o}rstad",
TITLE=" Mathematics, parallel computing and reservoir simulation",
BOOKTITLE="Proceedings of the Second European Congress of Mathematic",
NOTE="Budapest July 1996",
YEAR="1997",
EDITOR="Antal Balog",
PUBLISHER="Birkhauser Verlag",
URL="http://www.ii.uib.no/~petter/reports/budapest96.ps.gz"
}
Petter E. Bjørstad, Maksimillian Dryja and Eero Vainikko
Oktober 1996
We describe and compare some recent domain decomposition
algorithms of Schwarz type with respect to parallel performance.
A new, robust domain decomposition algorithm -- Additive Average
Schwarz is compared with a classical overlapping Schwarz code.
Complexity estimates are given in both two and three dimensions
and actual implementations are compared on a Paragon machine as
well as on a cluster of modern workstations.
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1996:PIS,
AUTHOR="Petter E. Bj{\o}rstad and Maksimilian Dryja and Eero Vainikko",
TITLE="Parallel implementation of a Schwarz Domain Decomposition Algorithm",
BOOKTITLE="Applied Parallel Computing in Industrial Problems and Optimization",
YEAR="1996",
EDITOR="Jerzy Wasniewski and Jack Dongarra and Kaj Madsen and Dorte Olesen",
PAGES="",
ORGANIZATION="",
PUBLISHER="Springer",
ADDRESS="",
MONTH="December",
NOTE="Lecture Notes in Computer Science volume 1184",
URL="http://www.ii.uib.no/~petter/reports/para96.ps.gz"
}
Petter E. Bjørstad and Bjørn Peter Tjøstheim:
January 1996.
We show that one can derive an $O(N^3)$ spectral-Galerkin method
for fourth order (biharmonic type) elliptic equations based on
the use of Chebyshev polynomials.
The use of Chebyshev polynomials provides
a fast transform between physical and spectral space which
is advantageous when a sequence
of problems must be solved e.g., as part of a nonlinear iteration.
This improves the result of Shen which reported an
$O(N^4)$ algorithm inferior to the $O(N^3)$ method developed
earlier based on Legendre polynomials, but less
practical in the case of multiple problems.
We further compare our method with an improved implementation
of the Legendre-Galerkin method based on the same approach.
BIBTEX reference:
@ARTICLE{Bjorstad:1996:EAS,
AUTHOR="Petter E. Bj{\o}rstad, Bj{\o}rn Peter Tj{\o}stheim",
TITLE="Efficient algorithms for solving a fourth order equation
with the Spectral-Galerkin method",
JOURNAL="SIAM J. Sci. Comp.",
VOLUME="18",
NUMBER="2",
MONTH="March",
YEAR = "1997",
URL="http://www.ii.uib.no/~petter/reports/Leg_Cheb.ps.gz"
}
P. Bjørstad and T. Sørevik:
Nov. 92
This paper discusses the implementation and performance of the
computational BLAS kernels in a data-parallel setting.
Two different programming languages are compared and several
compiler issues are discussed.
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1993:DDP,
AUTHOR="P. E. Bj{\o}rstad and T. S{\o}revik",
TITLE="Two Different Data-Parallel Implementations of the {BLAS}",
BOOKTITLE=" Software for Parallel Computation",
EDITOR="J. S. Kowalik",
YEAR=" 1993"
URL="http://www.ii.uib.no/~petter/reports/mpp_blas.ps.gz"
}
P. Bjørstad and T. Sørevik:
Nov. 92
We consider a data-parallel implementation of LU-factorization
based on the LAPACK routine DGETRF.
We analyze the performance
of the required BLAS routines and show that high performance
is inhibited by current compiler limitations.
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1993:DPB,
AUTHOR="P. E. Bj{\o}rstad and T. S{\o}revik",
TITLE="Data-parallel {BLAS} as a basis for {L}apack on massively
parallel computers",
BOOKTITLE="Linear Algebra for Large Scale and Real-Time Applications",
YEAR="1993",
EDITOR="M. Moonen and G. Golub and B. De Moor",
PAGES="13-20",
PUBLISHER="Kluwer Academic Publishers"
URL="http://www.ii.uib.no/~petter/reports/mpp_LU.ps.gz"
}
Petter E. Bjørstad and Terje Kårstad:
July 94
A prototype black oil simulator is described.
The simulator has a domain-based data structure whereby the
reservoir is represented by a possibly large number of smaller
reservoirs each having a complete local data structure.
This design is essential for effective use of preconditioning
techniques based on domain decomposition. The chapter describes
a splitting technique for the solution of the nonlinear system and
an effective implementation of the algorithm
on massively parallel computer systems.
Most communication is localized and long range communication
is kept at a minimum.
Results from
an implementation of the method
are reported for a 16384 processor MasPar MP-2.
Petter E. Bjorstad and Robert Schreiber:
May 94
Unstructured grids lead to unstructured communication on
distributed memory parallel
computers, a problem that has been considered difficult.
Here, we consider adaptive,
offline communication routing for a SIMD processor grid.
Our approach is empirical. We use large data
sets drawn from supercomputing applications instead of an analytic
model of communication load.
The chief contribution of
this paper is an experimental demonstration of the effectiveness of
certain routing heuristics.
Our routing algorithm is adaptive, nonminimal, and is
generally designed to exploit locality.
We have a parallel
implementation of the router, and we report on its performance.
Petter E. Bjørstad, Jon Brækhus and Anders Hvidsten:
1991
This paper reviews the development that has occurred in order
to adopt a large scale structural analysis package,
SESAM
(SESAM is marketed by Veritas Sesam Systems Inc.), to
the rapid changes in computer architecture as well as to the
algorithmic advances that has been made in the past few years.
We describe a parallel implementation of the sophisticated
direct solution algorithm, based on processing substructures in
parallel, but also allowing a high degree of parallelism
in the computation within each substructure.
We further discuss the use of iterative solution strategies.
The paper concludes that iterative techniques should be further
investigated and that the current knowledge about such methods
makes them attractive for certain special classes of problems
already today. We provide a few numerical examples in support
of our conclusions.
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1991:PSA,
AUTHOR="Petter Bj{\o}rstad and Jon Br{\ae}khus and Anders Hvidsten",
TITLE="Parallel substructuring algorithms in structural analysis,
direct and iterative methods",
BOOKTITLE="Fourth International Symposium on Domain Decomposition
Metods for Partial Differential Equations",
EDITOR="R. Glowinski and Y. A. Kuznetsov and
G\'{e}rard Meurant and J. P\'{e}riaux and O. B. Widlund",
PAGES="321-340",
PUBLISHER="SIAM",
ADDRESS="Philadelphia",
YEAR="1991"
URL="http://www.ii.uib.no/~petter/reports/moscow_siam.ps.gz"
}
Petter E. Bjørstad, Randi Moe and Morten Skogen:
Jan. 90
Algorithms for the solution of partial differential equations based
on a subdivision of the spatial domain, has received much interest
in recent years.
To a large extent this has been motivated by the
new generation of parallel computers. This algorithmic approach
can introduce independent parallel tasks of variable granularity,
depending on the subdivision and can therefore be adapted to a wide
range of parallel computers.
We review some of the progress that
has been made and report on numerical experiments that illustrate
the convergence behavior. We also describe parallel implementations
on both shared memory computers (Alliant FX/8) and on local
memory systems (Intel iPSC/2 and network connected workstations).
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1990:PDD,
AUTHOR=" Petter E. Bj{\o}rstad and Randi Moe and Morten Skogen",
TITLE=" Parallel Domain Decomposition and Iterative Refinement
Algorithms ",
EDITOR="Wolfgang Hackbusch",
BOOKTITLE="Parallel Algorithms for PDEs, Proceedings of the
6th GAMM-Seminar held in Kiel, Germany, January 19--21, 1990"
PUBLISHER="Vieweg-Verlag",
ADDRESS="Braunschweig, Wiesbaden",
YEAR="1990"
URL="http://www.ii.uib.no/~petter/reports/pbrmms.ps.gz"
}
Petter E Bjørstad and Erik Boman:
Nov. 90
We apply a preconditioned conjugate gradient algorithm to
the SLALOM benchmark, proving that the solution phase
of the benchmark is reduced to $O(N^2)$. The algorithm therefore performs well
over the full range of input parameters specified by the benchmark.
This has a dramatic impact on the benchmark for all
computers. We illustrate this with new implementations on
an 8192 processor MP-1 system and a Cray X/MP.
BIBTEX reference:
@TECHREPORT{Bjorstad:1991:NAS,
AUTHOR="Petter Bj{\o}rstad and Erik Boman",
TITLE="A New Algorithm for the SLALOM Benchmark",
INSTITUTION="Institutt for Informatikk, University of Bergen",
NUMBER = "55",
MONTH="May",
YEAR = "1991",
NOTE = "Also published in Supercomputing Review"
URL="http://www.ii.uib.no/~petter/reports/slalom.ps.gz"
}
Petter E. Bjørstad and Morten D. Skogen:
1991
We discuss implementation of additive Schwarz type algorithms
on SIMD computers. A recursive, additive algorithm is compared
with a two-level scheme.
These methods are based on a subdivision of the domain into
thousands of micro-patches that can reflect local
properties, coupled with a coarser, global discretization
where the `macro' behavior is reflected.
The two-level method shows very promising
flexibility,
convergence and performance
properties when implemented on a massively parallel
SIMD computer.
BIBTEX reference:
@INPROCEEDINGS{Bjorstad:1992:DAS,
AUTHOR=" Petter E. Bj{\o}rstad and Morten Skogen",
TITLE="Domain Decomposition Algorithms of {S}chwarz
Type, Designed for Massively Parallel Computers",
EDITOR="David E. Keyes and Tony F. Chan 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",
PUBLISHER="SIAM",
YEAR="1992",
ADDRESS="Philadelphia, PA",
PAGES="362--375"
URL="http://www.ii.uib.no/~petter/reports/mgas_siam.ps.gz"
}
Petter E Bjørstad and Olof B Widlund:
Sep. 88
More than one hundred years ago, H.A. Schwarz introduced a domain
decomposition method in which the original elliptic equation is solved on
overlapping subregions, one after another, in an iterative
process. A few years ago, Chan and Resasco, introduced a method that they
classified as a domain decomposition method
using nonoverlapping subdomains.
In this note, it is shown that their method is an accelerated
version of the classical method.
It is also shown that the error propagation operator of the method
can be expressed in terms of Schur complements of certain stiffness
matrices and that techniques previously developed for the study
of iterative substructuring algorithms can be used to derive estimates
on the rate of convergence.
BIBTEX reference:
@ARTICLE{Bjorstad:1989:OON,
AUTHOR=" Petter E. Bj{\o}rstad and Olof B. Widlund ",
TITLE=" To Overlap or Not to Overlap: {A} Note on a Domain
Decomposition Method for Elliptic Problems ",
JOURNAL=" SIAM J. Sci. Stat. Comput.",
YEAR="1989",
VOLUME="10",
NUMBER="5",
PAGES= "1053--1061"
URL="http://www.ii.uib.no/~petter/reports/overlap.ps.gz"
}
Petter E Bjørstad, Frederik Manne, Tor Sørevik and M. Vajtersic:
Aug. 91.
We describe efficient algorithms for matrix multiplication on
SIMD computers. We consider SIMD implementations of Winograd's
algorithm in the case where additions are faster than multiplications, as
well as classical kernels and the use of Strassen's algorithm.
Actual performance figures using the MasPar family of SIMD computers
are presented and discussed.
BIBTEX references:
@ARTICLE{Bjorstad:1992:EMM,
AUTHOR="P. Bj{\o}rstad and F. Manne and T. S{\o}revik and M. Vajter\v{s}ic",
TITLE="Efficient Matrix Multiplication on {SIMD} Computers",
JOURNAL="SIAM J. Matrix Anal. Appl.",
VOLUME="13",
NUMBER="1",
PAGES="386-401",
YEAR="1992",
MONTH="January",
KEY="Matrix multiplication, Winograd's algorithm, Strassen's algorithm,
SIMD computer, parallel computing"
URL="http://www.ii.uib.no/~petter/reports/matrix_sigene.ps.gz"
}
Petter E. Bjorstad, Jeremy Cook, Hans Munthe-Kaas and Tor Sorevik:
Oct. 1991
We describe the results of a three-week project to evaluate and
implement
a SAR algorithm from FFI on a MasPar MP-1208 at para//ab
in Bergen. The report shows that a quite complex
program written in Fortran, can be rewritten in
C and made to run efficiently on a massively parallel
SIMD computer with relatively little effort.
The performance shows that general purpose SIMD computers
are very competitive with specially designed computers
for SAR processing.
BIBTEX references:
@TECHREPORT{Bjorstad:1991:ISP,
AUTHOR=" Petter E. Bj{\o}rstad and Jeremy Cook and Hans Munthe-Kaas
and Tor S{\o}revik",
TITLE="Implementation of a {SAR} processing algorithm on {M}as{P}ar
{MP}-1208",
INSTITUTION="Institute of Informatics, University of Bergen ",
ADDRESS="H{\o}yteknologisenteret,N-5020 Bergen, Norway",
YEAR="1991",
NUMBER="57",
MONTH="October"
URL="http://www.ii.uib.no/~petter/reports/sar.ps.gz"
}
Petter E. Bjørstad and Jan Mandel:
Dec. 1989
Many parallel iterative algorithms for solving symmetric, positive
definite problems proceed by solving in each iteration, a number of
independent systems on subspaces. The convergence of such methods is
determined by the spectrum of the sums of orthogonal projections on
those subspaces, while the convergence of a related sequential method is
determined by the spectrum of the product of complementary
projections.
We study spectral
properties of sums of orthogonal projections and in the case of two
projections, characterize the spectrum of the sum completely in terms
of the spectrum of the product.
BIBTEX references:
@ARTICLE{Bjorstad:1991:SSO,
AUTHOR=" Petter E. Bj{\o}rstad and Jan Mandel",
TITLE=" On the Spectra of Sums of Orthogonal Projections
with Applications to Parallel Computing ",
JOURNAL="BIT",
PAGES="76--88",
VOLUME="31",
YEAR="1991"
URL="http://www.ii.uib.no/~petter/reports/projections.ps.gz"
}
Petter E Bjørstad and Jeremy Cook:
Nov. 92
We discuss
the use of a massively parallel
computer in large scale
structural analysis computations.
In particular, we consider the necessary modifications to
a standard industrial
code and a strategy where
the code may be allowed to evolve gradually
from a pure F77 version to a form more suitable for
a range of parallel computers.
We present preliminary computational results from
a DECmpp computer, showing that we can achieve
good price performance when compared to traditional
vector supercomputers.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1993:LSS,
AUTHOR="Petter Bj{\o}rstad and Jeremy Cook",
TITLE="Large Scale Structural Analysis on Massively Parallel Computers",
BOOKTITLE="Linear Algebra for Large Scale and Real-Time Applications",
YEAR="1993",
EDITOR="M. Moonen and G. Golub and B. De Moor",
PAGES="3-11",
PUBLISHER="Kluwer Academic Publishers",
NOTE="NATO ASI Series"
URL="http://www.ii.uib.no/~petter/reports/nato_sestra.ps.gz"
}
Petter E. Bjørstad:
Jan. 88
We consider the classical Schwarz alternating algorithm and an
additive version more suitable for parallel processing.
The two methods
are compared and analyzed in the case of two domains.
We show that the rate of convergence for both methods, can be directly
related to a generalized eigenvalue problem, derived
from subdomain contributions to the global stiffness matrix.
Analytical expressions are given for a model case.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1989:MAS,
AUTHOR=" Petter E. Bj{\o}rstad",
TITLE="{M}ultiplicative and {A}dditive {S}chwarz {M}ethods:
{C}onvergence in the 2 domain case",
BOOKTITLE="Domain Decomposition Methods ",
YEAR="1989",
EDITOR="Tony Chan and Roland Glowinski
and Jacques P{\'e}riaux and Olof Widlund",
PUBLISHER="SIAM",
ADDRESS="Philadelphia, PA",
PAGES="147--159"
URL="http://www.ii.uib.no/~petter/reports/two_domain.ps.gz"
}
Petter E. Bjørstad, W. M. Coughran, Jr. and Eric Grosse:
May 94
Modeling semiconductor devices is an important technological problem.
The traditional approach solves coupled advection-diffusion carrier-transport
equations in two and three spatial dimensions on either high-end scientific
workstations or traditional vector supercomputers.
The equations need specialized discretizations as well
as nonlinear and linear iterative methods.
We will describe some of these techniques and our preliminary experience with
coarse-grained domain decomposition techniques applied on a collection
of high-performance workstations connected at a 100Mb/s shared network.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1994:PDA,
AUTHOR="Petter E. Bj{\o}rstad and Coughran, Jr., W. M. and Eric Grosse",
TITLE="Parallel Domain Decomposition Applied to
Coupled Transport Equations",
BOOKTITLE="Seventh International Conference of Domain Decomposition
Methods in Scientific and Engineering Computing",
EDITOR="David E. Keyes and Jinchao Xu",
YEAR="1994",
PUBLISHER="AMS",
SERIES="Contemporary Mathematics",
VOLUME="180",
PAGES="43--47",
NOTE="Held at Penn State University,
October 27-30, 1993.",
URL="http://www.ii.uib.no/~petter/reports/semi_conductor.ps.gz"
}
Petter E. Bjørstad:
Apr. 89
Algorithms for the solution of partial differential equations based
on a subdivision of the spatial domain, has received much interest
in recent years.
To a large extent this has been motivated by the
new generation of parallel computers. This algorithmic approach
can introduce independent parallel tasks of variable granularity,
depending on the subdivision and can therefore be adapted to a wide
range of parallel computers.
We review some of the progress that
has been made and supply a few new numerical examples that illustrate
the convergence behavior.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1989:PDI,
AUTHOR= "Petter E. Bj{\o}rstad",
TITLE= "Parallel Domain Decomposition and
Iterative Refinement Algorithms",
YEAR="1989",
URL="http://www.ii.uib.no/~petter/reports/tatra.ps.gz"
}
Petter E. Bjørstad
1995
The laboratory for parallel computing - Parallab actively
pursues the porting of significant industrial codes
to parallel computing platforms. This work started already
in 1985 with the acquisition of Europe's first 64 processor Intel
hypercube.
As of today, the laboratory has two MIMD machines,
an Intel Paragon and a Parsytec GC/Power-Plus.
As part of the Europort effort, four industrial codes
are currently being ported by Parallab scientists.
The paper will describe this effort and
the issues, trends and experiences learned from working with
industrial codes using MIMD type parallel computers.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1995:EIA,
AUTHOR="Petter E. Bj{\o}rstad",
TITLE="Experience with industrial applications
on MIMD machines",
PUBLISHER="K.G. Saur Verlag",
NOTE="Proceedings from Supercomputer '95, June 22-24, Mannheim",
URL="http://www.ii.uib.no/~petter/reports/mannheim.ps.gz"
}
Petter E. Bjørstad, Maksymilian Dryja and Eero Vainikko
Oct. 1995
We develop two additive Schwarz methods with new
coarse spaces. The methods are designed for elliptic
problems in 2 and 3 dimensions with discontinuous
coefficients. The methods use no explicit overlap of the
subdomains, subdomain interaction is via the coarse space.
The first method has a rate of convergence
proportional to (H/h)^(1/2) when
combined with a suitable Krylov space iteration.
This rate
is
independent of discontinuities in the coefficients of the equation.
The method has good parallelization properties and do not
require a coarse grid triangulation, that is, one is free to use
arbitrary, irregular subdomains.
The second method uses a diagonal scaling in addition to the standard
coarse space. This method is not as robust and flexible as the
first method.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1996:ASM,
AUTHOR="Petter Bj{\o}rstad and Maksymilian Dryja and Eero Vainikko",
BOOKTITLE="Domain Decomposition Methods in Sciences and Engineering",
TITLE="Additive Schwarz Methods without Subdomain
Overlap and with New Coarse Spaces",
EDITOR="R. Glowinski and J. P\'{e}riaux and Z. Shi and O. B. Widlund",
PAGES="xx-yy",
PUBLISHER="John Wiley \& Sons",
NOTE="Proceedings from the
Eight International Conference on Domain Decomposition
Metods, May 1995, Beijing",
YEAR="1996",
URL="http://www.ii.uib.no/~petter/reports/dd8_jump_pbmdev.ps.gz"
}
Petter E. Bjørstad
Oct. 1995
The laboratory for parallel computing - Parallab actively
pursues the porting of significant industrial codes
to parallel computing platforms. This work started already
in 1985 with the acquisition of Europe's first 64 processor Intel
hypercube.
As of today, the laboratory has three MIMD machines,
an Intel Paragon, a Parsytec GC/Power-Plus and
a DEC $\alpha$-cluster.
As part of the Europort effort, four industrial codes
are currently being ported by Parallab scientists.
The paper will describe this effort and
the issues, trends and experiences learned from working with
industrial codes using MIMD type parallel computers.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1995:ICM,
AUTHOR="Petter E. Bj{\o}rstad",
TITLE="Industrial Computing on {M}{I}{M}{D} machines",
BOOKTITLE="NIK",
EDITOR="Magne Haveraaen",
PAGES="xx--yy",
PUBLISHER="NIK",
NOTE="Proceedings from NIK'95, Nov 20--22, Gran, Norway",
URL="http://www.ii.uib.no/~petter/reports/NIK.ps.gz",
YEAR="1995"
}
Petter E. Bjørstad, Randi Moe, Rudi Olufsen, Eero Vainikko
May 1995
We have studied the parallelization methods for
the pressure equation in the reservoir simulator
FRONTSIM\footnotemark[3]\
for 3-dimensional reservoirs.
In order to
obtain a faster simulator and finer resolution, we have
studied the use of domain decomposition methods combined with
the use of parallel processing.
Both the additive Schwarz
method and the multiplicative Schwarz method are implemented together
with coarse-grid solver techniques.
The purpose of the
investigation is to find the best strategies for different
problem sizes and different approximate solvers.
The code is
parallelized using the PVM message passing library for communication
and has been tested on a cluster of workstations.
This effort is
part of the EC-ESPRIT III / EUROPORT2 project.
Some implementation results and directions for further developments
are given.
BIBTEX references:
@INPROCEEDINGS{Bjorstad:1995:PPA,
AUTHOR="Petter E. Bj{\o}rstad and Randi Moe and Rudi Olufsen
and Eero Vainikko",
BOOKTITLE="Parallel Programming and Applications: Proceedings
of the Workshop on Parallel Programming and
Computation (ZEUS '95) and the 4th Nordic
Transputer Conference (NTUG '95)",
TITLE="Domain Decomposition Techniques in Parallelization of
the 3-dimensional FRONTSIM code",
Overlap and New Coarse Spaces",
EDITOR="Peter Fritzon and Leif Finmo",
PAGES="97-110",
PUBLISHER="IOS Press",
ORGANIZATION="Link\"{o}ping University, Department of Computer
and Information Science",
YEAR="1995",
URL="http://www.ii.uib.no/~petter/reports/frontsim.ps.gz"
}
Petter E. Bj{\o}rstad, Maksymilian Dryja and Talal Rahman
May 2002.
Two variants of the additive Schwarz
method for solving linear systems arising from the mortar finite element
discretization on nonmatching meshes of second order ellip\-tic
problems with discontinuous coefficients are designed and analyzed.
The methods are defined on subdomains without overlap, and they use
special coarse
spaces, resulting in algorithms that are well suited for parallel
computation. The condition number estimate for the preconditioned
system in each method is proportional to the ratio $H/h$,
where $H$ and $h$ are the mesh sizes, and it is independent of
discontinuous jumps of the coefficients.
For one of the methods presented the choice of
the mortar (nonmortar) side is independent of the coefficients.
BIBTEX reference:
@ARTICLE{Bjorstad:2002:ASM,
AUTHOR="Petter E. Bj{\o}rstad, Maksymilian Dryja and Talal Rahman",
Title="Additive Schwarz Methods for Elliptic Mortar Finite Element Problems",
Year="2002",
Journal="Submitted to Numerische Mathematik",
URL="http://www.ii.uib.no/~petter/reports/pbmdtr2002AddSchMort.ps.gz"
}
Petter E. Bjørstad, petter@ii.uib.no.
Maintained by: Petter E. Bjørstad, petter@ii.uib.no, © 1995