My list of preprints.
Petter E. Bjørstad, Maksimillian Dryja and Eero Vainikko
1996
The Additive Average method is used for solution of elliptic partial differential
equations on unstructured meshes.
The ways of dividing irregular regions into subdomains are discussed.
Numerical experiments with different
unstructured grids are carried out. Possibilities for improvement of
the coarse bilinear form are discussed.
BIBTEX reference:
@INPROCEEDINGS{3pbmdev,
AUTHOR="Petter E. Bj{\o}rstad and Maksimillian Dryja and
Eero Vainikko",
TITLE="Robust Additive Schwarz Methods on Unstructured Grids",
BOOKTITLE="Domain Decomposition in Science and Engineering",
NOTE="Proceedings from the 9th International Conference on
Domain Decomposition Metods, Bergen, June 1996",
YEAR="1997",
EDITOR="Petter E. Bj{\o}rstad and Magne Espedal and David Keyes",
PUBLISHER="John Wiley \& Sons",
URL="http://www.ii.uib.no/~eero/Thesis/PaperD.ps"
}
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{2pbmdev,
AUTHOR="Petter E. Bj{\o}rstad and Maksimillian Dryja and
Eero Vainikko",
TITLE="Parallel implementation of a Schwarz Domain
Decomposition Algorithm",
BOOKTITLE="Proceedings from Para96, Lyngby Aug. 1996",
NOTE="Lecture Notes in Computer Science",
YEAR="1997",
EDITOR="Jerzy Wasniewski",
PUBLISHER="Springer",
URL="http://www.ii.uib.no/~petter/reports/para96.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{pbmdev95,
AUTHOR="Petter Bj{\o}rstad and Maksymilian Dryja and Eero Vainikko",
BOOKTITLE="Domain Decomposition Methods in Sciences and Engineering",
TITLE="Additive Schwarz Methods with No Subdomain
Overlap and 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/~eero/preprints.html"
}
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{pbrmroev95,
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",
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/~eero/preprints.html"
}
Eero Vainikko
September 1994
We consider the inverse problem for ground water filtration. Courant elements
are used for discretization together with Tikhonov regularization method
for ill-posed problems. A special model problem is constructed for finding
out the best regularization parameter for the case when the input data
must be interpolated to get a regular mesh. Real-life problem is solved
on MasPar MP-2 computer.
BIBTEX references:
@INPROCEEDINGS{VaiFEM50,
AUTHOR = {Eero Vainikko},
TITLE = {Courant Elements for the Inverse Problem in the
Filtration Coefficient Identification},
YEAR = {1994},
PUBLISHER = {Marcel Dekker},
VOLUME = {164},
PAGES = {451 - 459},
BOOKTITLE = {Lecture Notes in pure and applied Mathematics}
URL="http://www.ii.uib.no/~eero/preprints.html"
}
Eero Vainikko, eero@ii.uib.no.©
1996