Petter E. Bjørstad, Maksimillian Dryja and Eero Vainikko 1996The 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 1996We 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. 1995We 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 1995We 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 1994We 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