My list of preprints.

Robust Additive Schwarz Methods on Unstructured Grids

Petter E. Bjørstad, Maksimillian Dryja and Eero Vainikko
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:

       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",
       EDITOR="Petter E. Bj{\o}rstad and Magne Espedal and David Keyes",
       PUBLISHER="John Wiley \& Sons",

Parallel implementation of a Schwarz Domain Decomposition Algorithm

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:

       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",
       EDITOR="Jerzy Wasniewski",

Additive Schwarz Methods with No Subdomain Overlap and New Coarse Spaces

       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:

         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",
         PUBLISHER="John Wiley \& Sons",
         NOTE="Proceedings from the
               Eight International Conference on Domain Decomposition
                    Metods, May 1995, Beijing",

Domain Decomposition Techniques in Parallelization of the 3-dimensional FRONTSIM code

       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:

         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",
         PUBLISHER="IOS Press",
         ORGANIZATION="Link\"{o}ping University, Department of Computer
                       and Information Science",

Courant Elements for the Inverse Problem in the Filtration Coefficient Identification

       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:

         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}

Eero Vainikko,© 1996