The Chemnitz
finite element package for potential problems over three-dimensional domains,
implemented for MIMD parallel computers:
#
SPC-PM Po 3D

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Research

At present time much effort is being spent in both developing and implementing
parallel algorithms. The experimental package SPC-PM Po 3D is part of the
ongoing research of the Chemnitz research group Scientific Parallel Computing
(SPC), now part of the SFB
393, into finite element methods for problems over three dimensional
domains. Special emphasis is paid to choose finite element meshes which
exhibit an optimal order of the discretization error, to develop preconditioners
for the arising finite element system based on domain decomposition and
multilevel techniques, and to treat problems in complicated domains as
they arise in practice.
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The program

SPC-PM Po 3D is a computer program to solve elliptic potential problems
over three-dimensional domains on a MIMD parallel computer. It is being
developed in our research group
under the supervision of Prof.
A. Meyer, Dr. Th.
Apel, and
Dr. M. Jung.
Other main contributors are Dr.
G. Globisch, D. Lohse,
F. Milde,
Dr.
M. Pester,
U. Reichel
and M. Theß.
In Version 3.x the program can solve the Poisson equation and the Lamé
system of linear elasticity with in general mixed boundary conditions of
Dirichlet and Neumann type. The domain can be a curved bounded
polyhedron. The input is a coarse mesh, a description of the data and some
control parameters. The program distributes the elements of the coarse
mesh to the processors, refines the elements, generates the system of equations
using linear or quadratic shape functions, solves this system and offers
graphical tools to display the solution. Further, the behavior of the algorithms
can be monitored: arithmetic and communication time is measured, the discretization
error is measured, different preconditioners can be compared. There exists
special versions using a multigrid solver (M.
Jung ), having an error estimator ( G.
Kunert), or using the Globisch-Nepomnyaschikh mesh transformation technique
in the solver (G.
Globisch). We plan to extend the program in the next future by
including adaptive mesh refinement with dynamic load balancing, as well
as the treatment of coupled thermo-elastic problems.

The program has been developed for MIMD computers; it has been tested
on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors
and GCel-192 on transputer basis) and on workstation clusters using PVM.
The special case of only one processor is included, that means the package
can be compiled for single processor machines without any change in the
source files.

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History

The historical roots of the program are at one hand in several parallel
programs for solving problems over twodimensional domains using domain
decomposition techniques. These codes have been developed since about 1988
by A. Meyer, M. Pester, and other collaborators. On the other hand, Th.
Apel developed 1987-89 a sequential program for the solution of the Poisson
equation over three-dimensional domains which was extended 1993-94 together
with F. Milde.
####
Manuals

The package in its version 3.x is documented in two manuals. The User's
Manual provides an overview over the program, its capabilities, its
installation, and handling. Moreover, test examples are explained. The
aim of the
Programmer's
Manual is to provide a description of the algorithms and their realization.
It is written for those who are interested in a deeper insight into the
code, for example for improving and extending. Note that the Programmer's
Manual is only available for version 2.x, but remains still useful for
version 3.x.
####
Benchmark

Here are the
results of an elasticity benchmark in three dimensions which was defined
by the
*DFG-Schwerpunkt Randintegralmethoden.*
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Related projects

Local: SPC-PM Po 2D, SPC-PM Po El, SPC-PM CFD, SPC-PM CONS, SPC-PM EP.

Global: see the German
Scientific Computing pages on Mathematical
Software.

Thomas Apel,
Uwe Reichel, 02-09-1999