The Chemnitz finite element package for potential problems over three-dimensional domains, implemented for MIMD parallel computers:


[Short description (German | English) | User's Manual | Programmer's Manual ]

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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.

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.


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.


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.


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

Related projects

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

Thomas Apel, Uwe Reichel, 02-09-1999