The paper describes a storage scheme for sparse symmetric or nonsymmetric matrices which has been developed and used for many years at the Technical University of Chemnitz. An overview of existing library subroutines using such matrices is included.

The paper mainly describes the user interface of some graphical visualization tools for parallel finite element applications in 2D (layer problems, deformation problems, fluid dynamics). There are presented some examples of various methods to display the numerical results.

The paper describes a method for Visualization of computational results in parallel finite element applications for 3D problems. The visualization itself is done on a workstation using a post- processing tool based on GRAPE, which interacts with the parallel program to obtain data.

This paper deals with the application of domain decomposition methods for the parallel solution of boundary value problems for partial differential equations over a domain $Omegabset R^d$, $d=2,3$. The attention is focused on the conception of efficient communication routines for the data exchange which is necessary for example in the preconditioned cg-algorithm for solving the resulting system of algebraic equations. The paper describes the data structure, different algorithms, and computational tests.

Abstract P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary re- sults for 1D case, condition number estimates and some inequalities for 2D reference element.

P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary results for 1D case, condition number estimates and some inequalities for 2D reference element. Part II is devoted to the derivation of the Schur complement preconditioner and conditionality number estimates for the p-version finite element matrixes. Also DD preconditioning is considered.

The realization of the finite element method on parallel computers is usually based on a domain decomposition approach. This paper is concerned with the problem of finding an optimal decomposition and an appropriate mapping of the subdomains to the processors. The quality of this partitioning is measured in several metrics but it is also expressed in the computing time for solving specific systems of finite element equations. The software environment is first described. In particular, the data structure and the accumulation algorithm are introduced. Then several partitioning algorithms are compared. Spectral bisection was used with different modifications including Kernighan-Lin refinement, post-processing techniques and terminal propagation. The final recommendations should give good decompositions for all finite element codes which are based on principles similar to ours. The paper is a shortened English version of Preprint SFB393/96-18 (Uwe Reichel: Partitionierung von Finite-Elemente-Netzen), SFB 393, TU Chemnitz-Zwickau, December 1996. To be selfcontained, some material of Preprint SPC95_5 (see below) is included. The paper appeared as Preprint SFB393/96-18a, SFB 393, TU Chemnitz-Zwickau, January 1997.

This paper deals with the characterization of multiplication operators, especially with its behavior in the ill-posed case. We want to classify the different types and degrees of ill-posedness. We give some connections between this classification and regularization methods.

Der Standard des Message Passing Interfaces (MPI) stellt dem Entwickler paralleler Anwendungen ein mächtiges Werkzeug zur Verfügung, seine Softwa- re effizient und weitgehend unabhängig von Details des parallelen Systems zu entwerfen. Im Rahmen einer Projektarbeit erfolgte die Umstellung der Kommunikationsbibliothek eines bestehenden FEM-Programmes auf den MPI-Mechanismus. Die Ergebnisse werden in der hier gegebenen Beschreibung der Cubecom-Implementierung zusammengefasst. In einem zweiten Teil dieser Arbeit wird untersucht, auf welchem Wege mit der in MPI verfügbaren Funktionalität auch die Koppelrandkommunikation mit einem einheitlichen und effizienten Verfahren durchgeführt werden kann. Sowohl fuer die Basisimplementierung als auch die MPI-basierte Koppelrandkommunikation wird die Effizienz untersucht und ein Ausblick auf weitere Anwendungsmoeglichkeiten gegeben.

We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the o ccupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find an evidence for a dynamical phase transition well below the transition temperature of the pure system.