Using material models on the basis of the flow theory of plasticity the asymptotic behaviour of solid mechanics solutions in crack tips, interface corners etc. strongly depends on the local realized load trajectory. For incrementally proportional load paths the equations determining the asymptotic fields are very simple ones. The paper considers two-dimensional statements in the neighbourhood of an interface corner consisting of two material ranges. At a distance from the corner the finite element nodes of a regular net are established in a polar co-ordinate system together with the displacement degrees of freedom. The main idea of the presented singular and non-singular stress and deformation field calculation at interface corners characterizes an replacement of the corner neighbourhood effect to the surrounding body by introducing stiffness actions which in usual manner can be assembled together with the other element stiffness matrices to the global stiffness matrix of the body. According to this there exists an in teresting invariant stiffness independence in corner and crack neighbourhoods. The applied technique allows extensions to non-proportional local load increments simplifying the mathematical calculations for the presentation of stress and strain fields in this general case. All computations are made on modern parallel computers. Concrete examples show the advantages of the presented approach.

The purpose of this paper is to supply a summary of library subroutines and functions for parallel MIMD computers. The subroutines have been developed at the University of Chemnitz during a period of the last five years. In detail, they are concerned with vector operations, inter-processor communication and simple graphic output to workstations. One of the most valuable features is the machine-independence of the communication subroutines proposed in this paper for a hypercube topology of the parallel processors (excepting a kernel of only two primitive system-dependend operations). They were implemented and tested for different hardware and operating systems including transputer, nCube, KSR, PVM. The vector subroutines are optimized by the use of C language and enrolled loops (BLAS1-like). The paper includes hints for using the libraries with both Fortran and C programs.

The investigation of new parallel algorithms for MIMD computers requires some postprocessing facilities for quickly evaluating the behavior of those algorithms We present two kinds of visualization tool implementations for 2D and 3D finite element applications to be used on a parallel computer and a host workstation.

For the basic algebraic vector operations several variants of a local implementation on distributed memory parallel computers are presented and discussed systematically. In particular necessary and sufficient conditions are shown for the local realizability of the multiplication matrix by vector.

In order to prepare modern finite element analysis a program for the efficient parallel generation of tetrahedral meshes in a wide class of three dimensional domains having a generalized cylindric shape is presented. The applied mesh generation strategy is based on the decomposition of some 2D-reference domain into single con- nected subdomains by means of its triangulations the tetrahedral layers are built up in parallel. Adaptive grid controlling as well as nodal renumbering algorithms are involved. In the paper several examples are incorporated to demonstrate both program's capabilities and the handling with.

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.

A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.

Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.

We discuss the pole placement problem for single-input or multi-input control models of the form _x=Ax+Bu. This is the problem of determining a linear state feedback of the formu=F xsuch that in the closed-loop system _x= (A+BF)x, the matrixA+BFhas a prescribed set of eigenvalues. We analyze the conditioning of this problem and show that it is an intrinsically ill-conditioned problem, and especially so when the system dimension is large. Thus even the best numerical methods for this problem may yield very bad results. On the other hand, we also discuss the question of whether one really needs to solve the pole placement problem. In most circum- stances what is really required is stabilization or that the poles are in a specified region of the complex plane. This related problem may have much better conditioning. We demonstrate this via the example of stabilization.

The purpose of this paper is to supply a summary of library subroutines and functions for parallel MIMD computers. The subroutines have been developed at the University of Chemnitz during a period of the last five years. In detail, they are concerned with vector operations, inter-processor communication and simple graphic output to workstations. One of the most valuable features is the machine-independence of the communication subroutines proposed in this paper for a hypercube topology of the parallel processors (excepting a kernel of only two primitive system-dependend operations). They were implemented and tested for different hardware and operating systems including transputer, nCube, KSR, PVM. The vector subroutines are optimized by the use of C language and enrolled loops (BLAS1-like). The paper includes hints for using the libraries with both Fortran and C programs.