H.-J. Payer:

"Optimierung von FE- und RE-Analysen unter Berücksichtigung der Verwendung eines Vektorrechners";

Supervisor, Reviewer: H.A. Mang, F. G. Rammerstorfer; Institute for Strength of Materials, Vienna University of Technology, 1995.

Despite of the enormous increase in computer-power during the last years large Finite- Element and Boundary-calculations (FE- and BE-calculations) may require excessive computer resources (CPU-time and disc-space), making it impossible to carry out the calculations with reasonable efforts. Even when using supercomputers an efficient execution of the employed computer program is very important for the feasibility and the efficiency of the calculations.Apart from using a vector-computer (SNI S100/10) the goal of this work was to optimize the chosen algorithms concerning CPU-time and disc-space, considering the characterisitc features of such a computer. In numerical simulations with a large number of degrees of freedom most of the CPU-time is consumed for the solution of systems of linear equations. Hence most of the described modifications deal with the solution-step.

Iteractive solvers were used instead of direct solvers. Explanations of relevant details of the employed iterative algorithms will be given. The algorithms were taken from the literature. The effectiveness of the implemented modifications and the advantages resulting from the use of a vector-computer were tested within the framework of different technical problems.

At first, results from 3D-FE-calculations of automobile tires with frictional contact will be presented. The respective analyses are based on a realistic numerical modelling of the rubber and the reinforced cords. Realistic modelling of the contact-area of the tire leads to systems of algebraic equations with a large number of degrees of freedom. The incremental-iterative solution of the geometrically and materially nonlinear problems results in long CPU-times and a large amount of data to be transferred between the main memory and the discs.

Apart from using iterative solvers modifications were done for the numerical calculations allowing reduction of the I/O-amount and the disc-space. In addition to providing for the possibility of using one computer for the solution of the algebraic equations and another one for the remaining calculation-steps, a substructure-strategy was developed. This strategy may be regarded as the basis for a parallel implementation of FE-calculations.

Furthermore strategies for the acceleration of coupled, three-dimensional simulations of the stress problem in the context of the excavation of tunnels were developed. The FEM is used for the discretization of the near-field of the tunnel and the BEM for the far-field. Consequently the coeffizient matrix of the system of equations consists of a symmetric, sparse matrix and an unsymmetric, fully populated matrix. The possibility of using iterative solvers for linear-elastic BE-simulations as well as the coupling strategy are described in detail. Apart from the description of a strategy, where only the system of equations for the coupling surface is solved by an iterative solver, a strategy with no need to reduce the degrees of freedom of the FE-subdomain to the coupling surface will be described.

Modifications were also made for pure BE-calculations. They refer to a computer program, which is used for the calculation of sound propagation. These calculations lead to a system of equations with complex coefficients. With the help of selected problems the advantages are demonstrated, which can be achieved with an iterative solver. The main goal of this part of the work is to show how to modify a step of the claculation in order to reduce the CPU-time on a vector computer. The modifications of the different operations are explained in detail.

In addition to explanations concerning C-routines, which can be used for the conversion from "IEEE" - to "M"-data-representation and in the opposite direction, this work includes a summary of test results for the "vfl"-file-system on the SNI S100/10 an the I/O-system of a HP-workstation.

The solution of the technical problems reported in this thesis demonstrates the superiority of iterative solvers in comparison to direct solvers. The reduction in CPU-time and disc-space has been demonstrated by means of various numerical tests. Moreover, the need for modifications of program codes, which originally have been designed for execution on general-purpose computers, to allow for efficient executions of these codes on a vector computer is emphasized. The vectors, which are needed in the calculations, should be long and the amount of I/O should be minimized.

Keywords: @contact, @dissertation, @tire

Created from the Publication Database of the Vienna University of Technology.