Parallel Software for Impliciet Differential Equations (CWI.4533)

The project aims at the development of parallel software for the numerical solution of initial value problems (WPs) for implicit differential equations (IDEs), which contain the classes of ordinary differential equations and differential-algebraic equations. A start has already been made in STW project CWI.2703 resulting two main software products, viz. the code PSIDE and the CWI Test set.

PSIDE stands for Parallel Software for Implicit Differential Equations. A lot of real-life IDE problems require the use of stable and robust methods. In project CWI.2703 we succeeded in designing the underlying numerical method for PSIDE in such a way that it enables the efficient implementation on a parallel computer, in spite of the sequential nature of the problems to be solved. The code PSIDE is based on advanced numerical integration techniques and fully tuned for use on multi-processor computer systems. The current status of PSIDE is that by using more processors, it beats the state-of-the-art solvers in terms of wall-clock time. At the same time, the class of problems that can be solved is larger. However, to make PSIDE suitable for the use in commercial environments, more facilities have to be implemented.

In testing new codes for the numerical solution of WPs, it would save a lot of time if one could give a generally accepted reference for test problems and use the same computer codes for the test problems, instead of describing and programming the problems oneself. Moreover, if everyone would use the same source of the test problem, i.e. the same formulation, parameters, integration interval, initial values, way of programming, etc., then the comparison of results obtained by different authors would become much easier. The Test set for IVP solvers is a tool to facilitate the numerical testing of codes on real-life problems and tries to fulfill these demands. Since the test set is available via the World Wide Web, it is very easy to use; to perform a test run, one only has to download the desired problem, solver and the interface between problem and solver, the so-called driver.

In this project we want to pursue our research in the following directions:

1. Design of a block-triangular Newton matrix strategy based on splitting of the Jacobian matrix as an optional facility for use in PSIDE.
2. Analysis of waveform relaxation type techniques and implementation in PSIDE.
3. Implementation of sparse matrix solvers in PSIDE.
4. Improvement of the theory for control strategies in numerical software for IDEs such as the code PSIDE.
5. Development of a test protocol for comparing numerical codes.
6. Extension of the CWI Test set by collecting further real-life test problems with reference solutions of high quality.

Er zijn nog geen resultaten bekend.

Er zijn drie bedrijven en twee andere universiteiten bij dit project betrokken.

Prof.dr. P.J. van der Houwen
Centrum voor Wiskunde en Informatica
Afd. Numerieke Wiskunde
Kruislaan 413
1098 SJ Amsterdam