Numerische Lösung großer strukturierter DAE-Systeme der chemischen Prozeßsimulation
- Borchardt, Jürgen
- Bruell, Ludger
- Grund, Friedrich
- Horn, Dietmar
- Hubbuch, Frank
- Michael, Tino
- Sandmann, Horst
- Zeller, Robert
2010 Mathematics Subject Classification
- 65Y05 80A30 65H10 65F50 80A30 92E20
- Algebraic-differential equations, systems of partitioned nonlinear equations, systems of sparse linear algebraic equations, parallelization of numerical methods, simulation of chemical processes in chemical plants
Parallelizable numerical methods for solving large scale DAE systems are developed at the level of differential, nonlinear and linear equations. For this the subsystem-wise structure of the DAE systems based on unit-oriented modelling is explored. Partitionings are used to parallelize waveform relaxation and structured Newton methods. Initial values are computed with a modified Newton method. To solve large sparse systems of linear equations a special Gaussian elimination method is used. The algorithms were implemented on a CRAY C90 vector computer, as well as on both, moderately parallel CRAY J90 vector computers and massively parallel CRAY T3D machines. The methods were tested using several real life examples.
- Mathematik Schluesseltechnologie fuer die Zukunft (Hoffmann, K.-H., Jaeger, W., Lohmann, T., and Schunk, H., eds.), Springer-Verlag Berlin Heidelberg New York, 1997, pp. 91-103.