Convergence criteria for waveform iteration methods applied to partitioned DAE systems in chemical process simulation
- Borchardt, Jürgen
- Michael, Tino
2010 Mathematics Subject Classification
- 65L05 80A30 65F50 65Y05 80A30 92E20
- Algebraic-differential equations, waveform iteration, partitioned systems, parallelization of numerical methods, chemical process simulation
The application of block waveform iteration methods to initial value problems for implicit DAE systems of index 1 arising in chemical process simulation is considered. These methods permit the concurrent treatment of blocks of subsystems of the entire system gaining a coarse granular parallelism. Their convergence properties strongly depend on the assignment of variables to equations and the partitioning of the system into subsystem blocks.
The convergence of block waveform iteration methods applied to semiexplicit DAE sytems of index 1 is proved. The convergence conditions are given in such a way that only the single blocksystems have to satisfy some corresponding conditions. It is shown that these conditions are fulfilled for a simplified modeling of distillation columns. Resulting from the convergence considerations an assignment and partitioning algorithm is given. A prototype of a waveform-iteration code has been implemented and tested by means of examples included in the user package of the chemical process simulator SPEEDUP.