Using sparse LU factorisation to precondition GMRES for a family of similarly structured matrices arising from process modelling
- Univ. of Bath (United Kingdom)
Process engineering software is used to simulate the operation of large chemical plants. Such simulations are used for a variety of tasks, including operator training. For the software to be of practical use for this, dynamic simulations need to run in real-time. The models that the simulation is based upon are written in terms of Differential Algebraic Equations (DAE`s). In the numerical time-integration of systems of DAE`s using an implicit method such as backward Euler, the solution of nonlinear systems is required at each integration point. When solved using Newton`s method, this leads to the repeated solution of nonsymmetric sparse linear systems. These systems range in size from 500 to 20,000 variables. A typical integration may require around 3000 timesteps, and if 4 Newton iterates were needed on each time step, then this means approximately 12,000 linear systems must be solved. The matrices produced by the simulations have a similar sparsity pattern throughout the integration. They are also severely ill-conditioned, and have widely-scattered spectra.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- OSTI ID:
- 433336
- Report Number(s):
- CONF-9604167-Vol.1; ON: DE96015306; TRN: 97:000720-0009
- Resource Relation:
- Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 1; PB: 422 p.
- Country of Publication:
- United States
- Language:
- English
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