30 October 2003
Dr Robert Scheichl
The simulation of sedimentary basins aims at reconstructing its historical evolution in order to provide quantitative predictions about phenomena leading to hydrocarbon accumulations. The kernel of this simulation is the numerical solution of a complex system of time dependent, three dimensional partial differential equations of mixed parabolic-hyperbolic type in highly heterogeneous media. A discretisation and linearisation of this system leads to large ill-conditioned non-symmetric linear systems with three unknowns per mesh element. \\ \\ In the seminar I will look at different preconditioning approaches for these systems and at their parallelisation. The most effective preconditioner which we developed so far consists in three stages: (i) a local decoupling of the equations which (in addition) aims at concentrating the elliptic part of the system in the "pressure block''; (ii) an efficient preconditioning of the pressure block using AMG; (iii) the "recoupling'' of the equations. Numerical results on real case studies, exhibit (i) a significant reduction of sequential CPU times, up to a factor 5 with respect to the current ILU(0) preconditioner, (ii) robustness with respect to physical and numerical parameters, and (iii) a speedup of up to 4 on 8 processors.
- Computational Mathematics and Applications Seminar