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.