Past

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.

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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.

Why does a spinning coin come to such a sudden stop? Why does a
spinning hard-boiled egg stand up on its end? And why does the
rattleback rotate happily in one direction but not in the other?
The key mathematical aspects of these familiar dynamical phenomena,
which admit simple table-top demonstration, will be revealed.

Rapidly oscillating problems, whether differential equations or

integrals, ubiquitous in applications, are allegedly difficult to

compute. In this talk we will endeavour to persuade the audience that

this is false: high oscillation, properly understood, is good for

computation! We describe methods for differential equations, based on

Magnus and Neumann expansions of modified systems, whose efficacy

improves in the presence of high oscillation. Likewise, we analyse

generalised Filon quadrature methods, showing that also their error

sharply decreases as the oscillation becomes more rapid.