Organisation : Delphine Lautier, Emmanuel Gobet, Clémence Alasseur

Lieu : Salle 01 – Institut Henri Poincaré, 11 rue Pierre et Marie Curie – Paris 5eme

Date : Vendredi 27 mai 2016

Heure : 14h00

Intervenants:  Dr Francisco Bernal (Instituto Superior Técnico, Lisbon)

Sujet: Accelerated probabilistic methods for domain decomposition of large-scale PDEs


Probabilistic Domain Decomposition (PDD) is an incipient approach which attempts to improve scalability in the numerical solution of large-scale boundary value problems (BVPs). It does so by relying on the much better parallelization properties of Monte Carlo methods for stochastic differential equations. In a gist, the idea is to solve first the BVP on the inter-subdomain artificial interfaces by exploting Feynman-Kac type representations, thus producing a set of well-posed small-scale BVPs. They can later be solved by individual processors independently from one another. Both stages of PDD minimize inter-processor communication and–in the most favourable scenario–allow for an optimal use of the computational resources. On the other hand, stochastic representations of BVPs typically lead to lengthy simulations if good accuracy is sought. In this talk, we will present an accelerated version of PDD, called IterPDD, which is inspired in the Multigrid method. The idea is to use a rough estimate of the solution to construct a control variate for the following, and more accurate, estimate, until reaching the desired accuracy. By balancing the various sources of error, this iteration leads to a substantial reduction in variance and thus to a shorter overall simulation time. A numerical example will be worked out where the speedup is about 100.

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