Abstract:

In this talk a recently developed probabilistic representation for
N-dimensional initial value semilinear parabolic problems based on
generalized random trees will be presented. Two different strategies have
been proposed, both requiring generating suitable random trees combined with
a Pade approximant for approximating accurately a given divergent series.
Such series are obtained by summing the partial contribution to the solution
coming from trees with arbitrary number of branches. The new representation
expands largely the class of problems amenable to be solved
probabilistically, and was used successfully to develop a generalized
probabilistic domain decomposition method. Such a method has been shown to
be suited for massively parallel computers, enjoying full scalability and
fault tolerance. A few numerical examples will be given to illustrate the
remarkable performance of the algorithm, comparing the results with those
obtained with a classical method.