Parallel computing of partial differential equations based-applications

Résumé

This thesis explores the parallel implementation of models involving Partial differential equations: 1) the analysis of the interaction between electromagnetic pulses with thin wire structures 2) the Anisotropic nonlinear diffusion technique for filtering three dimensional images and 3) the three dimensional bursting phenomena. For three such models, implementation developments or improvements have been presented, along with numerical results on several architectures. Besides, the appropriate communication model for each application on three parallel systems has been determined. The thesis includes the proposition of a novel classification scheme and communication interface. This works make important contributions in two ways: it contains information which will potentially benefit those interested in theoretical aspects of computational science and also those developing applications aiming to benefit from high performance computing resources.