Cellular Neural Networks and Least Squares for partial differential problems parallel solving

Nicolas Fressengeas (1) , Hervé Frezza-Buet (2)

1 LMOPS - Laboratoire Matériaux Optiques, Photonique et Systèmes
2 SUPELEC-Campus Metz

This paper shows how Cellular Neural Networks (CNN) can be harnessed into solving partial differential problems through an adaptation of the Least Squares Finite Elements Method. As CNNs can be implemented on distributed parallel architectures, this method allows the distribution of a resource demanding differential problem over a computer network.

Mots clés: Cellular Automata; Partial Differential Equations; Distributed computing

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Calcul parallèle, distribué et partagé [cs.DC]

Nicolas Fressengeas, Hervé Frezza-Buet. Cellular Neural Networks and Least Squares for partial differential problems parallel solving. 2009. ⟨hal-00107064v6⟩