Variationally adaptive support size in local maximum-entropy approximants (Poster)

ADRIAN ROSOLEN; DANIEL MILLÁN; MARINO ARROYO

Cardona, Barcelona

Workshop; 9th Workshop on Numerical in Applied Science and Engineering 2010; 2010

LaCàN - Universitat Politècnica de Catalunya

An advantage of meshfree methods over conventional mesh-based methods is the flexibility they offer to scatter nodes in the domain at will and to select the support size (or locality) of the basis functions. As it is known that the accuracy of the solutions depends strongly on those choices, several adaptive strategies to arrange optimally the nodes have been proposed in the literature. However, in spite of more than thirty years of meshfree developments, the systematic optimization of the basis functions support size has never been tackled. Here, the automatic adaption of the support size in the context of meshfree local maximum-entropy approximants and partial differential equations stemming from a minimum principle is proposed and investigated.