Computing derivatives in a meshless simulation using permutations in ADOL-C

Abstract

In order to compute derivatives in a meshless simulation one needs to take into account the ever changing neighborhood relationships in a point-cloud that describes the domain. This may be implemented using permutations of the independent and dependent variables during the assembly of the discretized system. Such branchings are difficult to handle for operator overloading AD tools using traces. In this paper, we propose a new approach that allows the derivative computations for an even larger class of specific branches without retracing. © 2012 Springer-Verlag.