Algorithms to reduce the computational cost of vector Preisach model in view of Finite Element analysis

The purpose of this work is to devise algorithms to reduce the memory consumption of the vector Preisach model in view of its usage in Finite Element analysis. Four algorithms, which all implement a vector Preisach hysteresis model, are presented and critically compared theoretically and by numerical experiments taken on with two materials and three signals. Several strategies are presented to reduce both the memory occupation and the computational cost of several orders of magnitude.