An adaptive treecode algorithm for computing the evolution of microstructures in an elastic media (Q2869164)

The authors consider a treecode algorithm in order to speed up the numerical formulation for computing the evolution of microstructures in an elastic media presented in [\textit{H.-J. Jou} et al., J. Comput. Phys. 131, No. 1, 109--148 (1997; Zbl 0880.73050)]. Only particle-cluster interactions are incorporated. Numerical examples are presented and show a significantly lower computation time.NEWLINENEWLINEUnfortunately, no empirical evidence is given of the additional numerical error due to the treecode algorithm. While treecodes converge exponentially, the same holds true for the alternating point quadrature used for space discretisation of the boundary integral operator. Therefore, it is possible that the error due to the treecode approximation actually dominates the spatial discretisation error in the given setup, making a careful choice of the treecode approximation parameters necessary.NEWLINENEWLINEFor the entire collection see [Zbl 1264.65002].