A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain where fine scale features need to be resolved, a continuum sub-domain which can adequately describe the macroscale deformation and an overlap interphase sub-domain that has a blended description of the two. The problem is formulated in terms of equilibrium equations with a blending between the continuum stress and the atomistic force in the interphase. Coupling between the continuum and the atomistics is established by imposing constraints between the continuum solution and the atomistic solution over the interphase sub-domain in a weak sense. Specifically, in the examples considered here, the atomistic domain is modeled by the aluminum embedded atom method (EAM) inter-atomic potential developed by Ercolessi and Adams [F. Ercolessi, J.B. Adams, Interatomic potentials from first-principles calculations: the force-matching method, Europhys. Lett. 26 (1994) 583] and the continuum domain is a linear elastic model consistent with the EAM potential. The formulation is subjected to patch tests to demonstrate its ability to represent the constant strain modes and the rigid body modes. Numerical examples are illustrated with comparisons to reference atomistic solution.
This article proposes a parallel implementation using a multicore environment with MPI to the solution of the linear system resulting from the discretization of the Poisson equation in 2D using finite differences and the iterative method of Jacobi. The size of the domain and its corresponding discretization result in a system of linear equations where the number of variables can be millions. The magnitude of the problem allows the algorithm to be highly scalable in parallel; this means that by increasing the number of processors available to solve the system, the execution time will improve considerably. However, as the number of processors increases, the communication work also increases, which stops its performance. Therefore, this article proposes re-engineering the parallel algorithm focused on memory management to speed up its execution and improve its effectiveness.
Abstract
This article proposes a parallel implementation using a multicore environment with MPI to the solution of the linear system resulting from the discretization of the Poisson equation [...]