To study static and dynamic dislocation properties that involve long-ranged elasticity, we have developed a 2D and 3D Green's Function (GF) method to treat the boundary conditions. In this flexible-boundary condition method, the simulation cell is divided into three regions, denoted as atomistic, GF and continuum. In the outer continuum region, the atomic positions are initially determined according to the anisotropic elastic displacement field for a dislocation line defect at the center of the atomistic region, and then are either relaxed (MS) or propagated (MD) by a GF method according to the forces in the GF region. The GF method uses 2D or 3D lattice and elastic GF solutions for line or point forces. Complete atomistic relaxation or propagation is performed in the atomistic region according to the interatomic forces generated from, for example, MGPT potentials. Forces developed in the GF region as the relaxation or propagation proceeds in the atomistic region are then used to relax or propagate those atoms in all three regions according to GF solutions. In such a way, the relaxation or propagation of those atoms in the atomistic region can proceed without causing a large force build-up in the continuum region.
In our GF simulation code, a spatial domain decomposition scheme called a layered-cake decomposition is implemented for all three computational regions, as illustrated in the Figure. The small domain cells defined in this scheme are connected via a cell-linked list method such that each cell has a fixed number of neighboring cells. This reduces the number of unnecessary interatomic separations considered in evaluating the interatomic potentials, in particular the MGPT potentials, which is crucial to their efficient application. In addition, to take advantage of the scalable architectures of the current state-of-the-art computer platforms, a mapping algorithm has also been developed for massively parallel computers. A 3D to 1D mapping list is built at the beginning of the simulation. This mapping list ensures the connectivity between different regions, so that no information is lost during the simulations. The mapping scheme also provides portability and flexibility to the MGPT-GF simulation code.
Maintained by Lorin X. Benedict