![\"\"](\"http:\/\/tasharp.com\/wp-content\/uploads\/2017\/09\/GFMDlogo.png\")
<\/a><\/p>GFMD stands for Greens Function Molecular Dynamics. \u00a0The method uses a function called the static surface Greens function (GF) of the material. \u00a0The concept will be described more in the next paragraph.\u00a0 Importantly, the GF essentially contains all the information about the linear behavior of the lattice without having to simulate the lattice. \u00a0What it means is that regions of the atomic lattice with small strains can be deleted from the simulation, and the single layer of atoms at the boundary of the region can be controlled in a more complicated way. \u00a0Being able to discard those large regions of the lattice means that the simulation reaps large savings in memory and CPU time.<\/p>
Campa\u00f1\u00e1 and M\u00fcser [1] introduced GFMD and showed how the method can be naturally used in molecular dynamics. \u00a0Our first paper rigorously developed GFMD based on the atomic interactions of lattice of molecules, making it an elegant and seamless boundary for MD simulations [2]. \u00a0 Our second paper (in preprint) extends GFMD to realistic, many-body interactions between atoms–which can be very slow and benefit the most from the speed-up [3].<\/p> To give an idea of the technical underpinning, we describe a few more details of the method. \u00a0The idea is that, as long as the strain is small, the atomic interactions can be considered at linear order. \u00a0In simulations of friction, for instance, large plastic strains occur near the surface of a solid, where a full, explicit, MD simulation must be used.\u00a0 But further away from the surface, the Hamiltonian of the system can be approximated to quadratic order in the atomic positions.<\/p> The first and second derivatives of the Hamiltonian compose the external forces and dynamical matrix of the atoms, and, given that the atoms form a regular crystalline structure, transfer function methods may be used to calculate the GF. \u00a0The surface GF is nothing other than the equilibrium displacements of the surface atoms when the surface is subject to a point force. \u00a0Given the linearized Hamiltonian, the effect of an arbitrary exerted force on the surface is given by the the super-position of the GF displacements.<\/p> For many-body potentials, complications arise. \u00a0False forces are generated, so called ghost forces, at the layer of atoms that connects the explicit region from the linearized substrate. \u00a0Also, the forces cannot be decomposed into having a single-atom source, complicating implementation into standard MD codes. Meticulous attention to the formalism and familiarity with MD codes allowed us to introduce the appropriate domain decomposition, into explicit, substrate, and GFMD layers.<\/p> This detailed work results in a dramatically faster code. The plot at the top of this post indicates the speed up from running GFMD as opposed to the full system. The time per simulation time step scales with system size <\/p> [1]\u00a0Campa\u00f1\u00e1, Carlos, and Martin H. M\u00fcser. “Practical Green\u2019s function approach to the simulation of elastic semi-infinite solids.”\u00a0Physical Review B<\/i>\u00a074.7 (2006): 075420.\u00a0https:\/\/journals.aps.org\/prb\/abstract\/10.1103\/PhysRevB.74.075420<\/a><\/p><\/a><\/p><\/a><\/p>