Multiscale Green's function
Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations. The main application of the MSGF technique is in modeling of nanomaterials. These materials are very small – of the size of few nanometers. Mathematical modeling of nanomaterials requires special techniques and is now recognized to be an independent branch of science. A mathematical model is needed to calculate the displacements of atoms in a crystal in response to an applied static or time dependent force in order to study the mechanical and physical properties of nanomaterials. One specific requirement of a model for nanomaterials is that the model needs to be multiscale and provide seamless linking of different length scales. Green's function (GF) was originally formulated by the British mathematical physicist George Green in the year 1828 as a general technique for solution of operator equations. It has been extensively used in mathematical Physics over the last almost two hundred years and applied to a variety of fields. Reviews of some applications of GFs such as for many body theory and Laplace equation are available in the Wikipedia. The GF based techniques are used for modeling of various physical processes in materials such as phonons, Electronic band structure and elastostatics. (Wikipedia).
