Authors: I. Tsukerman, G. Friedman and D. Halverson
Affilation: The University of Akron, United States
Pages: 458 - 461
Keywords: nanoparticle assembly, long-range forces, electrostatic interactions, magnetostatic interactions, variational-difference schemes, generalized finite-difference methods, flexible local approximation
The Flexible Local Approximation MEthod (FLAME) proposed recently by one of the authors is shown to be efficient for the simulation of long-range electromagnetic interactions between nanoparticles. Other promising applications of FLAME include charge or dipole interactions in explicit and implicit solvent models in macromolecular simulation, and unbounded electro- or magnetostatic problems. Mathematically, FLAME is a class of difference schemes having the ability to incorporate desirable accurate local approximations of the field. These approximations may reflect point charge or dipole singularities; boundary layers; field jumps at material interfaces, and so on. This flexibility of approximation is uncommon in traditional numerical methods. For instance, conventional Finite Difference schemes are based on Taylor expansions and do not normally take into account specific features of the solution. Finite Element methods employ piecewise-polynomial approximation and typically require complex meshes to represent the geometric and physical features of the problem. In contrast, FLAME relies more on algebraic (analytical) approximation than on geometrically conforming meshes. The paper describes some nanoscale applications of FLAME and in addition provides a tutorial-type illustration of its usage.