A new computational electromagnetics method based on discrete mechanics

It has been known since the late nineteenth century that electromagnetic phenomena can be simulated by the dynamics of a mechanical system, as long as the Hamiltonian of the mechanical and electromagnetic systems coincide. George Francis FitzGerald’s 1885 model of electromagnetic propagation meets this requirement. When implemented numerically it leads to a new computational method for the simulation of the interaction between electromagnetic fields and physically realistic media, that gives a principal role to the vector potential. In this model, the properties of free space and the constitutive properties of material media reside in physically distinct entities. Based on Discrete Mechanics, the simulation propagates the fields in time according to Newton’s laws, as strains and stresses due to the interacting forces in the medium. There is no inherent limitation to linear phenomena: dispersive as well as non-linear materials are just as easily accommodated. Furthermore, a limitation to purely electromagnetic entities need not be assumed. After derivation of the model for propagation in the presence of linear dispersive magnetodielectrics, its generality is demonstrated through the time-domain simulation of a non-linear transmission line for the generation of solitons. No assumption is made about a small signal limit. Finally, the ability of the model to simulate the interaction between matter and waves is illustrated by considering collisions between ponderable media and electromagnetic pulses. The Doppler shift of the pulse reflected from a moving object is correctly obtained, as well as a classical Compton Effect for the case of a very light object. Through collisions between an electromagnetic pulse and a penetrable dielectric obstacle, it is shown that conservation of total momentum arises naturally out of the simulation, without the need to impose any special moving boundary conditions on the field. The method is ideal for the simulation of environments where electromagnetic forces are on par with, and even may modify, the mechanical forces of the devices involved. Applications to electromagnetic propulsion, microelectromechanics, and nanomachines are envisioned.