Field Marshal is directed at achieving a working balance between cost, usability and power for electromagnetics R&D. Two elements necessary to cost-effectively achieve this (at least initially) are finite difference methods and multigrid techniques.

Finite Difference Methods

Numerous mathematical and numerical techniques have been developed (and are required) for electromagnetics; however, any “toolbox” of codes for solving electromagnetic problems should contain a grid-based, finite-difference solver for the Laplace/Poisson equations. This provides a simple-to-understand, straightforward-to-maintain and extend implementation of the physics involved in electromagnetics. As a minimum, the Field Marshal simulation environment requires a high-quality Laplace/Poisson solver that takes full advantage of the environment. The necessary high-accuracy finite difference formulas are delineated in a short paper, FDTech.pdf. A more detailed paper covering static and time dependent Helmholtz equations as well as the Laplace and Poisson equations will be posted in a few weeks.

Multigrid is a set of techniques for enhancing the solution of partial differential equations by utilizing nested grids of different resolutions. These techniques can be applied to increase solution speed, produce variable and adaptive grid resolutions, improve accuracy, and make finite difference techniques even more memory efficient. Fortunately, multigrid techniques do not have to be adopted en masse. Significant advantages can be gained from even the most basic implementations of multigrid. A short paper with two examples illustrating speed and accuracy improvements from simple multigrid implementations can be found here.