Finite-element solution of Maxwell's equations with Helmholtz forms

Interest in scattering and/or absorption involving three-dimensional penetrable bodies has driven numerous efforts to develop computational methods for such problems. When the object is geometrically and electrically complex, the finite-element method is a logical numerical choice. Helmholtz weak forms have recently been advocated, and computational successes have been achieved with the approach. An overview of the Helmholtz formulation, with particular emphasis on its spurious-mode-resistant properties, some efficient and reliable solution procedures for the algebra that it generates, and an approach to unstructured mesh generation, is presented. As a whole these procedures provide the basis for a methodology for realizing three-dimensional finite-element solutions of Maxwell's equations in a workstation computing environment Examples of calculations that demonstrate several important properties of the Helmholtz technique and illustrate the extent to which practical three-dimensional calculations can be accomplished with readily available computing power are shown.