Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints

The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given. ∗This work was supported by the United States Air Force Office of Scientific Research under grant F-49620-94-1-0311. †This work was supported by the United States Air Force Office of Scientific Research under grant F-49620-94-1-0311. This work was also supported in part by the National Aeronautics and Space Administration under NASA Contract NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE).