Reduced Vector Helmholtz Wave Equation Analysis on the Wave-Number Side
Open Access
- 1 January 2019
- journal article
- Published by Scientific Research Publishing, Inc. in Journal of Electromagnetic Analysis and Applications
- Vol. 11 (09), 161-172
- https://doi.org/10.4236/jemaa.2019.119011
Abstract
The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is motivated by solving an EM problem on the Fourier side in order to relate the resolvent and the Green’s function. Methods used include Matrix Theory, Fourier Transforms, and Green’s function. A closed form of the resolvent is derived for the electromagnetic Helmholtz reduced vector wave equation, with Dirichlet boundary conditions. The resolvent is then used to derive expressions for the solution of the EM wave equation and provide Sobolev estimates for the solution.Keywords
This publication has 1 reference indexed in Scilit:
- Boundary Value Problems of Mathematical Physics, Vol. 1Physics Today, 1967