UNIFIED MATRIX PRESENTATION OF MAXWELLS AND WAVE-EQUATIONS USING GENERALIZED DIFFERENTIAL MATRIX OPERATORS

In this paper, we introduce the concept of generalized differential ma trix operators (GDMO's) that are useful for the formulation of electro magnetic boundary value problems in arbitrary orthogonal coordinate sy stems, e.g., Cartesian, cylindrical, and spherical. The most significa nt attribute of the GDMO approach is that their use helps to simplify the complicated manipulation of vector differential equations, especia lly in problems dealing with an anisotropic media. We show that the us e of the GDMO's enable one to replace, for most problems in electromag netics, the complicated vector differential operations with manipulati on of 3 x 3 matrices. In addition, we demonstrate GDMO's are convenien t for deriving many differentiation identities and integral theorems w hich find extensive applications in electromagnetics.