Electromagnetic Theory With Discrete Exterior Calculus

Abstract

Abstract-A self-contained electromagnetic theory is developed on a simplicial lattice. Instead of dealing with vectorial field, discrete exterior calculus (DEC) studies the discrete differential forms of electric and magnetic fields, and circumcenter dual is adopted to achieve diagonal Hodge star operators. In this paper, Gauss' theorem and Stokes' theorem are shown to be satisfied inherently within DEC. Many other electromagnetic theorems, such as Huygens' principle, reciprocity theorem, and Poynting's theorem, can also be derived on this simplicial lattice consistently with an appropriate definition of wedge product between cochains. The preservation of these theorems guarantees that this treatment of Maxwell's equations will not lead to spurious solutions.

Modeling of the Electromagnetic Field of a Rectangular Waveguide With Side Holes

“…Calculations show that the reactive part of the effective impedance has a capacitive characteristic. The calculations are performed for the effective value of the surface impedance, obtained on the basis of the formulas of the article [5]:…”

“…Let us consider the propagation of magnetic waves in the current waveguide, provided that the surface impedance of a narrow wall is known, and it can be calculated from the relationships given in [12][13][14][15][16][17].…”

“…The representation of boundary conditions of components of the electric and magnetic fields on the coupling elements on openings of a rectangular waveguide and the boundary conditions of an impedance type outside the openings in the form of a linear combination of electric and magnetic fields allow us to construct a system of integral equations for the problem of radiation from a finite waveguide antenna array with an impedance flange. One approach to solving such problems is to use approximate boundary conditions [1][2][3][4][5][6]. If E τ and H τ are tangential components of an electromagnetic field on a certain interface between two regions, the concept of surface impedance Z s is introduced (in the general case, complex and anisotropic), connecting these components by the relation…”

Calculation of the Electromagnetic Field of a Rectangular Waveguide With Chiral Medium

“…Normal waves of TE-type in the considered waveguide have the form [17][18][19][20][21][22][23][24][25][26][27][28]:…”

Modeling Microwave Signals Transmitted Through a Rectangular Waveguide

“…In the practical use of waveguides, an important role is played by the methods of inputting energy into them, that is, methods of exciting waves of the required types, as well as methods for extracting the energy of these waves [1][2][3][4][5][6][7].…”