Cell-Vertex Based Multigrid Solution of the Time-Domain Maxwell's Equations

Abstract

Abstract-The time domain Maxwell's equations are numerically solved using a multigrid method in a scattered field formulation and a cell-vertex based finite volume time domain framework. The multilevel method is an adaptation of Ni's [9] cell-vertex based multigrid technique, proposed for accelerating steady state convergence of nonlinear Euler equations of gas dynamics. Accelerated convergence to steady state of the time domain Maxwell's equations, for problems involving electromagnetic scattering, is obtained using multiple grids without the use of additional numerical damping usually required in nonlinear problems. The linear nature of the Maxwell's system also allows for a more accurate representation of the fine-grid problem on the coarse grid.

A p-VARIABLE HIGHER-ORDER FINITE VOLUME TIME DOMAIN METHOD FOR ELECTROMAGNETIC SCATTERING

“…where a is the cylinder radius and λ the wavelength of the incident wave [6,14,18]. Results are shown in terms of bistatic RCS and the absolute value of surface current after time stepping fixed incident time periods usually adequate for desired steady state response in such problems.…”

“…[17]. The first problem considered is that of the circular cylinder subject to continuous harmonic incident TM illumination with a/λ = 4.8 where a is the cylinder radius and λ the wavelength of the incident wave [6,14,18]. Results are shown in terms of bistatic RCS and the absolute value of surface current after time stepping fixed incident time periods usually adequate for desired steady state response in such problems.…”

“…The next problem considered is that of illumination by a continuous harmonic incident TE wave and a/λ = 9.6 [6,14,18]. The "O" grid with 600 points in the circumferential direction is taken so that the resolution on the scatterer surface again corresponds to 10 PPW.…”

“…7. The airfoil chord length is 10 times the wavelength of the incident harmonic TM wave at broadside incidence [6,14,18]. Results are obtained using a body-fitted "O" grid with 200 points around the airfoil and 50 in the normal direction.…”