Title :
An Analytical Expression for 3-D Dyadic FDTD-Compatible Green´s Function in Infinite Free Space via z-Transform and Partial Difference Operators
Author_Institution :
Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan
fDate :
4/1/2011 12:00:00 AM
Abstract :
FDTD solutions have their own properties distinct from the discrete samples of corresponding continuous wave solutions. Thus, the discrete equivalent to the Green´s function is needed for applications like the one using a hybrid absorbing boundary condition which couples the FDTD algorithm with integral operators for nonconvex scatterers. In this paper we propose a new closed-form expression for the 3-D dyadic FDTD-compatible Green´s function in infinite free space via a novel approach with the ordinary z-transform along with the spatial partial difference operators. The final expression involves a summation of standing wave modes with time-varying coefficients. The propagation of waves in the Yee´s grid can be interpreted by the selective property of the time-varying coefficients, which is very different from the conventional concept of a traveling wave. The traditional dispersion analysis using plane waves for the FDTD algorithm in a source-free region may not be applicable to explain the wave propagation phenomenon through our analytic expression, because the corresponding z-transform diverges for z on the unit circle.
Keywords :
Green´s function methods; Z transforms; electromagnetic wave propagation; electromagnetic wave scattering; finite difference time-domain analysis; 3D dyadic FDTD-compatible Green function; Yee grid; continuous wave solutions; hybrid absorbing boundary condition; infinite free space; nonconvex scatterers; partial difference operators; plane waves; time-varying coefficients; traditional dispersion analysis; traveling wave cocept; wave propagation; z-transform; Algorithm design and analysis; Boundary conditions; Electric fields; Equations; Finite difference methods; Green´s function methods; Time domain analysis; FDTD methods; Green functions; Z transforms; operators (mathematics);
Journal_Title :
Antennas and Propagation, IEEE Transactions on
DOI :
10.1109/TAP.2011.2109363