Numerical Electromagnetics LN11_Local Subcell [email protected]
2 /31 A fundamental problem arises in any grid-based numerical
modeling tool. Modeler options: 1. a variable lattice of space
cells to precisely model shape and features of a structure. 2. a
simpler and much more uniform mesh than option 1. Simplest
Contour-path Sub-cell Models: These is a effective approach to
dealing material structures whose bounding surfaces do not conform
to grid planes in a uniform Cartesian mesh. There are two simple
sub-cell models as: Local Sub-cell Models Staircase model, TE grid,
Diagonal split-cell model for PEC surface, average-properties model
for material interface.
Slide 3
Numerical Electromagnetics LN11_Local Subcell [email protected]
3 /31 Others are updated using normal Yee algorithm. Contour-path
Model of Narrow Slot: Slot is assumed to provide a sub cell air
gap. Faraday's law contour paths C 1, C 2 and C 3 are used to
derive special FDTD updates: Contour C 1 : Contour C 2 : Contour C
3 : Local Sub-cell Models Taflove et al., IEEE Trans. Antennas and
Propagation, 1988. pp. 247-257, 1988 IEEE.
Slide 4
Numerical Electromagnetics LN11_Local Subcell [email protected]
4 /31 Test: Contour-path Model of Narrow Slot Comparison of
contour-path FDTD and frequency-domain moment-method results for
gap electric field distribution in a slotted PEC screen for
broadside TE, illumination: Magnitude phase
Slide 5
Numerical Electromagnetics LN11_Local Subcell [email protected]
5 /31 Faraday's law contour path for thin wire. Umashankar, IEEE
Trans. Antennas and Propagation, 1987, pp. 1248 1257, 1987 IEEE
Contour-path Model of Thin Wire: It permits incorporation of
near-field physics, yielding special purpose time-stepping
expressions that are not obvious from pure FDM. An excellent
example involves interaction of an EM with a PEC wire having a sub
cell diameter [2,5]. Looping H Components: Where: Radial E
Components: Where: For others components refer [2,5] in:
Contour-path Model of Thin Wire
Slide 6
Numerical Electromagnetics LN11_Local Subcell [email protected]
6 /31 Test: Contour-path Model of Thin Wire
Slide 7
Numerical Electromagnetics LN11_Local Subcell [email protected]
7 /31 Locally Conformal Models of Curved Surfaces: Contour-path
technique was proposed in [3,4] to implement conformal models of
structures having curved surfaces within a Cartesian FDTD lattice.
Yu-mitra Technique for PEC Structure: A TE z cut-plane in a 3D-FDTD
lattice is shown in: Free space is assumed to be to the left of
PEC. Results for PEC Structures: Twisted Elliptical Cross Section
Waveguide Cavity: [9] Using Ansoft HFSS: Locally Conformal Models
of Curved Surfaces Contour path for conformal FDTD PEC surface
model. Yu and Mitra, IEEE Antennas and Propagation Magazine, Oct.
2000, pp. 28-39, 2000 IEEE. Contour-path FDTD yields an error at a
mesh resolution of =/8 which is comparable to that obtained using
staircased FDTD at =/32. Therefore a very significant storage and
running- time reduction of approximately (32/8) 3 :1 or 64:1 and
(32/8) 4 :1 or 256:1, respectively.
Slide 8
Numerical Electromagnetics LN11_Local Subcell [email protected]
8 /31 Results for Wing like Object: Mono-static RCS at 10GHz of a
wing like aluminum plate having acute 11 o angles for its leading
and trailing edges [10]. Target specifications: 1. Length= 30.48cm
(10 o ) in vertical (z) direction, width=25.4cm (8.47 o ); 2. Cross
section shape (in x-y plane) of an isosceles triangle with base
angles=11.31 o ; 3. Triangle sides opposite to base are smoothly
joined by a 15.24cm (5.1 o ) radius cylindrical chamfer; 4. Base
has a vertical triangular slot centered in its span. Slot
dimensions: 1.27cm (0.42 o ) depth, and 2.54cm (0.85 o ) width.
Results: Validation of 2D contour-path FDTD model Source: Taflove,
Report to General Dynamics, 1990. Locally Conformal Models of
Curved Surfaces
Slide 9
Numerical Electromagnetics LN11_Local Subcell [email protected]
9 /31 Results for Pair of PEC Spheres: Discussion: Locally
conformal FDTD models of PEC structures with curved surfaces
provide clear advantages relative to use of stair casing. In a
number of simulations ranging from studies of cavity resonances to
calculations of RCS, conformal FDTD models achieve accuracy levels
at mesh resolutions of o /20 that staircased models might achieve
at mesh resolutions of o /80 or finer. Locally conformal FDTD
models may also provide advantages relative to use of unstructured
and partially structured space lattices. Away from PEC surface,
locally conformal models globally propagate numerical modes in
uniform and well-characterized Cartesian Yee lattice. In contrast,
unstructured-lattice models propagate numerical modes in
non-uniform, non-Cartesian meshes which have numerical dispersion
and stability properties that vary with spatial position, and from
problem to problem. Validation of 3D contour-path FDTD model of
bistatic RCS of two 1 0 diameter PEC spheres separated by a 1 0 air
gap, oblique incidence case. solid line =FDTD model; dots
=generalized multi pole technique. Source: Jurgens and Taflove,
IEEE Trans. Antennas and Propagation, 1993, pp. 1703-1708, 1993
IEEE. Locally Conformal Models of Curved Surfaces
Slide 10
Numerical Electromagnetics LN11_Local Subcell [email protected]
10 /31 Yu-Mitra Technique for Material Structures: Second conformal
FDTD technique reported by Yu and Mittra [12], which provides a
simple and efficient treatment of dielectric structures with curved
surfaces. This technique is much easier to use than contour-path
model or effective-dielectric-constant method of [13]. It shows a
significant improvement in accuracy relative to stair-casing that
is comparable to either of two previous approaches. Space-cell
geometry for Yu-Mittra model in a TE z cut-plane in a 3D-FDTD space
lattice is shown: Embedded a dielectric structure whose surface
intersects this cut plane such that a triangular part of cell is
filled with 2 whereas remainder of cell is filled with 1 An
effective permittivity eff is assigned as: Yu-Mittra technique is
simpler because it does not require area or volume calculations
pertaining to how space cells are cut in 3D by arbitrarily oriented
surfaces. Hence, mesh generation for this conformal technique is
quite simple. Yu-MiUra Technique for Material Structures Red walls
have not any problem Red-blue walls have a problem
Slide 11
Numerical Electromagnetics LN11_Local Subcell [email protected]
11 /31 Maloney-Smith Technique For Thin Material Sheets
Maloney-Smith Technique For Thin Material Sheets: It is a
contour-path method to model planar material sheets (dielectric and
conducting) of sub-cell thickness, where sheet is perpendicular to
one of major axes of FDTD space lattice [14]: By embedding a
material sheet of thickness d