EFIE-based MoM (Part IV)
- Dielectric Formulations
E8-202 Class 10
2
• 2D vs 2.5D vs. 3D Formulations
• Electrostatic Formulation: Capacitance matrix extraction
• Magnetostatic Formulation: Inductance matrix extraction
• Electric Field Integral Equation (EFIE): S-parameter extraction
• Partial Element Equivalent Circuit (PEEC) Method
• Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE)
• PMCHWT Formulation: Dielectric modeling
• Parallelization techniques
Module 2: Method of Moments
• D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral
modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag., vol.
AP-32, pp. 77–85, Jan. 1984.
References
4
Data Structures
• N2XYZ
• P2N
• E2P
• E2N
• P2E
Dielectric Handling
• Multilayered Green’s Functions (Not Full 3D)
• PMCHW
• Approximate quasi-static formulation
• Volumetric formulation (3D Maxwell Accurate)
6
• Is vector potential affected by permittivity?
• Is scalar potential affected by permittivity?
Approximate Quasi-Static Formulation
, ,
, ,
| |
| |
( ) ( )
4 | |
1 ( )
4 | | ( )
i j
i j
jk
j
ij i
T T
jk
j
i
T T
j e
ds ds
e ds r ds
j
r-r
r-r
Z f r f r
r r
f r f
r r
Approximate Quasi-Static Formulation
Boundary Condition
1 0
2
D n D s
n
Equation
E
3 0 0
,
2 ) ' (
' ) '
' 4 (
1
n r ds r
r r r r
E T T
8
• Current and related charge unknowns (RWG) on conductors
• Charge unknowns (Piecewise constant) on dielectrics
Approximate Quasi-Static Formulation
0 , f J E
Z Z
Z Z
d c dd
dc
cd cc
Volumetric Formulation (Preferred)
• Equation:
E j Dj
J r 0
0
r T
i
s j
E J E
E
j A
j E J
r i
0
j A
j
D E j
r i
0
10
Volumetric Formulation
• Basis Function:
D j
fs
D. H. Schaubert, D. R. Wilton, and A. W. Glisson, “A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,” IEEE Trans. Antennas Propag., vol. AP-32, pp. 77–85, Jan. 1984.
