CBFM work presented at IEEE AP-S International Symposium on Antenna and Propagation and UNSC/URS National Radio Science Meeting, Spokane, Washington, USA 03-08 July 2011

1. A Non-Overlapping Characteristic Basis
Function Method for the Electromagnetic
Analysis of Dielectric Objects
B. Babu, G. Bianconi and R. Mittra
The Pennsylvania State University
IEEE AP-S International Symposium on Antenna and Propagation
and UNSC/URS National Radio Science Meeting
Spokane, Washington, USA
03-08 July 2011

2. Advantages of the CBFM
Can solve large objects with limited
computing resources;
Shown to be highly successful for perfect
electric conductors;
Suitable for efficient parallelization on
shared memory with multi core processors;
 Can handle multiple RHSs efficiently
avoiding the problem to be solved iteratively.

3. 10/28/2016
Non-Overlapping CBFM for Dielectric Objects
A novel CBFM procedure for the EM analysis of
Dielectric objects is proposed;
 The main advantage of the technique is to avoid
the use of overlap (buffer-free) between adjacent
blocks;
 Buffer-free CBFs have proven to not suffer from
edge effect for the dielectric case;
 By avoiding overlap between adjacent blocks, the
total number of unknowns is reduced.

4. 10/28/2016
Non-Overlapping CBFM for Dielectric Objects
Current Distribution induced on a PEC/Dielectric Plate
PEC Plate Dielectric Plate

5. 10/28/2016
 The object has been divided into a number of blocks. Each block has been
illuminated by Nf plane-waves with a different incidence angle;
Non-Overlapping CBFM Procedure: Step I
 Each block has been discretized by using the EFIE and solved via the Method of
Moments (MoM).
 
     
   
 
0 cos
0
1 1 0 1 0 0 0
4
1
1 0 1 0 2
0 0
2 2
1 0
1
2 4
jkt i i n jn
z n
n
mn mn mn
nn
Z E E E e j J k e
Z C J k a J k R jH k R m n
C j
Z J k a jH k a
k k
C j a k n k
 f f

  

 

   
  
   
  

r r

6. 10/28/2016
 The MoM matrix relative to the previous example has been
decomposed into 9 blocks;
Non-Overlapping CBFM Procedure: Step II

7. 10/28/2016
Non-Overlapping CBFM Procedure: Step III
 Each block has been illuminated by Nf plane-waves with a different
incidence angle. Nf CBFs are generated for each block overestimating the
total Degrees of Freedom (DoFs) for each section.
1,2, ,ii i iZ J V i M   L
1 2
1 1 1
1 2
2 2 2
1 2
i i i
N
N
i
N
N N N
J J J
J J J
J
J J J
f
f
f
 
 
 
  
 
 
 
L
L
M M L M
L

8. 10/28/2016
Removing redundancy using SVD
Non-Overlapping CBFM Procedure: Step IV
 In order to discard the redundant CBFs, a SVD
algorithm has been applied to only retain the most
K linearly independent high-level basis functions;
 
1 2
1 2
1 2, , ,
i i
i
i i
i
i
H
i i i i
N N
i N
N N
i N
i N
J U S V
U u u u
V v v v
S diag   


  
   
   

r r r
L £
r r r
L £
L

9. 10/28/2016
Non-Overlapping CBFM Procedure: Step V
 The final induced current distribution J can be expressed as a linear
combination of the CBFs:
1 2
1, 1, 2, 2, , ,
1 1 1
tot tot tot
KN N N
n n n n K n K n
n n n
J J J J  
  
     
r r r r
L
 The final step to be performed is the
generation of the Reduced matrix ZR that can
be accomplished by applying the Galerkin
testing procedure employing the CBFs as
testing functions:
R T R R R T
Z J Z J Z V V J V      
r

10. 10/28/2016
Numerical Results
Circular cross section cylinder
 The object is illuminated by a normally incident TM plane wave;
 Frequency (MHz) = 300;
 Radius R = 0.5l, where l is the wavelength at the operating frequency;
 Relative permittivity er = 2-0.8j;
 Low level basis functions (LLBFs): pulse
 Total number of LLBFs: 225;
 Number of LLBFs per block: 105, 15, 105
 Number of CBFs per block: 13, 8, 13
 Threshold value d = 1e-4

11. 10/28/2016
 Excellent agreement among the analytical and numerical solutions is achived.
 Tangential Ez at z = 0 computed analytically, via the EFIE-MoM and the
CBFM procedure;
Circular cross section cylinder
Numerical Results

12. 10/28/2016
Numerical Results
Inhomogeneous circular cross section cylinder
 The object is illuminated by a normally incident TM plane wave;
 Frequency (MHz) = 300;
 Outer radius R1 = 0.5l
 Inner radius: R2=0.2l
 Inner relative permittivity er = 20-0.8j;
 Outer relative permittivity er = 2-0.8j;
 LLBFs: pulse
Total number of LLBFs: 225;
 Block number of LLBFs: 90, 45, 90

13. Summary of the CBFM parameter
Numerical Results

14. 10/28/2016
Numerical Results
Inhomogeneous circular cross section cylinder
 Et computed at z = 0 by using the EFIE-MoM and CBFM approach;
 Excellent agreement with the conventional numerical solution.

15. 10/28/2016
Numerical Results
Circular cross section cylinder
 The object is illuminated by a normally incident TM plane wave;
 Frequency (MHz) = 300;
 The cylinder side = 4.0l;
Relative permittivity er = 2-0.8j;
LLBFs: pulse
Total number of LLBFs: 3481;
 Block number of LLBFs: 1593, 295, 1593

16. 10/28/2016
Summary of the CBFM parameter
Numerical Results

17. 10/28/2016
Numerical Results
Test Case II
 Et computed at z = 0 by using the EFIE-MoM and CBFM approach;

18. 10/28/2016
Numerical Results
Test Case III
 Et computed at z = 0 by using the EFIE-MoM and CBFM approach;
 Excellent agreement with the conventional numerical solution.

19. 10/28/2016
Conclusions and future developments
 Excellent agreement among CBFM and analytical or
EFIE-MoM solutions;
 Non-Overlapping CBFs have been shown to do not suffer
from edge effects for dielectric objects;
 The dimension of the reduced matrix is much smaller in
comparison to that which would be generated by employing
the conventional Moment Method formulation allowing a
direct solution of the linear system;
 Development of a CBMoM code for general 3D dielectric
objects.

20. Thank You