DIAKOPTIC ANALYSIS OF COMPLEX 3-D ELECTROMAGNETIC SYSTEMS 1 School - - PowerPoint PPT Presentation
A.R. Djordjevi 1 , D.I. Ol an 1 , B.M. Kolundija 1 , J.R. Mosig 2 , I.M. Stevanovi 3 DIAKOPTIC ANALYSIS OF COMPLEX 3-D ELECTROMAGNETIC SYSTEMS 1 School of Electrical Engineering, University of Belgrade, Serbia 2 Ecole Polytechnique
1School of Electrical Engineering, University of Belgrade, Serbia 2Ecole Polytechnique Fédérale de Lausanne, Switzerland 3Freescale Semiconductor, Geneva, Switzerland
COST Action IC0603 Workshop Cyprus, April 2008
Present status of research and software
Plans for future work Collaboration among universities and STSMs
Split the original system into smaller nonoverlapping
Solve each subsystem individually Combine partial solutions to obtain the solution of
Diakoptic approach is based on
surface integral-equation (SIE) formulation equivalence theorem (Huygens’ Principle)
Diakoptic surface integral equation (DSIE)
One outer subsystem (for open systems) and
The total number of ports for the circuit is KM Brute-force solution, using tableau system of
More sophisticated solution results in KM
If topological elimination is used, then the
Nesting
Assumptions/conditions:
matrix inversion time dominates K congruent subsystems, each with N unknowns 2M unknowns for each diakoptic surface
Total number of unknowns for circuit solution: KM Efficient when overhead is small (M<<N) Storage reduction =1 for closed systems, =2 for open systems
2-D electrostatic problems with piecewise-
3-D electrostatic problems with piecewise-
2-D quasi-static and dynamic problems
3-D dynamic problems with piecewise-
new results
2 4 6
2
2 x [m] y [m] z [m]
Two metallic cubes
Original system Outer subsystem Inner subsystems
Potential (verification)
Original system Outer subsystem Inner subsystems
200 400 600 800 1000 1200 1 2 3 4 5 6
[%]
M
200 400 600 800 1000 1200 1 2 3 4 5 6
a M
200 400 600 800 1000 1200 0.0 0.5 1.0 1.5 2.0 2.5
s M
Error Acceleration Storage reduction
Metallic spheres with dielectric coating Diakoptic surfaces can be arbitrary; they
Metallic patches
Diakoptic surfaces
Metallic plates (scatterers) in dielectric cubes
0.25 0.50 0.75 1.00
Real MoM-SIE Imag MoM-SIE Real DSIE Imag DSIE
z - coordinate Js [mA/m]
5 10 15 20 25 30 35 40 0.0 0.2 0.4 0.6 0.8 1.0 1.2
y [mm] Ez [V/m]
MoM-SIE DSIE
Current distribution Near field
40 80 120 160 200 240 280 320 360 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25
[deg] /
2
MoM-SIE DSIE
Radar (monostatic) cross section (RCS)
Metallic cubes (1250)
One cluster Outer subsystem One inner subsystem
RCS
40 80 120 160 200 240 280 320 360
10
[deg] /
2 [dB] DSIE MoM-SIE
30 60 90 120 150 180
5 10 15
[deg] /
2 [dB] DSIE MoM-SIE
SIE
DSIE
SIE
DSIE
Patch antennas (cookies)
60 120 180
10
[deg]
g [dB] ( = 0)
Patch antennas (cookies)
congruent subsystems
771.9 93.0 6 000 82 200
92.5 4 860 66 582
91.7 3 840 52 608
90.3 2 940 40 278
87.5 2 160 29 592
81.6 1 500 20 550
68.7 960 13 152
43.5 540 7 398
13.7 240 3 288
Storage reduction Coefficients DSIE Coefficients MoM-SIE Array
Evaluation for arbitrary 3D dynamic problems
antennas, large arrays printed circuits, microwave devices
Fully incorporate the diakoptics into existing
subdomain and entire-domain basis functions
Software implementations of DSIE on