SA SKA project 2010 Postgraduate
Bursary Conference
Prof David B Davidson
SKA Research Chair
Dept. Electrical and Electronic
Engineering
Univ. Stellenbosch, South Africa

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 Electromagnetics (EM) as a core radio astronomy technology.
Computational EM.
Overview of previous research in CEM.
Five-year plan (2011-2015) for research chair.
Collaborators.
Summary.

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Controlling equations in classical EM are Maxwell’s eqns.
Two curl eqns (Faraday and
Ampere’s laws).
Two divergence eqns
(Gauss’s law).
Constitutive (material) parameters ε and μ.
 
H J

B
 t

D
 t
0

D
 
E
B
 
H

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Maxwell’s equations ("On Physical Lines of Force”,
Philosophical Magazine, Pts 1-4 1861-2) predict classical (non-quantum) EM interactions to extraordinary accuracy.

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From late 19 th century, these have formed basis for understanding of EM wave phenomena.
Classical methods of mathematical physics yielded solutions for canonical problems – sphere, cylinders, etc (Mie series opposite).
Astute use of these, physical insight and measurements produced great advances in understanding of antennas,
EM radiation etc.

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In common with Comp
Sci & Engr, CEM has its genesis in 1960s as a new paradigm.
First methods were
MoM (circa 1965),
FDTD (1966), FEM
(1969).

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Elevation of CEM to equal partner of analysis & measurement only since
1990s.
Widespread adoption of
CEM for general industrial
RF & microwave use delayed by computational cost of 3D simulations.
1990s saw first commercial products emerge (eg FEKO,
HFSS, MWS), and 2000s has seen these products become industry standards.
 RF & microwave industry:
– General telecoms
–
–
–
–
–
Cell phone designers & operators
Radio networks
Terrestrial & satellite broadcasting;
Radar and aerospace applications (esp. defence – which is where much of SA’s current expertise originated)
Radio astronomy.

 20 years back:
Computations – no-one believes them, except the person who made them.
Measurements – everyone believes them, except the person who made them.
(Attributed to the late Prof
Ben Munk, OSU).

CEM formulations
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Solutions to Maxwell’s eqns have been sought in time and frequency domains (d/dt → j ω, aka phasor domain).
Full-wave formulations have included:
–
–
–
Finite difference (usually in time domain)
Finite element (traditionally frequency, now increasingly time domain)
Green’s function based (boundary element, volume element; known as method of moments in CEM). (Usually frequency domain).
 Asymptotic methods have also been used (typically ray-optic based methods, eg geometrical theory of diffraction). Very powerful for a limited class of problems (reflectors!)

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Left: MoM (usually) meshes surfaces
Centre: FDTD meshes volumes with cuboidal elements
Right: FEM meshes volumes with tetrahedral elements.

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FEM in CEM shares much with computational mechanics.
Along with FDTD, FEM shares simple handling of different materials.
FEM offers systematic approach to higher-order elements.
Less computationally efficient than FDTD, but uses degrees of freedom more efficiently.
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Based on “minimizing” variational functional:
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 1
2

S



1 r
(

E ) ( E )
 k i
2
 r



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Uses “edge based” unknowns: w ij
  j
  i

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Application using higher-order functions:
Magic-T hybrid.
–
–
Solid: FEMFEKO (802 tets, h ≈ 6.5mm, LT/QN.
*: HFSS results (1458 tets) - adaptive.
Good results from coarse mesh!

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Application: Waveguide filter.
Uses explicit residualbased criteria (MM
Botha, PhD 2002)
Result for 2.5% of elements with highest error.
Can be used for selective adaptation.

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Method of Moments – usually a boundary element method - still most popular method in antenna engineering.
For perfectly or highly conducting narrow-band structures, very efficient.
Uses free-space (or geometry specific) Green’s function , incorporating Sommerfeld radiation condition.
Usually reduces problem dimensionality by at least one (surfaces), sometimes two (wires).

 Modelling thin-wires one of earliest apps.
 Based on integral eq:
 inc
E ( ) z


1 j

0 e
 jkR
4

R

L
[
 2

 z
2
 k
2

( , ')] ( ') z

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Generates a full interaction matrix, with complex entries, with moderate to poor conditioning.
Main challenge has been O(f 6 ) asymptotic cost for surfaces - although O(f 4 ) matrix fill and memory requirement often as significant.
Breakthroughs in fast methods, especially Multilevel
Fast Multipole Method (FLFMM) – have greatly extended scope of MoM.

Bistatic RCS computation of a PEC sphere: diameter 10.264 l
N=100005 unknowns
Memory requirement:
MLFMM 406 MByte
MoM (est) 149 GByte
Run-time (Intel Core 2
E8400):
MLFMM 5 mins
MoM not solved

Memory requirement:
MLFMM 1.17 GByte
MoM 209.08 GByte
Run-time (P4 1.8 GHz):
MLFMM 4 hours
MoM not solved
Mobile phone analysis in a car model at 1878 MHz

N=118 452 unknowns
(Surface impedance used for human)

 Work on DDMs, especially
Characteristic Basis
Functions, has yielded very promising results.
 Pioneered by
Maaskant & Mittra,
ASTRON.
 MSc – D Ludick,
2010.

The CBFM applied to a
7-by-1 Vivaldi array
Direct Solver
~ 8,000 RWG Unknowns
CBFM
Accuracy
11.77 %
Direct
Solution
Time
226.8 sec
CBFM
43.4 sec
~ 19 CBFM Unknowns
Synthesis (by recycling primary CBFs)
9 sec

x
( , ,
  x
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Finite Difference Time Domain
(FDTD) currently most popular full-wave method overall.
Usually refers to a specific formulation – [Yee 66], right.
Uses central-difference spatial and temporal approximation of
Maxwell curl equations on “Yee cell”. (2D eg below)
Basic Yee leap-frog implementation simple & 2 nd order accurate with explicit time integration.

 t
  s
[ H i j n z
( , , )
 z
( ,

1, )]

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Rat-race coupler in microstrip, 1.8 GHz center frequency.
“Open boundaries” –
Perfectly Matched
Layer – used to terminate upper space.

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Relatively easy to implement.
Regular lattice makes parallelization fairly straightforward.
Higher-order FDTD has not proven straightforward.
Have worked on finite element-finite difference hybrid to overcome this (N
Marais, PhD, 2009).

 Extensive use also made of CHPC platforms (Ludick, e1350):
 Work also in progress on use of GPGPUs for
CEM (Lezar).

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Core team:
– Prof DB Davidson
(SARChI chair); Prof HC
Reader (1/2 time on
SARChI chair 2011-12);
Dr DIL de Villiers (SKA funded), and post-docs.
Supported by RF & microwave group:
– Profs P Meyer, KD
Palmer, JB de Swardt. and MM Botha (new appointment), Dr RH
Geschke.
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Work closely with
Electronics &
Superconducting group:
– Prof WJ Perold, Dr C
Fourie
Also continued support from
Emeritus Professors Cloete and van der Walt.

 Focal plane arrays and computational methods for their efficient simulation
– Periodic array analysis
– Domain decomposition methods.

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Feed optics – especially offset
Gregorian (GRASP)
Broadband feeds.
Front-end devices – filters, LNAs, superconducting A/D convertors.
Small radio telescope for SU?

 Ongoing work on:
– Power provision
– Site base RFI
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Cabling and interfaces
Telescope RFI hardening
Lightning protection
Monitoring of site RFI emissions.
– Array feeding EMI issues .

 New course on radio astronomy for engineers (DBD).
 Electromagnetic theory (MMB ?)
 Established courses:
– Computational Electromagnetics (DBD/MMB).
– Antenna design (KDP).
– Microwave devices (PM, JBdS).
– EMC (HCR, RHG)

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Pinelands KAT office
HART-RAO
Centre of High
Performance
Computing (Flagship
Project)
EMSS
UCT (Prof MR Inggs);
UP (Profs Joubert &
Odendaal) and CPUT
New opportunities?
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Cambridge (HCR sabbatical 2010)
ASTRON (Post-doc Dr
Smith 2010).
Manchester University
(Prof Tony Brown) and
Jodrell Bank. (DBD sabbatical 2009).
CSIRO (KPD visit)
New opportunities?

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Talk has recapped career in CEM to date.
Plan for 2011-2015 outlined – main focus on CEM for antenna modelling and EMC, but also looking at front-end issues.
Very important aim of above to is train a new generation of electronic engineers - well versed in electromagnetics - who understand radio telescopes.
Will (try!) not to lose sight of upstream (overall interferometer design, eg uv coverage) and downstream (DSP, correlator, bunker) issues!