The SKA SA Stellenbosch Research Chair: Five year research plan
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SA SKA project 2010 Postgraduate Bursary ConferenceProf David B DavidsonSKA Research Chair
Dept. Electrical and Electronic Engineering
Univ. Stellenbosch, South Africa
The SKA SA Stellenbosch Research Chair: Five year research plan
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Outline of talk
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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Maxwell’s equations
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.
BE
t
DH J
t
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Maxwell contd
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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Using Maxwell’s equations
From late 19th 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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Computational Electromagnetics (CEM)
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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CEM as a viable design tool
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.
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CEM as a viable design tool (2)
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).
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CEM formulations
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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MoM, FDTD, FEM – basics
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
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.
Based on “minimizing” variational functional:
Uses “edge based” unknowns:
21 1( ) ( ) ( )2 riS r
F E E E k E E dS
ij i j j iw
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FEM application
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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FEM – p adaptation
Application: Waveguide filter.
Uses explicit residual-based 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 (MoM)
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).
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MoM formulation – (very) basics
Modelling thin-wires one of earliest apps.
Based on integral eq:
22
20
1 ( , ')( ) [ ( , ')] ( ')
( , ')4
incz z
L
jkR
z zE z k z z I z dz
j z
ez z
R
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MoM - issues
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.
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MLFMM application example: Sphere (FEKO)
Bistatic RCS computationof a PEC sphere: diameter 10.264 N=100005 unknowns
Memory requirement: MLFMM 406 MByte MoM (est) 149 GByte
Run-time (Intel Core 2 E8400): MLFMM 5 mins MoM not solved
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MLFMM application example: Mobile phone in a car
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 MHzN=118 452 unknowns(Surface impedance used for human)
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MoM – domain decomposition methods
Work on DDMs, especially Characteristic Basis Functions, has yielded very promising results.
Pioneered by Maaskant & Mittra, ASTRON.
MSc – D Ludick, 2010.
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The CBFM applied to a The CBFM applied to a 7-by-1 Vivaldi array7-by-1 Vivaldi array
Direct Solver
CBFM
Solution Time
43.4 sec226.8 sec11.77 %
CBFMAccuracy Direct Synthesis (by recycling primary CBFs)
9 sec
~ 8,000 RWG Unknowns
~ 19 CBFM Unknowns
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FDTD method (1)
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 & 2nd order accurate with explicit time integration.
( , , 1) ( , , ) [ ( , , ) ( , 1, )]x x z z
tE i j n E i j n H i j n H i j n
s
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FDTD method-MWS example
Rat-race coupler in microstrip, 1.8 GHz center frequency.
“Open boundaries” – Perfectly Matched Layer – used to terminate upper space.
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FDTD method (2)
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).
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Use of HPC platforms
Extensive use also made of CHPC platforms (Ludick, e1350):
Work also in progress on use of GPGPUs for CEM (Lezar).
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Wrapping up CEM to date:
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Dept E&E – SKA team
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.
Work closely with Electronics & Superconducting group:
– Prof WJ Perold, Dr C Fourie
Also continued support from Emeritus Professors Cloete and van der Walt.
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Five year plan – antennas
Focal plane arrays and computational methods for their efficient simulation– Periodic array
analysis– Domain
decomposition methods.
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Five year plan – antennas & front-end
Feed optics – especially offset Gregorian (GRASP)
Broadband feeds. Front-end devices –
filters, LNAs, superconducting A/D convertors.
Small radio telescope for SU?
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Five year plan – EMC/EMI
Ongoing work on:– Power provision– Site base RFI– Cabling and interfaces– Telescope RFI hardening– Lightning protection– Monitoring of site RFI
emissions.
– Array feeding EMI issues.
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Five year plan – Post-graduate teaching
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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Collaborators
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?
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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In summary
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!