sa ska project 2010 postgraduate bursary conference prof david b davidson ska research chair dept....
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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
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.
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.
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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.
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.
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).
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.
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).
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!)
MoM, FDTD, FEM – basics
Left: MoM (usually) meshes surfaces Centre: FDTD meshes volumes with cuboidal elements Right: FEM meshes volumes with tetrahedral elements.
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
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!
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.
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).
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
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.
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
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)
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.
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
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
FDTD method-MWS example
Rat-race coupler in microstrip, 1.8 GHz center frequency.
“Open boundaries” – Perfectly Matched Layer – used to terminate upper space.
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).
Use of HPC platforms
Extensive use also made of CHPC platforms (Ludick, e1350):
Work also in progress on use of GPGPUs for CEM (Lezar).
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.
Five year plan – antennas
Focal plane arrays and computational methods for their efficient simulation– Periodic array
analysis– Domain
decomposition methods.
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?
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.
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)
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?
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!