The SKA SA Stellenbosch Research Chair: Five year research plan

SA SKA project 2010 Postgraduate Bursary Conference

Prof David B Davidson SKA Research Chair Dept. Electrical and Electronic Engineering Univ. Stellenbosch, South Africa

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.

 

H

0  

B



t



D



t D

 

E B

 

H

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 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.

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: 1 2 

S

   1

r

( 

E E

) 

k i

2 

r



E E dS

 Uses “edge based” unknowns:

w ij

 

j i

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 engineering. – usually a boundary element method - still most popular method in antenna 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:

E z inc

   1

j

 0

e



jkR

4 

R L

 [  2  

z

2 

k

2 

z z I z dz z

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 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

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 MHz  N=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 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

FDTD method (1)

x x

    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 integration.

nd order accurate with explicit time   

t



s

[

z



z



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).

Wrapping up CEM to date:

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!