SA SKA project 2010 Postgraduate Bursary Conference Prof David B Davidson SKA 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 ( ) 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.

Maxwell contd Maxwell’s equations ("On Physical Lines of Force”, Philosophical Magazine, Pts ) 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: Uses “edge based” unknowns:

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:

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 N= 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 GByte Run-time (P4 1.8 GHz): MLFMM 4 hours MoM not solved Mobile phone analysis in a car model at 1878 MHz  N= 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 CBFM Solution Time 43.4 sec226.8 sec11.77 % CBFMAccuracyDirect 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 & 2 nd order accurate with explicit time integration.

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 ); 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 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!