The SKA SA Stellenbosch Research Chair: Five year research plan SA SKA project 2010 Postgraduate Bursary Conference Prof David B DavidsonSKA 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.
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:
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 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.
Accuracy Direct CBFM 11.77 % Solution Time 226.8 sec 43.4 sec The CBFM applied to a 7-by-1 Vivaldi array Direct Solver ~ 8,000 RWG Unknowns CBFM ~ 19 CBFM Unknowns Synthesis (by recycling primary CBFs) 9 sec
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.
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!