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Matematik former morgendagens satellitter Md MATH p KU 15-11-2018 This is a footer TIC TICRA One of the first spin-offs from Electromagnetics Institute at DTU (1971) 2 TIC TICRA A his istory ry of f excellence The glo lobal l

  1. Matematik former morgendagens satellitter Mød MATH på KU 15-11-2018 This is a footer

  2. TIC TICRA • One of the first spin-offs from Electromagnetics Institute at DTU (1971) 2

  3. TIC TICRA A his istory ry of f excellence The glo lobal l standard 3

  4. Matematikken former morgendagens satelli litter Vi skal fra højteknologiske kommunikationssatellitter i rummet ned på Jorden og ind i klasselokalet. Fokus er på matematik i anvendelse. Når I spørger jeres elever “Hvad er løsningen?” skal vi have dem til at svare “Hvor nøjagtigt et resultat skal du bruge - og hvor hurtigt?”. Der er læring og penge i den overvejelse. 4

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  6. Ele lectromagnetism – Maxwell’s Equations Illustrations from esa.int and terahertz.dk 6

  7. Customers Satellite Operators Satellite Manufacturers Space Agencies 7

  8. Product Lin ines Support & Maintenance Antenna Design Antenna Modelling SW ??? 8

  9. Working at t TIC TICRA 26 Employees: Hereof: 10 Ph.D.’s from DTU Electro 12 Ph.D./M.Sc./B.Sc. 4 Adm./Marketing/misc. 9

  10. Typisk udfordring for vores kunder Design Antennerne til en planlagt kommunikationssatellit 10

  11. INDHOLD TID RESOURCER 11

  12. Tel elecommunication satellite Test satellite meshed from a CAD file: S, C, X, Ku and Ka-band • Example frequencies: Solar panel span: 19.8 meters • 10 GHz Width: 7.1 meters • 30 GHz Height: 4.5 meters 450 λ Courtesy of Marco Sabbadini European Space Agency. 1980 λ 710 λ 12

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  14. Centralt spørgsmål ”Hvad er løsningen ?”. 14

  15. TICRA’s GRASP Product Targeting electrically large reflector antennas and • platforms Huge range of built-in models for reflectors => ease of use • Meets the space industry’s special requirements: • High accuracy (100 dB dynamic range with low • computational overhead…) High robustness • Multi-scale structures • 15

  16. MoM solution(s) Small reflector (20  )  MoM with RWG basis functions are the foundation of most with discretization density  /10 commercial solvers for large frequency-domain problems  Large number of small triangles in a mesh (  /10)  Piecewise linear current  130 unknowns per  2  TICRA’s MoM is based on a very different approach: Very high Small reflector (20  ) with discretization order MoM (HO-MoM) density 2   Large curved quads (2  , 4 th order)  Smooth currents using 1st - 10th order hierarchical Legendre basis functions  25 unknowns per  2  Memory and CPU of standard MoM reduced by a factor of 16 16

  17. MoM-solution(s)  Sphere with different meshes and polynomial orders Convergence rate of higher-order MoM: D=13  Coarse mesh Fine mesh • The MoM solution error decays as h p  h: mesh size  p: polynomial order  High accuracy: Increasing p is much better than decreasing h  Previous work on MLFMM-acceleration of higher-order MoM: x 2 nd order is optimal x Large memory penalty for higher orders  New modified MLFMM algorithm for higher-order MoM: 17

  18. MoM-Solution(s) Peak directivity: MoM 47.761 dBi PO/PTD 47.764 dBi Frequency 60 GHz Electrical 53,500 λ 2 size HO Unknowns 1.5 million Runtime 1 hour 6.5 million Equiv. RWG Total Memory 15 GB Currents on the 4 reflectors in the beam waveguide 18

  19. Solv lver Robustness – Survi rviving Mesh Err rrors • The standard MoM and MoM/MLFMM algorithms require a connected mesh When two surfaces are in physical contact, the meshes must connect properly along • the line joining the surfaces This is bad news when building complicated models • Meshing algorithms are sensitive to Meshes from different sources A local mesh change, e.g. inclusion of defective or missing connectivity cannot be joined a fine geometrical detail, requires a information in CAD files global update of the mesh -> modeling errors Edge AB not connected to edge AC in Detailed Antenna CAD file Platform mesh with hole mesh for accommodating Meshes are antenna incompatible! 19

  20. Solv lver Robustness – Survi rviving Mesh Err rrors • The mesh connectivity requirements originate in the continuous integral equation x The standard EFIE integral equation used everywhere requires continuous basis functions • Solution published recently: Discontinuous Galerkin IE • Closed PEC scatterers discretized with RWGs • Only discontinuous basis functions • • Our new higher-order MLFMM solver supports an extended version of this formulation:  Mixed continuous/discontinuous basis functions for maximum efficiency  Open/closed structures  Dielectric and composite PEC/dielectric materials  Higher-order basis functions 20

  21. Dis isconnected Meshes - Be Benefits Mesh of antenna Mesh of platform with hole for Valid mesh with currents flowing accommodating antenna continuously across the red line Valid mesh after import of CAD file Mesh refinement is performed locally with missing topological information 21

  22. Dis isconnected Meshes - Be Benefits • The new higher-order MLFMM solver is robust against meshing errors  Disconnected meshes have no impact on accuracy or iteration count • We use disconnected meshes extensively  More regular meshes  Easier to keep large efficient patches 22

  23. Central pointe • Flere løsninger til samme problem • Forskellig nøjagtighed – beregningstid – ressource forhold “Hvad er løsningen?” “Hvor nøjagtigt et resultat skal du bruge - og hvor hurtigt?” INDHOLD TID RESOURCER 23

  24. Tel elecommunications satellite – Computation mesh 2 GHz Platform meshed at 2 Ghz: – Two holes for accommodating helix antennas – Mesh file with helix antennas added S-band helix Ka-band feed array with 90 horns Ka-band feed array is tiny at S-band -> multiscale structure! Automatic mesh processing => Increased robustness – Single closed volume detected – Outward normals found – Topological information from CAD tool not needed S-band helix 24

  25. Tel elecommunications satellite – Results 2 GHz • The solution is obtained in 39 iterations Frequency 2 GHz • The preconditioner handles multiscale structures efficiently Electrical size 6,349  2 • The electrically small details provide the dominant contribution Patches 20,208 to the computational resources Smallest patch  /200 Largest patch 2.2  HO Unknowns 292,690 Equiv. RWG unknowns 1,500,000 Iterations 39 Runtime (2*Xeon @2.9 GHz) 15:45 min Memory 18 GB TTC1, interference from TTC2: 25

  26. Tel elecommunications satellite – Computation mesh 12 GHz 26

  27. Tel elecommunications satellite – Results 12 GHz Frequency 12 GHz Electrical size 167,762  2 Patches 105,436 Smallest patch  /200 2.2  Largest patch HO Unknowns 4,475,955 Equiv. RWG unknowns 22,000,000 Iterations 90 Runtime (2*Xeon @2.9 GHz) 2:50 hours 122 GB Memory 27

  28. Central pointe “Hvad er løsningen?” “Hvor nøjagtigt et resultat skal du bruge - og hvor hurtigt?” INDHOLD “Hvilken løsning er den rigtige for problemet?”. TID RESOURCER 28

  29. Nøjagtige løsninger Th The glo lobal l standard Hurtige løsninger Kostbare løsninger 29

  30. Dis iskussion • Den vigtigste pointe, jeg tager med mig hjem, er ….. • Jeg kan se pointen anvendt i min undervisning, ved at jeg …. 30

  31. Th Thank you TICRA Tel. +45 3312 4572 E-mail: info@ticra.com Follow us on LinkedIn

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