Matematik former morgendagens satellitter Md MATH p KU 15-11-2018 - - PowerPoint PPT Presentation

Matematik former morgendagens satellitter

Mød MATH på KU

This is a footer 15-11-2018

TIC TICRA

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

TIC TICRA

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A his istory ry of f excellence The glo lobal l standard

Matematikken former morgendagens satelli litter

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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.

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Ele lectromagnetism – Maxwell’s Equations

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Illustrations from esa.int and terahertz.dk

Customers

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Space Agencies Satellite Manufacturers Satellite Operators

Product Lin ines

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Antenna Modelling SW Antenna Design Support & Maintenance

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Working at t TIC TICRA

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26 Employees: Hereof: 10 Ph.D.’s from DTU Electro 12 Ph.D./M.Sc./B.Sc. 4 Adm./Marketing/misc.

Typisk udfordring for vores kunder

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Design Antennerne til en planlagt kommunikationssatellit

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INDHOLD TID RESOURCER

Tel elecommunication satellite

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Test satellite meshed from a CAD file:

• Solar panel span: 19.8 meters
• Width: 7.1 meters
• Height: 4.5 meters

Courtesy of Marco Sabbadini European Space Agency. S, C, X, Ku and Ka-band Example frequencies: 10 GHz 30 GHz 1980 λ 710 λ 450 λ

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Centralt spørgsmål

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”Hvad er løsningen?”.

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

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MoM solution(s)

• MoM with RWG basis functions are the foundation of most

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
• rder MoM (HO-MoM)
• Large curved quads (2, 4th 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

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Small reflector (20) with discretization density /10 Small reflector (20) with discretization density 2

MoM-solution(s)

• Sphere with different meshes and polynomial orders
• The MoM solution error decays as hp
• 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 2nd order is optimal x Large memory penalty for higher orders

• New modified MLFMM algorithm for higher-order MoM:

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Convergence rate of higher-order MoM:

Coarse mesh Fine mesh D=13

MoM-Solution(s)

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Currents on the 4 reflectors in the beam waveguide

MoM 47.761 dBi PO/PTD 47.764 dBi

Peak directivity:

Frequency

60 GHz

HO Unknowns

1.5 million

• Equiv. RWG

6.5 million

Electrical size

53,500 λ2

Runtime

1 hour

Total Memory

15 GB

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

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Meshes from different sources cannot be joined

Detailed Antenna mesh Platform mesh with hole for accommodating antenna

Meshes are incompatible! A local mesh change, e.g. inclusion of a fine geometrical detail, requires a global update of the mesh Meshing algorithms are sensitive to defective or missing connectivity information in CAD files

• > modeling errors

Edge AB not connected to edge AC in CAD file

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

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Dis isconnected Meshes - Be Benefits

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Mesh refinement is performed locally Mesh of platform with hole for accommodating antenna Mesh of antenna Valid mesh with currents flowing continuously across the red line Valid mesh after import of CAD file with missing topological information

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

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Central pointe

• Flere løsninger til samme problem
• Forskellig nøjagtighed – beregningstid – ressource forhold

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“Hvad er løsningen?” “Hvor nøjagtigt et resultat skal du bruge - og hvor hurtigt?”

INDHOLD TID RESOURCER

Tel elecommunications satellite – Computation mesh 2 GHz

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Platform meshed at 2 Ghz:

– Two holes for accommodating helix antennas – Mesh file with helix antennas added S-band helix S-band helix Ka-band feed array with 90 horns

Automatic mesh processing => Increased robustness

–Single closed volume detected –Outward normals found –Topological information from CAD tool not needed Ka-band feed array is tiny at S-band

• > multiscale structure!

Tel elecommunications satellite – Results 2 GHz

• The solution is obtained in 39 iterations
• The preconditioner handles multiscale structures efficiently
• The electrically small details provide the dominant contribution

to the computational resources

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Frequency 2 GHz Electrical size 6,349 2 Patches 20,208 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:

Tel elecommunications satellite – Computation mesh 12 GHz

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Tel elecommunications satellite – Results 12 GHz

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Frequency 12 GHz Electrical size 167,762 2 Patches 105,436 Smallest patch /200 Largest patch 2.2  HO Unknowns 4,475,955

• Equiv. RWG unknowns

22,000,000 Iterations 90 Runtime (2*Xeon @2.9 GHz) 2:50 hours Memory 122 GB

Central pointe

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

INDHOLD TID RESOURCER

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Nøjagtige løsninger Hurtige løsninger Kostbare løsninger

Th The glo lobal l standard

Dis iskussion

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Th Thank you

TICRA

• Tel. +45 3312 4572

E-mail: info@ticra.com Follow us on LinkedIn