Cluster configuration for 3D simulation of acoustic transducer and waveguide

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Cluster configuration for 3D simulation of
acoustic transducer and wave-guide

• Sylvain Ballandras, William Daniau
• Institut FEMTO-ST
• Département de Physique et Métrologie des
  Oscillateurs, Besançon, France

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Summary of the talk

• FEMTO-ST (brief presentation)
• Simulation of acoustic transducers
• Historical progression
• The new cluster configuration
• Some examples of application
• Perspectives

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FEMTO-ST Institute A new Research Unit 19
April 2007 Freiburg

• 3rd BFG Workshop

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FEMTO-ST components

• CREST
• Thermic, flow
• LCEP
• Quartz technology
• LMARC
• Mechanics
• LOPMD
• Optics
• LPMO
• Micro-systems,
• TimeFrequency

FEMTO-ST  Franche-comté Electronique Mécanique
Thermique et Optique - Sciences et Technologies
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FEMTOs Technology center MIMENTO

• 3D Microfabrication Isotropic and Anisotropic
  chemical etchning, DRIE, LIGA
• Microfabrication on piezoelectric
  materialsQuartz, LiNbO3, Piezocomposites, AlN
• Hybrid Micro-mechanics Silicon technologies
  dedicated to MEMS
• Nanotechnologies FIB etching, e-beam
  lithography, porous silicon, auto-assembling
  sinlge layers

• 370 m2 dedicated to clean room
• 230 m2 for chemics and back-end

• 7 M of technological equipments
• 18 engineers and techicians

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Simulation of acoustic transducersDifferent
kinds of transducers considered in these works

• Surface Acoustic Wave devices
• Source, filters, sensors
• Thin Film Bulk Acoutic Resonator
• filters and sensors
• Piezocomposite transducers
• Imaging and non destructive control
• Micomachined Ultrasound Transducers
• Imaging and sensors

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Elementary structure of a SAW Bandpass filter
Overlap shape of the fingers Fourier trasform
of the expected spectral function
0.5 µm
1 µm
10 µm
2 µm
Electrode width
Operating frequency
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Film Bulk Acoustic Resonators
Bragg mirror
Air or vacuum gap (surface micro-machining)
Piezolayer excited using 2 electrodes
Si substrate
Si substrate
Si membrane
HBAR for frequency source application
fr 2.497 GHz, Ks² 1, Q 2210
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Principle of MUTs
Implementation of piezoelectric MUTs
Simulation of a capacitive MUT
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General principle of an acoustic imaging system
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Mathematical problem Opas Physics
Hookes law
Electrical induction
Linear but anisotropic, layered, piezoelectric
materials with periodic inhomogeneous excitation
Newtons law
Poissons law
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Need for Intensive Computation

• Design choice of the right parameters for the
  considered application
• Temperature stability, coupling factor, figures
  of merit,
• ? Requires numerous fast computations
• Analysis understanding the actual operation of
  the device
• Assessment, deviation, model updating
• ? Requires large model implementation

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Nature of the implemented models
Finite Element Analysis
Boundary integrals or elements
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Definition of the Greens function
The Greens function defines the linear relation
between mechanical displacement and surface
stresses
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Spectral relations
Fourier transform along t
s is the slowness defined as s?/k (no
dispersion assumed)
Fourier transform along x
Piezoelectric, layered problems only is
easily accessible
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Main modeling constraints
20 nodes cubic element 4 dof/node ? Elementary
matrices Mass, Stifness 3240 complex16 each

• FEA 3D requires large algebraic systems to be
  solved
• BEM convolution techniques impose all the dof
  are connected one to another

No radiation
With radiation
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How to address the problem

• Operation in harmonic conditions
• No time dependent variables
• No Fourier transform
• Computation of the solution for each frequency
  point
• Periodic boundary conditions
• Applicable in harmonic and time domains as well
• Access to mutual terms require Fourier transform
• Enlarge the matrix profile
• Absorbing conditions for simulation of non
  periodic problems

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Computation conditions
Mutual terms deduced from the harmonic analysis
Harmonic excitation
Harmonic impedance
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Typical example of harmonic to mutual
transformation
Fourier transform
Sommerfeld integral ?convolution
Harmonic domain
Mutual parameters
Real space simulation
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Some historyof a small physicist team using
computers

• Paleonthology from µVAX (1MB RAM) and APPOLO
  Stations (8 MB RAM) to HP700 Workstations (64 MB
  RAM 25 k/machine)
• 1995 a Power Challenge machine _at_ LMARC Besançon
  (500 kF 75k)
• These approaches were expensive and did not
  provide very large computation capabilities

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1998 A new cluster approach

• Price reduction of personal computer together
  with Pentium-CPUs availability ? Increase of the
  PC park in labs
• Arising of libraries dedicated to cluster
  parallel processing for stand-alone machines
• Parallel Virtual Machine PVM
• MOSIX OpenMOSIX

Requires high data flow rate network connection
100 Mbit/s to 1Gbit/s
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2005 Return of the SMPs

• New SMP machines available
• Price reduction
• 64-bit-CPU
• Large RAM access and handling (larger than 4
  GBytes)
• These machines can deal with
• Numerous  small  computations
• Large model implementation
• For a moderate price (20 to 40 k), One can
  access intensive computation units

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Calculation unit Computer Coorp.

• 8 AMD Opteron DUAL CORE CPUs 875 2,2 GHz
• Mother Card chipset Nvidia NForce Pro 2200 AMD
  8131
• 128 GByte DDR PC3200 ECC Registered
• Two connectors PCI Express 16x
• Integrated grphic interface ATI Rage XL 8 MO
• Dual Interface Lan Gigabit 1000 BT, RJ45 connect.
• 2 x Hard Disks SATA Raptor 74 Go 10 000 tr/min
  (RAID 1 System)

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Operating system
Linux x86_64 Distribution under GPL licence based
on the RedHat Enterprise 4.0, Upgraded, Optimised
core (http//www.centos.org/)
Miscellaneous
Managing the grappe
Ressource statistics
Advanced parallel tools
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Programmation Fortan 95 Protland

• 2 simultaneous compilation licence with
• BLAS (Basic Linear Algebra Subprogs)
• LAPACK (Linear Algebra Package)
• FFTW (Fast Fourier Transform)
• This compiler support OpenMPI chosen for code
  parallelisation
• Parallel library MPICH, LAM/MPI, PVM (on demand)

Optimized for AMD64
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General outlook of the system distributed by
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SMP versus distributed machine cluster

• SMP is built once, poorly oriented to updating
• SMP can handle large memory resource at once (the
  equivalent to our system is 8 machines with 16 GB
  RAM)
• Due to technological improvements, SMP are
  dedicated to be overcome
• For addressing large 3D problems, SMP is well
  adapted to our demand because of large RAM
  handling

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How do we use parallel capabilities of the SMP

• Quite rustically at this time split of the
  wave-number and frequency ranges in 16 small
  parts launched on the SMP CPUs ? rebuild of the
  final result as a unique data set
• Real parallel computation (i.e. programming)
  investigated for large 3D models and time
  dependant problems

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Some examples of applications
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3D SAW modeling
Rayleigh wave on quartz (YX) p20µm, w5?
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pMUT in 2D-periodic time domain
Top Silicon plate
PZT
Silica spacer
PZT is excited by a 1V.Dirac voltage
Silicon base
The Silicon base is clamped
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pMUT Simulation results Harmonic vibration and
mutual coupling
Different phase excitations along x, In-phase
excitation along y
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CMUT with Hexagonal periodicity
In phase Fundamental
In phase S1 mode
Phase ?/4 Antisym.
In phase 2nd Harm.
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CMUT
Experimental response
Simulation results (3D)
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Conclusion

• Acoustics requires systematic computation tools
  for design and analysis as well
• SMP machines can nowadays answer small scientific
  group demands for moderate (accessible) prices
  but
• 64-bit CPU allows for large RAM resource managing
  well-suited for 3D computation
• There is still some distance for our industrial
  partners to share facilities and computation
  resourcebut

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Perspectives with SMP capabilities

• Simulation of whole transducer structures for
  imaging probes and image simulation
• Accounting for parasitic effects in 3D simulation
  of elastic wave-guides ? ultimate signal
  processing devices
• Non-linear periodic time domain simulations (with
  acoustic radiation effects)
• Actual behavior of acoustic sensors in organic
  environments
• Optimization of finite dimension devices using
  the harmonic approach combined with PMLs