Title: Cluster configuration for 3D simulation of acoustic transducer and waveguide
1Cluster 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
2Summary of the talk
- FEMTO-ST (brief presentation)
- Simulation of acoustic transducers
- Historical progression
- The new cluster configuration
- Some examples of application
- Perspectives
3FEMTO-ST Institute A new Research Unit 19
April 2007 Freiburg
4FEMTO-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
5FEMTOs 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
6Simulation 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
7Elementary 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
8Film 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
9Principle of MUTs
Implementation of piezoelectric MUTs
Simulation of a capacitive MUT
10General principle of an acoustic imaging system
11Mathematical problem Opas Physics
Hookes law
Electrical induction
Linear but anisotropic, layered, piezoelectric
materials with periodic inhomogeneous excitation
Newtons law
Poissons law
12Need 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
13Nature of the implemented models
Finite Element Analysis
Boundary integrals or elements
14Definition of the Greens function
The Greens function defines the linear relation
between mechanical displacement and surface
stresses
15Spectral 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
16Main 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
17How 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
18Computation conditions
Mutual terms deduced from the harmonic analysis
Harmonic excitation
Harmonic impedance
19Typical example of harmonic to mutual
transformation
Fourier transform
Sommerfeld integral ?convolution
Harmonic domain
Mutual parameters
Real space simulation
20Some 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
211998 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
222005 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
23Calculation 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)
24Operating 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
25Programmation 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
26General outlook of the system distributed by
27SMP 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
28How 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
29Some examples of applications
303D SAW modeling
Rayleigh wave on quartz (YX) p20µm, w5?
31 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
32pMUT Simulation results Harmonic vibration and
mutual coupling
Different phase excitations along x, In-phase
excitation along y
33CMUT with Hexagonal periodicity
In phase Fundamental
In phase S1 mode
Phase ?/4 Antisym.
In phase 2nd Harm.
34CMUT
Experimental response
Simulation results (3D)
35Conclusion
- 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
36Perspectives 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