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From unit cell to the whole array

Elastic, acoustic and piezoelectric physics coupled across every element of a finite array — not one pillar at a time.

Array-scale  •  Coupled multiphysics  •  AI-driven optimization

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“Quanscient Allsolve enables large-scale multiphysics simulations of PMUT and CMUT arrays that would be challenging to achieve with other simulation tools.”

Infineon Nilavazhagan Subbiah, PhD
Staff Engineer, Infineon
 

“With Quanscient Allsolve, we were able to test different parameters to find the working design from the first iteration, saving three months in product development time.”

IXI Antony Hartley
CAE Consultant, IXI
The gap

The unit cell can't show you the array

A unit cell assumes every pillar has identical neighbours, forever. A real array has edges, crosstalk and a diced aperture.

01

Infinite by assumption

Symmetry on every lateral face makes the model an infinite array: useful for the stack, silent on the device.

02

Crosstalk stays invisible

Energy spreads from a driven element into its neighbours, and a periodic model has no neighbours behaving differently.

03

No beam, no steering

Directivity, lateral modes, delays and apodization need a finite, diced aperture to exist at all.

04

The bench comes too late

The array's real behaviour shows up after it is built, when every correction is a manufacturing cycle.

What Allsolve does

Array-scale piezoelectric simulation, fully coupled

One model, all the physics, at array scale — carried from unit cell to finite array without rebuilding anything.

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The whole finite array

Absorbing PMLs replace the symmetry boundaries at the array edges. A 19×19-element array, about 9.1 million degrees of freedom, solves in under an hour on 112 cores.

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Natively coupled physics

Elastic waves, acoustic waves and electrostatics with piezoelectric coupling, solved together in one transient run that covers the whole band.

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Cloud scale, from code

The Python SDK builds and runs models through the API. Everything it creates is still an Allsolve project you can open and check.

Proven on real MUT designs

What that makes possible

Two studies that only become routine when a full array solves in under an hour.

Sub-diced matching layer · Design trade-off

53.8° → 65.7°

−6 dB element beam width, continuous epoxy vs sub-diced

Sub-dicing the matching layer and filling the cuts with silicone rubber widened the element beam by nearly 12°, for about 1.5 dB of peak sensitivity.

Watch the webinar →

AI-driven optimization · Pareto search

69% → 84%

−6 dB fractional bandwidth, with higher sensitivity too

Six stack parameters, two competing objectives, every candidate scored by a simulation. The design nearest the baseline gained bandwidth and sensitivity at once.

Read more about the example →

Real-world examples

FAQ

Piezoelectric array simulation questions

How large a piezoelectric array can Quanscient Allsolve simulate?
The array shown in the piezocomposite webinar was 19×19 elements, about 9.1 million degrees of freedom, and that is not the ceiling. Arrays in the 100-million-DoF range have been run, and a purely acoustic billion-DoF model solved on 3,500 cores in under three minutes. Large models are split with domain decomposition across hundreds or thousands of cloud cores.
How long does a full array model take to solve?
The 9.1-million-DoF, 19×19-element array solved in under an hour on 112 cores; the unit cell behind it solves in 39 seconds on 3 CPUs. At those run times, design studies on full array models are practical before anything is manufactured.
Does a unit-cell model capture crosstalk?
No. Symmetry on every lateral face makes a unit cell an infinite periodic array, so there is nothing for energy to leak into. Crosstalk, lateral modes across a diced aperture, element directivity and beam steering exist only in a finite array model.
How do you get beam patterns without modelling a large volume of water?
Acoustic extrapolation computes pressure outside the simulated domain from a Kirchhoff integral, so on-axis pressure and far-field beam patterns come out at any distance without meshing the propagation path. It is set up in the Allsolve UI as an arc, spot, line or 2D grid of points and drops into an existing model.
Does extrapolation work in inhomogeneous media?
Not currently. Beyond the simulated domain, extrapolation assumes a homogeneous medium with a specified density and velocity, so anything inhomogeneous has to sit inside the simulated region.
Can elements be driven individually for beam steering, or set up for transmit and receive?
Yes. Each element can carry its own electrodes, so elements can be driven independently with delays or apodization to steer and focus, and separate transmit and receive electrodes can be defined with circuits attached to them.
Which physics are coupled, and how are the materials defined?
Elastic waves in the solids, acoustic waves in the fluid, electrostatics with piezoelectric coupling in the PZT and the acoustic–structure interface where they meet, all solved simultaneously in one transient run. PZT is defined by its elasticity matrix and piezoelectric properties; elastic materials such as a silicone kerf fill by density with longitudinal and shear velocities, or by Young's modulus and Poisson's ratio.
Does AI replace the physics?
No. The optimizer proposes designs and decides where to spend compute, but every candidate is scored by an Allsolve simulation and the final designs are verified in Allsolve. Models built through the Python SDK are ordinary Allsolve projects that can be opened in the browser and inspected.
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Resources

Case examples and other resources

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Webinar + PDF summary

Simulating ultrasonic piezocomposite arrays

The unit cell, a 19×19-element array, acoustic extrapolation and a Pareto search, walked through live.

Download PDF summary →

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White paper

MultiphysicsAI for ultrasound transducer design

Thousands of simulations, a surrogate that predicts in milliseconds, and the trade-offs it exposes.

Open the white paper →

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Case example

SAW filter design optimization

A 200-point frequency sweep in 90 seconds instead of 73 minutes, fully coupled.

Read the full article →

Quanscient Allsolve

See how it could work for you

Submit the form to talk with our experts — we'll respond within one business day.

“Quanscient Allsolve's unique capabilities have helped us push the boundaries of what can be simulated in ultrasonic MEMS design.”

Nilavazhagan Subbiah, PhD — Staff Engineer, Infineon

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