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mems-pmut-visaulization
Unlimited scripting
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100x acceleration for versatile multiphysics

electromagnetics-1

Electromagnetics

Motors, superconductors, piezoelectrics, RF antennas, microwave engineering & more. 
mechanics

Mechanics

MEMS design, vibration analysis, general elasticity, nonlinear mechanics Electromagnetics & more.
fluid-dynamics-2-1

Fluid dynamics

Aerodynamics, fluid-structure interaction, microfluidics, laminar flow, turbulent flow & more.

Why Quanscient Allsolve?

Solve 10x faster in 10x more complex simulations.

Runtime from days to coffee breaks.

Run as many simulations in parallel as you like.

Parametric sweeps and optimization problems with blazing speed.

Say goodbye to upfront license costs.

No user limits. No hardware costs.

Work on projects together.

Share your work by sending a link. No licenses required.

Full support every step of the way
  • You can get support directly from the experts on our team. We can provide training, workshops and can even implement simulation models for you.
  • On our documentation site, we offer a collection of tutorial videos and documentation updated weekly.

Our clients are already running 100x faster simulations in

mems-min

MEMS 

Accelerate your MEMS development with Quanscient Allsolve.

READ MORE →

super-min

Superconductors 

Fast and accurate superconductor simulations with Quanscient Allsolve

READ MORE →

electric-min

Electric motors 

Streamline your electric motor simulations with Quanscient Allsolve.

READ MORE →

Specific cases where Quanscient Allsolve delivers

Proven speedups in multiple use cases across various industries.
mems-capacitive-accelerometer
Mode shapes of MEMS capacitive accelerometer

The first six mode shapes of the moving parts of the MEMS capacitive accelerometer are obtained. The four corners of the serpentine springs are anchored for the eigen mode analysis.

Large scale PMUT array simulation
Large scale PMUT array 15x15

The acoustic pressure radiated by 225 PMUTs resonating at 1 MHz is simulated. A thin piezoelectric layer (PZT crystal) is electrically actuated and vibrates a thin silicon membrane that acts as an ultrasound transducers.

IDT Finger device
Comb drives:
IDT finger device

The mechanical deflection of an electrostatically actuated comb drive is simulated. The nonlinear electrostatic force created by an electric potential difference is at the origin of the mechanical displacement.

SAW device
RF filters:
SAW device

The electric actuation of a piezoelectric IDT emits GHz-range elastic waves. The piezo-elastic physics are strongly coupled and the PZT and silicon wafer anisotropic behavior is taken into account.

backbone-curve
Backbone curve

Nonlinear frequency analysis (harmonic-balance) for general MEMS devices without limit on the Q-factor. No transient simulation required.

See the related publication.

accelometer-auto
GDS2 format drag and drop

Use your existing GDS2 files or draw your MEMS in the widely-used Klayout software then export as GDS2. Drag and drop the file into Quanscient Allsolve to automatically show in 3D your MEMS geometry.

ultrasound-waves-simulation-2-1
Nonlinear acoustics frequency analysis

An array of 16 transducers focuses 40 kHz ultrasound waves for-mid air haptic feedback. The pressure spot in air is so intense that nonlinear acoustic phenomena arise, such as a saw-tooth waveform. 

viscoelaticity
Viscoelasticity with PMLs

A 5 MHz wave travels through two materials respectively modeled as viscoelastic (generalized Maxwell model using 18 series of spring-dashpot branches) and elastic. PMLs surround the geometry to let the waves leave without artificial reflections.

Superconducting tube
High temperature superconductor

A thin superconducting tube is subject to an applied magnetic field that increases over time. As the magnetic field is increased it progressively penetrates in the tube until the tube is not able to perfectly shield its interior volume anymore.

Synchronous electric motor
Synchronous electric motor

The induction field and the motor torque of a permanent magnet synchronous electric motor are calculated for an increasing mechanical angle. Only 1/8 of the geometry has to be simulated (anti-periodicity). 

pmsmpadapt
Electric motor,
P-adativity

The interpolation order (right) in this PMSM magnetic field simulation is adapted to every mesh element based on an input criterion (e.g. field gradient). For a given accuracy this speeds up the simulation since the computational effort is added only where needed.

PZT crystal orientation
Influence of SI/PZT crystal orientation

A piezoelectric PZT layer grown on a monocrystalline silicon wafer is sandwiched between two electrically actuated electrodes, creating a harmonic deflection of the bilayer. The crystal orientation of both the PZT and the silicon can be changed to any direction.

Piezoresistor
Piezoresistor, nonmatching meshes

The deflection of a monocrystalline silicon cantilever causes a change in the resistance of the doped (piezoresistive) conducting track in it. The cantilever and track meshes do not match, field interpolation has to be used.

pmutaxisymair
Fluid coupled piezo actuated MEMS

A piezoelectric actuated micromembrane (PMUT) outputs ultrasound pressure waves in air. The simulation is performed in 2D using axisymmetry.

fsimicropillar
Fluid-structure interaction

A pair of micropillars placed in a microchannel bend due to a forced inlet water velocity. Geometric nonlinearity is taken into account in the mechanical model. A Laplace formulation is used to smooth the deformed fluid mesh.

viscousflow-1
Fluid flow in a microvalve

The flow speed magnitude (top) and the pressure field (bottom, 100 Pa at left inlet and 0 Pa at right outlet) are computed for a low Reynolds (Stokes) flow in a microvalve.

thermoacoustic
Thermoacoustics in a deformable cavity

The transient thermoacoustic response to a 0.1 us laser pulse in a 500 um deformable cavity with ambient air on top is simulated. The fields displayed are the fluid pressure, velocity, temperature and membrane deformation.

cmutcollapsemode
Contact mechanics, collapsed CMUT

The collapse mode of a CMUT ultrasonic transducer is simulated (in collapse mode the membrane touches the bottom of the cavity). The static deflection as well as the small signal vibration are simulated and illustrated on the image.

disk eigenmodes
Damped mechanical resonance modes

The damped eigenmodes and eigenfrequencies are obtained for a 3D disk clamped at its side. A proportional damping is used to model losses.

nl geomodes
Buckling, geometric nonlinearity

A prestressed 3D bilayer micromembrane is pushed downwards by the atmospheric pressure. The static deflection and resonance frequency shift is simulated thanks to a small-strain geometric nonlinearity formulation. This example can be adapted to simulate buckling in time.

General periodic conditions
General periodic conditions

The crosstalk between a central micromembrane and 6 neighbours is analyzed on only 1/6 of the geometry using a periodic condition between two faces with non-matching meshes. The available mortar finite element method allows to implement general periodic conditions.

Resistance and capacitance
Resistance and capacitance

The resistance and capacitance is computed for a 3D geometry made of a conducting trace connected to a circular-shaped, parallel-plate air capacitor. The simulated capacitance matches the parallel plate formula. The quadrature electric potential field is displayed on the picture above.

electric circuit coupling
Ports, electric circuit coupling

Lumped electric circuit elements can be accurately calculated from a FEM simulation or coupled to it in a strong or weak way. Additional lumped operations like computing mechanical reaction forces can be treated with the same tools.

A-V and H-phi formulation
A-v and H-phi formulation

The magnetic field and induction created by AC currents in three wires is simulated using an A-v and a H-phi formulation. Cohomology cuts are required in the H-phi case. The picture shows the magnetic induction field, the current density in each wire and the cuts.

magind
Magnetic induction, skin effect

An AC voltage is applied to a coil surrounding an aluminium tube in which currents are induced. In the current density cut displayed on the right, the skin effect in the thick copper wire of the coil is clearly visible.



Static magnetic saturation
Static magnetic saturation

A magnetic steel shell surrounds two insulated copper conductors with DC currents flowing in opposite directions. For large currents the shell is saturated. An iterative resolution of the A-v formulation is used to solve this nonlinear problem.

Permanent magnets
Permanent magnets, magnetic force

The static magnetic field created by an array of permanent magnets is simulated using the scalar magnetic potential formulation. The Halbach configuration shows as expected a magnetic field strength increase. The potential and the magnetic field lines are illustrated.

Magnetic stresses, magnetostriction
Magnetic stresses, magnetostriction

The magnetic stress state created by a DC current flow in a choke (inductor) is computed. The corresponding mechanical deformation is deduced. Magnetostrictive stresses are taken into account.

magstatvecpot3dtop-1
Magnetic shielding of a DC current

A 3D steel cylinder is placed nearby a wire with a given static current density. The magnetic vector potential formulation is used. A gauge condition is added in combination with a spanning tree to remove the singular matrix problem associated with the formulation.


heating tungsten DC current
Conductor heating due to DC current

A voltage is applied across a 3D tungsten conductor in vacuum. The (strong) DC current flow as well as the induced thermal heating (displayed) is simulated. The influence of the temperature on the material properties is taken into account with a nonlinear loop.

photonic waveguide
Optical waveguide coupling modes

The coupling (eigen)modes between two photonic SiN waveguides in a SiO2 cladding are calculated. The waveguide is designed for optical frequencies.

electromagnetic waveguide
Electromagnetic waveguide

A cross shaped perfectly conducting 3D waveguide is excited with an imposed electric field at one end.

dipoleantenna
Half-wave dipole antenna

The 1 GHz electromagnetic wave radiation of a half-wave dipole antenna is simulated. The electric field, magnetic field and Poynting vector are computed and can be visualized in time.

Stabilized advection diffusion
Stabilized advection diffusion

This is a sandbox example for stabilized (advection dominated) advection-diffusion problems. The isotropic, streamline anisotropic, SPG, SUPG, crosswind and crosswind-shockwave stabilization methods are predefined.

handconvection
Natural convection, hp-adaptivity 

The natural convection created by a hot disk in a colder air environment is simulated using hp-adaptivity. The fully compressible flow is considered and solved in time.

double diffusion
Double diffusion of salt fingers

A coupled thermal-salt concentration advection-diffusion problem is simulated in time in presence of a gravity force. The picture shows the appearing salt fingers as well as the density inversion phenomenon.

laminarflow
Laminar flow, hp-adaptivity

The nonlinear Navier-Stokes equations for incompressible laminar flow are solved with a Newton iteration to simulate the water flow past a step in a 1 mm pipe. HP-adaptivity is used. The top image is the flow velocity, the bottom image is the adapted mesh.

macnumber
Potential air flow around an airfoil

A NACA0012 airfoil is put in a subsonic air flow. The problem is nonlinear because the air density is a function of the air speed. The picture shows the Mach number everywhere around the airfoil.

von Karman vortex street
Unsteady fluid flow past an obstacle

The fluid flow past an obstacle is simulated in time with DNS for an increasing inlet velocity. A von Karman vortex street appears at a high enough inlet velocity.

stiffnessversustemperature
Working with experimental data

The deflection of a steel disk with a non-uniform temperature profile is calculated: the stiffness versus temperature dependence is obtained by interpolating between experimental data samples using natural cubic splines.

Specific cases where Quanscient Allsolve delivers

Proven speedups in multiple use cases across various industries.
mems-capacitive-accelerometer
Mode shapes of MEMS capacitive accelerometer

The first six mode shapes of the moving parts of the MEMS capacitive accelerometer are obtained. The four corners of the serpentine springs are anchored for the eigen mode analysis.

Large scale PMUT array simulation

Large scale PMUT array 15x15

The acoustic pressure radiated by 225 PMUTs resonating at 1 MHz is simulated. A thin piezoelectric layer (PZT crystal) is electrically actuated and vibrates a thin silicon membrane that acts as an ultrasound transducers.

IDT Finger device

Comb drives:
IDT finger device

The mechanical deflection of an electrostatically actuated comb drive is simulated. The nonlinear electrostatic force created by an electric potential difference is at the origin of the mechanical displacement.

SAW device

RF filters:
SAW device

The electric actuation of a piezoelectric IDT emits GHz-range elastic waves. The piezo-elastic physics are strongly coupled and the PZT and silicon wafer anisotropic behavior is taken into account.

backbone-curve

Backbone curve

Nonlinear frequency analysis (harmonic-balance) for general MEMS devices without limit on the Q-factor. No transient simulation required.

See the related publication.

accelometer-auto

GDS2 format drag and drop

Use your existing GDS2 files or draw your MEMS in the widely-used Klayout software then export as GDS2. Drag and drop the file into Quanscient Allsolve to automatically show in 3D your MEMS geometry.

ultrasound-waves-simulation-2-1

Nonlinear acoustics frequency analysis

An array of 16 transducers focuses 40 kHz ultrasound waves for-mid air haptic feedback. The pressure spot in air is so intense that nonlinear acoustic phenomena arise, such as a saw-tooth waveform. 

viscoelaticity

Viscoelasticity with PMLs

A 5 MHz wave travels through two materials respectively modeled as viscoelastic (generalized Maxwell model using 18 series of spring-dashpot branches) and elastic. PMLs surround the geometry to let the waves leave without artificial reflections.

More examples
 
Superconducting tube
High temperature superconductor

A thin superconducting tube is subject to an applied magnetic field that increases over time. As the magnetic field is increased it progressively penetrates in the tube until the tube is not able to perfectly shield its interior volume anymore.

 

Synchronous electric motor
Synchronous electric motor

The induction field and the motor torque of a permanent magnet synchronous electric motor are calculated for an increasing mechanical angle. Only 1/8 of the geometry has to be simulated (anti-periodicity). 

 
pmsmpadapt
Electric motor,
P-adativity

The interpolation order (right) in this PMSM magnetic field simulation is adapted to every mesh element based on an input criterion (e.g. field gradient). For a given accuracy this speeds up the simulation since the computational effort is added only where needed.

PZT crystal orientation
Influence of SI/PZT crystal orientation

A piezoelectric PZT layer grown on a monocrystalline silicon wafer is sandwiched between two electrically actuated electrodes, creating a harmonic deflection of the bilayer. The crystal orientation of both the PZT and the silicon can be changed to any direction.

 

 

Piezoresistor
Piezoresistor, nonmatching meshes

The deflection of a monocrystalline silicon cantilever causes a change in the resistance of the doped (piezoresistive) conducting track in it. The cantilever and track meshes do not match, field interpolation has to be used.

 

 

pmutaxisymair-1

Fluid coupled piezo actuated MEMS

A piezoelectric actuated micromembrane (PMUT) outputs ultrasound pressure waves in air. The simulation is performed in 2D using axisymmetry.

 

 

fsimicropillar

Fluid-structure interaction

A pair of micropillars placed in a microchannel bend due to a forced inlet water velocity. Geometric nonlinearity is taken into account in the mechanical model. A Laplace formulation is used to smooth the deformed fluid mesh.

 

 

viscousflow-1

Fluid flow in a microvalve

The flow speed magnitude (top) and the pressure field (bottom, 100 Pa at left inlet and 0 Pa at right outlet) are computed for a low Reynolds (Stokes) flow in a microvalve.

 

 

thermoacoustic

Thermoacoustics in a deformable cavity

The transient thermoacoustic response to a 0.1 us laser pulse in a 500 um deformable cavity with ambient air on top is simulated. The fields displayed are the fluid pressure, velocity, temperature and membrane deformation.

 

cmutcollapsemode

Contact mechanics, collapsed CMUT

The collapse mode of a CMUT ultrasonic transducer is simulated (in collapse mode the membrane touches the bottom of the cavity). The static deflection as well as the small signal vibration are simulated and illustrated on the image.

 

 

disk eigenmodes

Damped mechanical resonance modes

The damped eigenmodes and eigenfrequencies are obtained for a 3D disk clamped at its side. A proportional damping is used to model losses.

 

 

nl geomodesBuckling, geometric nonlinearity

A prestressed 3D bilayer micromembrane is pushed downwards by the atmospheric pressure. The static deflection and resonance frequency shift is simulated thanks to a small-strain geometric nonlinearity formulation. This example can be adapted to simulate buckling in time.

 

 

General periodic conditions

General periodic conditions

The crosstalk between a central micromembrane and 6 neighbours is analyzed on only 1/6 of the geometry using a periodic condition between two faces with non-matching meshes. The available mortar finite element method allows to implement general periodic conditions.

 

Resistance and capacitance

Resistance and capacitance

The resistance and capacitance is computed for a 3D geometry made of a conducting trace connected to a circular-shaped, parallel-plate air capacitor. The simulated capacitance matches the parallel plate formula. The quadrature electric potential field is displayed on the picture above.

 

 

electric circuit coupling

Ports, electric circuit coupling

Lumped electric circuit elements can be accurately calculated from a FEM simulation or coupled to it in a strong or weak way. Additional lumped operations like computing mechanical reaction forces can be treated with the same tools.

 

 

A-V and H-phi formulation

A-v and H-phi formulation

The magnetic field and induction created by AC currents in three wires is simulated using an A-v and a H-phi formulation. Cohomology cuts are required in the H-phi case. The picture shows the magnetic induction field, the current density in each wire and the cuts.

 

 

magind

Magnetic induction, skin effect

An AC voltage is applied to a coil surrounding an aluminium tube in which currents are induced. In the current density cut displayed on the right, the skin effect in the thick copper wire of the coil is clearly visible.

 

Static magnetic saturation

Static magnetic saturation

A magnetic steel shell surrounds two insulated copper conductors with DC currents flowing in opposite directions. For large currents the shell is saturated. An iterative resolution of the A-v formulation is used to solve this nonlinear problem.

 

 

Permanent magnets

Permanent magnets, magnetic force

The static magnetic field created by an array of permanent magnets is simulated using the scalar magnetic potential formulation. The Halbach configuration shows as expected a magnetic field strength increase. The potential and the magnetic field lines are illustrated.

 

 

Magnetic stresses, magnetostriction

Magnetic stresses, magnetostriction

The magnetic stress state created by a DC current flow in a choke (inductor) is computed. The corresponding mechanical deformation is deduced. Magnetostrictive stresses are taken into account.

 

 

magstatvecpot3dtop-1

Magnetic shielding of a DC current

A 3D steel cylinder is placed nearby a wire with a given static current density. The magnetic vector potential formulation is used. A gauge condition is added in combination with a spanning tree to remove the singular matrix problem associated with the formulation.

 

heating tungsten DC current

Conductor heating due to DC current

A voltage is applied across a 3D tungsten conductor in vacuum. The (strong) DC current flow as well as the induced thermal heating (displayed) is simulated. The influence of the temperature on the material properties is taken into account with a nonlinear loop.

 

 

photonic waveguide

Optical waveguide coupling modes

The coupling (eigen)modes between two photonic SiN waveguides in a SiO2 cladding are calculated. The waveguide is designed for optical frequencies.

 

 

electromagnetic waveguide

Electromagnetic waveguide

A cross shaped perfectly conducting 3D waveguide is excited with an imposed electric field at one end.

 

 

dipoleantenna

Half-wave dipole antenna

The 1 GHz electromagnetic wave radiation of a half-wave dipole antenna is simulated. The electric field, magnetic field and Poynting vector are computed and can be visualized in time.

 

Stabilized advection diffusion

Stabilized advection diffusion

This is a sandbox example for stabilized (advection dominated) advection-diffusion problems. The isotropic, streamline anisotropic, SPG, SUPG, crosswind and crosswind-shockwave stabilization methods are predefined.

 

 

handconvection
 

Natural convection, hp-adaptivity 

The natural convection created by a hot disk in a colder air environment is simulated using hp-adaptivity. The fully compressible flow is considered and solved in time.

 

 

double diffusion

Double diffusion of salt fingers

A coupled thermal-salt concentration advection-diffusion problem is simulated in time in presence of a gravity force. The picture shows the appearing salt fingers as well as the density inversion phenomenon.

 

 

laminarflow

Laminar flow, hp-adaptivity

The nonlinear Navier-Stokes equations for incompressible laminar flow are solved with a Newton iteration to simulate the water flow past a step in a 1 mm pipe. HP-adaptivity is used. The top image is the flow velocity, the bottom image is the adapted mesh.

 

 

macnumber
 

Potential air flow around an airfoil

A NACA0012 airfoil is put in a subsonic air flow. The problem is nonlinear because the air density is a function of the air speed. The picture shows the Mach number everywhere around the airfoil.

 

 

von Karman vortex street

Unsteady fluid flow past an obstacle

The fluid flow past an obstacle is simulated in time with DNS for an increasing inlet velocity. A von Karman vortex street appears at a high enough inlet velocity.

 

 

stiffnessversustemperature
 

Working with experimental data

The deflection of a steel disk with a non-uniform temperature profile is calculated: the stiffness versus temperature dependence is obtained by interpolating between experimental data samples using natural cubic splines.

 



Quanscient Allsolve roadmap

Next three years
Quantum-accelerated simulations. Seamless integration and automation for simulations in design workflow.
This year
Cloud API for Quanscient Allsolve. Cloud-based FEM for accelerating CFD simulations.
June 2023
Quanscient Allsolve v.1.2. Extruded meshing, optimized simulations startup-time, account management
March 2023
Quanscient Allsolve v.1.1. Parametric sweeps, usability improvements, script documentation
October 2022
The first version of Quanscient Allsolve is officially launched with a focus on electromagnetics
August 2022
First Early Access users are onboarded

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