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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.

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

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

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.

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

See the related publication.

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.

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.

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.

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.

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).

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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

See the related publication.

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.

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.

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.

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.

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).

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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