Stellarators present features such as steady-state operation and intrinsic stability that make them more attractive than tokamaks in their scaling to fusion power plants. By leveraging more possible configurations, stellarators can be optimized for better engineering feasibility, e.g., resilience to manufacturing tolerances, reduced mechanical load on conductor, material optimization, cost of fabrication. Finite Element Analyses are crucial for the design and optimization of High-Temperature Superconducting (HTS) REBCO non-planar coils. However, accurate simulation of large-scale magnetostatic, mechanical, and quench models can take days or even weeks to compute. In this work, we present a model of a real-size, HTS, non-insulated, non-planar stellarator coil and perform in Quanscient Allsolve, a transient simulation study including modelling quench, using the $H - \varphi $ formulation. It is shown that transient model benefits heavily from the built-in Domain Decomposition Method (DDM), which allows reaching reasonable computation times. Such models become then invaluable in predicting and understanding the complex behavior of non-insulated large-scale REBCO magnets, including their intrinsic energy imbalance.

Coated conductors based on high temperature superconductors (HTS), such as rare-earth barium copper oxide tapes, are expected to enable future electromagnetic applications to reach magnetic fields beyond 20 T. Understanding their mechanical behavior is crucial, but choosing the right tools and modeling methods can be challenging. This work introduces a new open-source simulation tool that can be used to analyze the strain and stress in HTS tapes. The built-in structural elastic solver in this multiphysics C++ based finite element library is enhanced with a linear hardening elastoplastic method by us. It also offers flexibility for future expansion based on user needs. Detailed and homogenized HTS tape models are explored using the mechanical model with both elastic and elastoplastic analyses. By comparing different approaches, the optimal method can be identified for specific applications. We believe this methodology and tool have the potential for large-scale electromagnetic applications, for instance solenoids and magnets, with the ability to be tailored to specific requirements.

Ultrasound transducers have diverse applications in medical imaging, consumer electronics, and automotive industries, offering advantages such as non-invasive medical imaging, reliable and non-mechanical transduction of input signals. Micro-Electro-Mechanical Systems (MEMS) based ultrasound transducer solutions, including Piezoelectric Micromachined Ultrasound Transducer (PMUT) and Capacitive Micromachined Ultrasound Transducer (CMUT) devices, exhibit superior performance compared to traditional piezo-ceramic based solutions due to their low cost, compact design, high efficiency and wideband operation capability, furthermore monolithic integration with electronics is possible. However, the development of these cutting-edge technologies requires sophisticated simulation tools to understand and manipulate the underlying ultrasound physics, which is essential for engineering applications. The newly developed simulation methodology will be utilized to model three-dimensional arrays of CMUT and PMUT cells. Simulations are performed on cutting-edge designs of Infineon-developed chips using the Quanscient Allsolve software. The results obtained through resonance frequency measurements on PMUT devices and CMUT devices will be evaluated and compared with the simulation results obtained using the presented methodology. Additional capabilities on building ultrasound simulation models with multiphysics is elaborated in this work and demonstrated. Projections for further development in the simulation environment arc also presented.

The use of the classical finite element method (FEM) to solve problems with magnetic composites leads to huge linear systems that are impossible to solve. Instead, homogenization and multiscale methods are often used with the composite material replaced by a homogeneous material with the homogenized constitutive law obtained by solving cell-problems representing the mesoscale material structure. For non-linear time-dependent problems, FEM is often used with a time-transient method (TTM) and the solution is obtained one time-step at a time. However, in cases where a steady-state solution is of interest, the multiharmonic method can be faster and more cost effective for the same accuracy of the time discretization. In addition, when solving magnetoquasistatic multiscale problems with TTM, the dynamic hysteresis in the homogenized fields can slow down or even impede the convergence of the macro-scale problem due to the possibly non-continuously differentiable homogenized material laws. This work presents a novel robust modelling approach for non-linear magnetoquasistatic problems combining multiharmonic method with the multiscale method.

Design and modeling of a stellarator fusion reactor is a multidisciplinary effort that requires a tight integration between simulation of highly nonlinear multi-physics and representation of non-planar complex geometries. The critical current calculation and the design of the mechanical structures are among the most crucial aspects as they set size, cost, and time to build the stellarator. Because of the asymmetric and non-planar nature of its components the modeling of such figures of merit needs to be carried out at large scale, without the possibility of taking advantage of any particular symmetry. In this work we develop a three-dimensional model for the analysis of the magnetic field and forces, necessary for such considerations, for complex coil geometries, such as stellarators, where a two-dimensional approach can not provide accurate analyses and verification of assumptions. Moreover, this method can quickly generate a large amount of critical modeling data (e.g. Lorentz load, displacement and stresses) that could be integrated into a workflow for coil design optimization based on machine learning or other recent optimization tools.

Due to the highly nonlinear electrical resistivity of high temperature superconducting (HTS) materials, computing the steady-state eddy current losses in HTS tapes, under time-periodic alternating current excitation, can be time consuming when using a time-transient method (TTM). The computation can require several periods to be solved with a small time-step. One alternative to the TTM is the multiharmonic method (MHM) where the Fourier basis is used to approximate the Maxwell fields in time. The method allows obtaining the steady-state solution to the problem with one resolution of the nonlinear problem. In this work, using the finite element method with the $H-\varphi$ formulation, the capabilities of the MHM in the computational eddy current loss modeling of HTS tapes are scrutinized and compared against the TTM.

Multilayer 2G high-temperature superconductor (HTS) tapes undergo various mechanical loading steps as part of a superconducting magnet operation. The mechanical loading steps include cool-down to cryogenic temperatures and Lorentz forces when powering up the magnets. Studying the mechanical behavior of the constituent layers in a HTS tape can reveal the strain or stress level in each layer and help in predicting the probability of mechanical failure or critical current degradation. A detailed finite element method (FEM)-based simulation models enable us to estimate the mechanical behavior in each layer. However, defining the model parameters for material mechanical properties or thickness of each material layer can have considerable uncertainty due to variation in manufacturing processes and missing measurements of material properties within these tapes. The material properties in thin layers may not exactly comply with bulk materials of the same kind. In this paper we present a sensitivity analysis for mechanical behavior dependence on material properties variation in the constituent layers of a HTS tape. The results give important insight about the accuracy and reliability of mechanical simulation results and guide the priorities in future material characterization. In addition, we will investigate the effect of the thickness of Hastelloy layer on effective macroscopic mechanical behavior of the tape. A nonlinear elastoplastic FEM model is used for performing the simulations.

The growing interest in the modeling of superconductors has led to the development of effective numerical methods and software. One of the most utilized approaches for magnetoquasistatic simulations in applied superconductivity is the $H$ formulation. However, due to the large number of degrees of freedom (DOFs) present when modeling large and complex systems (e.g. large coils for fusion applications, electrical machines, and medical applications) using the standard $H$ formulation on a desktop machine becomes infeasible. The $H$ formulation solves the Faraday's law formulated in terms of the magnetic field intensity $\mathbf {H}$ using edge elements in the whole modeling domain. For this reason, a very high resistivity is assumed for the non-conducting domains, leading to an ill-conditioned system matrix and therefore long computation times. In contrast, the $H$ - $\phi$ formulation uses the $H$ formulation in the conducting region, and the $\phi$ formulation (magnetic scalar potential) in the surrounding non-conducting domains, drastically reducing DOFs and computation time. In this work, we use the $H$ - $\phi$ formulation in 2D for the magnetothermal (AC losses and quench) analysis of stacks of REBCO tapes. The same approach is extended to a 3D case for the AC loss analysis of a twisted superconducting wire. All the results obtained by simulations in Sparselizard are compared with results obtained with COMSOL. Our custom tool allows us to distribute the simulations over hundreds of CPUs using domain decomposition methods, considerably reducing the simulation times without compromising accuracy.

This paper demonstrates an 11-by-11 PMUT array used as a high-bandwidth receiver and transmitter developed for underwater communications. The array is composed of a randomized distribution of elements with three different diameters. While each individual element has its own unique resonance frequency - around 61, 66 or 73 kHz depending on its dimensions - and a bandwidth around 5 kHz in water, the combination of multiple sizes within the same array is shown to result in an average frequency response exhibiting a single resonance peak around 63 kHz with a fractional bandwidth up to 18% in water. A transmit efficiency of 1.6 Pa/V is achieved at 10 cm, combined with a receive sensitivity of 0.23 μV/Pa.

This paper presents a Piezoelectric Micromachined Ultrasonic Transducer (PMUT) array targeting mid-air haptic feedback applications. Compared to existing bulk ultrasound transducer technologies, this array implements polymer-based micromachined ultrasound transducers fabricated in a display-compatible, large area technology. It is, thus, a good candidate for direct integration on top of large displays and allows to fabricate dense PMUT arrays for a fine non-contact haptic experience at interesting price point.

Multi-frequency piezoelectric micromachined transducer (PMUT) arrays have the potential to assist long-term monitoring with high resolution images at large penetration depth, paving the way for early diagnosis, follow-up and treatment. In this paper, we have demonstrated the design and characterization of multi-frequency polymer-based PMUT arrays intended for aforementioned applications. Starting from single PMUT devices, the resonance frequencies and mode shapes characterized in water agree well with the simulated counterparts. Based on these results, PMUT devices of 320 μm and 400 μm are selected to build up PMUT array. First, the maximum axial pressure of one 5×5 PMUT array has been measured in water at a frequency sweep of 1.7-20MHz. Moreover, the measured pressure map of a 16×32 PMUT array remains aligned with the acoustic simulation result. As an important step towards imaging applications, the pulse echo signal of the same PMUT array has been characterized by using a plate phantom in water.

In this paper, a physically representative electric equivalent lumped model of a fabricated 600 um diameter polymer-based piezoelectric micromachined ultrasonic transducer (PMUT) is detailed. All parameter values in the lumped model are identified based on electrical impedance measurements in air and in vacuum. The model is then used to predict the emitted ultrasound pressure, the radiated acoustic power and the overall power efficiency. The predictions are validated with experimental data and finite element simulations. Finally, the model is used to estimate the minimum PMUT array size required to reach the expected haptic sensing threshold at a given focus point.

This paper deals with the design, simulation and characterization of polymer-based piezoelectric micromachined ultrasound transducers (PMUT) (arrays) intended for short-range gesture recognition applications. The presented process flow is fully compatible with existing flat-panel display fabrication. Finite element models were developed for the evaluation of the frequency response, deflection and acoustic pressure output of single PMUT as a function of the membrane diameter. A laser Doppler vibrometer was used to measure the frequency response, membrane velocity and displacement, as well as mode shapes of the microfabricated PMUT in air. An optical microphone was used to measure the pressure emitted by a single PMUT at various distances along the normal axis of the oscillating membrane. A strong correlation between simulations and measurement results is shown. The device geometries most suitable for short-range gesture recognition purposes are selected and the radiation pattern of square arrays is analyzed using simulations. The resonance properties of single PMUT in an array are determined using measurements. An optimized array is used to demonstrate pulse-echo measurements, and the requirements for a simple gesture recognition platform are elucidated.

Mid-air acoustic holographic techniques allow the tempo-spatial reconstruction of the desired wave profile (in amplitude and/or phase), driving novel applications such as particle trapping and haptics in air. Piezoelectric micro-machined ultrasound transducer (pMUT) remains promising for these applications due to its potential to build up high density, cost effective phase arrays compatible with drive electronics. For this purpose, we characterized in-house fabricated discrete pMUT devices and assumed each element of pMUT phase array performs the same in this paper. Using these parameters as input of $25 \times 25$ pMUT arrays, we mainly demonstrated three different acoustic projection methodologies for reconstructing mid-air acoustic holograms 1 cm distant from the aperture by simulations: pure pseudo-inverse (PINV) algorithm, PINV algorithms together with iterative weighting, PINV methods integrated with Tikhonov regularization. The resulting drive performance of pMUT array, calculated as transducer drive efficiency for variant acoustic holograms, was increased by 3-6 times when adding iterative weighting or Tikhonov regularization. The trade-off was the side lobes distributed across the final pressure field compared to the reference of PINV but Tikhonov regularization outperformed iterative weighting especially in the central region.

This paper describes a robust and efficient method to obtain the steady-state, nonlinear behaviour of large arrays of electrically actuated micromembranes vibrating in a fluid. The nonlinear electromechanical behaviour and the multiple vibration harmonics it creates are fully taken into account thanks to a multiharmonic finite element formulation, generated automatically using symbolic calculation. A domain decomposition method allows to consider large arrays of micromembranes by efficiently distributing the computational cost on parallel computers. Two- and three-dimensional examples highlight the main properties of the proposed method.

This paper describes a method to automatically derive multiharmonic finite element formulations for coupled, nonlinear electromechanical problems. It focuses on models of electrically actuated micromembranes using both a staggered and a monolithic Newton iteration scheme. Two- and three-dimensional examples highlight the main properties of the proposed method.

This paper compares linearly as well as nonlinearly preconditionned domain decomposition methods for nonlinear, coupled electrovibromechanical problems. The iteration unknowns for the domain decomposition are either taken only at the subdomain interfaces or in the whole volume. Both staggered and monolithic electrostatic/elastic/acoustic formulations are considered for the multiphysics problem. Because of the nonlinearity a pure harmonic excitation leads to multiple harmonics in the displacement field, in the pressure field and in the electric potential. A novel multiharmonic resolution method is used to automatically generate the required multiharmonic formulations and thus avoid the need of time-stepping to reach steady state.