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This paper presents a framework for the simultaneous application of shape and topology optimization in electro-mechanical design problems. Whereas the design variables of a shape optimization are the geometrical parameters of the CAD description, the design variables upon which density-based topology optimization acts represent the presence or absence of material at each point of the region where it is applied. These topology optimization design variables, which are called densities , are by essence substantial quantities. This means that they are attached to matter while, on the other hand, shape optimization implies ongoing changes of the model geometry. An appropriate combination of the two representations is therefore necessary to ensure a consistent design space as the joint shape-topology optimization process unfolds. The optimization problems dealt with in this paper are furthermore constrained to verify the governing partial differential equations (PDEs) of a physical model, possibly nonlinear, and discretized by means of, e.g., the finite element method (FEM). Theoretical formulas, based on the Lie derivative, to express the sensitivity of the performance functions of the optimization problem, are derived and validated to be used in gradient-based algorithms. The method is applied to the torque ripple minimization in an interior permanent magnet synchronous machine (PMSM).

We present a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering by large, convex obstacles. This algorithm combines the use of an ansatz for the unknown density in a boundary-integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. We include numerical results illustrating the high-order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases.

In this paper, we study a high-order finite element approach to simulate an ultrahigh finesse Fabry-Pérot superconducting open resonator for cavity quantum electrodynamics. Because of its high quality factor, finding a numerically converged value of the damping time requires an extremely high spatial resolution. Therefore, the use of high-order simulation techniques appears appropriate. This paper considers idealized mirrors (no surface roughness and perfect geometry, just to cite a few hypotheses), and shows that under these assumptions, a damping time much higher than what is available in experimental measurements could be achieved. In addition, this work shows that both high-order discretizations of the governing equations and high-order representations of the curved geometry are mandatory for the computation of the damping time of such cavities.

Sweeping-type algorithms have recently gained a lot of interest for the solution of highfrequency time-harmonic wave problems, in particular when used in combination with perfectly matched layers. However, an inherent problem with sweeping approaches is the sequential nature of the process, which makes them inadequate for efficient implementation on parallel computers. We propose several improvements to the double-sweep preconditioner originally presented in [18], which uses sweeping as a matrix-free preconditioner for a Schwarz domain decomposition method. Similarly, the improved preconditioners are based on approximations of the inverse of the Schwarz iteration operator: the general methodology is to apply well-known algebraic techniques to the operator seen as a matrix, which in turn is processed to obtain equivalent matrix-free routines that we use as preconditioners. A notable feature of the new variants is the introduction of partial sweeps that can be performed concurrently in order to make a better usage of the resources. As these modifications still leave some unexploited computational power, we also propose to combine them with right-hand side pipelining to further improve parallelism and achieve significant speed-ups. Examples are presented on high-frequency Helmholtz and Maxwell problems, in two and three dimensions, to demonstrate the properties of our improvements on parallel computer architectures.

Accurate electromagnetic modeling of the head of a subject is of main interest in the fields of source reconstruction and brain stimulation. Those processes rely heavily on the quality of the model and, even though the geometry of the tissues can be extracted from magnetic resonance images (MRI) or computed tomography (CT), their physical properties such as the electrical conductivity are difficult to measure with non intrusive techniques. In this paper, we propose a tool to assess the uncertainty in the model parameters, the tissue conductivity, as well as compute a parametric forward models for electroencephalography (EEG) and transcranial direct current stimulation (tDCS) current distribution.

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.

A homology and cohomology solver for finite element meshes is represented. It is an integrated part of the finite element mesh generator Gmsh. We demonstrate the exploitation of the cohomology computation results in a finite element solver and use an induction heating problem as a working example. The homology and cohomology solver makes the use of a vector-scalar potential formulation straightforward. This gives better overall performance than a vector potential formulation. Cohomology computation also clarifies the lumped parameter coupling of the problem and enables the user to obtain useful postprocessing data as a part of the finite element solution. [PUBLICATION ABSTRACT]

This work uses multi-material topology optimization (MMTO) to maximize the average torque of a 3-phase permanent magnet synchronous machine (PMSM). Eight materials are considered in the stator: air, soft magnetic steel, three electric phases, and their three returns. To address the challenge of designing a 3-phase PMSM stator, a generalized density-based framework is used. The proposed methodology places the prescribed material candidates on the vertices of a convex polytope, interpolates material properties using Wachspress shape functions, and defines Cartesian coordinates inside polytopes as design variables. A rational function is used as penalization to ensure convergence towards meaningful structures, without the use of a filtering process. The influences of different polytopes and penalization parameters are investigated. The results indicate that a hexagonal-based diamond polytope is a better choice than the classical orthogonal domains for this MMTO problem. In addition, the proposed methodology yields high-performance designs for 3-phase PMSM stators by implementing a continuation method on the electric load angle.

Purpose The purpose of this paper is to deal with the correction of the inaccuracies near edges and corners arising from thin shell models by means of an iterative finite element subproblem method. Classical thin shell approximations of conducting and/or magnetic regions replace the thin regions with impedance-type transmission conditions across surfaces, which introduce errors in the computation of the field distribution and Joule losses near edges and corners. Design/methodology/approach In the proposed approach local corrections around edges and corners are coupled to the thin shell models in an iterative procedure (each subproblem being influenced by the others), allowing to combine the efficiency of the thin shell approach with the accuracy of the full modelling of edge and corner effects. Findings The method is based on a thin shell solution in a complete problem, where conductive thin regions have been extracted and replaced by surfaces but strongly neglect errors on computation of the field distribution and Joule losses near edges and corners. Research limitations/implications This model is only limited to thin shell models by means of an iterative finite element subproblem method. Originality/value The developed method is considered to couple subproblems in two-way coupling correction, where each solution is influenced by all the others. This means that an iterative procedure between the subproblems must be required to obtain an accurate (convergence) solution that defines as a series of corrections.

Evaluating uncertainties of geological features on fluid temperature and pressure changes in a reservoir plays a crucial role in the safe and sustainable operation of high-temperature aquifer thermal energy storage (HT-ATES). This study introduces a new automated surface fitting function in the Python API (application programming interface) of Gmsh (v4.11) to simulate the impacts of structural barriers and variations of the reservoir geometries on thermohydraulic behaviour in heat storage applications. These structural features cannot always be detected by geophysical exploration but can be present due to geological complexities. A Python workflow is developed to implement an automated mesh generation routine for various geological scenarios. This way, complex geological models and their inherent uncertainties are transferred into reservoir simulations. The developed meshing workflow is applied to two case studies: (1) Greater Geneva Basin with the Upper Jurassic (“Malm”) limestone reservoir and (2) the 5° eastward-tilted DeepStor sandstone reservoir in the Upper Rhine Graben with a uniform thickness of 10 m. In the Greater Geneva Basin example, the top and bottom surfaces of the reservoir are randomly varied by ± 10 and ± 15 m, generating a total variation of up to 25 % from the initially assumed 100 m reservoir thickness. The injected heat plume in this limestone reservoir is independent of the reservoir geometry variation, indicating the limited propagation of the induced thermal signal. In the DeepStor reservoir, a vertical sub-seismic fault juxtaposing the permeable sandstone layers against low permeable clay-marl units is added to the base case model. The fault is located in distances varying from 4 to 118 m to the well to quantify the possible thermohydraulic response within the model. The variation in the distance between the fault and the well resulted in an insignificant change in the thermal recovery (∼ 1.5 %) but up to a ∼ 10.0 % pressure increase for the (shortest) distance of 4 m from the injection well. Modelling the pressure and temperature distribution in the 5° tilted reservoir, with a well placed in the centre of the model, reveals that heat tends to accumulate in the updip direction, while pressure increases in the downdip direction.