Electromagnetics (EM) can be described, together with the constitutive laws, by four PDEs, called Maxwell's equations. "Quasi-static" approximations emerge from neglecting particular couplings of electric and magnetic field related quantities. In case of slowly time varying fields, if inductive and resistive effects have to be considered, whereas capacitive effects can be neglected, the magneto quasi-static (MQS) approximation applies. The solution of the MQS Maxwell's equations, traditionally obtained with finite differences and elements methods, is crucial in modelling EM devices. In this paper, the applicability of an unsupervised deep learning model is studied in order to solve MQS Maxwell's equations, in both frequency and time domain. In this framework, a straightforward way to model hysteretic and anhysteretic non-linearity is shown. The introduced technique is used for the field analysis in the place of the classical finite elements in two applications: on the one hand, the B-H curve inverse determination of AISI 4140, on the other, the simulation of an induction heating process. Finally, since many of the commercial FEM packages do not allow modelling hysteresis, it is shown how the present approach could be further adopted for the inverse magnetic properties identification of new magnetic flux concentrators for induction applications. Recently, deep learning emerges as a powerful technique in many applications, including computer vision, speech recognition, natural language process, and bioinformatics. There is This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Coupled fluid-particle simulations are routinely used in a variety of applications, ranging from respiratory droplet spreading to internal combustion engines, from ink-jet printing to in-flight ice accretion. The efficiency of parallel algorithms to simulate fluid-particle systems is strongly influenced by the different evolution of the flow and the particles dynamics. Indeed, a domain partitioning based on particle workload is possibly sub-optimal in terms of the number of fluid volume elements associated to each process. In this work, an efficient mesh partitioning based on graph representation is implemented. It can handle unstructured hybrid meshes composed by triangles and quadrilaterals in two spatial dimensions, and by tetrahedra, hexahedra, prisms, and pyramids in three dimensions. In order to obtain a domain decomposition to efficiently follow the particle trajectories, a preliminary solution is computed to suitably tag the fluid domain cells. The obtained weights represent the element probabilities to be crossed by particles. The algorithm is implemented using MPI distribute memory environment. The proposed approach is tested against reference cases for the coupled flow-particle simulation of ice accretion over 2D and 3D geometries. Two different cloud droplet impact test cases have been simulated: a NACA 0012 wing section and a NACA 64A008 swept horizontal tail. The computed collection efficiency compares fairly well with reference numerical and experimental data. The parallel efficiency of the algorithm is verified on a distributed memory cluster.
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