1,721,034 research outputs found
A Novel Mixed-Hybrid Formulation for Magnetostatics
No full textMixed-hybrid finite-element (MHFE) formulations for magnetostatic problems are appealing because - like the magnetic scalar potential (MSP) formulations - they yield to algebraic systems that can be effectively solved by black-box algebraic multigrid solvers. At the same time, the MHFE formulation is algebraically equivalent to the magnetic vector potential (MVP) formulation and therefore provides a conservative flux and superior accuracy. We introduce a novel mixed-hybrid (MH) formulation for magnetostatics which combines the best features of MSP and reduced MVP formulations. In particular, it avoids the explicit representation in the FE mesh of the shape of source current regions. Moreover, the new formulation - unlike the MHFE one - does not require the inversion of the local mass matrices, but still provides the same solution - on tetrahedral meshes and up to linear solver tolerance - of the corresponding MHFE formulation. Another advantage is that it can deal with very general polyhedral meshes, where div-conforming FE basis functions are not available
Calculation of 3D magnetic fields produced by MHD active control systems in fusion devices
No full textIn a magnetic confinement fusion device the presence of a conductive wall (shell) surrounding the plasma is important to guarantee a good magnetohydrodynamic (MHD) stability. However, due to the finite diffusion time of any resistive shell, a feedback control system of the plasma instabilities is also required. Recently, a very effective control scheme, named Clean Mode Control (CMC), has been proposed in RFX-mod. The CMC is based on the real-time correction (cleaning) of the sideband harmonics in the magnetic field due to the discrete nature of the local active coils. In this paper we describe how to exploit periodic boundary conditions in the frequency domain calculations of 3D magnetic fields produced by MHD active control systems, in view of possible optimization of the CMC scheme
Diagonal material matrices for arbitrary simplicial meshes for solving poisson problems with one unknown per element
No full textWe present a technique to construct diagonal material matrices for arbitrary triangular and tetrahedral meshes and arbitrary scalar material parameters. The recipe is based on a novel dual complex called folded Voronoï diagram. The proposed matrices are tailored to enable the use of a complementary-dual formulation for Poisson problems featuring one unknown per element
Fast halo currents computation in fusion reactors by electrokinetic complementary formulations
No full textThis paper presents a tool to estimate the halo current forces generated by disruptions that occurr during fusion reactors operations. The domain of the elektrokinetic problem is so complicated that two complementary formulations are used to monitor the discretization error. It turns out that thousands of cohomology generators are needed by the electric vector potential formulation, that would require an enormous amount of memory and computing power to retrieve all of them even using state-of-the-art algorithms. To solve this challenging problem, we present a novel algorithm to generate the absolute second cohomology group generators exploiting the idea of lazy cohomology generators stored as sparse vectors. The new algorithm is able to save orders of magnitude computational time
Cyclic Symmetry in Volume Integral Formulations for Eddy Currents: Cohomology Computation and Gauging
No full textThis contribution addresses the solution of eddy-current problems by means of a volume integral formulation based on the electric vector potential on a computational domain that exhibits a cyclic symmetry. Even if grids discretizing the domain are typically composed of tetrahedral or hexahedral elements, the proposed approach also works for general polyhedral meshes, such as those ones obtained by subgridding. In this article, an algorithm to compute a set of suitable cohomology generators needed when the conductors are not simply connected is introduced first. Besides being purely combinatorial, with linear-time worst case complexity and suitable with polyhedral meshes, it reuses a code that computes generators for triangular surface meshes, with obvious advantages concerning the implementation effort. Second, the formulation and the algorithm for cohomology computation are tweaked to be able to solve eddy-current problems with cyclic symmetry reserving specific attention to the construction of suitable tree-cotree decomposition for the problem gauging
Study and design of ratiometric inductive position sensors using area-of-overlap functions
No full textThis article presents a theoretical study of an absolute, ratiometric inductive position sensor (IPS) based on eddy currents. The aim is to describe the working principle of the sensor, having as key components a transmitting coil, the receiving coils and the conductive target, by introducing area-of-overlap functions. We show that each target–receiver pair needs the adoption of a different reconstruction formula for the identification of the target position, whereas in the literature the usual inverse tangent function is applied for every possible pair. Than, we seek the target–receiver pair that maximizes the amplitude of the induced voltages on the receivers. The results show that, to achieve the maximum value of the induced voltages, the best choice is to have rectangular target and rectangular receivers. In order to verify the theory, a simulation and optimization method has been applied to the rectangular receivers coils on two rotary IPS realized with Printed Circuit Board (PCB) technology. Measurements performed on the prototypes have shown an increment of the induced voltage of more than 57% with respect to the commonly used sinusoidal receivers. However, a linearity error of 1.5%FS is obtained by using the inverse tangent reconstruction formula. When using the formula provided from the theory, the linearity error becomes 0.6%FS for the non-optimized prototype and below 0.15%FS for the optimized one
Real-Time Design and Characterization of Inductive Position Sensors Through AI-Driven DesSS
No full textWe propose a fast method to characterize inductive position sensors with zero physical prototypes. The technique is based on an in-house developed electromagnetic simulation tool which shows three orders of magnitude improvement with respect to the most widely used commercial software. This simulation software is used for producing synthetic data for training a machine learning surrogate model based on a neural network. In this way, the characterization of a sensor takes just milliseconds. This opens the possibility of devising a Design Support System (DesSS), a software that guide the user in sensor design for the best possible outcome, thereby saving development time
A Novel Family of Inductance Matrix Compression Techniques
No full textIntegral methods for the solution of eddy current problems are very appealing since they avoid the meshing of the insulating regions. Yet, their main shortcoming is that they require the assembly and storage of a fully populated stiffness matrix K. To reduce the memory footprint and to enable a fast matrix construction, low-rank approximations techniques-like the Adaptive Cross Approximation (ACA)-have been considered a major breakthrough in the field. This paper presents a novel family of compression techniques that is enabled by a novel explicit factorization of the inductance matrix. Such a novel family exhibits orders of magnitude speedup and memory consumption with respect to state-of-the-art techniques. In particular, the aim of this paper is to compare for the first time the memory occupation, computation time and accuracy of the solution obtained with different compression techniques
Explicit geometric construction of sparse inverse mass matrices for arbitrary tetrahedral grids
No full textThe geometric reinterpretation of the Finite Element Method (FEM) shows that Raviart–Thomas and Nédélec mass matrices map from degrees of freedoms (DoFs) attached to geometric elements of a tetrahedral grid to DoFs attached to the barycentric dual grid. The algebraic inverses of the mass matrices map DoFs attached to the barycentric dual grid back to DoFs attached to the corresponding primal tetrahedral grid, but they are of limited practical use since they are dense. In this paper we present a new geometric construction of sparse inverse mass matrices for arbitrary tetrahedral grids and possibly inhomogeneous and anisotropic materials, debunking the conventional wisdom that the barycentric dual grid prohibits a sparse representation for inverse mass matrices. In particular, we provide a unified framework for the construction of both edge and face mass matrices and their sparse inverses. Such a unifying principle relies on novel geometric reconstruction formulas, from which, according to a well-established design strategy, local mass matrices are constructed as the sum of a consistent and a stabilization part. A major difference with the approaches proposed so far is that the consistent part is defined geometrically and explicitly, that is, without the necessity of computing the inverses of local matrices. This provides a sensible speedup and an easier implementation. We use these new sparse inverse mass matrices to discretize a three-dimensional Poisson problem, providing the comparison between the results obtained by various formulations on a benchmark problem with analytical solution
Simulation and measurements of a rotary inductive position sensor
No full textIn this work a method for the fast simulation of a rotary inductive position sensor with the Surface Integral Method in order to predict the non linearity error of the sensor is provided. Experimental analysis shows the effectiveness of the method and the effect of the rotation speed on the receivers
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