Conference Agenda

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Session Overview
PA-A3: Numerical Techniques
Tuesday, 16/Jul/2019:
2:20pm - 4:10pm

Session Chair: Thomas Henneron
Session Chair: Ruben Specogna
Location: Patio 44-55

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Reconstruction of Cracks in Carbon Fiber Reinforced Polymer Laminate Plate from Signals of Eddy Current Testing

Yali Du1,2, Xudong Li1, Shejuan Xie1, Shiyou Yang3, Zhenmao Chen1

1Xi’an Jiaotong University, China; 2Xi’an Polytechnic University, China; 3Zhejiang University, Hangzhou, China

To evaluate defects in carbon fiber reinforced polymer (CFRP) and to predict its size, a numerical scheme for quantitative eddy current testing (ECT) is proposed and validated in this study. At first, an efficient forward numerical solver based on a database approach is updated to simulate the ECT signals of defects in a CFRP plate. Second, a hybrid inverse analysis scheme is proposed and imple-mented for sizing the defects from measured ECT signals of high frequency. Third, both simulated signals with white noise and meas-ured signals are adopted to reconstruct the profile of the slits in CFRP plate as examples to validate the proposed numerical scheme. The good agreement of the true and the reconstructed values demonstrated the validity of the new scheme for sizing defects in CFRP.

Alternative proposal of the High Order Gauss Quadrature for reference triangle in the Generalized Finite Element Method

Werley Gomes Facco1, Renan Coswosk da Silva1, Kaio Fábio de Oliveira Santos1, Elson José da Silva2, Rodney Rezende Saldanha2, Alex Sander de Moura3

1Federal Institute of Espírito Santo, Brazil; 2Federal University of Minas Gerais; 3Federal University of Juiz de Fora,

In this paper the Generalized Finite Element Method (GFEM) with enriched plane wave is used to solve wave propagation problem in an electrically large domain. To calculate the integrals of the weak form of this method in the reference triangle two high order Gaussian quadrature approaches will be investigated: Traditional and one adaptive method. To validate the presented proposal the Generalized Finite Element Method will be used to solve a wave propagation problem.

Modeling and Analysis of GIC Effects on Power Grid and Power Transformer using Harmonic Balance Method

Junwei Lu1, Xiaojun Zhao2, Zhiguang Cheng3

1Griffith University, Australia; 2North China Electric Power University, Baoding, China; 33Institute of Power Transmission and Transformation Technology, Baoding, China

Geomagnetically induced currents (GICs) caused by geomagnetic disturbances (GMDs) have a significant impact to power system and high voltage (HV) power transformers. The paper introduces an effective Harmonic Balance Method (HBM) for modeling and analyzing GIC effects on power grid and power transformers. The DC biased problems in HV transformers caused by GIC can be solved by using Harmonic Balance Finite Element Method (HBFEM), while the power system model including DC-biased transformer in GIC analysis can be derived by using HBM based transformer impedance matrix and power system model. During GIC flow, harmonic currents and voltages generated by saturated DC-biased transformers, and harmonic power losses can be directly calculated by using proposed HBFEM and Harmonic Balance Impedance Matrix (HBIM) model.

An Integro-Differential Time Domain Scheme for Electromagnetic Field Modeling in HTS Materials

Hocine MENANA, Mohamad FARHAT, Melika HINAJE, Bruno DOUINE

Université de Lorraine, France

In this work, we developed an integro-differential model in the time domain for electromagnetic field computation in high temperature superconducting (HTS) composite materials which are characterized by a nonlinear anisotropic electrical conductivity and multiscale dimensions. A relaxation method is applied to improve the convergence of the solution and to reduce the computation time. In the aim validation, a numerical example is considered where the numerical evaluation of AC losses in a Bi-Sr-Ca-Cu-O type HTS tape is compared to analytical modeling using measured parameters.

Performance analysis of finite-difference contrast source inversion and increment contrast source inversion

Wencong Jiang1, Minjing Zhong1, Liang Guo1, Hong Yu2

1College of Information and Control Engineering, China University of Petroleum; 2College of Science, China University of Petroleum

Contrast source inversion (CSI) is one of the well-known methods for solving electromagnetic inverse scattering problem on the basis of integral equations. Two different approaches to reconstructing the unknown dielectric properties of objects are considered. These are finite difference contrast source inversion (FD-CSI) and increment contrast source inversion (Inc-CSI). Both are based on CSI method and applicable for models under an inhomogeneous background. The former uses finite difference method to solve the integral equations which can expand the application scope of CSI. The latter does some adjustments to CSI. It reconstructs objects with the increment of measured scattered data after placing the objects of interest in imaging domain. Each method is described briefly. The performances of both methods are analyzed and compared in imaging accuracy and scope of application. Numerical results are displayed to verify the superiority of Inc-CSI.

Nonlinear Eigenmode Computation of Plasmonic NanoResonators

Mondher Besbes, Christophe Sauvan

Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, France

This paper is dealing with the eigenmode computation of nanoresonators made of dispersive and absorptive materials. The presence of material dispersion leads to a non-linear eigenvalue problem. We present two different approaches to linearize the non-linear problem. The first one is based on the introduction of auxiliary fields and the second one uses a Taylor expansion. We present the implementation of these methods with the finite element method and apply them to calculate the quasinormal modes of a metallo-dielectric core-shell nanocube.

Numerically Inversed Multiscale Behavior Model and Vector Potential Formulation: Convergence Properties

Eduardo Leal Grade, Laurent Bernard, Nelson Sadowski, Patrick Kuo-Peng

Federal University of Santa Catarina, Brazil

Multiscale approaches are attractive solutions for the modelling of the magneto-elastic behavior of ferromagnetic materials in electromagnetic device simulations. For use in magnetic vector potential formulations, the material behavior model should consider the magnetic flux density as input parameter. To achieve this aim, a simplified multiscale model is considered with numerical inversion by Newton-Raphson’s method. This inverse model is implemented into the finite element method and a three-phase transformer is considered, as an example, to analyze convergence properties and computational cost. The results are compared to the ones obtained using direct approaches. It is shown that the use of the numerically inversed multiscale model is a viable solution with parallel computing capabilities.

Acceleration Techniques for Linear-System Solver in Shielding Current Analysis of Cracked High-Temperature Superconducting Film

Atsushi Kamitani, Teruou Takayama, Ayumu Saitoh

Yamagata University, Japan

Two acceleration techniques are applied to a linear system in the shielding current analysis of a cracked high-temperature superconducting (HTS) film. When the shielding current density is calculated in the HTS film, a linear system of special type has to be solved at each iteration cycle of the Newton method. Although the linear system can be stably solved by means of the variable-reduction method (VRM), its numerical solution costs much computation time. In order to accelerate the VRM, a large portion of matrix-vector multiplication is performed by means of the H-matrix method and the variable preconditioned GMRES is adopted as a linear system solver. Consequently, the accelerated VRM becomes about 4 times faster than the conventional VRM.

An Efficient Parallel Computing Method for the Steady-State Analysis of Electric Machines Using the Woodbury Formula

Bo He, Chuan Lu, Ningning Chen, Dingsheng Lin, Ping Zhou

Ansys, United States of America

This paper describes a parallel computing method for the steady-state analysis of electric machines. In this method, due to the low rank of the coupling matrix, the Woodbury formula is exploited to develop a highly efficient parallel algorithm to solve the formulated linearized block matrix.

An Efficient Parallel Computing Method for the Steady-State Analysis of Low-Frequency Electromagnetics Using an Anti-Periodic Condition

Bo He, Ningning Chen, Dingsheng Lin, Chuan Lu, Ping Zhou

Ansys, United States of America

This paper describes an efficient parallel computing method based on the Message Passing Interface (MPI) for the steady-state analysis of low-frequency electromagnetics. In this method, two frames of reference are used to account for rigid-body motions, and an anti-periodic condition is exploited to reduce simulation time.

Study of the combined effects of the airgap transfer for Maxwell Tensor and the tooth mechanical modulation in electrical machines

Raphaël Pile1,2, Yvonnick Le Menach1, Jean Le Besnerais2, Guillaume Parent3

1L2EP, France; 2EOMYS ENGINEERING, France; 3LSEE, France

The Maxwell Tensor (MT) method is widely used to compute global forces or local surface forces for vibroacoustic design of electrical machines under electromagnetic excitation. In particular the airgap Maxwell Tensor method is based on a cylindrical shell in the middle of the airgap. This communication proposes to quantify the differences between the airgap MT and the magnetic force wave experienced by the stator. In particular the airgap to stator transfer and the tooth mechanical modulation effect are studied. A numerical application is performed with a turbo-alternator to illustrate the respective and combined effects of both phenomena. The communication highlights that the tooth mechanical modulation alone is not necessary relevant for electrical machines with a high number of tooth. However the combination of both phenomena has a clear impact on the computed magnetic surface force.

Equivalent Circuit Allowing Loss Separation Synthesized from Field Computations: Application to Induction Heating

Toshihito Shimotani1,2, Hajime Igarashi2, Eiji Hashimoto1, Hiroyuki Imanari1

1TOSHIBA MITSUBISHI-ELECTRIC INDUSTRIAL SYSTEMS CORPORATION, Japan; 2Information Science and Technology Department, Hokkaido university, Japan

In this paper, the proper orthogonal decomposition (POD) is applied to reduce the electromagnetic finite element equation of the 3-D model of an induction heater (IH) for hot strip mill. Based on the result of POD, the equivalent circuit of IH is synthesized where the circuit parameters are determined by fitting to the input impedance at sampling frequencies. The copper losses in the coil and heating plate can be separately evaluated using the equivalent circuit synthetized by the proposed method.

FEM Formulation with Dirichlet-To-Neumann map boundary condition for Eddy Current problems.

Anton Efremov1, Antea Perrotta2, Salvatore Ventre2, Lalita Udpa1, Antonello Tamburrino1,2

1Michigan State University, United States of America; 2University of Cassino and Southern Lazio, Italy

In this work a differential formulation of the Eddy Current Problem, combined with exact boundary condition based on the Dirichlet-To-Neumann map (DTN) is proposed. The numerical model is obtained via a FEM discretization combined with the Galerkin approach. Specifically, the Reduced Vector Potential FEM formulation is truncated by an exact DTN boundary condition, thus reducing the size of the region to be discretized. An additional reduction of the computational cost can be achieved by properly sparsifying the dense submatrix corresponding to the DTN (boundary) operator. Several model problems are investigated, and the results are compared to those from classic approaches.

A neural approach for fast direct and inverse Preisach model

Gabriele Maria Lozito1, Ermanno Cardelli2, Antonio Faba2, Valentina Lucaferri1, Simone Quondam Antonio2, Francesco Riganti Fulginei1, Alessandro Salvini1, Antonino Laudani1

1Universita degli Studi Roma Tre; 2Università degli Studi di Perugia

A computationally efficient approach for the numerical modelling of hysteretic magnetic materials is presented. The approach exploits the simplicity of the identification procedure for the Preisach model of hysteresis and the reduced computational costs of Neural Networks. The model for hysteresis is implemented both in direct and inverse form. Validation is performed against independent dataset, with evident computational speedup, which can be a valuable asset for Finite Element Method simulations.

Boundary Element Methods for Field Reconstruction in Accelerator Magnets

Melvin Liebsch1,2, Stephan Russenschuck1, Stefan Kurz2

1CERN, Switzerland; 2Technical University of Darmstadt, Germany

Most established approaches for magnetic measurement of accelerator magnets aim for a characterization of the magnetic field by means of cylindrical eigenfunctions of the Laplace equation, which are known as field harmonics. These field harmonics are measured with long, rotating-coil magnetometers covering the magnet and its fringe-field region, and treating the results as a 2D field problem. There are four major limitations of this field representation:

  • 1) Limitation to circular apertures, and
  • 2) spectral coefficients correspond to global field distributions, i.e. uncertainties in coefficients do not correspond to local measurement uncertainties. Moreover,
  • 3) limitation to straight magnets and
  • 4) no feedback on local field distributions in the magnet extremities.

In this paper an alternative approach with the potential to migrate these issues is presented, which based on Kirchhoff's integral equation. Dirichlet and Neumann data are approximated on finite dimensional approximation spaces. It is shown that, dependent on the formulation, either the Dirichlet or Neumann data can be related to flux measurements along the chosen domain boundary. Exploiting Calderón's Projector, one can then recover the missing Cauchy datum in a numerical post-processing. Results for the reconstruction of integrated fields are presented. In this case, the stretched wire measurement system is used to acquire boundary fluxes. In the paper to be submitted for COMPUMAG 2019, results of 3D field reconstructions using a translating-coil magnetometer will be included. Additionally, the propagation of measurement uncertainties to the boundary data will be analyzed. In this way, local measurement uncertainties can be detected and eliminated by re-sampling.

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