Numerical methods for computing the modal decomposition of the magnetic polarizability of conducting objects

Numerical methods are presented for characterizing the wideband responses of conducting objects to excitation by electromagnetic induction sensors. Electromagnetic induction sensors can be used to measure the magnetic polarizability tensor of conducting targets, a tensor that encapsulates the entire scattering interaction between target and sensor. Wideband characterization of the magnetic polarizability tensor can be achieved by expanding the frequency response in pole-expansion form. The pole-expansion coefficients may then be used as a signature, which can be used for subsurface target detection. To derive the coefficients numerically, the interaction between a target of interest and the sensor is modeled as a linear system, which can then be set up as generalized eigenvalue problem. The eigenvalues of the system correspond to the pole locations of the pole expansion. The remaining coefficients can be derived from the eigenvectors of the system, which correspond to the that natural modes that are excited by the sensor. Integral methods are presented for numerically computing the pole-expansion coefficients of thin conducting sheets and shells, conducting volumes, and bodies of revolution. A differential method is also presented for conducting volumes. Computational results are compared to known analytical solutions when possible as well as to experimental measurements.Ph.D

Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.Comment: Paper accepted for publication in the SIAM MMS journa

Simulation Tools and Developments on Integral Formulations for the Computation of Eddy Currents

openComputational electromagnetics is a discipline that since many years ago has permitted deep innovations in the study of electromagnetic problems. Even if, nowadays, commercial softwares undeniably show a certain maturity when applied to practical problems, some research work has still to be done in going beyond the theoretical limits underneath the various approaches. With respect to this, integral formulations still present some open issues. Historically, the exploitation of these formulations to study eddy currents started around the 90s with the seminal works of G. Albanese, R. Martone and R. Rubinacci together with the research activity of L. Kettunen and L. R. Turner and then with G. Meunier, who more recently rediscovered them. Lately, the contributions of L. Codecasa, R. Specogna and F. Trevisan have further increased the possibilities offered by this approach by introducing a set of new shape functions for polyhedral grids that are based on a discrete geometrical reinterpretation of the physics of electromagnetic phenomena. One of the main features characterizing integral formulations to compute eddy currents stems from the fact that they do not require any discretization of the complement of the conductor to be studied. As a drawback, they lead to fully populated matrices whose assembly results to be remarkably time consuming and whose size can sometimes saturate the memory of the calculator. In this respect, this composition presents a new volume integral code for polyhedral grids describing how a fast and efficient cohomology computation can be implemented to treat also non-simply connected domains. Then, some tools are provided for the reduction of the size, and thus of the assembly time too, of the fully populated matrix. More precisely, the attention is focused on the exploitation of cyclic symmetry and on the novel topology-related issues arising when integral formulations have to be referred only to the symmetry cell of the complete conducting domain in order not to spoil the block-circulant property of the system matrix when building the cohomology generators or the gauging tree. Furthermore, also new iterative methods are considered as additional approaches to limit the size of the system matrix to be assembled: despite being already known to the computational electromagnetics community, their convergence behaviour has not been studied yet when they are applied to integral formulations as the one here proposed. Specifically, after presenting a purely iterative scheme derived from the volume integral formulation whose convergence can be somehow problematic, we propose a new direct-iterative method based on Krylov subspace techniques and on the domain splitting into multiple conductors that exhibits a much improved behaviour. The study of these methods leads to new interesting findings to be considered in addition to matrix compression techniques.Dottorato di ricerca in Ingegneria industriale e dell'informazioneopenPassarotto, Maur

Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface

Near-surface applied electromagnetic geophysics is experiencing an explosive period of growth with many innovative techniques and applications presently emergent and others certain to be forthcoming. An attempt is made here to bring together and describe some of the most notable advances. This is a difficult task since papers describing electromagnetic induction methods are widely dispersed throughout the scientific literature. The traditional topics discussed herein include modeling, inversion, heterogeneity, anisotropy, target recognition, logging, and airborne electromagnetics (EM). Several new or emerging techniques are introduced including landmine detection, biogeophysics, interferometry, shallow-water electromagnetics, radiomagnetotellurics, and airborne unexploded ordnance (UXO) discrimination. Representative case histories that illustrate the range of exciting new geoscience that has been enabled by the developing techniques are presented from important application areas such as hydrogeology, contamination, UXO and landmines, soils and agriculture, archeology, and hazards and climat

Transient eddy current response due to a subsurface crack in a conductive plate

Eddy current nondestructive evaluation (NDE) is usually carried out by exciting a time harmonic field using an inductive probe. However, a viable alternative is to use transient eddy current NDE in which a current pulse in a driver coil produces a transient field in a conductor that decays at a rate dependent on the conductivity and the permeability of the material and the coil configuration. By using transient eddy current, it is possible to estimate the properties of the conductive medium and to locate and size potential flaws from the measured probe response. The fundamental study described in this dissertation seeks to establish a theoretical understanding of the transient eddy current NDE. Compared with the Fourier transform method, the derived analytical formulations are more convenient when the transient eddy current response within a narrow time range is evaluated. The theoretical analysis provides a valuable tool to study the effect of layer thickness, location of defect, crack opening as well as the optimization of probe design;Analytical expressions have been developed to evaluate the transient response due to eddy currents in a conductive plate based on two asymptotic series. One series converges rapidly for a short time regime and the other for a long time regime and both of them agree with the results calculated by fast Fourier transform over all the times considered. The idea of asymptotic expansion is further applied to determine the induced electromotive force (EMF) in a pick-up coil due to eddy currents in a cylindrical rod;Starting from frequency domain representation, a quasi-static time domain dyadic Green\u27s function for an electric source in a conductive plate has been derived. The resulting expression has three parts; a free space term, multiple image terms and partial reflection terms. The dyadic Green\u27s function serves as the kernel of an electric field integral equation which defines the interaction of an ideal crack with the transient eddy currents in a conductive plate. The crack response is found using the reciprocity theorem. Good agreement is observed between the predictions of the magnetic field due to the crack and experimental measurements

Towards MRI scanner design: the Proper Generalised Decomposition in the context of coupled magneto-mechanical problems

Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners, with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their high-strength transient magnetic fields induce unwanted eddy currents in shielding components, which result in high-frequency vibrations, noise, imaging artefacts and, ultimately, heat dissipation and boiling off of the helium used to super-cool the magnets. Optimum MRI scanner design requires the capturing of complex electro-magneto-mechanical interactions with high fidelity computational tools. Moreover, manufacturing new MRI scanners still represents a computational challenge to industry due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of user-friendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where high-dimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time.This thesis presents a novel a priori Proper Generalised Decomposition (PGD) computational framework for the analysis of the electro-magneto-mechanical inter-actions in the context of MRI scanner design to address the urgent need for the development of new cost-effective methods, whereby previously performed compu-tations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. The PGD methodology is derived for coupled electro-magneto-mechanical problems in an axisymmetric Lagrangian setting, in-cluding the possibility to vary several material and geometrical parameters (as part of the high-dimensional offline solution), that are relevant for the industrial part-ner of the project, Siemens Healthineers. A regularised-adaptive strategy and a staggered PGD approach are proposed in order to enhance the accuracy and robust-ness of the PGD algorithm while preserving its a priori nature. The Lagrangian adaptation of the governing equations will allow for a comparison between staggered and monolithic solvers, where the staggered approach will be shown to enhance the robustness and accuracy of the PGD technique. Moreover, geometric changes in the computational domain will be accounted for in the PGD solution by using a PGD-projection technique that will enable the computation of a separable expression even for geometrical variations, preserving thus the efficiency of the online PGD stage. A set of numerical problems will be presented in order to validate the PGD formula-tion, which will be benchmarked against the full order (reference) model. Moreover, a comparison between two families of ROM methods, the a priori PGD and the a posteriori Proper Orthogonal Decomposition (POD), will also be performed in order to assess and compare different ROM strategies

Optimization of a boundary element approach to electromagnet design with application to a host of current problems in Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) has proven to be a valuable methodological approach in both basic research and clinical practice. However, significant hardware advances are still needed in order to further improve and extend the applications of the technique. The present dissertation predominantly addresses gradient and shim coil design (sub-systems of the MR system). A design study to investigate gradient performance over a set of surface geometries ranging in curvature from planar to a full cylinder using the boundary element (BE) method is presented. The results of this study serve as a guide for future planar and pseudo-planar gradient systems for a range of applications. Additions to the BE method of coil design are developed, including the direct control of the magnetic field uniformity produced by the final electromagnet and the minimum separation between adjacent wires in the final design. A method to simulate induced eddy currents on thin conducting surfaces is presented. The method is used to predict the time-dependent decay of eddy currents induced on a cylindrical copper bore within a 7 T MR system and the induced heating on small conducting structures; both predictions are compared against experiment. Next, the method is extended to predict localized power deposition and the spatial distribution of force due to the Lorentz interaction of the eddy current distribution with the main magnetic field. New methods for the design of actively shielded electromagnets are presented and compared with existing techniques for the case of a whole-body transverse gradient coil. The methods are judged using a variety of shielding performance parameters. A novel approach to eliminate the interactions between the MR gradient system and external, non-MR specific, active devices is presented and its feasibility is discussed. A completely new approach to shimming is presented utilizing a network of current pathways that can be adaptively changed on a subject-by-subject basis and dynamically controlled. The potential benefits of the approach are demonstrated using computer simulations and a prototype coil is constructed and tested as a proof-of-principle

Doctor of Philosophy

dissertationModeling of induced polarization (IP) phenomena is important for developing effective methods for remote sensing of subsurface geology and is widely used in mineral exploration. However, the quantitative interpretation of IP data in a complex 3D environment is still a challenging problem of applied geophysics. In this dissertation I use the regularized conjugate gradient method to determine the 3D distribution of the four parameters of the Cole-Cole model based on surface induced polarization (IP) data. This method takes into account the nonlinear nature of both electromagnetic induction (EMI) and IP phenomena. The solution of the 3D IP inverse problem is based on the regularized smooth inversion only. The method was tested on synthetic models with DC conductivity, intrinsic chargeability, time constant, and relaxation parameters, and it was also applied to the practical 3D IP survey data. I demonstrate that the four parameters of the Cole-Cole model, DC electrical resistivity, p0 (or electrical conductivity <r0 = 1 / p 0 ), chargeability, r ; time constant, r ; and the relaxation parameter, , can be recovered from the observed IP data simultaneously. There are four Cole-Cole parameters involved in the inversion, in other words, within each cell, there are DC conductivity ( ), chargeability ( ), time parameters ( ), and relaxation parameters ( ) compared to conductivity only, used in EM only inversion. In addition to more inversion parameters used in IP survey, dipole-dipole configuration which requires more sources and receivers. One the other hand, calculating Green tensor and Frechet matrix time consuming and storing them requires a lot of memory. So, I develop parallel computation using MATLAB parallel tool to speed up the calculation