Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls

1972 ◽  
Vol 56 (1) ◽  
pp. 121-141 ◽  
Author(s):  
J. S. Walker ◽  
G. S. S. Ludford ◽  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Boundary Layers ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Flow Direction ◽  
Three Dimensional ◽  
Side Wall ◽  
Transverse Magnetic ◽  
Wall Boundary ◽  
Strong Transverse

The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.

scholarly journals 2D and 3D fault basis for fuel cell diagnosis by external magnetic field measurements

2017 ◽  
Vol 79 (2) ◽  
pp. 20901 ◽  
Author(s):  
Lyes Ifrek ◽  
Gilles Cauffet ◽  
Olivier Chadebec ◽  
Yann Bultel ◽  
Sébastien Rosini ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Fuel Cell ◽  
External Magnetic Field ◽  
Current Density ◽  
Field Measurements ◽  
Magnetic Field Measurements ◽  
Uniqueness Of The Solution ◽  
Ill Posed ◽  
Value Decomposition

An original approach used for the identification of faults in fuel cell stacks is presented. It is based on the 3D reconstruction of the current density from external magnetic field measurements which is an ill-posed magnetostatic linear inverse problem. A suitable and original current density and magnetic field basis are proposed in order to define both local and global faults on a fuel cell stack. The inverse problem is regularized by truncated singular value decomposition (SVD) to ensure the uniqueness of the solution.

Eigenvector Model Descriptors for the Seismic Inverse Problem

2020 ◽  
Author(s):  
Florian Faucher ◽  
Otmar Scherzer ◽  
Hélène Barucq
Keyword(s):  
Image Processing ◽  
Inverse Problem ◽  
Diffusion Equation ◽  
Surface Reconstruction ◽  
Wave Speed ◽  
Three Dimensional ◽  
Low Frequency ◽  
Minimization Algorithm ◽  
Iterative Minimization ◽  
Ill Posed

<p>We consider the quantitative inverse problem for the recovery of subsurface Earth's properties, which relies on an iterative minimization algorithm. Due to the scale of the domains and lack of apriori information, the problem is severely ill-posed. In this work, we reduce the ill-posedness by using the ``regularization by discretization'' approach: the wave speed is described by specific bases, which limits the number of coefficients in the representation. Those bases are associated with the eigenvectors of a diffusion equation, and we investigate several choices for the PDE, that are extracted from the field of image processing. We first compare the efficiency of these model descriptors to accurately capture the variation with a minimal number of coefficients. In the context of sub-surface reconstruction, we demonstrate that the method can be employed to overcome the lack of low-frequency contents in the data. We illustrate with two and three-dimensional acoustic experiments.</p>

THE LOCATION OF SPHERICAL CAVITIES USING A TRIPOTENTIAL RESISTIVITY TECHNIQUE

Geophysics ◽  
1969 ◽  
Vol 34 (5) ◽  
pp. 780-784 ◽  
Author(s):  
G. M. Habberjam
Keyword(s):  
Magnetic Field ◽  
Apparent Resistivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Spherical Body ◽  
Numerical Results ◽  
Detailed Account ◽  
Conducting Sphere ◽  
Spherical Cavities ◽  
Conductivity Contrast

The surface gravitational and magnetic field anomalies due to a contrasting spherical body at depth are well known and appear in geophysical textbooks. The corresponding problem of the anomaly in apparent resistivity arising from such a body, owing to its conductivity contrast, is less frequently referred to because of the lengthy potential solutions involved. In electrical interpretation, few potential solutions exist for buried bodies of limited three‐dimensional extent, and consequently the simplest of these problems, the buried sphere, has received particular attention. Following early work by Hummel (1928), Webb (1931) produced potential solutions for this problem, and more recently Lipskaya (1949) has derived solutions and computed extensive numerical results. For the particular case of an infinitely conducting sphere, Van Nostrand (1953) has computed comprehensive numerical solutions, and more recently Van Nostrand and Cook (1966) presented a very detailed account of work on the buried sphere.

scholarly journals CONTINUOUS ANALOG OF THE GAUSS–NEWTON METHOD

1999 ◽  
Vol 09 (03) ◽  
pp. 463-474 ◽  
Author(s):  
R. G. AIRAPETYAN ◽  
A. G. RAMM ◽  
A. B. SMIRNOVA
Keyword(s):  
Inverse Problem ◽  
Newton Method ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Nonlinear Problems ◽  
Nonlinear Inverse Problem ◽  
Derivative Operator ◽  
Continuous Analog ◽  
Ill Posed ◽  
Practical Recommendations

A Continuous Analog of discrete Gauss–Newton Method (CAGNM) for numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Fréchet derivative operator, some regularization function is introduced. For the CAGNM, a convergence theorem is proved. The proposed method is illustrated by a numerical example in which a nonlinear inverse problem of gravimetry is considered. Based on the results of the numerical experiments, practical recommendations for the choice of the regularization function are given.

"In Situ" Evaluation of Ferromagnetic Bodies Magnetic Characteristics

2014 ◽  
Vol 792 ◽  
pp. 177-182 ◽  
Author(s):  
Horia Gavrila ◽  
Marilena Stanculescu ◽  
Mihai Maricaru ◽  
Marian Vasilescu ◽  
Paul Andrei ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Magnetic Induction ◽  
The Body ◽  
Magnetic Field Distribution ◽  
Magnetic Characteristics ◽  
Field Problem ◽  
Ill Posed ◽  
The Magnetic Field

The B-H characteristic of an iron body material influences the magnetic field measured in the air. On principle, one can pose the problem of B-H relation determination, by making measurements of the magnetic induction in the neighbourhood of the body. Unfortunately, we have an ill-posed inverse magnetic field problem, for which there is possible that, big variations of the BH characteristic to produce only very small modifications of the magnetic field in the air. It is essential to use a sufficiently sensitive computation procedure in order to produce credible results. This paper proposes a device for the B-H characteristic evaluation, admitting that inside the ferromagnetic bodies the magnetic field distribution is not uniform.

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