Global identifiability for an inverse problem for the Schr�dinger equation in a magnetic field

1995 ◽  
Vol 303 (1) ◽  
pp. 377-388 ◽  
Author(s):  
Gen Nakamura ◽  
Ziqi Sun ◽  
Gunther Uhlmann
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Dinger Equation

The interface of a uniform plasma enveloped by the magnetic field of a system of line currents

1969 ◽  
Vol 3 (4) ◽  
pp. 651-660 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Complex Variable ◽  
Field Boundary ◽  
Equilibrium Configurations ◽  
Minimum Number ◽  
The Magnetic Field ◽  
Uniform Plasma

It is shown that complex variable transformations, suitable for obtaining the solution for the field boundary of a system of line currents confined in one cavity by a perfectly conducting uniform plasma, can be used for obtaining the solution to the inverse problem where a perfectly conducting uniform plasma is confined in one cavity by a system of line currents. It is deduced that the minimum number of line currents for confining (not stably) a plasma is two. The equilibrium configurations for several special but simple cases are investigated and discussed.

Magnetic field inverse problem of grounding grid and its application

2012 ◽  
Vol 40 (3) ◽  
pp. 173-183 ◽  
Author(s):  
Fan Yang ◽  
Yan Jiang ◽  
Qinyan Shi ◽  
Tao Chen ◽  
Wei He
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Grounding Grid

EQUIVALENT SOURCES USED AS AN ANALYTIC BASE FOR PROCESSING TOTAL MAGNETIC FIELD PROFILES

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 339-348 ◽  
Author(s):  
David A. Emilia
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Amplitude Spectrum ◽  
Linear Inverse Problem ◽  
Total Magnetic Field ◽  
Vertical Derivative ◽  
Equivalent Sources

Equivalent sources are useful in processing total magnetic field profiles. A lines‐of‐dipoles distribution, obtained by solving the linear inverse problem, provides an analytic base for computing the following quantities from an observed field: first and second vertical derivative fields, upward‐ and downward‐continued fields, field reduced to the pole, amplitude spectrum of the field, and band‐passed field. A theoretical example demonstrates the validity of the approach, and a field example shows that reasonable results are readily obtained.

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.

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