scholarly journals A finite‐difference, time‐domain solution for three‐dimensional electromagnetic modeling

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 797-809 ◽  
Author(s):  
Tsili Wang ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Execution Time ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Transient Electromagnetic ◽  
The Earth ◽  
The Magnetic Field

We have developed a finite‐difference solution for three‐dimensional (3-D) transient electromagnetic problems. The solution steps Maxwell’s equations in time using a staggered‐grid technique. The time‐stepping uses a modified version of the Du Fort‐Frankel method which is explicit and always stable. Both conductivity and magnetic permeability can be functions of space, and the model geometry can be arbitrarily complicated. The solution provides both electric and magnetic field responses throughout the earth. Because it solves the coupled, first‐order Maxwell’s equations, the solution avoids approximating spatial derivatives of physical properties, and thus overcomes many related numerical difficulties. Moreover, since the divergence‐free condition for the magnetic field is incorporated explicitly, the solution provides accurate results for the magnetic field at late times. An inhomogeneous Dirichlet boundary condition is imposed at the surface of the earth, while a homogeneous Dirichlet condition is employed along the subsurface boundaries. Numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth‐order difference method at early times and a second‐order method at other times. Numerical checks against analytical, integral‐equation, and spectral differential‐difference solutions show that the solution provides accurate results. Execution time for a typical model is about 3.5 hours on an IBM 3090/600S computer for computing the field to 10 ms. That model contains [Formula: see text] grid points representing about three million unknowns and possesses one vertical plane of symmetry, with the smallest grid spacing at 10 m and the highest resistivity at 100 Ω ⋅ m. The execution time indicates that the solution is computer intensive, but it is valuable in providing much‐needed insight about TEM responses in complicated 3-D situations.

scholarly journals A parallel finite‐difference approach for 3D transient electromagnetic modeling with galvanic sources

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1192-1202 ◽  
Author(s):  
Michael Commer ◽  
Gregory Newman
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electric Field ◽  
Electric Fields ◽  
Time Derivative ◽  
Stable Solution ◽  
Parallel Computer ◽  
Staggered Grid ◽  
Electromagnetic Modeling ◽  
Transient Electromagnetic

A parallel finite‐difference algorithm for the solution of diffusive, three‐dimensional (3D) transient electromagnetic field simulations is presented. The purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources (grounded wires) over arbitrarily complicated distributions of conductivity and magnetic permeability. Using a staggered grid and a modified DuFort‐Frankel method, the scheme steps Maxwell's equations in time. Electric field initialization is done by a conjugate‐gradient solution of a 3D Poisson problem, as is common in 3D resistivity modeling. Instead of calculating the initial magnetic field directly, its time derivative and curl are employed in order to advance the electric field in time. A divergence‐free condition is enforced for both the magnetic‐field time derivative and the total conduction‐current density, providing accurate results at late times. In order to simulate large realistic earth models, the algorithm has been designed to run on parallel computer platforms. The upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two‐dimensional parallel fast Fourier transform. Example simulations are compared with analytical, integral‐equation and spectral Lanczos decomposition solutions and demonstrate the accuracy of the scheme.

scholarly journals Two-dimensional hybrid model for magnetic field calculation in electrical machines: exact subdomain technique and magnetic equivalent circuit

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Brahim Ladghem Chikouche ◽  
Kamel Boughrara ◽  
Dubas Frédéric ◽  
Rachid Ibtiouen
Keyword(s):  
Magnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Current Density Distribution ◽  
Electrical Machines ◽  
Field Calculation ◽  
Two Dimensional ◽  
Content Type ◽  
The Magnetic Field ◽  
Load Conditions

Purpose The purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions. Design/methodology/approach In this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke. Findings It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique. Originality/value The main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.

scholarly journals Numerical modelling analysis of multi-source semi-airborne TEM systems using a TFEM

2020 ◽  
Vol 17 (3) ◽  
pp. 399-410
Author(s):  
He Li ◽  
Zhipeng Qi ◽  
Xiu Li ◽  
Yingying Zhang
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Specific Area ◽  
Multiple Sources ◽  
Electromagnetic System ◽  
Transient Electromagnetic ◽  
Vector Finite Element ◽  
Data Collections ◽  
The Magnetic Field

Abstract Traditional transient electromagnetic methods use single sources for excitation and extract the characteristics of underground media by improving interpretation technology. This study focused the improvements of transient electromagnetic interpretation using complex source technology. A time-domain vector finite element method (TFEM) was applied on three-dimensional forward modelling of semi-airborne transient electromagnetic (TEM) with multiple electrical sources, and it analysed the characteristics of fields with multiple sources. The study used a model of an isolated anomalous body in a homogeneous medium as an example. The effects of different combinations of excitation sources on the distributions of the magnetic field characteristics were analysed. Numerical results showed that the magnetic field components in a specific area could be strengthened by changing the layout of the sources, which was significant for future field data collections. By comparing the transient electromagnetic fields of the vertical array dipole sources with that of the loop source, the anomaly transient electromagnetic field of multi-source was more obvious than the field with a single source. Taking a complex orebody model as an example, a cross-electric source was used to calculate the magnetic field components of the semi-airborne TEM method. The resistivity distribution characteristics of the underground medium were obtained using an apparent resistivity interpretation method of the vertical magnetic field, which fully demonstrated that a multi-source transient electromagnetic system had the ability to determine abundant resistivity information of a complex medium.

scholarly journals Reevaluation and correction of Maxwell’s Equations: a magnetic field has a source, a moving electric charge

F1000Research ◽  
2020 ◽  
Vol 9 ◽  
pp. 1092
Author(s):  
M.J. Koziol
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Charge ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electric And Magnetic Fields ◽  
The World ◽  
New Equation ◽  
The Magnetic Field

Maxwell’s Equations are considered to summarize the world of electromagnetism in four elegant equations. They summarize how electric and magnetic fields propagate, interact, how they are influenced by other objects and what their sources are. While it is widely accepted that the source of a magnetic field is a moving charge, one of the equations instead states that the magnetic field has no source. However, it is widely accepted that a magnetic field cannot be created without a moving electric charge. As such, here, after carefully reevaluating how Maxwell derived his equation, a limitation was identified. After adjustments, a new equation was derived that instead demonstrates that the source of a magnetic field is a moving charge, confirming experimentally verified and widely accepted observations.

A three-dimensional kinematic dynamo

1975 ◽  
Vol 344 (1637) ◽  
pp. 235-258 ◽  
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Characteristic Size ◽  
Steady Flows ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
The Earth ◽  
Induction Equation ◽  
High Degree ◽  
The Magnetic Field

A number of steady (marginal) solutions of the induction equation governing the magnetic field created by a particular class of threedimensional flows in a sphere of conducting fluid surrounded by an insulator are derived numerically. These motions possess a high degree of symmetry which can be varied to confirm numerically that the corresponding asymptotic limit of Braginsky is attained. The effect of altering the spatial scale of the motions without varying their vigour can also be examined, and it is found that dynamo action is at first eased by decreasing their characteristic size. There are, however, suggestions that the regenerative efficiency does not persistently increase to very small length scales, but ultimately decreases. It is further shown that time varying motions, in which the asymmetric components of flow travel as a wave round lines of latitude, can sustain fields having co-rotating asymmetric parts. It is demonstrated that, depending on their common angular velocity, these may exist at slightly smaller magnetic Reynolds numbers than the corresponding models having steady flows and fields. The possible bearing of the integrations on the production of the magnetic field of the Earth is considered, and the implied ohmic dissipation of heat in the core of the Earth is estimated for different values of the parameters defining the model.

Simulation of Maxwell's Equations on GPU Using a High-Order Error-Minimized Scheme

2017 ◽  
Vol 21 (4) ◽  
pp. 1039-1064 ◽  
Author(s):  
Tony W. H. Sheu ◽  
S. Z. Wang ◽  
J. H. Li ◽  
Matthew R. Smith
Keyword(s):  
Parallel Computing ◽  
Graphics Processing Units ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Order Error ◽  
Parallel Speedup ◽  
Explicit Finite Difference ◽  
Graphics Processing

AbstractIn this study an explicit Finite Difference Method (FDM) based scheme is developed to solve the Maxwell's equations in time domain for a lossless medium. This manuscript focuses on two unique aspects – the three dimensional time-accurate discretization of the hyperbolic system of Maxwell equations in three-point non-staggered grid stencil and it's application to parallel computing through the use of Graphics Processing Units (GPU). The proposed temporal scheme is symplectic, thus permitting conservation of all Hamiltonians in the Maxwell equation. Moreover, to enable accurate predictions over large time frames, a phase velocity preserving scheme is developed for treatment of the spatial derivative terms. As a result, the chosen time increment and grid spacing can be optimally coupled. An additional theoretical investigation into this pairing is also shown. Finally, the application of the proposed scheme to parallel computing using one Nvidia K20 Tesla GPU card is demonstrated. For the benchmarks performed, the parallel speedup when compared to a single core of an Intel i7-4820K CPU is approximately 190x.

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