Three Dimensional Finite Element Vector Potential Formulation of Magnetic Fields in Electrical Apparatus

1981 ◽  
Vol PAS-100 (8) ◽  
pp. 4104-4111 ◽  
Author(s):  
N. Demerdash ◽  
F. Fouad ◽  
T. Nehl ◽  
O. Mohammed
Keyword(s):  
Finite Element ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Three Dimensional ◽  
Potential Formulation ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Electrical Apparatus

scholarly journals The three-dimensional finite element forward modelling of complex excitation source NMR

2019 ◽  
Vol 17 (1) ◽  
pp. 127-137
Author(s):  
Zhipeng Qi ◽  
Xiu Li ◽  
Kerui Fan ◽  
Qingquan Zhi
Keyword(s):  
Finite Element ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Excitation Source ◽  
Magnetic Vector Potential ◽  
Forward Modelling ◽  
Dimensional Finite Element ◽  
Nmr Sensitivity ◽  
Three Dimensional Finite Element ◽  
Nuclear Magnetic

Abstract Traditional nuclear magnetic resonance (NMR) is mainly applied to horizontal ground and one-dimensional electrical structures. However, calculations of the excitation fields rarely consider the three-dimensional electrical changes of the subsurface medium and undulating terrain, or the deformations caused by emission sources. Therefore, to analyse the influences of terrain fluctuations, emission source deformations and three-dimensional electrical changes on NMR, three-dimensional finite element forward modelling of undulating terrain NMR was conducted in this study. First, based on a scalar finite element method, the direct calculations of the excited magnetic fields of a three-dimensional electrical medium were realised, which improved calculation accuracy by avoiding the finite element calculations of magnetic vector potential and vector on the magnetic field. During the source loading process, the equivalent thin wire source of the pseudo δ function was used to load the source function directly into the equation for the purpose of achieving total field calculations. This was completed to enable the calculations to be applied to any shape of the transmitting loop and undulating terrain. Then, the components of the excitation magnetic fields perpendicular to the geomagnetic fields were calculated using the rotation matrix. Finally, the NMR sensitivity function and 3D responses were calculated. The calculations of the excitation magnetic fields were verified using a uniform half-space model. The overall algorithm was tested by the nuclear magnetic responses of the layered medium. Also, a typical undulating terrain model was adopted and the complex excitation source NMR was simulated using the algorithm proposed in this study. The algorithm provided a three-dimensional forward basis for the NMR inversion in the cases of determining the electrical medium for the subsequent undulating terrain.

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