Geodesic
Finite-difference algorithm for solving two-dimensional quasi-stationary electromagnetic problems with moving transmitter
Matematičeskoe modelirovanie, Tome 19 (2007) no. 9, pp. 79-93

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We consider a problem of calculating the electromagnetic field in and nearby the metal pipe walls in the cylindrical coordinate system. Transmitter with low-frequency exciting current is slowly moved along the axis. The quasistationary approximation is used to model the field. We propose a second-order finite difference algorithm with exact non-uniform boundary conditions on the open boundaries of the computational domain in axial direction. The matrix sweep method is used to solve a given problem with multiple right-hand sides generated by the transmitter. Numerical tests to demonstrate efficiency of the proposed method is describe. 
@article{MM_2007_19_9_a5,
     author = {N. A. Zaitsev and I. L. Sofronov},
     title = {Finite-difference algorithm for solving two-dimensional quasi-stationary electromagnetic problems with moving transmitter},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {79--93},
     publisher = {mathdoc},
     volume = {19},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_9_a5/}
}
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N. A. Zaitsev; I. L. Sofronov. Finite-difference algorithm for solving two-dimensional quasi-stationary electromagnetic problems with moving transmitter. Matematičeskoe modelirovanie, Tome 19 (2007) no. 9, pp. 79-93. http://geodesic.mathdoc.fr/item/MM_2007_19_9_a5/