Finite-difference algorithm for solving two-dimensional quasi-stationary electromagnetic problems with moving transmitter

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.