Numerical Simulation of Shielding Current Density in High-Temperature Superconductor by Parallel Processing on PC Cluster

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The numerical method has been investigated for analyzing the time evolution of the shielding current density in the high-temperature superconductor. Although the finite element method has been widely used in the various fields of the engineering, it has been plagued by two inherent difficulties : the limited smoothness ofthe approximate solution and the time-consuming element generation. In order to resolve the difficulties, several meshless approaches have been proposed.In the present study, the 3D numerical simulation code has been developed on the basis of the meshless approach and it has been employed for calculating the time evolution of the shielding current density In order to discretize the governing equations with respect to space and time, the backward Euler method and the element free Galerkin method are employed, respectively. For the purpose of solving the resulting nonlinear system stably, the adaptively deaccelerated Newton method has been proposed. Furthermore, to achieve the high-performance computing, the parallel processing by using the MPI on a PC cluster is applied to the numerical simulation.By using the above simulation method, the inductive method for measuring the critical current density is investigated. When the high-temperature superconductor is exposed to the magnetic field generated by the ac coil current, the voltage induced in the coil contains not only a linear component but higher harmonics. The harmonic voltages are numerically calculated as a function of the coil current. The results of computations show that, above a certain limit of the coil current, The third harmonic voltage is suddenly excited. In addition, it is also found that the square root of the third harmonic voltage is approximately a linear function of the coil current.