Three-dimensional analysis on time evolution of shielding current density in HTS

The numerical method for calculating the shielding current density in the high-T_c superconductor (HTS) is developed by use of the element-free Galerkin method. The behavior of the shielding current density is expressed by the integro-differential equations. In order to solve the initial-boundary-value problem of the equations, the weak form is derived that is equivalent to the problem. Since the essential boundary conditions are directly incorporated into the weak form by using the Lagrange multipliers, both the test and the trial functions do not need to satisfy the conditions. The numerical code for analyzing the time evolution of the shielding current density has been developed by using the above method. The time sequence of the magnetic field is calculated by means of the code and its spectral analysis is performed.