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A high-speed analysis of a shielding current density in a high-temperature superconducting film containing cracks has been proposed. To this end, a numerical code has been developed for analyzing the shielding current density in an HTS film. In the code, the GMRES(k) with the H-matrix method has been implemented to solve a linear-system obtained by discretizing an initial-boundary-value problem of a nonlinear integro-differential equation with respect to time and space. The results of the computations show that, if the Jacobi scaling is not applied to the linear-system, the Newton method does not converge at a certain time step. Therefore, the Jacobi scaling is an necessary tool for analyzing the shielding current density. Furthermore, by using the GMRES(k) method with the H-matrix method as a linear-system solver, the time evolution of the shielding current can be analyzed with high speed. In conclusion, the speed of the GMRES(k) with H-matrix method is about 221.3 times as fast as that of the LU decomposition.

High-speed method for analyzing shielding current density in HTS with cracks: implementation of <i>H</i>-matrix method to GMRES