Numerical Simulation of Shielding Current Density in HTS Film by Using Acceleration Technique With $\mathcal {H}$-Matrix Method

Numerical techniques are proposed for fast solving a linear system appearing in the shielding current analysis in a cracked high-temperature superconducting (HTS) film. After discretized with respect to time and space, an initial-boundary-value problem of the shielding current density reduces to a problem in which a linear system is solved at each iteration of the Newton method. Although the coefficient matrix of the system is dense, a fast iterative linear-system solver can be realized by implementing the H-matrix method to matrix-vector multiplications. On the other hand, the CPU time required for the iterative solver increases with the number of elements adjacent to cracks. To remove such unfavorable characteristics, the QR factorization is applied to a part of the linear system so that all unknowns other than correction of the current vector potential may be eliminated from the linear system. The performance of the techniques is evaluated and, as an application of the techniques, detectability of multiple cracks in an HTS film is investigated numerically.