A fast and stable method is proposed for calculating the time-varying shielding current density in a high-temperature superconducting (HTS) film containing cracks. If an initial-boundary-value problem of the shielding current density is formulated by the T -method, integral forms of Faraday's law on crack surfaces are also imposed as boundary conditions. As a result of the spatial discretization of the initial-boundary-value problem, semi-explicit differential algebraic equations (DAEs) are obtained. Although the DAEs can be solved with standard ordinary-differential-equation (ODE) solvers, much CPU time is required for their numerical solution. In order to shorten the CPU time, the following high-speed algorithm is proposed: the block LU decomposition is incorporated into function evaluations in ODE solvers. A numerical code is developed on the basis of the proposed algorithm and detectability of cracks by the scanning permanent-magnet method is numerically investigated. The results of computations show that, when multiple cracks is contained in an HTS film, resolution of the scanning permanent-magnet method will be degraded remarkably.
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