Abstract
A fast and stable method is proposed for calculating the shielding current density in a high-temperature superconducting film containing cracks. After discretized with the finite-element method, the initial-boundary-value problem of the shielding current density reduces to semi-explicit differential algebraic equations (DAEs). Although the DAEs can be solved with standard ordinary-differential-equation (ODE) solvers, much CPU time is required for its numerical solution. In order to shorten the CPU time, a high-speed algorithm is proposed. In the algorithm, the block LU decomposition is incorporated into function evaluations in ODE solvers. A numerical code is developed on the basis of the proposed method, and detectability of cracks by the scanning permanent-magnet method (SPM) is numerically investigated. The results of computations show that the SPM can realize high-speed crack detection. In addition, it is also found that, for multiple cracks, resolution of the SPM will be remarkably degraded.
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