Convergence-property improvement of GMRES in shielding current analysis of cracked high-temperature superconducting film

摘要

A high-performance method is proposed for solving a linear system in the shielding current analysis of a cracked high-temperature superconducting film. After discretized with respect to time and space, the initial-boundary-value problem of the shielding current density reduces to a linear system at each iteration cycle of the Newton method. Although the linear system can be easily solved with GMRES, both crack length and the number of cracks affect convergence property significantly. In order to improve convergence property of GMRES, other variables than corrections of the current vector potential are all eliminated from the linear system. As a result, convergence property of GMRES is hardly influenced by either crack length or the number of cracks.