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

Abstract

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.

Improvement of Convergence Property of Communication Avoiding Conjugate Gradient Method for Linear System Obtained from Meshless Approaches

“…To improve above behavior of the system, the variable reduction method is adopted as the preconditioning strategy of CG. It is known that the variable reduction method is a very effective preconditioning strategy for the linear system with constraint condition [4]. In EFG, the boundary conditions are imposed using constraint condition such as Lagrange multiplier method, and only unknown vector x is required as a solution of (1).…”

Acceleration Techniques for Linear-System Solver in Shielding Current Analysis of Cracked HTS Film

“…In the present study, the shielding current analysis is applied to the scanning permanent-magnet method (SPMM) [2,4] that is one of contactless methods for measuring the spatial distribution of the critical current density in an HTS film. A schematic view of the SPMM is shown in Fig.…”

“…Under the thin-plate approximation, there exists a scalar function T (x, t) such that J = (2/b)∇ × (T e z ), and its time evolution is governed by the following integrodifferential equation [1][2][3]:…”

“…In order to conceptually design the contactless methods, the shielding current density must be accurately evaluated in a cracked HTS film. For this reason, the authors have developed numerical methods for analyzing the shielding current density on the basis of the current-vector-potential method [1][2][3].…”

“…In fact, even if the Krylovspace method such as GMRES is applied to the linear system, its residual history shows a degraded convergence property. In order to resolve this problem, the authors developed the variable-reduction method (VRM) [2,3]. As a result, it is found that the VRM is effective in speeding up the shielding current analysis of a cracked HTS film.…”