High-Performance Simulation of Shielding Current Density in HTS by Constitutive-Relation Relaxation Method

The high-performance method has been investigated for calculating the shielding current density in a high-temperature superconducting thin film. After discretized with the finite element method, the initial-boundary-value problem of the shielding current density is transformed to the nonlinear system of ordinary-differential equations. When the Runge-Kutta method with an adaptive step-size control is applied to the system, an overflow might be caused in the step-size correction iteration. In order to suppress the overflow, the constitutive relation is modified so that its solution may satisfy the original relation. This method is called the constitutive-relation relaxation method. A numerical code for analyzing the shielding current density has been developed on the basis of the method and, as an application of the code, the permanent-magnet method for measuring the critical current density has been investigated numerically.