Application of Hierarchical Matrices to Large-Scale Electromagnetic Field Analyses of Coils Wound With Coated Conductors

Because the coefficient matrix is dense in the electromagnetic-field-analysis models of coated conductors using current vector potentials, the analyses of large-scale coils require a large amount of memory and long computation time. In this paper, we introduce hierarchical matrices by using the HACApK library in order to reduce both memory consumption and computation time. The effect of the method with respect to memory consumption and computation time is examined in numerical tests using a pancake coil wound with a coated conductor. The effect of parallel computations is also examined. Finally, we analyzed a large-scale magnet, with 1.5 million unknown values.