A Fast Matrix Compression Method for Large Scale Numerical Modelling of Rotationally Symmetric 3D Passive Structures in Fusion Devices

Abstract

This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER).

Keywords

• plasma fusion
• integral formulations
• fast methods
• eddy current
• QR-MGS sparsification
• H-matrix