The Problem of Eigenvalues in the Problem of Calculating the Pattern of Current Spreading over the Spacecraft Surface

The aim of the work is to identify an optimal way to take into account all the eigenvalues and eigenvectors of the sparse matrix of the system and their further use to build a macromodel of the equivalent linear electrical circuit of the spacecraft. For the problem of numerically accounting for eigenvectors and eigenvalues of a sparse matrix, two algorithms were compared and discussed: the QR algorithm and the Rayleigh iteration algorithm. We reasonably chose the optimal algorithm for taking into account eigenpairs in the problem of the spacecraft charge. An important result of the work is the proposed approach of combining sparse matrix compression methods with macro-modeling to build a new mathematical model of the spacecraft electrical circuit.