Simulation of Nonlinear Magnetic Systems by the Finite Element Method Using BLR-Factorization

Abstract

The possibility of practical application of BLR-factorization (low-rank approximation of the matrix of un-knowns of a system of linear equations) for finite element modeling of the electromagnetic field topology of nonlinear magnetic systems is considered. A method for estimating the accuracy of the computed solution of the SLAE and the nature of the influence of the given accuracy of the low-rank approximation of the matrix of un-knowns on the upper limit of the relative forward error of the computed solution of the SLAE are shown. Using a model problem as an example, the dependence of the accuracy of calculating the integral characteristics of an electromechanical apparatus on the tolerance of the low-rank approximation of the matrix of unknowns is shown, as well as its effect on the convergence of the process of solving a nonlinear numerical problem. A quantitative assessment of the reduction in the computational complexity of the process of solving a numerical problem and the required amount of computer memory for solving the SLAE is carried out. The applicability of BLR-factorization for finite element modeling of the topology of the electromagnetic field without the use of numerical methods of the Krylov subspace is estimated.