Reduced-Order Modeling of Transient Diffusive Electromagnetic Fields.

摘要

The authors present a reduced-order modeling technique for the computation of three-dimensional electromagnetic diffusive fields. The first-order Maxwell system is taken as a starting point. After a spatial discretization procedure that preserves the structure of Maxwell's equations, an algebraic system of equations is obtained in which the time coordinate appears as a continuous parameter. Approximations to the solution of this system are constructed with the help of a Lanczos algorithm for skew-symmetric matrices. These approximations, called reduced-order models, give an accurate representation of the transient diffusive electromagnetic field on a certain bounded interval in time. The length of this interval can be extended by increasing the number of iterations of the underlying Lanczos algorithm. The structure and the convergence properties of the reduced-order models is discussed and some numerical examples illustrate the performance of the proposed technique.