PNNL

Abstract

The motion or, generally, the deformation of an electromagnetic medium makes it numerically difficult to implement the electromagnetic field boundary conditions and hence solve the conventional set of Maxwell's equations. The difficulty lies in the fact that the domain of solution and its boundary can be significantly distorted. A Lagrangian numerical treatment of Maxwell's equations is therefore a viable way to numerically deal with the initial-boundary-value problem of electromagnetics under the condition of deformation of the medium. The objective of the present work is to solve the set of Maxwell's equations in a material frame of reference, hence follow a Lagrangian approach to the problem. The deformation of the medium brings in the matter flow field and the Cauchy's finite strain tensor into the final set of Maxwell's equations. In effect, these deformation-kinematics fields map the geometrical changes in the domain of solution continuously to the initial configuration. The Crank-Nicolson integration scheme, with second order accuracy in time, is used to treat the time derivatives, rendering the set of Maxwell's equations elliptic at every time increment. The elliptic set is then treated using the First-Order Systems Least-Squares (FOSLS) variational formalism which results in a symmetric, positive definite bilinear form. Numerical results are presented for the transient electromagnetic fields and the eddy current in a bounded conducting medium undergoing time-dependent deformation. The Lorentz force field and the Joule heating are accurately computed.