Numerical approximation of asymptotically disappearing solutions of Maxwell's equations (Q2870697)

The present paper deals with the study of the numerical approximation of asymptotically disappearing solutions of the Maxwell system with the unknowns electric field and magnetic field. This study is performed in the exterior of a polyhedron, whose boundary approximates the sphere.NEWLINENEWLINEIn the first part, the authors state the strong form of the boundary value problem for Maxwell's equations. Next, the variational weak formulation is described. The main result of this section establishes the energy decay of the corresponding system. The authors also discuss the discretization of this variational form and how it can be guaranteed a good approximation of the asymptotically disappearing. In the next section, the authors describe the matrix representation of the semi-discrete system and the properties of the Crank-Nicolson scheme. Numerical results for the sphere are performed in the final part.