THE USE OF PLANE WAVES TO APPROXIMATE WAVE PROPAGATION IN ANISOTROPIC MEDIA

In this paper we extend the standard Ultra Weak Variational Formulation （UWVF） of Maxwell＇s equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media （however error estimates are not yet available） and completely describe the new scheme. We then consider TM mode scattering, show how this results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.     

THE COMPUTATION OF GREEN'S FUNCTION FOR THE LAPLACE OPERATOR IN A RECTANGLE

Abstract

The note gives an efficient method to compute Green's function for Laplace's operator in an arbitrary rectangle.     

DECAY OF ENERGY FOR A DISSIPATIVE ANISOTROPIC ELASTIC SYSTEM

In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua’s estimate technique, we prove the decay property of energy for anisotropic elastic system.