Event Type:

Department Colloquium

Date/Time:

Friday, June 1, 2007 - 08:00

Location:

Kidd 364

Local Speaker:

Abstract:

We consider the behavior of the electromagnetic field in a material presenting heterogeneous microstructures (composite materials), which are described by spatially periodic parameters. When such composite materials are subject to electromagnetic fields generated by currents of varying frequencies and the period of the structure is small compared to the wavelength, the coefficients in Maxwell's equations oscillate rapidly. These oscillating coefficients are difficult to treat numerically in simulations. Homogenization is a process in which the composite material having a microscopic structure is replaced with an equivalent material having macroscopic, homogeneous properties. In this process of homogenization the rapidly oscillating coefficients are replaced with new effective constant coefficients. In this talk we present a numerical method for the homogenized problem constructed using the periodic unfolding method, which has been introduced in the abstract framework of stationary elliptic equations. The numerical method uses finite elements for the spatial discretization and a fast recursive approach to numerically compute the convolution terms that appear in the homogenized equations. A comparison is made between the effective parameters obtained by the numerical method presented here and those computed by traditional mixture formulae, such as the Maxwell Garnett formula, which are based on physical arguments.