12:30pm
EQuad E415
Title:
Wavelet-Based Numerical Homogenization
Abstract: We consider the numerical solution of linear partial differential equations with coefficients that vary on scales much smaller than the computational domain. A direct discretization on a coarse grid, will in general give a very inaccurate discrete approximation. Instead, we derive an effective coarse grid operator whose structure is similar to the one given by direct discretization, but with a locally altered stencil that takes the effect of subgrid scales into account. We show a general procedure for doing this, based on wavelet projections of the discrete fine grid operator followed by sparse approximation. We give results from numerical experiments and in particular show an application of the method to the simulation of an optical waveguide filter.