Where: 362C (ACS building)
Speaker: Elsie Cortes
Title: Modified Grid for EEC-BIE Framework for Optical Cloaking Models
Abstract: Boundary integral equation (BIE) methods are useful for reducing the complexity of problems by one dimension - in our case, allowing us to work on a two-dimensional problem in 1D. As part of these methods, our solution is represented by layer potentials that allow us to evaluate the solution anywhere in our domain. We are not restricted by the mesh constructed on the boundary, which is used to solve our system. The model used in this project consists of multiple, concentric boundaries separating layers defined by different properties. The layers are defined by a body-fitted grid such that the layer each point belongs to is easily identifiable. For this project, it was necessary to modify the grid such that it would be more refined near the boundaries. Furthermore, in order to treat the close evaluation problem near the boundaries, this refined sub-grid needed to be constructed from the boundary's inward or outward unit normal. The reduction in the error of our method from this modified grid is shown in the results.