From <yoelsh@post.tau.ac.il> Fri Apr 19 16:30:05 2013 Date: Fri, 19 Apr 2013 16:35:14 +0300 From: Yoel Shkolnisky <yoelsh@post.tau.ac.il> To: <AMATH-IL@LISTSERV.TAU.AC.IL> Subject: Applied Mathematics Seminar - next week ----=-=-=-=.-.=-=-=-=--- Tel Aviv University Applied Mathematics Seminar Date: Tuesday April 23, 2013, 15:10 Place: Schreiber Bldg, Room 309 Speaker: Michael Medvinsky, Tel Aviv University Title: A High Order Accurate Algorithm for Transmission & Scattering Problems with Interfaces Unaligned to the grid Abstract: We study the propagation of waves over large regions of space with smooth, but not necessarily constant, material characteristics, separated into sub-domains by interfaces of arbitrary shape. We consider a divide and conquer approach based on wave splitting into incoming and outgoing waves. We assemble the overall solution from the set of individual solutions to an auxiliary problem (AP). The AP is defined independently for each sub-domain. The choice of the AP is relatively flexible; it can be formulated to enable an easy and economical numerical solution. Our new method uses only simple structured grids, e.g., Cartesian or polar, regardless of the shape of the boundaries or interfaces. In the regions of smoothness, it employs high order accurate finite difference schemes on compact stencils. They do not require any additional boundary conditions besides those needed for the underlying differential equation itself. Our approach is based on Calderon's operators and the method of difference potentials [1]. It has a number of important advantages; it easily handles curvilinear boundaries, variable coefficients and general boundary conditions while the complexity is that of a finite-difference scheme on a regular structured grid. A main advantage is that this methodology provides high order accuracy and overcomes the difficulties inherent in more traditional approaches. Furthermore, our new method uses only simple structured grids, e.g., Cartesian or polar, regardless of the shape of the interface or external boundaries. [1] V.S. Ryaben'kii. Method of Difference Potentials and Its Applications, volume 30 of Springer Series in Computational Mathematics. Springer-Verlag. Berlin, 2002. Webpage of the applied mathematics seminar: <https://sites.google.com/site/tauamathseminar/> ______________________________________________________________________ Dr. Yoel Shkolnisky Department of Applied Mathematics School of Mathematical Sciences phone: 972-3-640-8705 Tel Aviv University, fax : 972-3-640-9357 Tel Aviv, 69978 Israel email: <yoelsh@post.tau.ac.il> ______________________________________________________________________ --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yoel Shkolnisky <yoelsh@post.tau.ac.il>