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
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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>
______________________________________________________________________
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yoel Shkolnisky   <yoelsh@post.tau.ac.il>