Tel Aviv University
  School of Mathematical Sciences
    Applied Mathematics Seminar
 
Date:          Tuesday May 17, 2011, 15:10
Place:             Schreiber Bldg, Room 309
 
Speaker:     Amir Boag
          Tel Aviv University
 
Title: Non-uniform Grid Based Acceleration of
  Iterative and Direct Integral Equation Solvers
 
Abstract:
 
In this presentation we describe the Non-uniform Grid (NG) approach and
demonstrate that it can be employed to accelerate both iterative and
direct integral equation-based solvers.  The NG approach stems from the
observation that, locally, phase and amplitude compensated field
radiated by a finite size source is an essentially bandlimited function
of the angular and radial coordinates of the source centered spherical
coordinate system.  Therefore, the radiated field can be sampled on a
non-uniform spatial grid (NG) and subsequently evaluated at any point by
phase and amplitude compensated interpolation.  Using such NG field
representation and conventional hierarchical domain decomposition, the
multilevel non-uniform grid (MLNG) algorithm reduces the complexity of
field evaluation from o(N^2)  to O(N log N)  (N  being the number of
unknowns), thus facilitating fast iterative solution of electromagnetic
and acoustic problems.  Recently, we developed a direct solver using
NG-based matrix compression for scattering from quasi-planar objects.
In this context, we show that approximately O(N^1.5) complexity is
attained for the matrix compression, and the computational cost of the
solution for each right-hand-side is approximately of O(N).
 
For information about future seminars, see
 <http://www.tau.ac.il/~adid/AM_seminar_2010-201/AM_seminar_2010-2011.html>
 
______________________________________________________________________
 
Dr. Adi Ditkowski                                                     |
Department of Applied Mathematics                                     |
School of Mathematical Sciences          phone:  972-3-640-5987       |
Tel Aviv University,                     fax  :  972-3-640-9357       |
Tel Aviv, 69978 Israel                   email:   <adid@post.tau.ac.il>  |
______________________________________________________________________
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Adi Ditkowski   <adid@post.tau.ac.il>