News Description

Non-uniform Grid Based Acceleration of Iterative and Direct Integral Equation Solvers

Presentation given by Amir Boag, School of Electrical Engineering, Tel Aviv University, Israël

Monday October 24th 2016, 3pm, Louvain-la-Neuve, Maxwell Building, Shannon Room

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(N²) to O(NlogN) (N being the number of unknowns), thus facilitating fast iterative solution of electromagnetic and acoustic problems.  Furthermore, 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)

Amir Boag received the B.Sc. degree in electrical engineering and the B.A. degree in physics in 1983, both Summa Cum Laude, the M.Sc. degree in electrical engineering in 1985, and the Ph.D. degree in electrical engineering in 1991, all from Technion - Israel Institute of Technology, Haifa, Israel. 

From 1991 to 1992 he was on the Faculty of the Department of Electrical Engineering at the Technion.  From 1992 to 1994 he has been a Visiting Assistant Professor with the Electromagnetic Communication Laboratory of the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign.  In 1994, he joined Israel Aircraft Industries as a research engineer and became a manager of the Electromagnetics Department in 1997.  Since 1999, he is with the Physical Electronics Department of the School of Electrical Engineering at Tel Aviv University, where he is currently a Professor.

Dr. Boag's interests are in computational electromagnetics, wave scattering, imaging, and design of antennas and optical devices.  He has published over 100 journal articles and presented more than 200 conference papers on electromagnetics and acoustics.  In 2008, Amir Boag was named a Fellow of the IEEE for his contributions to integral equation based analysis, design, and imaging techniques.