Fast Solvers Based on Generalized Source Integral Equations with Improved Kernels
Recent years have seen an increasing interest in the development of fast direct integral equation solvers. These do not rely on the convergence of iterative procedures for obtaining the solution. Instead, they compute a compressed factorized form of the impedance matrix resulting from the discretization of an underlying integral equation. The compressed form can then be applied to multiple right-hand sides, at a relatively low additional cost. The most common class of direct integral equation solvers exploits the rank-deficiency of the off-diagonal blocks of the impedance matrix, in order to express them in a compressed manner. However, such rank deficiency is inherent to problems of small size compared to the wavelength as well as to problems of reduced dimensionality, e.g., elongated and quasi-planar problems.
The present work proposes a class of Generalized Source Integral Equation (GSIE) formulations, which aim to extend the range of problems exhibiting inherent rank-deficiency. The new formulations effectively reduce the problem’s dimensionality and, thus, allow for efficient low-rank matrix compression. When these formulations are used with hierarchical matrix compression and factorization algorithms, fast direct solvers are obtained. Shielded-source and multipole-based types of directional kernels to be employed in the GSIEs are proposed. The computational bottlenecks introduced by the shielded-source kernels are reduced by using non-uniform grid (NG) sampling techniques. The NG techniques, originally developed for fast iterative solvers, are employed for efficient computation of fields produced by the shielded sources. On the other hand, recently developed multipole-based kernels facilitate simpler and more efficient field computation. The two formulations’ properties and limitations are studied and their use for the development of fast direct solvers is showcased.
Date and Time
Location
Hosts
Registration
- Date: 28 Apr 2024
- Time: 02:00 PM to 04:00 PM
- All times are (UTC+08:00) Beijing
-
Add Event to Calendar
- Caoan Road 4800
- shanghai, Shanghai
- China
- Building: Zhixin Building
- Starts 27 April 2024 12:00 AM
- Ends 29 April 2024 12:00 AM
- All times are (UTC+08:00) Beijing
- No Admission Charge
Speakers
Amir Boag
Biography:
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 and acoustics, numerically efficient algorithms for quantum-electromagnetic simulations, radar imaging, and design of antennas and optical devices. He has published over 130 journal articles and presented more than 300 conference papers on electromagnetics and acoustics. Prof. Boag served as an Associate Editor for IEEE Transactions on Antennas and Propagation. He is a Fellow of the Electromagnetics Academy. In 2008, Amir Boag was named a Fellow of the IEEE for his contributions to integral equation based analysis, design, and imaging techniques.