Berkeley Lab – CS Seminar
Date:
Thursday, February 6, 2025
Time:
3:00pm – 4:00pm
Location:
Shyh Wang Hall – Bldg. 59, Room 3070
Speakers(s) and Affiliations(s):
Yaniv Brick
Ben-Gurion University of the Negev, Beer-Sheva, Israel
Title:
Generalized Integral Equation Formulations for Efficient High-Frequency Wave Analysis
Abstract:
High-fidelity wave simulation of large and intricate systems has been enabled greatly thanks to advances to the numerical solution of integral equation (IE) formulations of scattering problems. Fast solution algorithms and more stable formulations have been progressively developed to combat the high computational costs and degradation in problem conditioning associated with the increase in the electrical size, model detail, and numbers of simulated scenarios. Recent research in these fronts has focused on the development of fast direct solvers, relying on algebraic compression and compressed factorization of impedance matrices. Among these, notable are the classes of first generation low-rank compression-based hierarchical matrix solvers and the more sophisticated butterfly-compression solvers. The latter exhibit superior asymptotic cost scaling, even for geometric settings that do not exhibit inherent (asymptotic) rank-deficiency, i.e., ones that are not of reduced dimensionality. The appeal of the former is in their relative simplicity and effectiveness for systems that include large quasi-planar or elongated parts. Complementary to the search for faster and more compressive algebraic structures is that for IE formulations that are of enhanced compressibility, which will be the focus of our talk (selected publications listed below). Generalized IE formulations use modified Green’s function kernels to turn, where possible, broadside wave interactions between large sub-structures, which are of fast-scaling ranks, into reduced dimensionality ones. The resulting moment matrix blocks exhibit slower scaling of the ranks and greater rank-deficiency. This translates to greater compression and faster compressed factorization and solution. In the talk, we will review the evolution of generalized IEs, discuss the various types of such formulations, and present algorithms for removal of the bottlenecks associated with the computations of their more complex IE kernels. We will then demonstrate the algorithmic utilization of the reduced effective dimensionality (e.g., by employing non-uniform and randomized field sampling technique) for the design of fast solvers.
[1] Y. Brick, V. Lomakin, and A. Boag, “Fast Green's function evaluation for sources and observers near smooth convex bodies,” IEEE Trans. Antennas Propag., vol. 62, no. 6, pp. 3374 – 3378, June 2014.
[2] A. Sharshevsky, Y. Brick, and A. Boag, “Direct solution of scattering problems using generalized source integral equations,” IEEE Trans. Antennas Propag., vol. 68, no. 7, pp. 5512-5523, July 2020.
[3] D. Zvulun, Y. Brick, and A. Boag “A generalized source integral equation for enhanced compression in three dimensions,” IEEE Trans. Antennas Propag., vol. 72, no. 12, pp. 9316-9325, Dec. 2023.
[4] Y. Dahan and Y. Brick , “Fast direct solvers with arbitrary admissibility using generalized source integral equations,” IEEE Trans. Antennas Propag., vol. 72, no. 10, pp. 7872-7882, Oct. 2024.
Bio:
Yaniv Brick received the B.Sc. (2005, magna cum laude), M.Sc. (2007, summa cum laude), and Ph.D (2015) degrees in electrical and electronics engineering from the School of Electrical Engineering, Tel Aviv University. From 2014 to 2017, he was a Post-Doctoral Fellow with the Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin. Since 2017, he has been with the School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, where he is an associate professor. He is currently a visiting scholar at the University of California San Diego Center for Memory and Recording Research (CMRR). He has been an associate editor for the IEEE Journal on Multiscale and Multiphysics Computational Techniques and the IEEE Antennas and Propagation Magazine. He is a senior member of the IEEE and the International Union of Radio Science (URSI), and a recipient of the IEEE AP-S Doctoral Research Award, the Peter O’Donnell Jr. Post-Doctoral
2 Fellowships in Computational Engineering and Sciences, the Fulbright Post-Doctoral Fellowship Program Grant, and the Fulbright Alumni Prize.
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Meeting ID: 972 2981 2706
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Meeting ID: 972 2981 2706
Host of Seminar:
Yang Liu
Scalable Solvers Group (SSG)
Applied Mathematics and Computational Research Division
Lawrence Berkeley National Laboratory