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Speaker: Hari Sundar
Title:
Scalable Data Structures and Algorithms for Parallel PDE Solvers
Abstract:
Our ever-increasing computing capabilities promises to catalyze breakthroughs in our ability to understand, predict, and optimize complex natural, engineered, and societal systems. Amongst the many hurdles faced in scaling today’s simulations to the next generation of machines, one of the most challenging is the design of solvers that can make effective use of billion-way concurrency and exhibit optimal work and depth complexity. In my talk I will discuss my work on developing such scalable parallel algorithms for three problems: (1) multi-resolution spatial discretization schemes using octrees; (2) geometric multigrid; and (3) the fast Gauss transform. Octrees are used for adaptive mesh refinement, an important component for the numerical solution of partial differential equations (PDEs). Elliptic PDEs are encountered in several physical and biological problems such as electromagnetism, quantum mechanics and cardiac electrophysiology. They are also used in nonphysical applications such as mesh generation, image segmentation and registration and various inverse problems. Multigrid is one of the most effective methods for solving elliptic PDEs and is algorithmically optimal and robust when combined with Krylov methods. The fast Gauss transform (FGT) is an optimal complexity algorithm for the calculation of the sum of N Gaussians at M points. It is an effective solver for parabolic PDEs on moving boundaries and has wider applications in fields like signal analysis, regression, computational finance and computer graphics. I will conclude with results that demonstrate the scalability and performance of these methods on problems with over 10^{11}$ unknowns and on machines with 2^{18} cores.
Bio
Hari Sundar is a post-doctoral researcher at the Institute for Computational Engineering & Sciences at the University of Texas at Austin. The central focus of his research is the development of computationally optimal parallel, high-performance algorithms that are efficient and scalable on state-of-the-art architectures. Hari received his Ph.D. from the University of Pennsylvania, advised by Christos Davatzikos and George Biros. His work has been nominated for Best Student Paper at ACM/IEEE Supercomputing in 2007 and for Best Paper in 2010.
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