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Fast linear algebra algorithms with applications in computational flow-physics

Event Type: 
Date and Time: 
Friday, April 7, 2017 - 16:15
Location: 
CTR Conference Room 103
Event Sponsor: 
Parviz Moin, Director of Center for Turbulence Research
Speaker(s): 
Dr. Hadi Pouransari, Mechanical Engineering and Computer Science, Stanford University

In the realm of scientific computing, solving a linear system of equations is often the main bottleneck of the calculations. We extend ideas from the fast multipole method and propose a novel fast linear solver for sparse and dense matrices. The proposed algorithm is fully algebraic and has numerically proved linear complexity with the problem size. Our method relies on the low-rank compression of the new fill-in blocks generated during the elimination process. The compressed fill-ins are computed and stored in a hierarchical tree structure. The proposed solver can be used as a stand-alone direct solver with tunable accuracy determined a priori, or can be employed as a preconditioner in conjunction with an iterative method.

In addition, we present our high performance computational framework developed to simulate heated particle-laden flows. We present various results on the effects of particle preferential concentration. Simulation of the heated particle-laden flows involves solving a variable coefficient Poisson equation. We use this case, as well as many other applications, to benchmark our proposed fast linear solver.

Bio: 
Dr. Hadi Pouransari received his B.S. in Computer Science and Mechanical Engineering from Sharif University of Technology in 2011. He joined Stanford University at the same year and received his M.S. in Mechanical Engineering in 2013. In his Ph.D. studies at Stanford, he worked with Professors Eric Darve and Ali Mani on fast linear algebra algorithms with applications in computational flow-physics. He also obtained a Ph.D. minor in Computer Science from Stanford University.