Efficient solvers for space-fractional diffusion equations

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This work discusses recent developments in the numerical approximation of space fractional diffusion equations using particle-based and finite-volume discretizations. We first analyze the performance of the resulting approximations, and then turn our attention to efficient solution of the resulting dense-matrix systems. To this end, we develop block low-rank and hierarchical matrix approaches, and illustrate the scalability of the resulting codes in a multidimensional
variable property setting.

Brief Biography

Omar Knio received his Ph.D. in Mechanical Engineering from MIT.  He was a member of the Mechanical Engineering Faculty at Johns Hopkins from 1991-2011, and of the Mechanical Engineering and Materials Science Department at Duke from 2011-2018.  In 2013, he joined Applied Mathematics and Computational Science Program at KAUST, where he currently serves as Interim Dean of the CEMSE.