Fast Algorithms for Structured Matrices in Simulations of Physical Systems

Real-world complex phenomena are typically characterized by interacting physical processes, uncertain parameters, dynamic boundaries, and close coupling over a wide span of spatial and temporal scales. Predictive computational models of such phenomena inherit these characteristics and require many novel algorithmic components.

In this talk, I will identify some common features and challenges in physical modeling, focusing on cellular hemodynamics and cell biomechanics, and outline algorithms that enable predictive simulations of these processes. I will discuss some recent advances in efficiently solving large linear systems arising from the discretization of such models.

This is a joint work with Denis Zorin, Michael Shelley, and George Biros.

Abtin Rahimian is a Postdoctoral Research Associate at the Courant Institute of Mathematical Sciences at New York University. He earned his Ph.D. in Computational Science and Engineering from Georgia Institute of Technology under the supervision of Professor George Biros. His thesis work primarily focused on designing parallel algorithms for direct numerical simulation of cellular-scale hemodynamics using boundary integral methods. He holds M.Sc. in Mechanical Engineering from University of Pennsylvania and M.Sc. in Mathematics from Georgia Institute of Technology.

His research interests include scientific computing, multi-scale computational modeling, cellular biomechanics, and parallel algorithms for physical simulations. His current research projects include Tensor-Train accelerated solvers for structured matrices, large-scale boundary integral solvers for partial differential equations in complex and moving geometries, microstructure optimization and design, and modeling mesoscale biophysical systems. Rahimian has publications in the Journal of Computational Physics, the Physical Review Letters, and the ACM/IEEE Supercomputing conference.  After receiving his Ph.D., he worked as a Quant at Goldman Sachs and WorldQuant.

Rahimian is a recipient of the Gordon Bell award from the Association for Computing Machinery’s for “outstanding achievement in high-performance computing applications.”