Mathematics Colloquium: Fast algorithms for the simulation of biofluids

Fast algorithms for the simulation of biofluids

Dr. Minghao Wu Rostami
Assistant Professor
Department of Mathematics
Syracuse University

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Abstract:
The simulation of a fluid around dynamic biological structures, such as bacteria, cilia and sperm, entails the solution of challenging systems of linear and differential equations. In this talk, we present several efficient numerical algorithms for tackling them. The talk consists of the following two parts, which are joint work with Sarah Olson (WPI) and Weifan Liu (Syracuse), respectively. Some of the most popular methods for calculating fluid-structure interactions give rise to dense matrices, that is, matrices with very few zero entries; and they tend to be large and very costly to work with for practical models in which the number of structures is large. We extend the Kernel-Independent Fast Multipole Method (KIFMM) to calculate the matrix-vector products involving these large, dense matrices and develop efficient preconditioners for solving the linear systems involving them as well. The methods that we propose are matrix-free, that is, they do not require explicit construction of the matrices. In order to track the dynamics of the biological structures over a period of time, we need to solve a system of nonlinear Ordinary Differential Equations (ODEs). When multiple computer cores are available, we can parallelize the computation of fluid-structure interactions at each time step; however, the parallel speedup of this approach tends to “saturate” as the number of cores increases. We propose to apply the Parareal algorithm to parallelize the solution of the ODEs in the time domain instead. Roughly speaking, we divide the time domain into “slices” and solve the ODEs on these slices simultaneously. In order to further improve its speedup, we develop several new ODE solvers by extrapolating existing ones.

Speaker Bio:
Minghao received her PhD’s degree in Applied Mathematics and Scientific Computation from University of Maryland, College Park in 2012. She was a Postdoctoral researcher at Worcester Polytechnic Institute from 2013 to 2016. Minghao has been a tenure-track Assistant Professor at the Department of Mathematics, Syracuse University since 2016. Minghao’s research interests lie in numerical linear algebra, computational fluid dynamics, and mathematical biology.

Intended Audience:
All are welcome. Those with interest in the topic.