Abstract

The dynamics of microswimmers immersed in viscous fluid can be described by incompressibleStokes equation. We will discuss our recent work on the algorithms for two numerical challenges ofthe simulations of such problems.(1) Parallel-in-time algorithm: The long-ime numericasimulations of biofluid applications often require the use of parallel computing methods due to highcomputation costs. However, the parallel speedup saturates as the number of computer coresincreases if spatial parallelization alone is used. To resolve this problem, we develop a parallel-intime method based on the Parareal algorithm for simulating biofluid problems. in particular, wedevelop novel non-intrusive coarse solvers for the serial sweeps of the Parareal algorithm. (2)Multigrid method: With numerical methods such as Method of Regularized Stokeslet (MRS), theBoundary lntegral Equation (BlE) formulation, and the Boundary Element Method (BEM), given theluid velocities at these points, the hydrodynamic forces can be obtained by solving the dense linearsystem described by a kernel function. We propose a multigrid solver for solving such a linealsystem using the data-sparsity of the matrix and the regularity of the geometry of the structuresNumerical experiments on a variety of bio-inspired microswimmers immersed in a Stokes flowdemonstrate the effectiveness and efficiency of the proposed solvers.

Speaker Intro

Weifan Liu is a lecturer of Department of Mathematics at Beijing Forestry University. Shereceived her Ph.D from Duke University in 2019, and was a Philip T. Church Postdoctoral Fellow atSyracuse University from 2019 to 2022. Her research interests are in fast algorithms andmathematical modeling for various problems that arise from biology and physics.