Beijing Institute of Mathematical Sciences and Applications

Xiao Pei Jiao , Zhi Ting Ma , Fan Sheng Xiong , Wu Yue Yang

Weifan Liu

Thursday, May 30, 2024 3:30 PM - 5:00 PM

A3-1-301

Zoom 815 762 8413 (BIMSA)

The dynamics of microswimmers immersed in viscous fluid can be described by incompressible Stokes equation. We will discuss our recent work on the algorithms for two numerical challenges of the simulations of such problems. (1) Parallel-in-time algorithm: The long-time numerical simulations of biofluid applications often require the use of parallel computing methods due to high computation costs. However, the parallel speedup saturates as the number of computer cores increases if spatial parallelization alone is used. To resolve this problem, we develop a parallel-in-time method based on the Parareal algorithm for simulating biofluid problems. In particular, we develop 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), the Boundary Integral Equation (BIE) formulation, and the Boundary Element Method (BEM), given the fluid velocities at these points, the hydrodynamic forces can be obtained by solving the dense linear system described by a kernel function. We propose a multigrid solver for solving such a linear system using the data-sparsity of the matrix and the regularity of the geometry of the structures. Numerical experiments on a variety of bio-inspired microswimmers immersed in a Stokes flow demonstrate the effectiveness and efficiency of the proposed solvers.

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