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Fast and accurate evaluation of boundary integrals in 3D Stokes flow

Banff International Research Station for Mathematical Innovation and Discovery

We present a numerical method for computing the Stokeslet and stresslet integrals in Stokes flow, motivated by applications such as swimming of microorganisms, particle and drop motion, or biomembrane and red blood cell mechanics. Evaluating the integrals accurately for points near the boundary, e.g., when two interfaces are close together, is the most difficult case. The accurate solution is obtained by regularizing the kernels and adding analytically derived correction terms to eliminate the largest error. On the surface, high order regularizations are designed so that corrections are not required. To evaluate the resulting sums efficiently, we developed a kernel-independent treecode based on barycentric Lagrange interpolation.

Mathematics; Numerical analysis; Partial differential equations; Women and early careers in math

video/mp4

Author affiliation: Farmingdale State College

2019-11-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72280

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/