Convergent slender-body quadrature (CSBQ)

Principal author Dhairya Malhotra, with additional code by Alex Barnett. This work was done at the Center for Computational Mathematics at the Flatiron Institute, NY, NY.

CSBQ is a high-performance parallel C++ implementation of a high-order adaptive Nyström quadrature for the boundary integral equations arising in 3D Laplace and Stokes Dirichlet and rigid mobility boundary-value problems for closed loop filaments of arbitrarily small circular cross-section. Its quadrature setup cost is independent of the slenderness parameter, being around 20000 unknowns/sec per core, at 6-digit accuracy, away from close-to-touching regions. Close-to-touching geometries may be handled to close to machine accuracy using adaptivity. Open-ended fibers with rounded ends are possible and will be added soon.

This repository also contains MATLAB codes implementing the classical slender-body theory asymptotic approximation, and solving its linear inverse problem as needed for a mobility solve.

It is research software; use at your own risk. The following figures show some of the capabilities of the code (see the publication below for details).

_images/tangle-stokes-streamlines_sm.png — Stokes flow solution around rigid slender fiber with aspect ratio \(10^3\), max error \(10^{-10}\).

_images/close-to-touching-streamlines_sm.png — Stokes flow solution near close-to-touching rings, max error \(10^{-11}\).

_images/sed512-117_sm.png — Sedimentation of 512 rings each of aspect ratio 20, timestepped to 7-digit accuracy on 160 cores.

Citing this work

If you find this code useful in your research, please cite our publication:

Dhairya Malhotra and Alex Barnett, “Efficient Convergent Boundary Integral Methods for Slender Bodies,” Journal of Computational Physics, vol. 503, p. 112855, Apr. 2024. DOI: [10.1016/j.jcp.2024.112855](http://dx.doi.org/10.1016/j.jcp.2024.112855)