  The method of regularized stokeslets is extensively used in biological fluid
dynamics due to its conceptual simplicity and meshlessness. This simplicity
carries a degree of cost in computational expense and accuracy because the
number of degrees of freedom used to discretise the unknown surface traction is
generally significantly higher than that required by boundary element methods.
We describe a meshless method based on nearest-neighbour interpolation that
significantly reduces the number of degrees of freedom required to discretise
the unknown traction, increasing the range of problems that can practically
solved, without excessively complicating the task of the modeller. The
nearest-neighbour technique is tested against the classical problem of rigid
body motion of a sphere immersed in very viscous fluid, then applied to the
more complex biophysical problem of calculating the diffusion timescales of a
macromolecular structure modelled by three closely-spaced non-slender rods. A
heuristic for finding the required density of force and quadrature points by
numerical refinement is suggested. Matlab/GNU Octave code for the key steps of
the algorithm are given, which predominantly use basic linear algebra
operations, with a full implementation being provided on github. Compared with
the standard Nystr\"om discretisation more accurate and substantially more
efficient results can be obtained by de-refining the force discretisation
relative to the quadrature discretisation: a cost reduction of over 10 times
with improved accuracy is observed. This improvement comes at minimal
additional technical complexity. Future avenues to develop the algorithm are
then discussed.
