## Boundary integral equation analysis for suspension of spheres in Stokes flow. (arXiv:1707.06551v2 [math.NA] UPDATED)

We show that the standard boundary integral operators, defined on the unit
sphere, for the Stokes equations diagonalize on a specific set of vector
spherical harmonics and provide formulas for their spectra. We also derive
analytical expressions for evaluating the operators away from the boundary.
When two particle are located close to each other, we use a truncated series
expansion to compute the hydrodynamic interaction. On the other hand, we use
the standard spectrally accurate quadrature scheme to evaluate smooth integrals
on the far-field, and accelerate the resulting discrete sums using the fast
multipole method (FMM). We employ this discretization scheme to analyze several
boundary integral formulations of interest including those arising in porous
media flow, active matter and magneto-hydrodynamics of rigid particles. We
provide numerical results verifying the accuracy and scaling of their
evaluation.查看全文