  An accelerated boundary integral method for Stokes flow of a suspension of
deformable particles is presented for an arbitrary domain and implemented for
the important case of a planar slit geometry. The computational complexity of
the algorithm scales as O(N) or $O(N\log N$), where $N$ is proportional to the
product of number of particles and the number of elements employed to
discretize the particle. This technique is enabled by the use of an alternative
boundary integral formulation in which the velocity field is expressed in terms
of a single layer integral alone, even in problems with non-matched
viscosities. The density of the single layer integral is obtained from a
Fredholm integral equation of the second kind involving the double layer
integral. Acceleration in this implementation is provided by the use of General
Geometry Ewald-like method (GGEM) for computing the velocity and stress fields
driven by a set of point forces in the geometry of interest. For the particular
case of the slit geometry, a Fourier-Chebyshev spectral discretization of GGEM
is developed. Efficient implementations employing the GGEM methodology are
presented for the resulting single and the double layer integrals. The
implementation is validated with test problems on the velocity of rigid
particles and drops between parallel walls in pressure driven flow, the Taylor
deformation parameter of capsules in simple shear flow and the particle
trajectory in pair collisions of capsules in shear flow. The computational
complexity of the algorithm is verified with results from several large scale
multiparticle simulations.
