A boundary element method featuring the : Green’s function for the circular cylinder has been used to compute particle hydrodynamic mobilities in a channel. The Green’s function has very slowly converging Fourier-Bessel sums; consequently, construction of the integral equation kernel, i.e. the matrix assembly, accounts for essentially all of the CPU time in the sequential algorithm. A Single Program Multiple Data (SPMD) model was used to assign the matrix assembly to N processors. The validity of the SPMD model was verified using Condor, a batch job scheduler designed to pool idle workstation cycles in the network. Our work is typical of many CPU intensive computations in engineering and suggests that a SPMD approach that uses idle resources over a network is an attractive option. Our results are in excellent agreement with established mobilities for simple test cases, and can be readily extended to more interesting geometries.