We present an integral equation formulation for the unsteady Stokes equations in two
dimensions. This problem is of interest in its own right as a model for slow viscous flow, but …

One of the critical steps in Brownian dynamics simulation with hydrodynamic interactions is
to generate a normally distributed random vector whose covariance is determined by the …

We present in this paper a new kernel-independent fast multipole method (FMM), named as
FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI …

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet
problem of the biharmonic equation in three dimensions. A fast numerical algorithm is …

A system of Fredholm second kind integral equations (SKIEs) is constructed for the modified
biharmonic equation in two dimensions with gradient boundary conditions. Such boundary …

A major avenue of research in numerical analysis is creating algorithms in order to decrease
the amount of computational time in numerical simulations while maintaining high accuracy …

In this dissertation, we contributed on three fundamental parts of Brownian dynamics
simulations with hydrodynamic interactions. The first part of the dissertation is to derive the …