In one exemplary approach, a Schur complement-based boundary element method (BEM) is employed for predicting the motion of arbitrarily shaped three-dimensional particles under combined external and fluidic force fields. The BEM relies on modeling the surface of the computational domain, significantly reducing the number of unknowns when compared to volume-based methods. In addition, the Schur complement-based scheme enables a static portion of the computation to be computed only once for use in subsequent time steps, which leads to a tremendous reduction in solution time during time-stepping in the microfluidic domain. Parallelized oct-tree based O(N) multilevel iterative solvers are also used to accelerate the setup and solution costs.