University of North Carolina at Chapel Hill Graduate School
Doi
Abstract
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 formulas for computing the electric field gradients by the new version of fast multipole method(FMM) and to implement them as new functions for existing FMM solvers. In the second part of the dissertation, we discuss how to decompose the far-field Rotne-Prager-Yamakawa potential into four far-field Laplace FMM calls including electrostatic potential, electric field and field gradient terms. A parallelized Rotne-Prager-Yamakawa solver based on the new version of fast multipole method has been developed with tunable accuracy. The solver makes it computationally viable for large-scale, long-time Brownian dynamic simulations with hydrodynamic interactions. In the third part, a model is built toward an accurate description of hydrodynamic effects on the translational and rotational dynamics of complex, rigid macromolecules with arbitrary shape in suspension. The grand diffusion matrix is calculated by employing the bead-shell model for describing the shape and structure of macromolecules in the many-body system. Two fast algorithms based on block conjugate gradient method and the Schur complement method are developed for computing the translational and angular velocities, as well as the displacements and orientations in order to track the trajectories of the macromolecules in the complex structured biological system.Doctor of Philosoph
