Fast numerical methods and biological problems.
详细信息
文摘
This thesis encompasses a number of efforts towards the development of fast numerical methods and their applications,particularly in light of the simulation of biochemical systems. Scientific computing as a discipline requires considerations from computer science； namely those of algorithmic efficiency and software automation. Also required is knowledge of applied mathematics in order to bridge the gap between computer science and specific application. This thesis spans these fields,with the study and implementation of optimal numerical techniques encompassing two chapters,and the development and application of numerical techniques to biochemical problems encompassing another two. The first of these efforts is the construction of robust,optimal geometric unstructured multigrid methods in the face of difficult problem and mesh conditions. The second was the construction of optimal discrete function spaces for problems arising in quantum mechanics and electronic structure calculations. The third and fourth were the development of fast and flexible methods for nanoscale implicit solvent electrostatics. The development of fast and parallel methods for an important quantity of interest in classical density functional theory calculations is discussed. Also,the derivation and implementation of a finite element method for improved solvent models using automated scientific computing tools is described.