New parallel iteration methods, new nonlinear multigrid analysis, and application in computational chemistry.

摘要

This dissertation first presents and analyzes three new parallel iterative methods (the JSOR method, the PSOR method and a new parallel multigrid scheme) and a general multigrid smoother (the PM smoother), along with their parallel performance analysis on shared memory and distributed memory MIMD computers. Then a new nonlinear multigrid analysis, which is an extension of the multigrid theory by J. H. Bramble, et al. in the nonlinear case, is presented. Finally, the Shake method, a widely-used solver for Molecular Dynamics simulations, is developed into a family of methods, and two particular Shake methods, the Shake-Jacobi and the Shake-SOR methods, are proposed and analyzed.