| 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. |
