Parallel Preconditioners for Finite Element Computations

Abstract

This thesis sought to explore numerical methods for solving partial differential equations and to determine the best method of updating the deal.II software to utilize new Trilinos software packages. The one dimensional heat equation with Dirichlet boundary conditions and nonzero initial conditions was solved analytically, using the Forward in Time, Central in Space scheme of the finite difference method, and the Crank-Nicolson scheme of the finite element method. The solutions from using the finite difference method and the finite element method were then compared to the analytic solution to determine accuracy. An example using the same Trilinos packages that are utilized in deal.II currently was updated to use the newer Trilinos packages to determine how to update deal.II and to analyze any performance increases resulting from these changes to the software