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Michael Heroux, Computer Science; Michael Tangredi, Mathematics


This thesis will explore various Trilinos packages to determine a method for updating the deal.ii library. The deal.ii library specialize in solving partial differential equations by finite element methods. This thesis will begin with introducing some related concepts and the goals of this project, following the methods of achieving those goals by exploring analytical solution of one-dimensional Boussinesq equations and developing of newer prototypes based on Trilinos packages. After demonstrating the reduction of solving time in prototypes, the same methods have been applied to update the deal.ii library. Finally, an example program from the deal.ii library, step-32, will be used to demonstrate the performance improvement.