Document Type


Publication Date



Applied Mathematics | Computer Sciences | Hydraulic Engineering | Numerical Analysis and Scientific Computing | Partial Differential Equations | Physical Sciences and Mathematics


Michael Heroux, Computer Science; Michael Tangredi, Mathematics


This thesis explores various Trilinos packages to determine a method for updating the deal.ii library, which specializes in solving partial differential equations by finite element methods. It begins with introducing related concepts and general goals, followed by exploring computational and mathematical methods which are analytical solutions of one-dimensional Boussinesq equations and developing newer prototypes for solvers in deal.ii based on Trilinos packages. After demonstrating the methods, it indicates the reducing solving time in newer prototypes. Based on results from the prototype, similar methods are applied to update the deal.ii library. In the end, a testing program is exploited to demonstrate the improvement in performance for deal.ii.