High Performance Techniques Applied in Partial Differential Equations Library

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

The deal.II Library, Version 8.5

This paper provides an overview of the new features of the finite element library deal.II version 8.5

Deal2lkit: a Toolkit Library for High Performance Programming in deal.II

We propose a software design for the efficient and flexible handling of the building blocks used in high performance finite element simulations, through the pervasive use of parameters (parsed through parameter files). In the proposed design, all the building blocks of a high performance finite element program are built according to the command and composite design patterns.We present version 1.1.0 of the deal2lkit (deal.II ToolKit) library, which is a collection of modules and classes aimed at providing high level interfaces to several deal.II classes and functions, obeying the command and composite design patterns, and controlled via parameter files. Keywords: Object-orientation, Software design, Finite element methods, C+

The deal.II Library, Version 9.0

This paper provides an overview of the new features of the finite element library deal.II version 9.0

Parallel Preconditioners for Finite Element Computations

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

Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing

Magnetic Induction Tomography (MIT) is a non‐invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. With the exploitation of parallelism, it is possible to achieve high quality inexpensive MIT images for biomedical applications on clinically relevant time scales. In this paper we investigate the performance of different parallel implementations of the forward eddy current problem, which is the main computational component of the inverse problem through which measured voltages are converted into images. We show that a heterogeneous parallel method that exploits multiple CPUs and GPUs can provide a high level of parallel scaling, leading to considerably improved runtimes. We also show how multiple GPUs can be used in conjunction with deal.II, a widely‐used open source finite element library