A Parallel Implementation of the Galerkin Method for Solving Partial Differential Equations on a Triangular Mesh

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dc.contributor.advisorKirby, Robert C.
dc.contributor.authorHess, Rachel Nicole.
dc.contributor.departmentApplied Mathematics.en_US
dc.contributor.otherBaylor University.en_US
dc.contributor.schoolsHonors College.en_US
dc.date.accessioned2015-05-28T19:40:38Z
dc.date.available2015-05-28T19:40:38Z
dc.date.copyright2015
dc.description.abstractFinite Element Methods are techniques for estimating solutions to boundary value problems for partial differential equations from an approximating subspace. These methods are based on weak or variational forms of the BVP that require less of the problem functions than what the original PDE would suggest in terms of order of differentiability and continuity. In the scope of this project, we focused on implementing the Galerkin Finite Element Method, which provides a best approximation to the true solution from a finite-dimensional subspace of piecewise polynomial functions defined on a triangular mesh. For this thesis, we developed a shared memory parallel implementation of the Galerkin Method that can be executed on a GPU to minimize runtime by means of multiple processors working simultaneously in unison on each calculation. For this purpose, we used the open-source libraries PyOpenCL and Loo.py. Thus we are able to explore how essential tasks in the solution process map onto shared memory platforms, such as the construction of the stiffness matrix from the connectivity data of the triangular mesh that may then be used to approximate the true solution with numerical methods.en_US
dc.identifier.urihttp://hdl.handle.net/2104/9363
dc.language.isoen_USen_US
dc.rightsBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.en_US
dc.rights.accessrightsWorldwide accessen_US
dc.subjectParallel Computation.en_US
dc.subjectFinite Element Methods.en_US
dc.subjectMesh Queries.en_US
dc.titleA Parallel Implementation of the Galerkin Method for Solving Partial Differential Equations on a Triangular Meshen_US
dc.typeThesisen_US

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