Thesis

Bernstein-Bézier techniques and optimal algorithms in finite element analysis

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Awarding institution
  • University of Strathclyde
Date of award
  • 2013
Thesis identifier
  • T13753
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • This thesis focuses on the development of algorithms for the effiecient computation of the element system matrices associated with simplicial elements of arbitrary polynomial order. The algorithms make use of properties intrinsic to Bernstein-Bézier polynomials, allowing for sum factorizations techniques to be applicable. In particular, the presented algorithms are the first to achieve optimal complexity for H¹ elements on simplicial partitions in Rd, for d = 1, 2, 3. The optimal complexity result is extended to two-dimensional vector finite elements presents a clear distinction between the gradient and rotational comonents of the vector field. Numerical results illustrate the optimal cost associated with the computation of the elemental matrices, as well as the efficiency of the Bernstein-Bézier elements. The thesis contains the documentation of BBFEM, a C⁺⁺ implementation of the newly developed algorithms which is available under a GNU General Public Licence. In addition, a report on the work done for a shorter Knowledge Transfer Partnership project on edge elements, with Cobham Technical Services, is also included.
Resource Type
DOI
Date Created
  • 2013
Former identifier
  • 1032903

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