Title page for ETD etd-08172010-151435


Type of Document Dissertation
Author Pond, Kevin R
Author's Email Address kevin.pond@vt.edu
URN etd-08172010-151435
Title Multidimensional Adaptive Quadrature Over Simplices
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Borggaard, Jeffrey T. Committee Chair
Burns, John A. Committee Member
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Zietsman, Lizette Committee Member
Keywords
  • multidimensional
  • quadrature
  • adaptive
  • simplices
Date of Defense 2010-08-06
Availability unrestricted
Abstract
The objective of this work is the development of novel, efficient and reliable multidi- mensional adaptive quadrature routines defined over simplices (MAQS). MAQS pro- vides an approximation to the integral of a function defined over the unit hypercube and provides an error estimate that is used to drive a global subdivision strategy. The quadrature estimate is based on Lagrangian interpolation defined by using the vertices, edge nodes and interior points of a given simplex. The subdivision of a given simplex is chosen to allow for the reuse of points (thus function evaluations at those points) in successive refinements of the initial tessellation. While theory is developed for smooth functions, this algorithm is well suited for functions with discontinuities in dimensions three through six. Other advantages of this approach include straight-forward parallel implementation and application to integrals over polyhedral domains.
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