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Virginia Tech

Multidimensional Adaptive Quadrature Over Simplices

Abstract

dc:description.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.

Degree

thesis:*
Name thesis:degree_name
Ph. D.
Level thesis:degree_level
doctoral
Discipline thesis:degree_discipline
Mathematics
Department dc:contributor.department
Mathematics
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
2010

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Pond, Kevin R.
Chair dc:contributor.committeechair
  • Borggaard, Jeffrey T.
Committee members dc:contributor.committeemember
  • Cliff, Eugene M.
  • Herdman, Terry L.
  • Zietsman, Lizette
  • Burns, John A.

Subjects

dc:subject × 4

Rights

dc:rights
Statement dc:rights
  • In Copyright

Identifiers

dc:identifier.*
Dc Identifier Other
etd-08172010-151435
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/28699

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Pond, Kevin R.. Multidimensional Adaptive Quadrature Over Simplices. doctoral thesis, Virginia Tech, 2010. http://hdl.handle.net/10919/28699