Abstract
dc:description.abstractThe 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 × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-08172010-151435
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/28699