Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures

Bibliographic Details
Main Author:	Lee, Seung-Cheol
Language:	English
Published:	The Ohio State University / OhioLINK 2003
Subjects:	Electrical Engineering
Online Access:	http://rave.ohiolink.edu/etdc/view?acc_num=osu1394730392

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spelling	ndltd-OhioLink-oai-etd.ohiolink.edu-osu13947303922021-08-03T06:22:36Z Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures Lee, Seung-Cheol Electrical Engineering In this thesis, the finite element method (FEM) is extended into hierarchical higher order bases and the inexact Helmholtz decomposition. With the help of hierarchical basis functions, the approach can well adopt into p version adaptive process. On the other hand, the inexact Helmholtz decomposition enhances the stability of the finite element procedure when the operating frequency is low, or the element size is very small compared to the wavelength. This approach can also enhance the h version adaptive mesh refinement process since the process may cause very small elements near a singular region. To accomplish the inexact Helmholtz decomposition for the edge elements, the lowest order curl conforming basis functions, the tree-cotree splitting is utilized, and the general procedure is presented. As a result, a combination of hierarchical higher order basis functions with the inexact Helmholtz decomposition can improve the efficiency and the stability of the hp adaptive mesh refinement process. The accuracy and the stability of the improved FEM are also discussed through numerical examples. 2003 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1394730392 http://rave.ohiolink.edu/etdc/view?acc_num=osu1394730392 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection	NDLTD
language	English
sources	NDLTD
topic	Electrical Engineering
spellingShingle	Electrical Engineering Lee, Seung-Cheol Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures
author	Lee, Seung-Cheol
author_facet	Lee, Seung-Cheol
author_sort	Lee, Seung-Cheol
title	Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures
title_short	Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures
title_full	Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures
title_fullStr	Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures
title_full_unstemmed	Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures
title_sort	enhanced finite elements using hierarchical higher order bases and inexact helmholtz decomposition for wave guiding structures
publisher	The Ohio State University / OhioLINK
publishDate	2003
url	http://rave.ohiolink.edu/etdc/view?acc_num=osu1394730392
work_keys_str_mv	AT leeseungcheol enhancedfiniteelementsusinghierarchicalhigherorderbasesandinexacthelmholtzdecompositionforwaveguidingstructures
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Enhanced Finite Elements Using Hierarchical Higher Order Bases and Inexact Helmholtz Decomposition for Wave Guiding Structures

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