High Order Edge Finite Elements
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2008
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ndltd-OhioLink-oai-etd.ohiolink.edu-akron12171137552021-08-03T05:25:36Z High Order Edge Finite Elements Stoynov, Kiril Electrical Engineering Electromagnetism Engineering High Order Edge Finite Elements hexahedra differential forms The Finite Element Method (FEM) is an extremely powerful and versatile computa-tional technique. The standard (nodal) FEM, however, cannot be used universally incomputational electromagnetics. In particular, the method fails to solve for the fullvector Maxwell equations. The introduction of the vector FEM overcame most of theproblems associated with nodal FEM. The present thesis extends some of the workdone by Z. Ren and N. Ida on tetrahedral finite elements to hexahedral elements.The goal of the present thesis is twofold. First, to provide detailed mathematicaland theorethical background, required to better understand the construction of thep-th order 1-form basis functions from a geometrical point of view. Second, to con-struct higher order basis functions for hexahedral elements, conforming in the spaceH(curl, Ω). To take full advantage of the insights the vector elements provide, onehas to master the theory of differential forms, which is much more general tool thanthat of the vector analysis. The basis functions that are constructed in the presentwork are designed to model correctly the range space and null space of the exteriordifferential operator. They are hierarchical, so they can be used in p-refinement al-gorithms. In addition, by virtue of their construction the basis functions match thecontinuity conditions of the physical quantity modeled. 2008-09-02 English text University of Akron / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755 http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755 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 Electromagnetism Engineering High Order Edge Finite Elements hexahedra differential forms |
| spellingShingle |
Electrical Engineering Electromagnetism Engineering High Order Edge Finite Elements hexahedra differential forms Stoynov, Kiril High Order Edge Finite Elements |
| author |
Stoynov, Kiril |
| author_facet |
Stoynov, Kiril |
| author_sort |
Stoynov, Kiril |
| title |
High Order Edge Finite Elements |
| title_short |
High Order Edge Finite Elements |
| title_full |
High Order Edge Finite Elements |
| title_fullStr |
High Order Edge Finite Elements |
| title_full_unstemmed |
High Order Edge Finite Elements |
| title_sort |
high order edge finite elements |
| publisher |
University of Akron / OhioLINK |
| publishDate |
2008 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755 |
| work_keys_str_mv |
AT stoynovkiril highorderedgefiniteelements |
| _version_ |
1719419952106045440 |