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High Order Edge Finite Elements

Stoynov, Kiril
http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755

Abstract Details

2008, Master of Science, University of Akron, Electrical Engineering.
The Finite Element Method (FEM) is an extremely powerful and versatile computa-tional technique. The standard (nodal) FEM, however, cannot be used universally in computational electromagnetics. In particular, the method fails to solve for the full vector Maxwell equations. The introduction of the vector FEM overcame most of the problems associated with nodal FEM. The present thesis extends some of the work done 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 mathematical and theorethical background, required to better understand the construction of the p-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 space H(curl, Ω). To take full advantage of the insights the vector elements provide, one has to master the theory of differential forms, which is much more general tool than that of the vector analysis. The basis functions that are constructed in the present work are designed to model correctly the range space and null space of the exterior differential 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 the continuity conditions of the physical quantity modeled.
Nathan Ida, PhD (Advisor)
149 p.
Electrical Engineering; Electromagnetism; Engineering
High Order Edge Finite Elements; hexahedra differential forms

Recommended Citations

Citations

  • Stoynov, K. (2008). High Order Edge Finite Elements [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755

    APA Style (7th edition)

  • Stoynov, Kiril. High Order Edge Finite Elements. 2008. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755.

    MLA Style (8th edition)

  • Stoynov, Kiril. "High Order Edge Finite Elements." Master's thesis, University of Akron, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1217113755

    Chicago Manual of Style (17th edition)

akron1217113755
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© 2008, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.