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A Finite Element Boundary Element Method for Infinite Periodic Structures on Non-Periodic Meshes Using an Interior Penalty Formulation
Lee, Seung-Cheol

2012, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
This dissertation presents a hybrid finite element boundary element (FEBE) method for infinite periodic structures. Infinite periodic structures have been efficiently analyzed by solving for a single unit cell utilizing Floquet's theorem. However, most of the previous works require periodic meshes to properly impose the boundary conditions on the outer surfaces of the unit cell. To alleviate this restriction, interior penalty method is adopted and implemented in this work. The method is applied only on the outer surface by assuming that the interior mesh is conformal. For the boundaries that are exposed to infinite free space, boundary element method with periodic Green’s function is used. Also, a proper treatment for the boundary element part is addressed to account for non-conformity at the boundary of the boundary elements. Another ingredient of this work is the use of the efficient boundary element computation, accelerated by the Ewald transformation for the calculation of the periodic Green's function. Furthermore, a h-version of adaptive mesh refinement scheme is attempted for reliability and efficiency of the computation. A residual based a posteriori error estimator is proposed to identify the elements that require further refinement. Finally, the presented method is validated through some real life examples which are discretized without the constraint of a periodic mesh.
Lee Jin-Fa (Advisor)
Fernando Teixeira (Committee Member)
Robert Burkholder (Committee Member)

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Lee, S. (2012). A Finite Element Boundary Element Method for Infinite Periodic Structures on Non-Periodic Meshes Using an Interior Penalty Formulation. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Lee, Seung-Cheol. "A Finite Element Boundary Element Method for Infinite Periodic Structures on Non-Periodic Meshes Using an Interior Penalty Formulation." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 21 Sep 2017.

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Lee, Seung-Cheol "A Finite Element Boundary Element Method for Infinite Periodic Structures on Non-Periodic Meshes Using an Interior Penalty Formulation." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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