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Direct Evaluation of Hyper-singularity in Integral Equation with Adaptive Mesh Refinement

Peng, Shaoxin
http://rave.ohiolink.edu/etdc/view?acc_num=osu1557107644500354

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
This dissertation investigates three effective methods in solving practical engineer ing problems using discontinous Galerkin integral equation (IEDG) method. IEDG method, based on domain decomposition method, is very useful in modeling complicated structrues, allowing different parts of the structure to be modeled and meshed independently, without considering the continuity condition at the touching interface. Yet, the IEDG formulation incorporates a contour-contour integration derived from integration-by-part, which can sometimes be troublesome to implement because of the difficulty to identify the contour, especially for irregular mesh. To alleviate this problem, a novel method called quadrature-by-expansion (QBX) is introduced to get rid of integration-by-part all together. This method relies on expansion of dyadic Green’s function with spherical harmonics for the near region. Detailed derivation of formula- tion is presented. Numerical test shows a regularization effect of the hyper-singular integration. H-convergence validation shows O(h) convergence rate. A full-size mock up aircraft example is used to demonstrate the capability of QBX. The second method is constraint equation method. In practical engineering applications, electromagnetic characteristics of a target at different frequency is usually desired. A common practice is to mesh the target at a preferred mesh density, e.g. h = λ/10 according to the λ. However, meshing can be a laborous process, especially for target with many components or multi-pyhsica features. The proposed constraint equation method is aimed to remedy this problem by using one mesh for all frequencies. It starts with a mesh of high geometry fedelity, construct constraint equation from the continuity condition and reduce the original large linear system to a smaller one. Thus memory reduction and computation speed-up is achieved. The third method is adaptive mesh refinement. A real life problem usually embodies a handful of geometry features, such as sharp edges, entrant corners, and flat or curved surface. A uniformly refined mesh usually does not perform as well as a customized mesh designed to capture the smoothness of solution, in terms of accuracy for the same degree-of-freedom. This dissertation investigates an h-version fully automatic adaptive mesh refinement method. The energy reaction norm is used to guide local error refinement and global convergence. The effectivenesss of proposed error indicator is validated using a canonical cubic target. A superior convergence rate compared to uniformly refined mesh is observed. Finally electrically larger targets are computated to demonstrate the effectiveness of the proposed method.
Jin-Fa Lee (Advisor)
Robert Lee (Committee Member)
Fernando Teixeira (Committee Member)
121 p.
Electrical Engineering; Electromagnetics; Electromagnetism

Recommended Citations

Citations

  • Peng, S. (2019). Direct Evaluation of Hyper-singularity in Integral Equation with Adaptive Mesh Refinement [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1557107644500354

    APA Style (7th edition)

  • Peng, Shaoxin. Direct Evaluation of Hyper-singularity in Integral Equation with Adaptive Mesh Refinement. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1557107644500354.

    MLA Style (8th edition)

  • Peng, Shaoxin. "Direct Evaluation of Hyper-singularity in Integral Equation with Adaptive Mesh Refinement." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1557107644500354

    Chicago Manual of Style (17th edition)

osu1557107644500354
358
© 2019, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.