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Efficient Error-Controllable High-Order Electromagnetic Modelling of Scattering on Electrically Large Targets with the Locally Corrected Nyström Method

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dc.contributor.supervisor Okhmatovski,Vladimir (ECE, University of Manitoba) en_US
dc.contributor.author Shafieipour, Mohammad
dc.date.accessioned 2016-04-06T19:35:51Z
dc.date.available 2016-04-06T19:35:51Z
dc.date.issued 2014 en_US
dc.date.issued 2015 en_US
dc.identifier.citation IEEE TAP en_US
dc.identifier.citation IEEE TAP en_US
dc.identifier.uri http://hdl.handle.net/1993/31181
dc.description.abstract This dissertation is about efficient computation of the electromagnetic fields with the locally corrected Nyström (LCN) method as a point-based boundary element method (BEM). The concept of surface integral equations is discussed and the electric field integral equation (EFIE) is derived from the Maxwell’s equations. Due to its point-based nature, the LCN discretization of the EFIE has some advantages over discretizing the EFIE by the method-of-moments (MoM) which is an element-based BEM. On the other hand, due to maturity of the MoM, a large body of work is available to resolve the numerical issues arising in MoM while there has been less work related to the relatively new LCN. To combine the benefits of the LCN method and the classical Rao-Wilton-Glisson MoM, equivalence between these BEMs are established and their exact relationships are derived. Both the vector-potential EFIE and the mixed-potential EFIE are covered. Various aspects of achieving HO convergence to the correct answer using high-order (HO) LCN method are discussed. In particular, the patch size limitation, predicting the optimal degrees of freedom, and the effect of dynamic range in the solution are discussed both analytically and numerically to provide concrete motivations towards HO LCN. The benefits of an HO BEM can not be realized unless an HO geometry representation is used in conjunction with the BEM. Non-uniform rational b-spline (NURBS) surfaces are the most widely adopted HO geometry modelling technique in various disciplines due to their many advantages. However, a typical mesh created out of NURBS surfaces contain both triangular and quadrilateral elements while formulating LCN based on Gaussian quadrature rules on triangular elements have limitations. As a result, the LCN community has mostly adopted LCN based on curvilinear quadrilateral modelling of the geometry. A new class of Newton-Cotes quadrature rules for triangles is proposed to facilitate incorporating NURBS surfaces into the HO LCN. en_US
dc.publisher IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION en_US
dc.publisher IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION en_US
dc.subject Computational Electromagnetics, Locally Corrected Nystrom (LCN) Method en_US
dc.title Efficient Error-Controllable High-Order Electromagnetic Modelling of Scattering on Electrically Large Targets with the Locally Corrected Nyström Method en_US
dc.degree.discipline Electrical and Computer Engineering en_US
dc.contributor.examiningcommittee LoVetri, Joe (ECE, University of Manitoba) Wang, Bing-Chen (Department of Mechanical Engineering, University of Manitoba) Gedney, Stephen (ECE, University of Colorado) en_US
dc.degree.level Doctor of Philosophy (Ph.D.) en_US
dc.description.note May 2016 en_US


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