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Numerical solution of multiscale ele...

Duke University.

Numerical solution of multiscale electromagnetic systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical solution of multiscale electromagnetic systems.
Author:	Tobon Llano, Luis Eduardo.
Description:	117 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.
Notes:	Adviser: Qing H. Liu.
Contained By:	Dissertation Abstracts International75-02B(E).
Subject:	Engineering, Electronics and Electrical.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3599580
ISBN:	9781303489808

Numerical solution of multiscale electromagnetic systems.
Tobon Llano, Luis Eduardo.

Numerical solution of multiscale electromagnetic systems. - 117 p.

Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.

Thesis (Ph.D.)--Duke University, 2013.

The Discontinuous Galerkin time domain (DGTD) method is promising in modeling of realistic multiscale electromagnetic systems. This method defines the basic concept for implementing the communication between multiple domains with different scales.

ISBN: 9781303489808Subjects--Topical Terms:

226981
Engineering, Electronics and Electrical.

Numerical solution of multiscale electromagnetic systems.
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020 $a 9781303489808
035 $a (MiAaPQ)AAI3599580
035 $a AAI3599580
040 $a MiAaPQ $c MiAaPQ
100 1 $a Tobon Llano, Luis Eduardo. $3 660397
245 1 0 $a Numerical solution of multiscale electromagnetic systems.
300 $a 117 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.
500 $a Adviser: Qing H. Liu.
502 $a Thesis (Ph.D.)--Duke University, 2013.
520 $a The Discontinuous Galerkin time domain (DGTD) method is promising in modeling of realistic multiscale electromagnetic systems. This method defines the basic concept for implementing the communication between multiple domains with different scales.
520 $a Constructing a DGTD system consists of several careful choices: (a) governing equations; (b) element shape and corresponding basis functions for the spatial discretization of each subdomain; (c) numerical fluxes onto interfaces to bond all subdomains together; and (d) time stepping scheme based on properties of a discretized system. This work present the advances in each one of these steps. First, a unified framework based on the theory of differential forms and the finite element method is used to analyze the discretization of the Maxwell's equations. Based on this study, field intensities (E and H) are associated to 1-forms and curl-conforming basis functions; flux densities (D and B) are associated to 2-forms and divergence-conforming basis functions; and the constitutive relations are defined by Hodge operators.
520 $a A different approach is the study of numerical dispersion. Semidiscrete analysis is the traditional method, but for high order elements modal analysis is prefered. From these analyses, we conclude that a correct discretization of fields belonging to different p-form (e.g., E and B ) uses basis functions with same order of interpolation; however, different order of interpolation must be used if two fields belong to the same p-form (e.g., E and H). An alternative method to evaluate numerical dispersion based on evaluation of dispersive Hodge operators is also presented. Both dispersion analyses are equivalent and reveal same fundamental results. Eigenvalues, eigenvector and transient results are studied to verify accuracy and computational costs of different schemes. Two different approaches are used for implementing the DG Method. The first is based on E and H fields, which use curl-conforming basis functions with different order of interpolation. In this case, the Riemman solver shows the best performance to treat interfaces between subdomains. A new spectral prismatic element, useful for modeling of layer structures, is also implemented for this approach. Furthermore, a new efficient and very accurate time integration method for sequential subdomains is implemented. The second approach for solving multidomain cases is based on E and B fields, which use curl- and divergence-conforming basis functions, respectively, with same order of interpolation. In this way, higher accuracy and lower memory consumption are obtained with respect to the first approach based on E and H fields. The centered flux is used to treat interfaces with non-conforming meshes, and both explicit Runge-Kutta method and implicit Crank-Nicholson method are implemented for time integration.
520 $a Numerical examples and realistic cases are presented to verify that the proposed methods are non-spurious and efficient DGTD schemes.
590 $a School code: 0066.
650 4 $a Engineering, Electronics and Electrical. $3 226981
650 4 $a Engineering, Computer. $3 384375
650 4 $a Physics, Electricity and Magnetism. $3 227483
690 $a 0544
690 $a 0464
690 $a 0607
710 2 $a Duke University. $b Electrical and Computer Engineering. $3 531041
773 0 $t Dissertation Abstracts International $g 75-02B(E).
790 $a 0066
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3599580

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