Maxwell’s equations are a set of partial differential equations that describe the classic electromagnetic problems, electrodynamics etc. Effective numerical methods are derived to solve the equations in the past decades, and continued to be of great interest to be developed to its completion. In this thesis, we introduce and propose numerical methods using staggered meshes that deal with both two dimensional and three dimensional space problem in polygonal and general curved domains. / Finite difference method, finite volume method, spectral method and staggered discontinuous Galerkin method are discussed in the thesis. A forth order finite difference method using Taylor expansion technic is proposed. The integral form of the original Maxwell’s equations give rise to methods based on more general domain. For the finite volume method, covolume methods both on the cyclic polygon elements and noncyclic polygon elements are derived. To derive a higher order accurate method, staggered discontinuous Galerkin method based on the same domain decomposition present in the finite volume method use Nedelec elements is derived in two dimensional space, and spectral method using nodal high-order method operate on a general domain in 3D with flexible domain geometry is introduced. Numerical results are shown to show the performance oft he above mentioned approximation methods in 2D case. / 麥克斯韋方程組是一組描述經典電磁問題，電磁力學的偏微分方程。在過去數十年，行之有效的偏微分方程數值解已經被推導出並用於求解該方程，該問題現在仍然吸引著學者極大的興趣，並日臻完善。在這篇論文中，我們介紹並提出一些運用曲域交錯網格數值方法在二維和三維的多面體和更一般幾何體處理麥克斯韋方程組問題。 / 本論文對有限差分法，有限體積法，光譜法和交錯間斷有限元方法進行了討論。利用泰勒展開式這一方法推導出一個二維的四階有限差分方法。基於原來的麥克斯韋方程組的積分形式所得到的數值方法更適用於更普遍的域。對於有限體積法，對循環多邊形元素和非環狀多邊形元素的有限體積方法都將被導出。為了得到一個更高階準確的方法，基於有限體積法中使用的域分解方法，使用Nedelec元素，推導了二維空間的高階有限元方法。基於頂點高階數值方法的光譜法對於三維一般定義域的幾何形態更為靈活適用。在二維的定義域中，數值模擬結果驗證上述數值方法的精確性。 / Jian, Fangqiong. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 62-65). / Abstracts also in Chinese. / Title from PDF title page (viewed on 07, October, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1291492 |
| Date | January 2014 |
| Contributors | Jian, Fangqiong (author.), Chung, Tsz Shun Eric (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Mathematics. (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (62 leaves, 3 unnumbered leaves) : illustrations (some color), computer, online resource |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-NoDerivatives 4.0 International" License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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