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| 題 名 | Adaptively Reducing Boundary Error in Finite Element Analysis of Unbounded Electromagnetic Wave Problems=減低適應性有限元素法應用於電磁波散射與輻射問題邊界錯誤的方法 |
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| 作 者 | 蔡德明; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
| 卷 期 | 25:6 2001.11[民90.11] |
| 頁 次 | 頁384-394 |
| 分類號 | 448.5 |
| 關鍵詞 | 適應性有限元素法; 電磁波; 散射; 輻射; Adaptive finite element; Wave-envelope method; Hierarchal finite elements; Radiation; Scattering; Open boundary problems; Boundary error; Discretization error; |
| 語 文 | 英文(English) |
| 中文摘要 | 本論文以p型適應性有限元素方法（p-adaptive finite element method）計算二 維無邊界電磁波散射與輻射問題。雖然已經有不少研究是以適應性有限元素計算電磁問題， 但至今仍未有以自動減少邊界錯誤（ boundary error ）與離散錯誤（ discretization error ）為題的研究。本論文以下列方法自動減低邊界錯誤與一般的有限元素離散錯誤：（ 1 ） p 型適應性三角階級有限元素法（ p-adaptive hierarchal triangular finite elements ）， （ 2 ）電磁波封法（ wave-envelope method ），（ 3 ）吸收邊界條件（ absorbing boundary condition ）。 階級型有限元素（ Hierarchal finite elements ） 是以元素的階數（ element order ）控制自由度（ degrees of freedom ）的分佈， 因此 比 h 型有限元素（ h-type finite element ）更有效率， 因 h 型有限元素需要重新製作 所有有限元素才可增加或重新分佈自由度。電磁波封法是利用變數的調整來移除類似電磁波 浪性質的數值結果。電磁波封元素遠比傳統有限元素大（例如：每一個波長通常需要 10 至 20 個傳統元素， 但每一個波長只需要一個電磁波封元素，這將減少 10 至 20 倍的自由度 ）。吸收邊界條件能有效的吸收從內所發出的電磁波。在本論文的方法中：電磁散射或輻射 本體（ scattering or radiating object ）都以階級的有限元素模擬。在此之外，大片空 間是以階級電磁波封元素（ Hierarchal wave-envelope elements ）模擬。 最後在此之邊 界加上吸收邊界條件。因此片空間可以相當厚，而令邊界反射大大的減少。而此邊界錯誤與 在外的電磁波封元素之有效性極有關聯。若增加在外的電磁波封元素之階數，使其可以更有 效的模擬在外的電磁波﹣邊界錯誤因此而減少。而且，這邊界錯誤是有方向性的。在強度電 磁波散射或輻射的方向，邊界錯誤減少更多。 |
| 英文摘要 | An adaptive finite element method is developed to solve two dimensional unbounded electromagnetic radiation and scattering problems. Though there has been considerable research in adaption in electromagnetics, to date, there have been few attempts to deal with adaptively reducing the error introduced by a boundary that artificially truncates the unbounded domain in finite element analysis. The technique proposed here adapts on this boundary error, as well as on the usual finite element discretization error. It combines three techniques: (1) p-adaptive hierarchal triangular finite elements, (2) wave-envelope elements, and (3) absorbing boundary conditions. Hierarchal finite elements allow the polynomial orders of the elements to be used to control the distribution of degrees of freedoom; therefore, they make p-adaption possible, i.e., adaption by varying the element orders. This is more efficient that h-adaption, which requires actual re-meshing of the finite elements. The wave-envelope method uses a change of the dependent variable to remove the wave-like qualities of the solution and thereby permits the use of very large elements, i.e., elements much larger than a wavelength, in the external domain. An absorbing boundary condition is a boundary operator which approximately absorbs all the radiation incident on the boundary from within. In the new method, the scattering or radiating object itself, and its immediate surroundings, are meshed with hierarchal finite elements. Outside this, a thick layer of free space is meshed with hierarchal wave-envelope elements. The layer is thick enough such that when an absorbing boundary condition is imposed on its outer surface, there is very small reflection from it. Such a thick layer can be meshed with relatively few wave-envelope elements. The boundary error seen by the finite element region is, then, a function of how well the wave-envelope region is discretized. During p-adaption, increasing the order of the wave-evelope elements increases their ability to model the field accurately and, therefore, reduces the boundary error. Moreover, this reduction in the boundary error is selective: in directions of strong radiation, the error reduction is greater. |
本系統中英文摘要資訊取自各篇刊載內容。