復(fù)合矩形域上二維電磁場邊值問題的直線法分析
ANALYSIS OF 2-D ELECTROMAGNETIC BOUNDARY PROBLEMS WITH A COMPOUND RECTANGULAR CROSS-SECTION BY THE METHOD OF LINES
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摘要: 本文基于直線法的基本思想提出了一種分析復(fù)合矩形域上二維電磁場邊值問題的新方法,即將偏微分方程沿一維離散化,從而轉(zhuǎn)化為對于另一維變量的常微分方程組。在離散化過程中,本文引入了截?cái)嗾`差O(h4)的高精度格式,提出了在各種齊次邊界條件下確定離散化常微分方程組通解的反推法,最后用最小二乘逼近提高解的精度。對矩形同軸線和脊波導(dǎo)的主模和高次模截止波長以及矩形域內(nèi)靜電位分布的數(shù)值計(jì)算結(jié)果與有關(guān)文獻(xiàn)中的結(jié)果吻合得很好,體現(xiàn)了該方法簡便、精度高和計(jì)算量小的優(yōu)點(diǎn)。
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關(guān)鍵詞:
Abstract: A method based on the method of lines which discretizes a partial differential equation (PDE) into a system of ordinary differential equations (ODEs) is presented. A difference scheme with an error of O(h4) is introduced and a simple method for determining the general solutions of the ODEs is given. Finally, the least-square approximation is used for improving the accuracy of the numerical results. Some numerical results for rectangular coaxial line, ridge waveguide, and shielded stripline are also given. These results are in good agreement with that published in literatures. -
南京大學(xué)編,偏微分方程數(shù)值解法,科學(xué)出版社,1979年,PP. 392-417.[2]章文勛,無線電技術(shù)中的微分方程,國防工業(yè)出版社,1982年,第九、十二章.[3]S. T. Saad.[J].et al (E D): Microwave Engineers Handbooks Vol. 1, Artech House, Inc.1972,:-[4]N. Marcuvitz: Waveguide Handbook, McGraw-Hill, N. Y. (1951), pp. 400-402. -
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