复合矩形域上二维电磁场边值问题的直线法分析
ANALYSIS OF 2-D ELECTROMAGNETIC BOUNDARY PROBLEMS WITH A COMPOUND RECTANGULAR CROSS-SECTION BY THE METHOD OF LINES
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摘要: 本文基于直线法的基本思想提出了一种分析复合矩形域上二维电磁场边值问题的新方法,即将偏微分方程沿一维离散化,从而转化为对于另一维变量的常微分方程组。在离散化过程中,本文引入了截断误差O(h4)的高精度格式,提出了在各种齐次边界条件下确定离散化常微分方程组通解的反推法,最后用最小二乘逼近提高解的精度。对矩形同轴线和脊波导的主模和高次模截止波长以及矩形域内静电位分布的数值计算结果与有关文献中的结果吻合得很好,体现了该方法简便、精度高和计算量小的优点。
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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. -
南京大学编,偏微分方程数值解法,科学出版社,1979年,PP. 392-417.[2]章文勋,无线电技术中的微分方程,国防工业出版社,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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