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应用科学学报 ›› 1991, Vol. 9 ›› Issue (1): 1-7.

• 论文 •    下一篇

电磁场理论中几何化·数论消发散方法*(Ⅰ) GNES方法的理论表述

戴显熹   

  1. 复旦大学
  • 收稿日期:1989-12-30 出版日期:1991-03-31 发布日期:1991-03-31
  • 基金资助:
    国家自然科学基金(1987-1989年)、上海自然科学基金(1990-1991年)及通过CEEC授予的Cha Chi-Ming Fellowshop (199-1991年)的支持

GEOMETRIZATION NUMBER THEORY ELIMINATINGSINGULARITY APPROACH TO THE THEORYOF ELECTROMAGNETISM (I) The Theoretical Formulation of GNES Approach

DAI XIANXI   

  1. Fudan University
  • Received:1989-12-30 Online:1991-03-31 Published:1991-03-31

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摘要： 为对电磁场理论的高精度计算(如微波定向耦合器等),建议用"几何化·数论消发散"方法.作为这系列论文的第一篇,这里给出整体的理论表述;并利用作者发展的Ω级数理论,建立相当一般的严格的一维、非对称、非厄密奇性积分方程组.以后的论文将给出一般的解法,GNES方法细节,技术以及数值结果.

关键词: 几何化, 奇性积分方程组, 数论, 电磁理论, 消发散

Abstract: In order to realize highly accurate calculations for the theories of eleotromagnetism(e. g., microwave directive coupler et. al), the "geometrization number theory eliminating singularity approach" is suggested. This paper, the first one in the paper series, gives a general theoretical formulation of the GNES approach. And a fairly general class of exact, asymmetric, non-Hermitian, singular integral equation systems is formulated, with the aid of the Ω-series theory developed by us. The general formal solutions, the details of the GNES approach, techniques and numerical results will be presented in the succeeding papers.

Key words: Thery of electromagnetism, Singulau integral equation system, Eliminating singularity, Number theory, Geometrization