An Approximate Method to Solve Two-Dimensional Laplace's Equation by Means of Superposition of Green's Functions on a Riemann Surface

スポンサーリンク

概要

• 論文の詳細を見る

• A new method of solving two dimensional Laplace equation is presented. This method is a superposition method of Green's function on a Riemann surface constructed by a complex transformation and is suitable for analyzing potential problems in aregion that contains curved arcs as its boundary. This method originates from the research of the charge simulation method used often in some part of electrical engineering as an effective and simple method of solving Laplace equation. The essential and evident defect of this method is that the error of the analysis becomes large for the exterior problem of a very thin region or a region without thickness due to the singularity of Green's function superposed in this method. To overcome this difficulty, in this paper, Rimann surface constructed by two-valued complex transformation z=1/2(t+(1/t)) is used. The poles of Green's functions are placed on one of two sheets of the Riemann surface and their influence on the other sheet is superposed similarly to the ordinary charge simulation method. By using this complex transformation, the curved arc without area is transformed into a closed region with wide area. Then we can keep the poles of Green's functions apart from the boundary. This fact enables us to reduce the influence of the singularity of Green's function. Above technique is verified by analyzing the test problems in electrostatics. The results are fully satisfactory. This method is applicable to the problems in a region 1hat contains many curved arcs of arbitrary shape. Hence it will be widely used for various problems in electrostatics or hydrodynamics.

• 一般社団法人情報処理学会の論文
• 1980-09-30

著者

• Murashima Sadayuki

  Department Of Electronics Faculty Of Engineering Kagoshima University

• Murashima Sadayuki

  Department Of Electrical Engineering Kyoto Technical University

• KUHARA HIDEO

  Department of Information and Electronic Engineering, Yatsushiro National College of Technology

• Kuhara Hideo

  Department Of Information And Electronic Engineering Yatsushiro National College Of Technology

関連論文

• Correction Devisors for the Four-Point Probe Resistivity Measurement on Cylindrical Semiconductors
• An Approximate Method to Solve Two-Dimensional Laplace's Equation by Means of Superposition of Green's Functions on a Riemann Surface
• Correction Devisors for the Four-Point Probe Resistivity Measurement on Parallelepiped Semiconductors
• Correction Devisors for the Four-Point Probe Resistivity Measurement on Cylindrical Semiconductors (II)
• Information Capacity of Rudiographic Images for Circular Defects
• Information Capacity of Radiographic Images for the Random Signal and Continuous Objects
• Analyses of Some Potential Problems in Cylindrical Coordinates in Connection with Four-Point Probe Technique
• On the Problem of the Flow of Electricity in a Right Cylindrical Conductor
• Lossless Fractal Representation of Digital Images
• Neumann Functions for Laplace's Equation for a Circular Cylinder of Finite Length

スポンサーリンク