Response Function Method for Solving Dirichlet's Problems

概要

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Laplace equation Δψ(x, Z)=0 for the boundary condition of an infinitely long strip or arectangle is solved numerically by using the technique of Fourier transform and by samplingthe boundary value ψ(x,0) with equidistant spacing h as ψ(nh,O). The solution is represented by the sum Σ_nψ(nh, 0)Ω(n), where the response function φΩ(n) is the solution for animpulse function. As φΩ(n) depends only on h and the boundary shape, and the sampled boundary values ψ(nh, 0) are explicitly used in the form of the solution, this expression is suitable formachine calculation. The upper limit of the frequency component Ω which is contained in ψ(x,0) determines the appropriate sampling density 1/h for the solution of the problem.Applying this technique to electrostatics, it is also shown that the electric field components as the solutions are represented in similar forms, where the electrostatic potential ψ(nh, 0) are used as the sampled boundary values.
社団法人応用物理学会の論文
1977-05-05