普因卡雷-斯特克洛夫算子的明确数值可实现公式

Pub Date : 2024-04-01 DOI:10.1134/s0965542524020040

A. S. Demidov, A. S. Samokhin

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引用次数: 0

摘要

摘要本文提出了与二维拉普拉斯方程有关的波恩卡莱-斯特克洛夫算子的明确数值可实现公式，如狄利克特-诺伊曼算子、狄利克特-罗宾算子、罗宾1-罗宾2算子和格林伯格-马耶格兹算子。这些公式基于封闭解析曲线到圆的单等价等距映射的定理。对于狄利克特-诺伊曼和狄利克特-罗宾算子的几个测试谐函数，获得了具有非常复杂几何形状的域的数值结果。

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Explicit Numerically Implementable Formulas for Poincaré–Steklov Operators

Abstract

The paper presents explicit numerically implementable formulas for the Poincaré–Steklov operators, such as the Dirichlet–Neumann, Dirichlet–Robin, Robin1–Robin2, and Grinberg–Mayergoiz operators, related to the two-dimensional Laplace equation. These formulas are based on the lemma about a univalent isometric mapping of a closed analytic curve onto a circle. Numerical results for domains with very complex geometries were obtained for several test harmonic functions for the Dirichlet–Neumann and Dirichlet–Robin operators.

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