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In this paper, we derive analytical solutions to the Laplace equation in a hemispherical domain subject to two different idealized Neumann boundary conditions. The solutions are given as infinite series, and their convergence is analysed. The theoretical results have been validated by comparing them with numerical results obtained using EIDORS.

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Analytical Solutions to the Laplace Equation on a Hemispherical Domain

  • 会议论文

  • 发表日期：

    2025年

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  • Cristiana Sebu,
  • Andrei Amaira,
  • Michael Pidcock

摘要

In this paper, we derive analytical solutions to the Laplace equation in a hemispherical domain subject to two different idealized Neumann boundary conditions. The solutions are given as infinite series, and their convergence is analysed. The theoretical results have been validated by comparing them with numerical results obtained using EIDORS.