Scholarlink

<p>This paper introduces a finite difference numeric scheme designed for the computational solution of the nonlinear heat conduction problem in a homogeneous silicon rod. It is shown that the numerical method is consistent with the conservation law, is conditionally stable and convergent. Focusing on the implicit schemes, an efficient Newton multigrid method with Gauss-Seidel red-black smoother is developed. Computational experiments confirm the stability theory as well as the robustness of the multigrid method.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the stability of a finite difference scheme for the nonlinear silicon problem

  • 期刊论文

  • 发表日期：

    2026年1月3日

查看全文
  • Adriano Rodrigues de Melo,
  • Marcio Augusto Villela Pinto,
  • Sebastião Romero Franco,
  • Priscila Dombrovski Zen

摘要

This paper introduces a finite difference numeric scheme designed for the computational solution of the nonlinear heat conduction problem in a homogeneous silicon rod. It is shown that the numerical method is consistent with the conservation law, is conditionally stable and convergent. Focusing on the implicit schemes, an efficient Newton multigrid method with Gauss-Seidel red-black smoother is developed. Computational experiments confirm the stability theory as well as the robustness of the multigrid method.