V2EX robin condition

Robin Condition

Definition / 释义

Robin condition(罗宾条件):一种常见的边界条件(也常说 Robin boundary condition),把函数在边界上的取值与其法向导数按线性方式组合起来,典型形式为
\[ a\,u + b\,\frac{\partial u}{\partial n}=g \quad (\text{在边界上}) \]
常用于热传导、扩散、波动等问题中,表示“介于”Dirichlet(定值)与 Neumann(定通量)之间的混合边界条件

Pronunciation / 发音

/rbn kndn/

Examples / 例句

We used a Robin condition on the wall to model heat loss.
我们在墙面上使用罗宾条件来模拟热量散失。

In solving the Laplace equation on a bounded domain, imposing a Robin condition can represent convection at the boundary and leads to a well-posed boundary-value problem.
在有界区域上求解拉普拉斯方程时,施加罗宾条件可以表示边界处的对流效应,并使边值问题具有良好的适定性。

Etymology / 词源

“Robin condition”得名于法国数学家/物理学家 Victor Gustave Robin(维克托古斯塔夫罗宾)。该术语用来指代由“函数值 + 法向导数”线性组合构成的边界约束,因此也常被归类为“混合(mixed)边界条件”的一种。

Related Words / 相关词

Literary Works / 作品

  • Partial Differential Equations(Lawrence C. Evans)
  • Partial Differential Equations for Scientists and Engineers(Stanley J. Farlow)
  • Methods of Mathematical Physics(Richard Courant & David Hilbert)
  • Conduction of Heat in Solids(H. S. Carslaw & J. C. Jaeger)
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