- #1
azzaz
- 4
- 0
I have the following 2D Poisson equation (which can also be transformed
to Laplace) defined on a triangular region (refer to plot):
\begin{equation}
\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation}
with the following three boundary conditions:
\begin{equation}
\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=0\end{equation}
\begin{equation}
u=0\,\,\,\,\,\,\,\mathrm{at}\, y=ax+b\end{equation}
\begin{equation}
c\frac{\partial u}{\partial x}+d\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=ex+f\end{equation}
where C,a,b,c,d,e,f are constants.
What is the easiest way to solve this problem (preferably analytically)?
https://www.physicsforums.com/attachments/75674
to Laplace) defined on a triangular region (refer to plot):
\begin{equation}
\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation}
with the following three boundary conditions:
\begin{equation}
\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=0\end{equation}
\begin{equation}
u=0\,\,\,\,\,\,\,\mathrm{at}\, y=ax+b\end{equation}
\begin{equation}
c\frac{\partial u}{\partial x}+d\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=ex+f\end{equation}
where C,a,b,c,d,e,f are constants.
What is the easiest way to solve this problem (preferably analytically)?
https://www.physicsforums.com/attachments/75674