# 2D formulation for Electrostatic Problems

From KratosWiki

(Difference between revisions)

Line 8: | Line 8: | ||

\begin{cases} | \begin{cases} | ||

\left . V - \bar V = 0 \right |_{\Gamma_{V}} & in ~ \Gamma_{\varphi} \\ | \left . V - \bar V = 0 \right |_{\Gamma_{V}} & in ~ \Gamma_{\varphi} \\ | ||

+ | \, \\ | ||

\left . \hat n \vec{D} - \bar D_n = 0 \right |_{\Gamma_{q}} & in ~ \Gamma_{q} \\ | \left . \hat n \vec{D} - \bar D_n = 0 \right |_{\Gamma_{q}} & in ~ \Gamma_{q} \\ | ||

− | \left . \frac{\partial V}{\partial r} \right |_{\Gamma_{\infty}} \approx - \frac{V}{r^{ | + | \, \\ |

+ | \left . \frac{\partial V}{\partial r} \right |_{\Gamma_{\infty}} \approx - \frac{V}{r^{exp}} & in ~ \Gamma_{\infty} | ||

\end{cases} | \end{cases} | ||

</math> | </math> | ||

Line 85: | Line 87: | ||

− | ::<math>\alpha = \frac{1}{|r-r_0|^{ | + | ::<math>\alpha = \frac{1}{|r-r_0|^{exp}} \qquad with \quad exp=0.5, 1, 2...</math> |

## Revision as of 15:24, 30 October 2009

The 2D Electrostatic Poisson's equation given by the governing PDE and its boundary conditions:

can be written as (see the General formulation for Electrostatic Problems):

with (* n* is the number of nodes of the element):