# 2D formulation for Magnetostatic Problems

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(Difference between revisions)

Line 88: | Line 88: | ||

\mathbf{D}= | \mathbf{D}= | ||

\begin{bmatrix} | \begin{bmatrix} | ||

− | \frac{1}{\mu_y} & 0 \\ | + | \displaystyle \frac{1}{\mu_y} & 0 \\ |

\, \\ | \, \\ | ||

− | 0 & \frac{1}{\mu_x} | + | 0 & \displaystyle \frac{1}{\mu_x} |

\end{bmatrix} | \end{bmatrix} | ||

</math> | </math> |

## Revision as of 10:03, 2 February 2010

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

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

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

## 2D formulation for Triangular Elements

After applying the numerical integration for triangular elements by using the natural coordinates, we obtain:

### Stiffness Matrix K^{(e)}

### Source Vector f^{(e)}

**Linear case**(**n**=1 integration point):_{p}

**Quadratic case**(**n**=3 integration points):_{p}