# 2D formulation for Magnetostatic Problems

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(Difference between revisions)

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− | ::<math> | + | ::<math> A_z(x,y) \cong \hat A_z(x,y) = \sum_{i=0}^n N_i (x,y) a_i = \mathbf{N}^{(e)} · \mathbf{a}^{(e)}</math> |

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

\qquad | \qquad | ||

− | \mathbf{ | + | \mathbf{D}= |

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

− | \ | + | \frac{1}{\mu_y} & 0 \\ |

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

− | 0 & \ | + | 0 & \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}