# 2D formulation for Magnetostatic Problems

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\int_{\Omega} \mathbf{N^T} J_S \partial \Omega - | \int_{\Omega} \mathbf{N^T} J_S \partial \Omega - | ||

\oint_{\Gamma_q} \mathbf{N^T} \bar q_n \partial \Gamma_q - | \oint_{\Gamma_q} \mathbf{N^T} \bar q_n \partial \Gamma_q - | ||

− | \oint_{\ | + | \oint_{\Gamma_{A_z}} \mathbf{n^T} \mathbf{N^T} \mathbf{q_n} \partial \Gamma_{\varphi} |

} | } | ||

</math> | </math> |

## Latest revision as of 10:11, 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}