# 2D formulation for Magnetostatic Problems

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::<math>\mathbf{f}^{(e)}= | ::<math>\mathbf{f}^{(e)}= | ||

− | \int_{\Omega^{(e)}} \mathbf{N^T} | + | \int_{\Omega^{(e)}} \mathbf{N^T} J_S \partial \Omega^{(e)} - |

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

\oint_{\Gamma_{{A_z}^{(e)}}} \mathbf{n^T} \mathbf{N^T} \mathbf{q_n} \partial \Gamma_{\varphi^{(e)}} | \oint_{\Gamma_{{A_z}^{(e)}}} \mathbf{n^T} \mathbf{N^T} \mathbf{q_n} \partial \Gamma_{\varphi^{(e)}} |

## Revision as of 10:01, 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}