# 2D formulation for Magnetostatic Problems

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(New page: The 2D Magnetostatic Poisson's equation given by the governing PDE and its boundary conditions: ::<math>A(A_z) = \left[ \frac{\partial}{\partial x}\cdot \left( \frac{1}{\mu_y} \frac{\par...) |
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::<math>A(A_z) = \left[ \frac{\partial}{\partial x}\cdot \left( \frac{1}{\mu_y} \frac{\partial}{\partial x}\right) | ::<math>A(A_z) = \left[ \frac{\partial}{\partial x}\cdot \left( \frac{1}{\mu_y} \frac{\partial}{\partial x}\right) | ||

− | + \frac{\partial}{\partial y}\cdot \left( \frac{1}{\mu_x} \frac{\partial }{\partial y}\right) \right] A_z(x,y) | + | + \frac{\partial}{\partial y}\cdot \left( \frac{1}{\mu_x} \frac{\partial }{\partial y}\right) \right] A_z(x,y)+ J_z(x,y)=0 ~~ in ~ \Omega </math> |

## Revision as of 19:14, 1 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}