MaxwellIntegrators::DivCurl Namespace Reference

Classes
class	Eigen
class	Matrix

Detailed Description

Integrator for curl-curl problems in weakly divergence free subspace.

The weak formulation for this system is: find \(u,\phi\in V_h\times \Psi_h\) such that

\[ \begin{array}{cccclcl}\arraycolsep1pt \bigl(\mu \nabla\times u,\nabla\times v\bigr) + \bigl(\sigma u,v\bigr) &+& \bigl(v,\nabla \phi\bigr) &=& \bigl(f,v) &\qquad&\forall v\in V_h \\ \bigl(u,\nabla \psi) && &=& 0 &&\forall \psi\in\Psi_h \end{array} \]

The finite element system is expected to consist of a vector-valued curl conforming element in first position and an H¹-conforming scalar element in second.

We are building a single matrix in the end, but the cell matrices come in a two-by-two block structure in the order

1. The curl-elliptic operator
2. The gradient operator
3. The divergence operator as transpose of the gradient
4. Empty