Reducing the curl-curl matrix bandwidth in 2D magnetostatics using tree-cotree method

An approach for reducing the vector FEM curlcurl matrix bandwidth in 2D magnetostatics is proposed. In the tree cotree method, the cotree edges are chosen so that the resulting curl-curl matrix bandwidth stays as close to the main diagonal as possible. It is shown that it is possible to obtain a tridiagonal matrix in the case of rectangular elements. In the case of triangular elements it is possible to obtain a curl-curl matrix that is very close to a tridiagonal one. An advantage of direct LU decomposition over the iterative method is shown.