A LOGOS solution of a Locally Corrected Nystrom formulation for the magnetostatic volume integral equation

Local-global solution (LOGOS) modes have been proven to be an effective framework for developing fast, direct solution methods for electromagnetic simulations. The LOGOS method provides an efficient direct factorization that sparsifies dense linear systems of equations with controlled accuracy. In this paper, the LOGOS method is applied to analyze the magnetostatic problem. The analysis of magnetic materials in a magnetostatic field is a challenging problem. To add to the challenge, magnetic materials are usually non-linear and are often inhomogeneous. An efficient solution is proposed for this class of problems that is based on a magnetostatic volume integral equation (MVIE) discretized via a Locally Corrected Nystrom method combined with a fast, direct LOGOS solver. The MVIE is posed such that only the diagonal operator is influenced by the magnetic material parameters. The dense linear system can be pre-factored via a LOGOS factorization. Thus, each iteration of a non-linear solution does not require the system matrix to be re-factorized and the problem can be solved in 0(N) operations. In this paper, the Locally Corrected Nystrom solution of the proposed MVIE and the efficiency of the fast direct LOGOS solution are validated.