An automatic strategy for solving ill-conditioned linear systems of equations resulting from a finite element method

Electromagnetic fields problems discretized by means of finite elements lead to sparse linear systems of equations which can be very difficult to solve. For instance, the coupling of magnetic and electric circuits equations often leads to badly scaled matrices. Inversion of ill-conditioned linear systems can potentially result in very inaccurate solutions when direct solvers are used and it can cause the slow convergence and even the divergence of iterative methods. In this paper, we present a general strategy to solve large sparse linear systems when no estimate of the condition number is available a priori