Binormalized Factorizations for Magnetostatic Integral Equations

Localization-based sparse direct solvers provide a general framework for preconditioning sparse representations of integral equation formulations of magnetostatic field problems. However, problems involving complex meshes and geometries often lead to poorly conditioned system matrices. In some cases, localization-based preconditioners fail to yield convergent iterative solutions for these matrices. In this presentation it is shown that incorporating a multilevel matrix binormalization significantly increases the effectiveness of localization-based preconditioners.