Hierarchical EM preconditioners with spectral domain partitioning

The authors introduce an innovative approach to the problem that eliminates both the need for geometrical partitioning and the necessity of defining associated hierarchical basis functions. The main idea is to obtain the required Sobolev norm equivalencies directly at the matrix level and, in addition, to substitute the geometrical partitioning of the domain with a spectral partitioning. After presenting some background material, the authors delineate the main formulation. Numerical results were presented to corroborate the theory and to show the effectiveness of this approach when dealing with real case scenarios.