An H-matrix direct method with improved solution for finite element analysis of scattering problems

An efficient direct method based on hierarchical matrices (H-matrices) was developed for the solution of large sparse finite element systems. H-matrix technique provides a data-sparse way to approximate the inverse of a finite element matrix which is dense originally. The approximate inverse can be computed and stored in the algebra of hierarchical matrices with almost linear complexity. The accuracy of this approximation is controllable with different choices of the related parameters. A modification algorithm was introduced to iteratively improve the accuracy of an approximate solution generated from H-matrix inversion. Some numerical examples are provided to illustrate the accuracy and efficiency of this method.