H- and H2-matrix-based fast integral-equation solvers for large-scale electromagnetic analysis

Integral-equation (IE)-based methods generally lead to dense systems of linear equations. The resulting matrices, although dense, can be thought of as `data sparse`, that is, they can be specified by few parameters. Based on this observation, two fast IE-based methods were developed for large-scale electromagnetic analysis. One is a centre-point H-matrix-based method of linear complexity for large-scale analysis of static problems or problems having small electric sizes. The other is an H²-matrix-based method of controlled accuracy and linear complexity for large-scale analysis of electrodynamic problems across a wide range of electric sizes. Numerical simulations from a small number of unknowns to over 1 million unknowns, from small electric sizes to over 60 wavelengths have demonstrated the accuracy and efficiency of the proposed methods. The methods are kernel independent, and hence suitable for any IE-based formulation. In addition, they are applicable to arbitrarily shaped structures.