Fast H2-based integral equation solvers with an optimal H2-representation for large-scale electromagnetic analysis

We propose an algorithm to construct an optimal H²-based representation of integral operators, which has both optimized H²-partition and minimized rank, for accelerating integral equation based solutions of large-scale electromagnetic problems. The computational cost of this algorithm is small, since the cost associated with each admissible block depends on the block rank only. The proposed algorithm is also kernel independent. With the proposed H²-representation, both H²-based fast direct and iterative solvers are developed. They significantly outperform state-of-the-art H²-based solvers in computational efficiency without sacrificing accuracy.