Hierarchical LU decomposition and its application in tangential equivalence principle algorithm

In this paper, hierarchical (ℋ-) LU decomposition is used to calculate inverse of impedance matrix in tangential equivalence principle algorithm (T-EPA). The T-EPA is a kind of domain decomposition method based on integral equation. In T-EPA, the inverse impedance matrix of object needs to be solved. However, the computational complexity of traditional direct solver is O(N³). The ℋ-LU decomposition can be used as a direct solver with the computational complexity of O(N²). Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.