Layered H-matrix based direct matrix inversion of significantly reduced complexity for finite-element-based large-scale electromagnetic analysis

The matrix generated from a finite-element method (FEM) based analysis of electromagnetic problems is sparse, however, it can be computationally challenging to solve the matrix directly. The optimal complexity of the direct solution of an FEM matrix is shown to be 0(N1´5) with TV being the matrix size. An 7Y-matrix-based fast direct solver is developed for the FEM based analysis of large-scale electromagnetic problems. A detailed theoretical analysis is developed for the complexity and accuracy of the H-matrix-based direct FEM solver. It is shown that although the inverse of an FEM matrix is generally dense, it can be computed in O(Nlog²N) complexity and stored in O(Nlog²N) memory.