An explicit inverse based fast direct volume integral equation solver for electromagnetic analysis

A fast direct solver that bypasses the need of a numerical inversion and factorization is developed to reduce the computational cost of a volume integral equation (VIE) based analysis of electromagnetic problems. The explicit inverse is achieved by analytically converting the inverse of the VIE system matrix to the sum of a few matrix-matrix multiplications. The matrix solution thus becomes a few matrix-vector multiplications, the computation of which is accelerated by the ℋ²-matrix based fast algorithms, achieving linear CPU cost and memory consumption across a range of electric sizes. The proposed method applies to inhomogeneous materials having a very large contrast ratio. Numerical results demonstrate its superior performance compared to conventional VIE solvers.