Direct Finite-Element Solver of Linear Complexity for Large-Scale 3-D Electromagnetic Analysis and Circuit Extraction

In this paper, we develop a linear-complexity direct finite-element solver for the electromagnetic analysis of general 3-D problems containing arbitrarily shaped lossy or lossless conductors in inhomogeneous materials. Both theoretical analysis and numerical experiments have demonstrated the solver's linear complexity in CPU time and memory consumption with prescribed accuracy satisfied. The proposed direct solver has successfully analyzed an industry product-level full package involving over 22.8488 million unknowns in approximately 16 h on a single core running at 3 GHz. It has also rapidly solved large-scale antenna arrays of over 73 wavelengths with 3600 antenna elements whose number of unknowns is over 10 million. The proposed direct solver has been compared with the finite-element methods that utilize the most advanced direct sparse solvers and a widely used commercial iterative finite-element solver. Clear advantages of the proposed solver in time and memory complexity, as well as computational efficiency, have been demonstrated.