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.