Next-generation fast algorithms for electromagnetics-based design and analysis of high-performance integrated circuits, packages, and boards

The fast and large-scale design automation of next-generation IC, packages, and boards calls for a continuous reduction of the computational complexity of electromagnetic solvers. In general, to solve problems with N parameters, the optimal computational complexity is linear complexity O(N). State-of-the-art fast computational methods rely on iterative matrix solutions to solve large-scale problems. The optimal complexity of an iterative solver is O(NN it N rhs ) with N being matrix size, N it the number of iterations and N rhs the number of right-hand sides. How to invert or factorize a dense matrix or a sparse matrix of size N in O(N) (optimal) complexity has been a challenging research problem, but of critical importance to the continual advancement of computational electromagnetics and electronic design automation. In this talk, I will present recent progresses in developing both direct finite element solvers and integral equation-based solvers of optimal complexity for fast and large-scale electromagnetics-based analysis and design of integrated circuits and systems.