Fast Electromagnetic Transient Simulation Based on Hierarchical Low-Rank Approximation

In electromagnetic transient (EMT) simulation, 80-97% of the time is used to solve the network equations. Traditional approaches to solve the network equation are through sparse LU factorization, which is inherently sequential. In this paper, we propose a new approach to solve the network equations through hierarchical low-rank approximation of the inverse of the conductance matrix. The key observation is that the interaction between two groups of nodes, where nodes within each group are close to each other but nodes belonging to different groups are far apart, can be approximated by a low-rank matrix. Taking advantage of such observation, the proposed low-rank approximation permits $\mathrm{O}(N)$ time matrix-vector multiplication during each step of the EMT simulation, which is significant improvement over the $\mathrm{O}(N^{2})$ time by direct matrix-vector multiplication. Numerical studies on a series of large systems demonstrate that even without using any dedicated computing devices or parallelism, the proposed approach is about 2 times faster than the most widely used sparse LU factorization based direct solver without compromising the accuracy of the EMT simulation.