EI-PIT: A Parallel-in-Time Exponential Integrator Method for Transient Linear Circuit Simulation

In this paper, we introduce a parallel-in-time exponential integrator (EI) method, EI-PIT, designed to expedite the transient simulation of linear circuits. By leveraging the linear superposition principle, we decompose the solution at each time point into two components: one resulting from the natural decay of the initial state and the other induced from input excitation. The decay components are processed by computing a single matrix-exponential-vector product over the entire simulation span using the rational Krylov subspace method. Subsequently, the back-scaling technique exploits the scaling invariant property of the Krylov subspace to derive solutions at intermediate time points. The excitation component at any given time point is obtained by approximating a sequence of composite matrix exponential functions, each multiplied by input vectors at varying time points. Given that these inputs are predefined and independent, and the system matrix is constant, the computation-intensive process of generating Krylov subspaces can be performed in parallel. Two enhancement techniques, fast computation of the functions with input slopes based on subspace reuse, and parallelization in batches, are also developed to further boost the performance of EI-PIT.