2 research outputs found
Circuit simulation via matrix exponential method for stiffness handling and parallel processing
We propose an advanced matrix exponential method (MEXP) to handle the transient simulation of stiff circuits and enable parallel simulation. We analyze the rapid decaying of fast transition elements in Krylov subspace approximation of matrix exponential and leverage such scaling effect to leap larger steps in the later stage of time marching. Moreover, matrix-vector multiplication and restarting scheme in our method provide better scalability and parallelizability than implicit methods. The performance of ordinary MEXP can be improved up to 4.8 times for stiff cases, and the parallel implementation leads to another 11 times speedup. Our approach is demonstrated to be a viable tool for ultra-large circuit simulations (with 1.6M ∼ 12M nodes) that are not feasible with existing implicit methods. © 2012 ACM.published_or_final_versio
MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks
We proposed MATEX, a distributed framework for transient simulation of power
distribution networks (PDNs). MATEX utilizes matrix exponential kernel with
Krylov subspace approximations to solve differential equations of linear
circuit. First, the whole simulation task is divided into subtasks based on
decompositions of current sources, in order to reduce the computational
overheads. Then these subtasks are distributed to different computing nodes and
processed in parallel. Within each node, after the matrix factorization at the
beginning of simulation, the adaptive time stepping solver is performed without
extra matrix re-factorizations. MATEX overcomes the stiff-ness hinder of
previous matrix exponential-based circuit simulator by rational Krylov subspace
method, which leads to larger step sizes with smaller dimensions of Krylov
subspace bases and highly accelerates the whole computation. MATEX outperforms
both traditional fixed and adaptive time stepping methods, e.g., achieving
around 13X over the trapezoidal framework with fixed time step for the IBM
power grid benchmarks.Comment: ACM/IEEE DAC 2014. arXiv admin note: substantial text overlap with
arXiv:1505.0669