From Circuit Theory, Simulation to SPICE&lt;sup&gt;Diego&lt;\/sup&gt;: A Matrix Exponential Approach for Time-Domain Analysis of Large-Scale Circuits

Zhuang, Hao; Wang, Xinyuan; Chen, Quan; Chen, Pengwen; Cheng, Chung‐Kuan

doi:10.1109/mcas.2016.2549947

Cited by 12 publications

(1 citation statement)

References 52 publications

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“…Introduction. Exponential time integration is an actively developing research field [41], with numerous successful applications in challenging large scale computations, such as elastic wave equations [43], wind farm simulations [30], power delivery network analysis [69], large circuit analysis [70] vector finite element discretizations of Maxwell's equations [12] and photonic crystal modeling [9,11].…”

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confidence: 99%

A residual concept for Krylov subspace evaluation of the $φ$ matrix function

Botchev,

Knizhnerman,

Tyrtyshnikov

2020

Preprint

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An efficient Krylov subspace algorithm for computing actions of the ϕ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many other applications. Our algorithm is based on a reliable residual based stopping criterion and a new efficient restarting procedure. For matrices with numerical range in the stable complex half plane, we analyze residual convergence and prove that the restarted method is guaranteed to converge for any Krylov subspace dimension. Numerical tests demonstrate efficiency of our approach for solving large scale evolution problems resulting from discretized in space time-dependent PDEs, in particular, diffusion and convection-diffusion problems.

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