Time-Domain Analysis of Large-Scale Circuits by Matrix Exponential Method With Adaptive Control

MATEX: A distributed framework for transient simulation of power distribution networks

“…The standard Krylov subspace may not be computationally efficient when simulating stiff circuits based on MEXP [15,16]. For the accuracy of approximation of e A v, large dimension of Krylov subspace basis is required, which not only brings the computational complexity but also consumes huge memory.…”

“…2.4, standard Krylov subspace approximation in MEXP [15] is not computationally efficient for stiff circuit. The reason is that Hessenberg matrix Hm of standard Krylov subspace tends to approximate the large magnitude eigenvalues of A [13].…”

“…We test the part of circuit solver within MATEX using MEXP [15], as well as our proposed I-MATEX and R-MATEX. We create stiff RC mesh cases with different stiffness by changing the entries of matrix C, G. The stiffness here is defined as…”

“…However, building scalable and efficient distributed algorithmic framework for transient linear circuit simulation framework is still a challenge to leverage these powerful computing tools. Previous works [7,[14][15][16] have been made in order to improve circuit simulation by novel algorithms, parallel processing and distributed computing.…”

“…MEXP utilizes standard Krylov subspace method based on [11] to approximate matrix exponential and vector product. MEXP can solve the DAEs with high polynomial approximations [11,15] than traditional ones. Another merit of using MEXP-like SPICE simulation for linear circuit is the adaptive time stepping, which can proceed without re-factorizing matrices on-the-fly, while the traditional counterparts cannot avoid such timeconsuming process during the adaptive time marching.…”