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

Abstract

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 stiffness 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.

An algorithmic framework for efficient large-scale circuit simulation using exponential integrators

“…However, when the values in C vary in magnitudes caused by stiff circuit system, standard Krylov subspace demands large dimension of subspace to approximate MEVP, then degrades performance of matrix exponential-based circuit simulation. Such phenomenon has been observed in power distribution network simulation using matrix exponential framework [18], [19]. Besides, C should not be singular during the process of standard Krylov subspace strategy.…”

“…Beyond those conventional low order schemes, a high order matrix exponential based time integration kernel [3] has been recently triggering academic researchers' interests because of the progress of efficient matrix function computation using Krylov subspace methods [13]- [16]. In VLSI CAD and EDA research, this exponential integration kernel has been applied in time domain electromagnetic and technology semiconductor device simulation [17], power distribution network analysis [18], [19] as well as general circuit simulation [20], [21]. Those frameworks provide analytical solution for transient simulation of linear system, and better properties in numerical accuracy, stability and time step controlling, etc [3], [16], [18], [19].…”

A new tightly-coupled transient electro-thermal simulation method for power electronics

“…Nevertheless, our target step size is rather aggressive (∼ µs) compared to those reported in [3,16], and MEXP based on the ordinary Krylov subspace is not efficient for approximating large-magnitude eigenvalues (corresponding to the slow transients) [4]. Therefore, we choose to use the shift-and-invert (SAI) Krylov subspace method, which is essentially an "inverse" version of the standard Krylov subspace methods and can provide a better approximation to slow manifold of the waveform to allow larger step sizes [17,18]. The main step of SAI-Krylov is an m-step Arnoldi process applied to (I − γA) −1…”

Simulation Algorithms With Exponential Integration for Time-Domain Analysis of Large-Scale Power Delivery Networks

“…For the time step choice, breakpoints (also known as input transition spots (TS) [47]) are the time points where slopes of input vector change. Therefore, for Eq.…”

“…However, building scalable and efficient distributed algorithmic framework for transient linear circuit simulation is still a challenge to leverage these powerful computing tools. The papers [47], [48] show great potentials by parallelizing matrix exponential based method to achieve the runtime performance improvement and maintain high accuracy.…”