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

TL;DR

This paper introduces R-MATEX and DR-MATEX, innovative exponential integration algorithms for large-scale power delivery network simulation, enabling variable step sizes and distributed parallel processing for significantly faster runtimes.

Contribution

The paper presents a novel exponential integration framework with variable step sizes and a distributed parallel implementation, improving efficiency over traditional fixed-step solvers.

Findings

R-MATEX achieves up to 14.4X speedup over traditional methods.

DR-MATEX achieves up to 98.0X speedup with parallel processing.

The methods effectively handle large-scale PDN simulations with variable step sizes.

Abstract

We design an algorithmic framework using matrix exponentials for time-domain simulation of power delivery network (PDN). Our framework can reuse factorized matrices to simulate the large-scale linear PDN system with variable stepsizes. In contrast, current conventional PDN simulation solvers have to use fixed step-size approach in order to reuse factorized matrices generated by the expensive matrix decomposition. Based on the proposed exponential integration framework, we design a PDN solver R-MATEX with the flexible time-stepping capability. The key operation of matrix exponential and vector product (MEVP) is computed by the rational Krylov subspace method. To further improve the runtime, we also propose a distributed computing framework DR-MATEX. DR-MATEX reduces Krylov subspace generations caused by frequent breakpoints from a large number of current sources during simulation. By virtue of the superposition property of linear system and scaling invariance property of Krylov subspace, DR-MATEX can divide the whole simulation task into subtasks based on the alignments of breakpoints among those sources. The subtasks are processed in parallel at different computing nodes without any communication during the computation of transient simulation. The final result is obtained by summing up the partial results among all the computing nodes after they finish the assigned subtasks. Therefore, our computation model belongs to the category known as Embarrassingly Parallel model. Experimental results show R-MATEX and DR-MATEX can achieve up to around 14.4X and 98.0X runtime speedups over traditional trapezoidal integration based solver with fixed timestep approach.