Algorithm 907

Abstract

KLU is a software package for solving sparse unsymmetric linear systems of equations that arise in circuit simulation applications. It relies on a permutation to Block Triangular Form (BTF), several methods for finding a fill-reducing ordering (variants of approximate minimum degree and nested dissection), and Gilbert/Peierls’ sparse left-looking LU factorization algorithm to factorize each block. The package is written in C and includes a MATLAB interface. Performance results comparing KLU with SuperLU, Sparse 1.3, and UMFPACK on circuit simulation matrices are presented. KLU is the default sparse direct solver in the Xyce TM circuit simulation package developed by Sandia National Laboratories.

A holistic fast and parallel approach for accurate transient simulations of analog circuits

“…As a base line of comparison we choose the KLU solver [23,38] within the TITAN simulator. This solver is well suited for sparse matrices that arise from analog circuit simulation, and this solver is also widely used in open-source [4,5] and commercial SPICE simulators.…”

“…This solver is well suited for sparse matrices that arise from analog circuit simulation, and this solver is also widely used in open-source [4,5] and commercial SPICE simulators. Since KLU [23,38] does not have a parallel version, we consider the elapsed time of the sequential simulation as a reference for the sequential and parallel simulations with our approach.…”

“…As it is shown in Table 2, turning on the partition bypassing in sequential mode does not have any significant effect on the number of time steps nor on the number of iterations. Therefore The base line for comparison is a simulation with the KLU solver [23,38]. The sequential run with the BBD1 solver is the presented approach but without partition bypassing.…”

“…Therefore for large circuits the solver step (1.5) is the most dominant part of the Newton loop and was the subject of several research work. In several publications [20][21][22][23] the authors present various methods to speed up and to parallelize the linear solver step in the inner loop. These approaches are limited not just by Amdahl's law for parallelization, but they also have limited speedup capability due to their pure linear algebra view on the problem [10].…”

Asynchronous Power Flow on Graphic Processing Units

“…The Dome's implementation uses KLU, a highly optimized library for sparse matrix factorization, particularly suited to deal with matrices from circuit analysis [21]. The proposed method is tested on the Tesla K40c GPU, and the NR on the Xeon E5645 CPU.…”