GPU-Accelerated Sparse LU Factorization for Circuit Simulation with Performance Modeling

Chen, Xiaoming; Ren, Ling; Wang, Yu; Yang, Huazhong

doi:10.1109/tpds.2014.2312199

Cited by 67 publications

(57 citation statements)

References 28 publications

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“…As interesting works on similar problematic to this article we can point out [1][2][3][4]. It is without a doubt that the accuracy of a simulation of the electronic circuits is essential.…”

Section: Introductionmentioning

confidence: 63%

An Efficient Procedure for Transient Analysis of Electronic Circuits with Increased Precision

Cerny

Dobeš

2016

MATEC Web Conf.

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Abstract. This article presents an efficient procedure allowing to increase the final accuracy of the electronic circuits simulation. To obtain Transient Analysis of a nonlinear circuit the simulator needs to perform various algorithms, from an evaluation of initial DC state through a nonlinear iterative algorithm, to a numerical integration. These complex computations have to be implemented effectively with regards to memory and processor usage. Direct implementation of arbitrary precision types can directly lead to increased simulation accuracy but also significantly decrease simulation performance. As a compromise, we suggest using an additional algorithm based on Newton Iteration method for the solution of matrix inversion. The method was modified to be comparable to direct LUF solver.

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“…As interesting works on similar problematic to this article we can point out [1][2][3][4]. It is without a doubt that the accuracy of a simulation of the electronic circuits is essential.…”

Section: Introductionmentioning

confidence: 63%

An Efficient Procedure for Transient Analysis of Electronic Circuits with Increased Precision

Cerny

Dobeš

2016

MATEC Web Conf.

View full text Add to dashboard Cite

show abstract

“…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].…”

Section: Q(x(t K )) -Q(x(t K-1 ))mentioning

confidence: 99%

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

2017

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The accurate analog simulation of critical circuit parts is a key task in the R&D process of integrated circuits. With the increasing complexity of integrated circuits it is becoming cumulatively challenging to simulate in the analog domain and within reasonable simulation time. Previous speedup approaches of the SPICE (Simulation Program with Integrated Circuit Emphasis) analog circuit simulator included either solver improvements and speedup or model order reduction of the semiconductor devices.In this paper we present a comprehensive approach to significantly speedup a SPICE-based analog circuit simulator while keeping the single-rate characteristic of time domain simulations. The novelty of our approach consists in the combination and extension of existing approaches in a unique way, enabling fast transient SPICE-level simulations. The main component of our approach is the circuit partitioner that combines relevant aspects from circuit theory and linear algebra in a unifying way. This enables the construction of an efficient and parallel BBD (bordered block diagonal) solver. Furthermore, this BBD structure allows for intrinsic model order reduction of the partitions during the Newton iteration, transforming the Newton method to a Quasi-Newton method.For mid-sized and large-sized circuits our BBD approach leads to significant sequential and parallel accelerations of transient simulations. Additional speedup can be gained from our block-bypass strategies exploiting the latency in the partitioned circuit. Altogether our approach leads to a speedup of up to two orders of magnitude compared to the state-of-the-art KLU solver while maintaining SPICE-level accuracy.

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“…There exists some work on accelerating the construction of preconditioners with GPU. For example, the incomplete Cholesky factorization preconditioners on GPU, 25,26 the incomplete LU factorization preconditioners on GPU, [27][28][29][30][31][32][33] the FSAI preconditioners on GPU, [34][35][36][37] and the SPAI preconditioners on GPU, [38][39][40] and the preconditioners that consist of an incomplete factorization, followed by an approximate inversion of the incomplete factors on GPU. [41][42][43][44] Especially, some public libraries such as CUSPARSE, 45 CUSP, 46 and ViennaCL 47,48 also include parallel preconditioners on GPU.…”

Section: Introductionmentioning

confidence: 99%

An efficient sparse approximate inverse preconditioning algorithm on GPU

Yin

Gao

2019

Concurrency and Computation

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Summary The sparse approximate inverse (SPAI) preconditioner has proven to be effective in accelerating the convergence of iterative methods. Recently, accelerating it on the graphics processing unit (GPU) has attracted considerable attention due to the fact that the cost of constructing it is high. This motivates us to investigate how to accelerate the construction of SPAI preconditioners on GPU in this paper. We propose an efficient sparse approximate inverse algorithm on GPU, called SPAI‐Adaptive. For our proposed SPAI‐Adaptive, there are the following novelties: (1) an adaptive thread allocation strategy for SPAI‐Adaptive is proposed to assign the optimal thread number for each column of the preconditioner, and (2) Each component of the preconditioner, which includes finding indices I and J, constructing local submatrix, decomposing the local matrix into QR, and solving the upper triangular linear system, is computed in parallel inside a thread group of GPU. Experimental results show that the proposed SPAI‐Adaptive is effective, and has good performance and high parallelism.

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GPU-Accelerated Sparse LU Factorization for Circuit Simulation with Performance Modeling

Cited by 67 publications

References 28 publications

An Efficient Procedure for Transient Analysis of Electronic Circuits with Increased Precision

An Efficient Procedure for Transient Analysis of Electronic Circuits with Increased Precision

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

An efficient sparse approximate inverse preconditioning algorithm on GPU

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