CKTSO: High-Performance Parallel Sparse Linear Solver for General Circuit Simulations (2411.14082v2)

Abstract: This paper introduces CKTSO (abbreviation of "circuit solver"), a novel sparse linear solver specially designed for the simulation program with integrated circuit emphasis (SPICE). CKTSO is a parallel solver and can be run on a multi-core, shared-memory computer. The algorithms of CKTSO are designed by considering the features of matrices involved in SPICE simulations. CKTSO is superior to existing similar solvers mainly in the following three aspects. First, the matrix ordering step of CKTSO combines different types of ordering algorithms such that it can generally obtain the fewest fill-ins for a wide range of circuit matrices. Second, CKTSO provides a parallel fast LU factorization algorithm with pivot check, which behaves good performance, scalability, and numerical stability. Third, CKTSO provides a structure-adaptive hybrid parallel triangular solving algorithm, which can adapt to various circuit matrices. Experiments including both benchmark tests and SPICE simulations demonstrate the superior performance of CKTSO. The libraries of CKTSO are available at https://github.com/chenxm1986/cktso.

• The paper introduces CKTSO by integrating advanced matrix ordering and pivot-check based LU factorization to reduce fill-ins and boost computational efficiency.
• It employs a structure-adaptive hybrid parallel triangular solving strategy that partitions matrices according to sparsity patterns for optimized performance.
• Empirical evaluations show that CKTSO outperforms NICSLU and Intel oneMKL PARDISO, achieving significant improvements in simulation speed and scalability.

Insights into CKTSO: A High-Performance Parallel Sparse Solver for Circuit Simulations

This paper presents CKTSO, a specialized parallel sparse linear solver designed to enhance the efficiency of the Simulation Program with Integrated Circuit Emphasis (SPICE). SPICE is a cornerstone of electronic design automation (EDA), and CKTSO addresses certain performance bottlenecks inherent in existing solver implementations used in such simulations.

CKTSO distinguishes itself in three primary ways: it integrates advanced matrix ordering techniques, executes rapid LU factorization with numerical stability, and implements a hybrid parallel triangular solving strategy. These are purposefully crafted to respond to the unique characteristics of matrix sparsity and numerical behaviours encountered in circuit simulation tasks.

Matrix Ordering and Pre-processing

One of the initial challenges in SPICE simulations is the ordering of matrices to minimize fill-ins during LU factorization. CKTSO introduces a robust ordering strategy encompassing both the approximate minimum degree and nested dissection methods. By evaluating the fill-in count post-ordering with both techniques and selecting the optimal one, CKTSO achieves a balance that neither method could independently reach. The experimental results validate that this combined approach consistently achieves a reduction in fill-ins, thereby accelerating numerical factorization.

Pivot Check-Based Fast LU Factorization

CKTSO introduces an innovative pivot check-based LU factorization approach aimed at optimizing performance while maintaining numerical stability. Traditional approaches may not efficiently balance performance and stability, especially as matrix values evolve during the iterative SPICE simulation processes. CKTSO, therefore, initializes with a "guessed" elimination graph and monitors pivots throughout the factorization. If an unsatisfactory pivot is detected, a re-pivoting mechanism ensures accuracy without prohibitive performance costs. During typical iterations, when changes are gradual, the proposed strategy closely mirrors the speed of re-factorization but upholds the integrity typical of traditional factorization processes.

Structure-Adaptive Hybrid Parallel Triangular Solving

Addressing the inherent challenges of triangular solving, especially its sequential nature and low computation-to-communication ratio, CKTSO utilizes a structure-adaptive partitioning technique. Given the typical distribution patterns where denser blocks reside in matrix corners, CKTSO implements different solving strategies tailored to particular matrix sub-structures. This partitioning allows for parallelization of computationally intensive slices while maintaining efficient solving for dense lower triangular sub-matrices.

Performance Evaluation

The empirical evaluation conducted corroborates CKTSO’s advanced performance. When applied across a suite of benchmark circuit matrices from the SuiteSparse Matrix Collection, CKTSO outperformed other notable solvers such as NICSLU and Intel oneMKL PARDISO. More precisely, CKTSO’s matrix ordering leads to fewer fill-ins, reducing overall computational load, which, when coupled with its efficient parallel factorization and solving techniques, delivers marked improvements in simulation times.

Implications and Future Directions

CKTSO’s development marks a significant stride forward in the optimization of circuit simulation solvers, underpinning its practical utility in EDA. By integrating nuanced matrix-specific strategies and harnessing parallel computing capabilities, CKTSO sets a new benchmark for solver efficiency in SPICE simulations. As computational hardware continues to advance, these techniques suggest promising scalability and broader applicability in more generalized sparse matrix applications.

Looking forward, further exploration could involve refining CKTSO's strategies for even greater adaptability or expanding its scope to accommodate emerging circuit simulation challenges linked to novel semiconductor technologies. The exploration of domain-specific adaptations for varying EDA contexts may also yield actionable insights that further enhance solver performance across distinct application landscapes.