求解电路方程组的改进分块对角加边方法

Improved Bordered Block Diagonal Method for Solving Circuit Equation Systems

针对电路仿真中瞬态分析底层产生的超大规模稀疏线性方程组的求解,分块对角加边(Bordered Block Diagonal,BBD)方法是一类经典的方法。本文提出了一种改进的BBD方法,通过在边界分解时引入以列为基础单位的动态并行分解,缓解了经典BBD方法中线程负载不均的问题,同时增强了并行性。使用8个电路方程的矩阵进行了数值实验,实验结果显示对于测试矩阵的LU分解速度,本文提出的改进方法在2线程和8线程情况下相比经典BBD方法均有一定的提升。

The Bordered Block Diagonal(BBD)method is a classic approach for solving the large and sparse linear equation systems generated at the bottom level in transient analysis of circuits simulation.In this paper,an improved BBD method is proposed,which introduces a fine-grained parallel decomposition based on columns during the boundary decomposition to alleviate the issue of uneven thread workload in the classical BBD method,while enhancing parallelism.Numerical experiments were conducted using a matrix of 8 circuit equations,and the results show that the proposed improvement method achieves a certain speedup in LU decomposition for the test matrix compared to the classical BBD method when using 2-thread and 8-thread scenarios.