鲁棒电网分析的快速泊松解预处理方法

Jianlei Yang, Yici Cai, Qiang Zhou, Jin Shi
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引用次数: 14

摘要

稳健、高效的电网分析算法对于超大规模集成电路的设计和优化至关重要。随着电网规模的不断扩大,IR下降分析在运行时和内存消耗方面变得越来越具有计算挑战性。本文提出了一种非结构电网非理想边界条件下的快速泊松预条件求解方法。实际上,利用电网的解析公式,这种解析预调节器可以看作是一种稀疏近似逆技术。通过将该分析预调节器与鲁棒共轭梯度方法相结合,我们证明了该方法对于超大规模电网模拟具有完全的鲁棒性。实验结果表明,一旦确定焊盘密度和金属电阻值分布范围,该方法的迭代次数几乎不会随栅格尺寸的增加而增加。我们证明了该方法在经典ICCG求解器的1/3迭代中解决了具有2.56M节点的非结构化电网,并且在运行时比经典ICCG求解器实现了近20倍的加速。
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Fast poisson solver preconditioned method for robust power grid analysis
Robust and efficient algorithms for power grid analysis are crucial for both VLSI design and optimization. Due to the increasing size of power grids IR drop analysis has become more computationally challenging both in runtime and memory consumption. This work presents a fast Poisson solver preconditioned method for unstructured power grid with unideal boundary conditions. In fact, by taking the advantage of analytical formulation of power grids this analytical preconditioner can be considered as sparse approximate inverse technique. By combining this analytical preconditioner with robust conjugate gradient method, we demonstrate that this approach is totally robust for extremely large scale power grid simulations. Experimental results have shown that iterations of our proposed method will hardly increase with grid size increasing once the pads density and the range of metal resistances value distribution have been decided. We demonstrated that this approach solves an unstructured power grid with 2.56M nodes in only 1/3 iterations of classical ICCG solver, and achieves almost 20X speedups over the classical ICCG solver on runtime.
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