IC thermal analyzer for versatile 3-D structures using multigrid preconditioned krylov methods
IC thermal analyzer for versatile 3-D structures using multigrid preconditioned krylov methods
复制标题
使用多重网格预处理 krylov 方法的多功能 3D 结构 IC 热分析仪
DOI：
10.1145/2966986.2967045
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Ladenheim S
中科院分区：
文献类型：
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作者：
Ladenheim S
在先进的集成电路技术中，热分析对于确定热的传播和跟踪热点的形成至关重要。集成电路热分析的核心是热方程的数值求解。现有的学术热分析工具通常通过在均匀网格上应用有限差分方法来计算温度，其中时间积分方法具有固定的时间步长。此外，由离散热方程产生的线性系统使用基于矩阵分解的直接方法求解。然而，直接方法不能很好地随问题规模的增加而扩展。此外，大多数工具仅支持2D或有限数量的3D技术。为了解决这些问题，本文提出了一种新的热分析仪，能够模拟2-D和3-D电路技术。该分析仪使用有限元法进行空间离散化，再加上隐式时间积分法，以及时推进解决方案，从而求解热方程。它还提供完全自适应的时空细化功能，以提高精度和计算效率。所得到的线性系统求解的多重网格预处理Krylov子空间迭代法，这给3-D瞬态分析的上级性能。该分析仪被证明可以准确地捕获集成系统的水平和垂直方向上的热传播。
Thermal analysis is crucial for determining the propagation of heat and tracking the formation of hot spots in advanced integrated circuit technologies. At the core of the thermal analysis for integrated circuits is the numerical solution of the heat equation. Prior academic thermal analysis tools typically compute temperature by applying finite difference methods on uniform grids with time integration methods having fixed time step size. Additionally, the linear systems arising from the discretized heat equation are solved using direct methods based on matrix factorizations. Direct methods, however, do not scale well as the problem size increases. Moreover, most of the tools support only 2-D or a limited number of 3-D technologies. To address these issues, this paper presents a novel thermal analyzer with the ability to model both 2-D and 3-D circuit technologies. The analyzer solves the heat equation using the finite element method for the spatial discretization coupled with implicit time integration methods for advancing the solution in time. It also offers fully adaptive spatio-temporal refinement features for improved accuracy and computational efficiency. The resulting linear systems are solved by a multigrid preconditioned Krylov subspace iterative method, which gives superior performance for 3-D transient analyses. The analyzer is shown to accurately capture the propagation of heat in both the horizontal and vertical directions of integrated systems.