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Parallel iterative methods for dense linear systems in inductance extraction

机译:电感提取中密集线性系统的并行迭代方法

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Accurate estimation of the inductive coupling between interconnect segments of a VLSI circuit is critical to the design of high-end microprocessors. This paper presents a class of parallel iterative methods for solving the linear systems of equations that arise in the inductance extraction process. The coefficient matrices are made up of dense and sparse submatrices where the dense structure is due to the inductive coupling between current filaments and the sparse structure is due to Kirchoff's constraints on current. By using a solenoidal basis technique to represent current, the problem is transformed to an unconstrained one that is subsequently solved by an iterative method. A dense preconditioner resembling the inductive coupling matrix is used to increase the rate of convergence of the iterative method. Multipole-based hierarchical approximations are used to compute products with the dense coefficient matrix as well as the preconditioner. A parallel formulation of the preconditoned iterative solver is outlined along with parallelization schemes for the hierarchical approximations. A variety of experiments is presented to show the parallel efficiency of the algorithms on shared-memory multiprocessors.
机译:VLSI电路互连段之间的电感耦合的准确估算对于高端微处理器的设计至关重要。本文提出了一类并行迭代方法,用于求解在电感提取过程中出现的线性方程组。系数矩阵由密集和稀疏的子矩阵组成,其中密集的结构是由于电流细丝之间的电感耦合而稀疏的结构是由于Kirchoff对电流的约束。通过使用螺线管基础技术来表示电流,该问题被转换为不受约束的问题,随后通过迭代方法解决了该问题。类似于电感耦合矩阵的密集预处理器用于提高迭代方法的收敛速度。基于多极点的层次逼近用于计算具有密集系数矩阵以及前置条件的乘积。概述了预条件迭代求解器的并行公式以及用于层次近似的并行化方案。提出了各种各样的实验来显示算法在共享内存多处理器上的并行效率。

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