• Corpus ID: 125378861

Stochastic and hybrid linear equation solvers and their applications in vlsi design automation

  title={Stochastic and hybrid linear equation solvers and their applications in vlsi design automation},
  author={Sachin S. Sapatnekar and Haifeng Qian},
This thesis presents two new linear equation solvers, and investigates their applications in VLSI design automation. Both solvers are derived in the context of a special class of large-scale sparse left-hand-side matrices that are commonly encountered in engineering applications, and techniques are presented that can potentially extend the theory to more general cases. The first is a stochastic solver that performs the computation by establishing the equivalence between linear equations and… 
2 Citations

Thermally-Aware Design

The onus on thermal management is beginning to move from the package designer toward the chip designer, and a set of thermal optimization techniques, for controlling on-chip temperatures and limiting the level to which they degrade circuit performance, are described.



A hybrid linear equation solver and its application in quadratic placement

The new solver is a combination of stochastic solver and iterative solver: it is proven in this paper that an approximate LDL factorization can be obtained from random walks, and used as a preconditioner for conjugate gradient solver.

FastPlace: efficient analytical placement using cell shifting, iterative local refinement, and a hybrid net model

FastPlace-a fast, iterative, flat placement algorithm for large-scale standard cell designs based on the quadratic placement approach that produces a global placement with even cell distribution in a very short time and a hybrid net model that is a combination of the traditional clique and star models.

Sequential monte carlo techniques for the solution of linear systems

A sequential Monte Carlo method is applied, in which the sampling scheme is iteratively improved, and the number of steps is dramatically reduced.

A stochastic algorithm for high speed capacitance extraction in integrated circuits

Matrix inversion by a Monte Carlo method

The following unusual method of inverting a class of matrices was devised by J. von Neumann and S. M. Ulam. Since it appears not to be in print, an exposition may be of interest to readers of MTAC.

Probabilistic potential theory applied to electrical engineering problems

The mathematical equivalence between a potential satisfying a deterministic Laplace-type equation within a closed region and a certain probability associated with a particle exercising Brownian

A note on the inversion of matrices by random walks

1 W. E. Milne, "The remainder in linear methods of approximation," NBS, Jn. Research, v. 43, 1949, p. 501-511. This gives a more general approach to step errors of integration formulas based upon

Power grid analysis using random walks

A class of power grid analyzers based on a random-walk technique, with linear runtime and the desirable property of localizing computation is presented, and a single-level hierarchical method is built and extended to multilevel and "virtual-layer" hierarchy.

Efficient large-scale power grid analysis based on preconditioned Krylov-subspace iterative methods

In this paper, we propose preconditioned Krylov-subspace iterative methods to perform efficient DC and transient simulations for large-scale linear circuits with an emphasis on power delivery