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We present some superfast (O((m + n) log 2 (m + n)) complexity) and stable struc-tured direct solvers for m × n Toeplitz least squares problems. Based on the displacement equation, a Toeplitz matrix T is first transformed into a Cauchy-like matrix C, which can be shown to have small off-diagonal numerical ranks when the diagonal blocks are rectangular. We… (More)

We present an algorithm for the fast and accurate simulation of nano-scale devices not attainable using current techniques. The idea underlying the algorithm is a novel divide-and-conquer method based on the non-equilibrium Green's function formalism. This formalism has provided a unifying conceptual framework for the analysis of quantum transport in… (More)

We provide a new representation for the inverse of block tridiagonal and banded matrices. The new representation is shown to be numerically stable over a variety of block tridiagonal matrices, in addition of being more computationally efficient than the previously proposed techniques. We provide two algorithms for commonly encountered problems that… (More)

We introduce a technique that utilizes distributing computing resources for the efficient optimization of a traditional physical design problem. Specifically, we present a detailed placement strategy designed to exploit distributed computing environments, where the additional computing resources are employed in parallel to improve the optimization time. A… (More)

The simulation of realistically sized devices under the Non-Equilibrium Greens Function (NEGF) formalism typically requires prohibitive amounts of memory and computation time. In order to meet the rising computational challenges associated with quantum-scale device simulation we offer a 2-D domain decomposition technique. This technique is applicable to a… (More)

We present an algorithm for the fast and accurate simulation of power/ground mesh structures. Our method is a direct (non-iterative) approach for simulation based upon a parallel matrix inversion algorithm. Through the use of additional computational resources, this distributed computing technique facilitates the simulation of large-scale power/ground… (More)

ABOUT THIS CHAPTER Clock distribution networks and power delivery systems are the two largest types of on-chip interconnect networks. They both play a crucial role in the correct operation of a circuit. A clock network delivers a synchronizing signal across the chip to coordinate the flow of data. A power/ground (P/G) supply network provides a reference… (More)

We propose a fast structured selected inversion method for extracting the diagonal blocks of the inverse of a sparse symmetric matrix A, using the multifrontal method and rank structures. When A arises from the discretization of some PDEs and has a low-rank property (the intermediate dense matrices in the factorization have small off-diagonal numerical… (More)

Information processing with a single multifunctional nanofluidic diode Appl. Subthreshold swings below 60mV/dec in three-terminal nanojunctions at room temperature Appl. Electrical stabilities and carrier transport mechanisms of flexible organic bistable devices based on CdSe-InP core-shell nanoparticle/polystyrene nanocomposites APL: Org. Electrical… (More)