Nestor E. Evmorfopoulos

A 3-D Fast Transform-based preconditioner for large-scale power grid analysis on massively parallel architectures

Efficient analysis of on-chip power delivery networks is one of the most challenging problems that EDA is confronted with. This paper addresses the problem of simulating general multi-layer power delivery networks with significant via resistances. An iterative solution method is combined with an efficient and extremely parallel preconditioning mechanism based on the application of a 3D Fast Transform solver, which enables harnessing the computational resources of massively parallel architectures, such as GPUs. Experimental evaluation of the proposed methodology on a set of large-scale industrial benchmarks demonstrates a speed-up of 290.2X for a 2.62M-node design over a state-of-the-art parallel direct solver, and a speed-up of 75.5X for a 10.51M-node design over a parallel iterative solver with a general-purpose preconditioner, when GPUs are utilized.

Selective Inversion of Inductance Matrix for Large-Scale Sparse RLC Simulation

The inverse of the inductance matrix (reluctance matrix) is amenable to sparsification to a much greater extent than the inductance matrix itself. However, the inversion and subsequent truncation of a large dense inductance matrix to obtain the sparse inverse is very time-consuming, and previously proposed window-based techniques cannot provide adequate accuracy. In this paper we propose a method for selective inversion of the inductance matrix to a prescribed sparsity ratio, which is also amenable to parallelization on modern architectures. Experimental results demonstrate its potential to provide efficient and accurate approximation of the reluctance matrix for simulation of large-scale RLC circuits.

Parallel Fast Transform-Based Preconditioners for Large-Scale Power Grid Analysis on Graphics Processing Units (GPUs)

Efficient analysis of on-chip power delivery networks is one of the most challenging problems facing the electronic design automation industry today. The fast dc and transient simulation of power grids is necessary to determine the proper operation of the integrated circuits at the design phase, but is made very difficult by the sheer size of modern power grids, reaching quite a few million nodes in nanometer-scale integrated circuits. This paper presents two efficient and highly parallel preconditioning mechanisms for the analysis of large-scale power grids of near-2-D structure (with small via resistances) or 3-D structure (with large via resistances) by iterative solution methods. The proposed preconditioners approximate the matrices of practical power grids well enough to ensure fast convergence of the iterative method, while their application within the core of the method is based on a fast transform solver which makes use of a series of independent fast Fourier transforms. Apart from the near-optimal operation complexity, the main characteristics of a fast transform solver are the large degree of multilevel parallelism and low memory requirements, which enable harnessing the computational resources of massively parallel architectures like graphics processing units (GPUs). Experimental evaluation of the proposed methodology on a set of large-scale industrial benchmarks demonstrates nearly two orders of magnitude speedup and reduction in memory footprint over parallel implementations of state-of-the-art direct and iterative methods, when GPUs are utilized.

On the statistical memory architecture exploration and optimization

The worsening of process variations and the consequent increased spreads in circuit performance and consumed power hinder the satisfaction of the targeted budgets and lead to yield loss. Corner based design and adoption of design guardbands might limit the yield loss. However, in many cases such methods may not be able to capture the real effects which might be way better than the predicted ones leading to increasingly pessimistic designs. The situation is even more severe in memories which consist of substantially different individual building blocks, further complicating the accurate analysis of the impact of variations at the architecture level leaving many potential issues uncovered and opportunities unexploited. In this paper, we develop a framework for capturing non-trivial statistical interactions among all the components of a memory/cache. The developed tool is able to find the optimum memory/cache configuration under various constraints allowing the designers to make the right choices early in the design cycle and consequently improve performance, energy, and especially yield. Our, results indicate that the consideration of the architectural interactions between the memory components allow to relax the pessimistic access times that are predicted by existing techniques.

Placement-based SER estimation in the presence of multiple faults in combinational logic

Susceptibility of modern ICs to radiation-induced faults constitutes a matter of great concern in the recent years. Particularly, the transient faults and their impact on the combinational logic remain an intriguing issue, since the evaluation of their behavior is quite significant, especially for critical systems, for the development of error-resistant techniques in design process. For an accurate estimation of Soft Error Rate both single and multiple transient faults should be regarded since the appearance of the latter is more noticeable as technology downscales. The proposed tool, i.e. SER estimator, is based on Monte-Carlo simulations, in order to obtain an accurate result, and takes advantage of placement information to identify the vulnerable parts of a circuit. Finally, the verification shows a fairly good accuracy compared with SPICE.

Fast and accurate BER estimation methodology for I/O links based on extreme value theory

This paper introduces a novel approach towards the statistical analysis of modern high-speed I/O and similar communication links, which is capable of reliably to determine extremely low (∼10−12 or lower) bit error rates (BER) by using techniques from extreme value theory (EVT). The new method requires only a small amount of voltage values at the received eye center, which can be generated by running circuit/system level simulations or measuring fabricated I/O circuits, to predict link BERs. Unlike conventional techniques, no simplifying assumptions on link noise and interference sources are required making this approach extremely portable to any communication system operating with very low BER. Our experimental results show that the BER estimates from the proposed methodology are on the same order of magnitude as traditional time domain, transient eye diagram simulations for links with BER of 10−6 and 10−5 operating at 9.6 and 10.1 Gbps respectively.