In this paper we present some preliminary basic results on the performance of the Cedar multiprocessor memory system. Empiricai results are presented and used to calibrate a memory system simulator which is then used to discuss the scalability of the system.

In this paper, we investigate the combined use of static techniques and dynamic feedback information to achieve a high level of optimization of both compiler e ciency and code performance. In previous work, we have introduced a new compiler approach, iterative compilation, to select the best tile sizes and unrolling factors. In this approach, many versions of programs are generated and their worth is determined by the actual execution time. We found that this approach can obtain a much higher level of optimization than conventional static techniques. To further achieve both compiler e ciency and high code performance, we have incorporated cache models in the iterative compilation system. We utilize feedback information in two ways: Post-Selection and Pre-Selection. Experimental results show that even a very simple cache model can achieve a high level of optimization with Post-Selection verifying the worth of transformed programs, especially when the number of program executions is limited. Pre-Selection is superior if more program executions are allowed.

We present recent results from the design of the GFDL ocean circulation model for the Cedar multicluster architecture. The model simulates the basic aspects of largescale, baroclinic ocean circulation, including treatment of irregular bottom topography. We concentrate on several modifications and versions of the code that are designed to exploit the memory and computational hierarchy of Cedar, and to exploit the details of the land topography in the three dimensional domain.

In this paper we discuss the convergence of a stabilization algorithm based on a singular version of the discrete Riccati difference equation. This method is particularly appealing for large scale linear time invariant dynamical systems since one can nicely exploit the sparsity of such systems in order to reduce the complexity of the algorithm.

While significant progress has been made in developing efficient algorithms for vector machines, the same cannot be said of parallel processors which provide concurrency and vectorization along with a complex memory system. The three aspects of these architectures must be addressed simultaneously and are often contradictory; increasing vector length may destroy data locality and thereby lead to inefficient use of the hierarchical memory system. In this paper, we consider the tradeoffs involved in designing algorithms for such architectures and present some results for a single cluster of the CEDAR machine. 22 refs., 14 figs.

In this paper, we establish a connection between Krylov subspace techniques for Multipoint Padé interpolation, and the use of Sylvester equations for constructing reduced-order models. We also briefly point out that this connection partly extends to ADI-type techniques and to the Smith iteration for computing approximate solutions of Lyapunov equations.

In this paper, we focus our attention on linear time invariant continuous time linear systems with one input and one output (SISO LTI systems). We consider the problem of constructing a reduced order system via truncation of the original system. Given a SISO strictly proper transfer function T(s) of McMillan degree N and a strictly proper SISO transfer function (T) over cap (s) of McMillan degree n < N, we prove that (T) over cap (s) can always be constructed via truncation of the system T(s). The proof is mainly based on interpolation theory, and more precisely on multipoint Pade interpolation. Moreover, new results about Krylov subspaces are developed. (C) 2003 Elsevier Inc. All rights reserved.

this paper holds for both continuous-time anddiscrete-time systems, we only cover here the continuous-time case. Extensions of the theoryfor discrete-time systems are straightforward. Every linear time-invariant continuoustimesystem can be represented by a generalized state-space model :E x = Ax +Buy = Cx +Du(1)with input u(t), state x(t)Nand output y(t). Without loss of generality,we can assume that the system is controllable and observable since otherwise we...

A method is presented for generating a broad-band rational interpolant approximation of the reflection coefficient of multiple-screen frequency-selective surfaces (FSSs). The technique is structured around a linearization of the system provided by a spectral domain moment method-based analysis of the FSS, followed by a model-order reduction of the linearized system using the dual rational Arnoldi method. This process creates a rational interpolant of the linearized system that matches its transfer function and its derivatives at several expansion points in the Laplace domain. Numerical results indicate that a reduced-order model with a system matrix of dimension less than 20/spl times/20 can accurately reproduce the broad-band behavior of multiscreen FSSs originally modeled with several hundreds or thousands of unknowns.

A model order reduction technique for systems depending on two parameters is developed. Given a large system model, the method generates the descriptor matrices of a system model of lower order that is a rational interpolant of the transfer function of the large system—the transfer functions have identical values and derivatives for a finite set of parameter values. The new technique is a generalization of recently developed algorithms for one-parameter systems that are based on projections onto Krylov subspaces defined by the descriptor matrices.

In this paper, we have presented the major features and some preliminary results from the parallel fast multipole library, ScaleME (scalable multipole engine). We have briefly outlined the major features of the library and its applications.

Multiscreen frequency selective surfaces (FSSs) are useful over a broad part of the electromagnetic spectrum as frequency or angular filters, and they have been especially important as subreflectors in dish antennas. The most popular method for the calculation of the reflection from FSSs due to incident plane wave excitation is the method of moments (MoM). This method results in a system of equations for the weighting coefficients for the basis functions representing the current, and a linear relation between the weighting coefficients and the screen reflection coefficient. Unfortunately, iterating the MoM to calculate the reflection coefficient over a band of frequencies is computationally costly. At each frequency, it involves both the construction and solution of large linear systems. Therefore, the goal of this paper is to construct a reduced order model of the system of equations.

It is found that the fast multipole algorithm (FMA), used to compute interactions between M bodies, can be used effectively in computing the electrostatic potential due to M bodies. This paper describes some of the few combinations of a parallel fast multipole algorithm and a capacitance solver. Another group has also combined the parallel FMA with a capacitance solver (Wang et al. 1996). The main difference between this and previous implementations of the fast multipole algorithm is the way parallelization was implemented. The current implementation performs well when compared to previous implementations. Other advances include precomputation, multiprocessor scalability, and a focus on data memory layout techniques. Many of these concepts that have been utilized in this implementation can be used in developing distributed memory implementations.

This paper describes FALCON, an environment for the development of numerical programs using MATLAB. FALCON supports an algebraic language to provide the developer the freedom of algorithm representation and reduced development time. This is combined with a compiler and transformation system to convert the algebraic language into source code which can call other programs and libraries developed with the system or independently and which can be embedded in an application code. During the compilation and transformation process, the developer is able to interactively apply optimizations and transformations to the code, including both traditional compiler techniques and other transformations which utilize algebraic information about the operations performed and target libraries in which they are implemented. The environment includes modules that allow MATLAB programs to be analyzed and then optimized, both automatically and semi-automatically. Fortran 90, C++, or restructured MATLAB code implementing the transformed algorithm can be produced by the code generators included in the environment.

This paper presents a model reduction method for large-scale linear systems that is based on a Lanczos-type approach. A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield a rational interpolant (multi-point Padé approximant) for the large-scale system. An exact expression for the error in the interpolant is derived. Examples are utilized to demonstrate that the rational Lanczos method provides opportunities for significant improvements in the rate of convergence over single-point Lanczos approaches.

A coarse-grain parallel solver for systems of linear algebraic equations with general sparse matrices by Gaussian elimination is discussed. Before the factorization two other steps are performed. A reordering algorithm is used during the first step in order to obtain a permuted matrix with as many zero elements under the main diagonal as possible. During the second step the reordered matrix is partitioned into blocks for asynchronous parallel processing (normally the number of blocks is equal to the number of processors). It is possible to obtain blocks with nearly the same number of rows, because there is no requirement to produce square diagonal blocks. The first step is much more important than the second one and has a significant influence on the performance of the solver. A straightforward implementation of the reordering algorithm will result in O(n2) operations. By using binary trees this cost can be reduced to O(NZ log n), where NZ is the number of non-zero elements in the matrix and n is its order (normally NZ is much smaller than n2). Some experiments on parallel computers with shared memory have been performed. The results show that a solver based on the proposed reordering performs better than another solver based on a cheaper (but at the same time rather crude) reordering whose cost is only O(NZ) operations.

We summarize our work consisting of the development of FALCON, a programming environment based on MATLAB. This environment includes capabilities for the rapid prototyping of algorithms, and for the interactive and automatic transformations at both the operation-level and the function-or algorithmic-level in order to obtain good numerical and computational performance. FALCON supports the development and reuse of numerical programs and libraries, and combines the transformation and analysis techniques used in restructuring compilers with the algebraic techniques used by developers to express and manipulate their algorithms in an intuitively useful manner.