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The talk will consist of two parts. In the first part, I will present prior work aimed at developing new algorithms for materials science applications. I developed a novel numerical method to optimize the shape of mechanical parts and maximize their strength. This optimization problem was extremely challenging as it involved changing the topology and therefore classical optimization methods do not apply. A similar idea can be applied to model shape memory alloys and plasticity in metals. In this project, the optimization led to the construction of a tree of laminated microstructures. Constraints from mechanical equilibrium were used to construct an adaptive tree and to determine the optimal number of levels. The second part involves more recent work. I will present the implementation of a new heat flux algorithm to understand failures in micro-devices in LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator); LAMMPS is a high performance code which was benchmarked on Blue Gene L with 90% parallel efficiency. Also I am currently extending the capabilities of ParaDiS (Parallel Dislocation Simulator), another high performance code which has run on 135k processors of Blue Gene L. ©2008 Microsoft Corporation. All rights reserved.

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

This report documents the numerical algorithms used in an explicit Lagrangian finite element hydrocode. One, two, and three dimensional implementations of the numerical solution of the conservation equations are covered. Triangular and tetrahedral continuum elements and shell elements are described. SPH (Smooth Particle Hydrodynamics) techniques are discussed. Slideline techniques are explained. Material models are presented for constitutive behavior and equation of state behavior for several categories of materials. This report is a comprehensive presentation of the numerical techniques used in a current production hydrocode.

The results from a verification with pilot reports of four aircraft icing algorithms applied to Navy global numerical model data are presented. Significant differences in forecast performance among algorithms are closely related to differences in temperature and moisture thresholds utilized to infer icing. Near 850 mb (-5000 ft), three of the icing routines correctly forecast over 70% of observed icing occurrences, and obtained Hanssen and Kuipers skill scores (difference between hits and false alarms) in excess of 0.5 (0, random performance; I, perfect skill). Statistical tests indicated that differences in skill scores as a function of forecast lead time (0 to 24 hr) were generally not significant. The use of higher vertical resolution data was found very important for enhanced icing prediction performance. Overall results indicate that the ability of icing routines to differentiate icing type and intensity based on temperature, moisture and stability criteria is clearly limited. In terms of forecast skill and computational efficiency, algorithm comparisons indicate that the icing routine currently used as operational guidance at the National Centers for Environmental Prediction Aviation Weather Center would be a good selection for the Naval Research Laboratory's aviation support product suite.

An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by finding the space of dual functionals that annihilate it, reducing the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.

An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by finding the space of dual functionals that annihilate it, reducing the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.

In this paper we introduce the design and implementation of two parallel algorithms for solving the general tridiagonal linear system of equations using two new parallel algorithms: Parallel splitting Gauss – Jordan and the general parallel splitting Gauss Jordan algorithms. These algorithms are very easily distributed over different number of processors. In addition our implementations are very efficient, generally a linear speed-up is obtained by increasing the number of processors

In this paper we introduce the design and implementation of two parallel algorithms for solving the general tridiagonal linear system of equations using two new parallel algorithms: Parallel splitting Gauss – Jordan and the general parallel splitting Gauss Jordan algorithms. These algorithms are very easily distributed over different number of processors. In addition our implementations are very efficient, generally a linear speed-up is obtained by increasing the number of processors

Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized.

8 p. 28 cm

8 p. 28 cm

8 p. 28 cm

Abstract : The paper is devoted to the development and analysis of approximation-iteration algorithms based on the method of grids and the method of lines for solving an elliptic optimal control problem with a power-law nonlinearity. For the numerical solution of the main boundary value problem and the adjoint one, the second order of accuracy difference schemes are applied using the implicit method of simple iteration. Computational schemes of the method of lines for solving the above-mentioned elliptic boundary value problems are implemented in combination with the shooting method for the approximate solution of boundary value problems for the corresponding ordinary differential equations systems arising in the considered domain after lattice approximation. To minimize the objective functional, well-known gradient-type methods (gradient projection and conditional gradient methods) of constrained optimization are used. The essence of the proposed approximation-iteration approach consists in replacing the original extremal problem with a sequence of grid problems that approximate it on a set of refining grids, and applying an iterative gradient-type method to each of the "approximate" extremal problems. In this case, we propose to construct only a few approximations to the solution for each of the "approximate" problems and to take the last of these approximations, using piecewise linear interpolation, as the initial approximation in the iterative process for the next "approximate" problem. The sequence of the corresponding piecewise linear interpolants is considered as a sequence of approximations to the solution of the original extremal problem. The paper discusses the theoretical foundations of this combined approach, as well as its advantages over traditional methods using the example of solving a model optimal control problem.

This research involves higher order methods for solving partial differential equations. A common theme of this research is the use of spectral methods. One of the challenges of the spectral Fourier method is approximating smooth functions that are non-periodic. The rate of convergence deteriorates to O(1/N) away from the boundaries and there are spurious oscillations at the boundary points, known as the Gibbs phenomenon. We discuss an analytic but non-periodic function f(x) defined on -1,1, for which the first 2N+1 Fourier coefficients are known, and focuses on two methods that successfully eliminate the Gibbs phenomenon based on the information obtained from the Fourier coefficients. A new method is suggested to improve upon the results that have been obtained thus far. Also discussed is the Gibbs phenomenon for spherical harmonic spectral methods applied to functions that are piecewise analytic on spheres. We prove that knowledge of the first N spherical harmonic coefficients yield an exponentially convergent approximation to a spherical piecewise smooth function, hence completely overcoming the Gibbs phenomenon. Higher order numerical methods are applied to a specific one-dimensional hyperbolic system that describes the shallow water dynamics of a linearly sloping gulf. This problem is challenging due to the constantly changing location of where the water touches the shore. At this point the equation loses its strong hyperbolicity, and conventional numerical methods may not produce the correct solution. Also, any discontinuities that may arise as a result of the nonlinearity cannot be predicted, and this must be considered in selecting a numerical method.

Our research under the RASSP program focussed on the development of new signal processing algorithms to exploit the advantages and opportunities of rapid prototyping for signal processing systems. Our work was carried out in the Research Laboratory of Electronics at MIT with close collaboration and interaction with industrial partners including Lockheed Sanders. Our primary accomplishments were in several categories. We developed and explored new classes of signals and algorithms related to chaotic behavior in nonlinear systems. We also developed and explored the use of fractal signals for communications. A third new nonlinear signal class that we explored exploits the solution behavior of certain nonlinear wave equations. A significant part of our effort was directed at the exploration of algorithm-based fault tolerant architectures for signal processing and for the use of approximate processing techniques which can be exploited in the contexts of low-power signal processing architectures and in other aspects of processor resource management. We also explored opportunities to exploit multirate signal processing. In the following section we briefly summarize our results in each of these areas. Section 3 contains a bibliography of the journal articles, book chapters, and conference papers in which the details of our work is presented.

Yves - Performance Python for Numerical Algorithms [EuroPython 2014] [23 July 2014] This talk is about several approaches to implement high performing numerical algorithms and applications in Python. It introduces into approaches like vectorization, multi-threading, parallelization (CPU/GPU), dynamic compiling, high throughput IO operations. The approach is a practical one in that every approach is illustrated by specific Python examples. ----- This talk is about several approaches to implement high performing numerical algorithms and applications in Python. It introduces into approaches like multi-threading, parallelization (CPU/GPU), dynamic compiling, high throughput IO operations. The approach is a practical one in that every approach is illustrated by specific Python examples. The talk uses, among others, the following libraries: * NumPy * numexpr * IPython.Parallel * Numba * NumbaPro * PyTables

On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein's prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detection of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole binaries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest, and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. Our emphasis is on the synergy between these disciplines, and how mathematics, broadly understood, has historically played, and continues to play, a crucial role in the development of GW science. We focus on black holes, which are very pure mathematical solutions of Einstein's gravitational-field equations that are nevertheless realized in Nature, and that provided the first observed signals.

This paper discusses two algorithms for nonlinearly constrained optimization. These algorithms -- the penalty and barrier trajectory algorithms -- are based on an examination of the trajectories of approach to the solution that characterize the quadratic penalty function and the logarithmic barrier function, respectively. Although closely related in principle, the two algorithms display important differences in their implementation as well as in the properties of the generated iterates. The discussion will emphasize the numerical aspects of implementation of the trajectory algorithms, with particular attention to the choice of reliable methods for carrying out the required computations. (Author)

The work of several graduate students which relate to the NASA grant is briefly summarized. One student has worked on a detailed analysis of the so-called ijk forms of Gaussian elemination and Cholesky factorization on concurrent processors. Another student has worked on the vectorization of the incomplete Cholesky conjugate method on the CYBER 205. Two more students implemented various versions of Gaussian elimination and Cholesky factorization on the FLEX/32.

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

During the period of this grant, our detailed technical accomplishments are reported through journal articles and technical reports. Each of our semi-annual reports will highlight certain technical areas and provide a summary listing of our technical articles related to the project.

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

In this paper, we introduce various numerical methods for the solutions of ordinary differential equations and its application. We consider the Taylor series, Runge Kutta, Euler's methods problem to solve the Adam's Predictor, Corrector and Milne's Predictor, Corrector to get the exact solution and the approximate solution.  by Subhashini | Srividhya. B "Comparison of Several Numerical Algorithms with the use of Predictor and Corrector for solving ode"  Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019,  URL: https://www.ijtsrd.com/papers/ijtsrd29318.pdf  Paper URL: https://www.ijtsrd.com/mathemetics/other/29318/comparison-of-several-numerical-algorithms-with-the-use-of-predictor-and-corrector-for-solving-ode/subhashini

Work by Prof. Oppenheim and his collaborators is summarized here. The first step in one aspect of our research in the RASSP program involves evaluating the abilities and limitations of current DSP system design tools. We are concerned with what algorithms the tools support, and how the tool abilities might be expanded in the future to support emerging signal processing techniques. Major accomplishments in our recent approximate processing research include: (1) conceptual and mathematical elaboration of approximate process- ing concepts, (2) formulation and implementation of a class of incremental refinement algorithms for the short-time Fourier transform, (3) illustration of design issues in the context of incremental refinement algorithms , (4) continued development of the IPUS-C++ software environment for supporting the design of application systems with embedded approximate signal processing capabilities, and (5) initiation of a project to build a software environment to support algorithm design for approximate signal processing.

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

This paper describes the development and evaluation of a numerical roll reversal predictor-corrector guidance algorithm for the atmospheric flight portion of the Mars Surveyor Program 2001 Orbiter and Lander missions. The Lander mission utilizes direct entry and has a demanding requirement to deploy its parachute within 10 km of the target deployment point. The Orbiter mission utilizes aerocapture to achieve a precise captured orbit with a single atmospheric pass. Detailed descriptions of these predictor-corrector algorithms are given. Also, results of three and six degree-of-freedom Monte Carlo simulations which include navigation, aerodynamics, mass properties and atmospheric density uncertainties are presented.

The objective of this research project is to derive and evaluate versatile, accurate and efficient numerical algorithms for solution of aerodynamic flowfields at large Reynolds number. The concept of a dissipative finite element algorithm has been refined and extended to solution of a complete equation set in aerodynamics. The resultant numerical results are highly encouraging with respect to shock resolution and overall performance, utilizing both a linear quadratic finite element embodiment of the theory. The theoretical formulational statement of the algorithm has been extended to a multi-dimensional description in generalized coordinates. The key efficiency feature is identification of the tensor matrix resolution of the Jacobian of the Newton algorithm for this statement. The concept of application of the continuity equation solution, as a differential constraint on the momentum equation algorithm, has been validated. The formulation is directly useful for viscous marching procedures, and with some modifications could be equally useful for a low Mach number Navier - Stokes solution algorithm. (Author)

The ellipsoid algorithm associated with Shor, Khachiyan and others has certain theoretical properties that suggest its use as a linear programming algorithm. Some of the practical difficulties are investigated here. A variant of the ellipsoid update is first developed, to take advantage of the range constraints that often occur in linear programs (i.e., constraints of the form l or = aTx or = u, where u - l is reasonably small). Methods for storing the ellipsoid matrix are then discussed for both dense and sparse problems. In the large-scale case, a major difficulty is that the desired ellipsoid cannot be represented compactly throughout an arbitrary number of iterations. Some schemes are suggested for economizing on storage, but any guarantee of convergence is effectively lost. At this stage there remains little room for optimism that an ellipsoid-based algorithm could complete with the simplex method on problems with a large number of variables. (Author)

Two activities were pursued under this grant. The first was a visitor program to conduct research on numerical algorithms for MIMD computers. The program is summarized in the following attachments. Attachment A - List of Researchers Supported; Attachment B - List of Reports Completed; and Attachment C - Reports. The second activity was a workshop on the Control of fluid Dynamic Systems held on March 28-29, 1989. The workshop is summarized in attachments. Attachment D - Workshop Summary; and Attachment E - List of Workshop Participants.

The realization of high-speed numeric computation is a sought-after commodity for real world applications, including high-speed scientific computation, digital signal processing, and embedded computers. An example of this is the generation of elementary functions, such as sin( ) x , x e and log( ) x . Sasao, Butler and Reidel Ref. 1 developed a high speed numeric function generator using a look-up table (LUT) cascade. Their method used a piecewise linear segmentation algorithm to generate the functions Ref. 1. In this thesis, two alternative segmentation algorithms are proposed and compared to the results of Sasao, Butler and Reidel Ref.1. The first algorithm is the Constant Approximation. This algorithm uses lines of slope zero to approximate a curve. The second algorithm is the power-of-2-approximation. This method uses 2i x to approximate a curve. The constant approximation eliminates the need for a multiplier and adder, while the power-of-2-approximations eliminates the need for multiplier, thus improving the computation speed. Tradeoffs between the three methods are examined. Specifically, the implementation of the piecewise linear algorithm requires the most amount of hardware and is slower than the other two. The advantage that it has is that it yields the least amount of segments to generate a function. The constant approximation requires the most amount of hardware to realize a function, but is the fastest implementation. The power-of-2 approximation is an intermediate choice that balances speed and hardware requirements.

A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.

A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.

We provide a framework to bound the probability that accumulated errors were never above a given threshold on numerical algorithms. Such algorithms are used for example in aircraft and nuclear power plants. This report contains simple formulas based on Levy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one out of a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.

The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

This is a bibliography on numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are also listed.

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

Flash-algorithm track-reconstruction routines with speed factors 3000-4000 in excess those of traditional iterative routines are presented. The methods were successfully tested in the alignment of the Test Beam setup for the ATLAS Pixel Detector MCM-D modules yielding a 60 fold increase in alignment resolution over iterative routines, for the same amount of alocated CPU time.

In the dual formulation of d=3 SU(2) LGT, the link variables are group representations and valid configurations are those satisfying a number of triangle inequalities. In \cite{lat99} algorithms for local updates that automatically respect these constraints were described. It was also pointed out there that these local updates were not ergodic. In this presentation, we describe two different quasi-local updating algorithms which, in conjunction with the local updates, appear to be ergodic.

In the dual formulation of d=3 SU(2) LGT, the link variables are group representations and valid configurations are those satisfying a number of triangle inequalities. In \cite{lat99} algorithms for local updates that automatically respect these constraints were described. It was also pointed out there that these local updates were not ergodic. In this presentation, we describe two different quasi-local updating algorithms which, in conjunction with the local updates, appear to be ergodic.

Research concentrated on designing and implementing a microprocessor based concurrent computing environment consisting of a number of Intel microprocessors with IEEE floating point arithmetic implemented in hardware. The major focus of our work was the design of a concurrent tasker in software to locate code can data, monitor computation and communication and report results to the user. The construction of viable numerical algebra modules in an IEEE floating point arithmetic was and continues to be part of the research. (Author)

Several fast signal processing algorithms applicable in target detection and recognition techniques have been developed. These include a novel accurate and efficient method for replacing IIR filters by FIR filters, a method for multiresolution implementation of operators via filter banks, a multiresolution strategy for numerical homogenization and an algorithm for Unequally Spaced Fast Fourier Transform (USFFT) in multiple dimensions. The USFFT algorithm was one of the specific goals of the proposal. This algorithm was shown to be about 20% more efficient than the previous approach. It was also used as a part of a code for computing antenna far field patterns from near field measurements.

The purpose of this grant was to purchase a hypercube computer to support DoD-sponsored research, and other research, in parallel numerical computation. The plans that were outlined in the proposal were followed very closely. We have purchased a 32-node Intel iPSC-D5 hypercube computer with the funds from this grant, and have used the matching University contribution to support the maintenance of this computer. This computer has been used, over the past year, for research in parallel numerical computation in areas including global optimization, VLSI design, large sparse systems of linear equations, and eigenvalue problems, as well as for research in the languages for parallel computation and in the debugging and measurement of parallel programs.

The long term goals of this research activity are derived from concurrent computing with emphasis on numerical algorithms that support a variety of scientific applications. Among the applications of immediate interest are signal processing, high statistical methods such as the bootstrap. The shorter term focus has been the refinement and enhancement of the concurrent computing environment itself and the numerical algorithms that form the foundation for the applications. The computer systems that support this research use hardware manufactured by Intel -- with the 8086 cpu and the 8087 floating point processor at the heart of each node. The nodes are contained in workstations (with up to seven Workers and a Manager in a workstation) that can operate independently or can be linked together during execution. Worker structure and memory are configurable to support experiments conducted in the course of this research. Keywords: Parallel processing; Synchronization(electronics).

Latent Dirichlet Allocation (LDA) is a scheme which may be used to estimate topics and their probabilities within a corpus of text data. The fundamental assumptions in this scheme are that text is a realisation of a stochastic generative model and that this model is well described by the combination of multinomial probability distributions and Dirichlet probability distributions. Various means can be used to solve the Bayesian estimation task arising in LDA. Our formulations of LDA are applied to subject matter expert text data elicited through carefully constructed decision support workshops. In the main these workshops address substantial problems in Australian Defence Capability. The application of LDA here is motivated by a need to provide insights into the collected text, which is often voluminous and complex in form. Additional investigations described in this report concern questions of identifying and quantifying di erences between stake-holder group text written to a common subject matter. Sentiment scores and key-phase estimators are used to indicate stake-holder di erences. Some examples are provided using unclassi ed data.

During this project several new numerical algorithms were designed, analyzed, and implemented with the goal of accelerating computational experiments in time-domain electromagnetics and acoustics. Novel results include a new family of radiation boundary conditions used for truncating computational domains used in external scattering simulations. A new filter and also local time stepping method were created for stabilizing coarse temporal approximations for discontinuous Galerkin time-domain computations. In additional work a new tiling algorithm was developed allowing large numbers of polyomino tiles to be arranged to cover a two dimensional shape without leaving gaps. This abstract algorithm has application in the design of passive array antenna to minimize side-lobe radiation.

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