Advances in the dataflow computational model

The dataflow program graph execution model, or dataflow for short, is an alternative to the stored-program (von Neumann) execution model. Because it relies on a graph representation of programs, the strengths of the dataflow model are very much the complements of those of the stored-program one. In the last thirty or so years since it was proposed, the dataflow model of computation has been used and developed in very many areas of computing research: from programming languages to processor design, and from signal processing to reconfigurable computing. This paper is a review of the current state-of-the-art in the applications of the dataflow model of computation. It focuses on three areas: multithreaded computing, signal processing and reconfigurable computing.     

Neural networks in computational mechanics

Summary In this paper, recent neural network applications, epecially to the fields related with the computational mechanics, were surveyed. The most outstanding characteristics of the neural network aided computation is that neither complicated programmings nor rigid algorithms are needed. Another important point is that the neural network's inherent parallelism, that is, concurrent signal transmissions over numerous, information processing elements suits the massively parallel computer architectures. First, we briefly review the neural network applications to the computational mechanics fields from recent publications, and describe the mathematical basis of the neural network. Next, the following topics are detailed: quantitative nondestructive evaluation, structural identification, modeling of viscoplastic material behaviors, crack growth analysis of welded specimens, structural design, parameter estimation for nonlinear finite element analyses, and equation solver.     

Rotations in computational solid mechanics

Summary A survey of variational principles, which form the basis for computational methods in both continuum mechanics and multi-rigid body dynamics is presented: all of them have the distinguishing feature of making an explicit use of the finite rotation tensor. A coherent unified treatment is therefore given, ranging from finite elasticity to incremental updated Lagrangean formulations that are suitable for accomodating mechanical nonlinearities of an almost general type, to time-finite elements for dynamic analyses. Selected numerical examples are provided to show the performances of computational techniques relying on these formulations. Throughout the paper, an attempt is made to keep the mathematical abstraction to a minimum, and to retain conceptual clarity at the expense of brevity. It is hoped that the article is self-contained and easily readable by nonspecialists. While a part of the article rediscusses some previously published work, many parts of it deal with new results, documented here for the first time.     

Wall functions in computational fluid mechanics

Wall functions are a powerful tool in complex flows calculations. Unfortunately, often blind and inappropriate use of them have given the impression that they should be avoided. Our aim though this paper is, without being exhaustive, to correct some of these prejudges and to point some advantages of wall functions, not only from the complexity point of view but also from their greater modeling capacity.     

Functional programming on a dataflow architecture: Applications in real-time image processing

This paper presents a dataflow functional computer (DFFC) developed at the Etablissement Technique Central de l'Armement (ETCA) and dedicated to real-time image processing. Two types of data-driven processing elements, dedicated respectively to low-level and mid-level processings are integrated in a regular 3D array. The design of the DFFC relies on a close integration of the dataflow-architecture principles and the functional programming concept. An image processing algorithm, expressed with a syntax similar to that of functional programming (FP) is first converted into a dataflow graph. The nodes of this graph are real-time operators that can be implemented on the physical processors of the dataflow machine. This dataflow graph is then mapped directly onto the processor array. The programming environment includes a complete compilation stream from the FP specification to hardware implementation, along with a global operator database. Apart from being a research tool for real-time image processing, the DFFC may also be used to perform the automatic synthesis of autonomous vision automata from a high-level functional specification. An experimental system, including 1024 lowlevel custom dataflow processors and 12 T800 transputers, was built and can perform up to 50 billion operations/s. Several image processing algorithms were implemented on this system and run in real-time at digital video speed.     

Applications of power series in computational geometry

A number of algorithms are presented for obtaining power series expansions of curves and surfaces at a point. Some results on the radius of convergence are given. Two applications of series are given:

1. • for curve tracing algorithms, where a truncated series is used to approximate the curve of intersection of two surfaces

2. • to define nth degree geometric continuity, for arbitrary

On application of differential geometry to computational mechanics

Developments in the fields of computational science—the finite element method—and mathematical foundations of continuum mechanics result in many new algorithms which give solutions to very complicated, complex, large scaled engineering problems. Recently, the differential geometry, a modern tool of mathematics, has been used more widely in the domain of the finite element method. Its advantage in defining geometry of elements [13–15] or modeling mechanical features of engineering problems under consideration [4–7] is its global character which includes also insight into a local behavior. This fact comes from the nature of a manifold and its bundle structure, which is the main element of the differential geometry.

Manifolds are generalized spaces, topological spaces. By attaching a fiber structure to each base point of a manifold, it locally resembles the usual real vector spaces; e.g. ³. The properties of a differential manifold M are independent of a chosen coordinate system. It is equivalent to say, that there exists smooth or C^r differentiable atlases which are compatible.

In this paper a short survey of applications of differential geometry to engineering problems in the domain of the finite element method is presented together with a few new ideas.

The properties of geodesic curves have been used by Yuan et al. [13–15], in defining distortion measures and inverse mappings for isoparametric quadrilateral hybrid stress four- and eight-node elements in ². The notion of plane or space curves is one of the elementary ones in the theory of differential geometry, because the concept of a manifold comes from the generalization of a curve or a surface in ³.

Further, the real global nature of differential geometry, has been used by Simo et al. [4,6,7]. A geometrically exact beam finite strain formulation is defined. The mechanical basis of such a nonlinear model can be found in the mathematical foundation of elasticity [18]. An abstract infinite dimensional manifold of mappings, a configuration space, is constructed which permits an exact linearization of algorithms, locally. A similar approach is used by Pacoste [5] for beam elements in instability problems.

Special attention is focused on quadrilateral hybrid stress membrane elements with curved boundaries which belong to a series of isoparametric elements developed by Yuan et al. [14]. The distortion measures are redefined for eight-node isoparametric elements in ² for which geodesic coordinates are used as local coordinates.     

Random matrix theory for modeling uncertainties in computational mechanics

This paper deals with data uncertainties and model uncertainties issues in computational mechanics. If data uncertainties can be modeled by parametric probabilistic methods, for a given mean model, a nonparametric probabilistic approach can be used for modeling model uncertainties. The first part is devoted to random matrix theory for which we summarize previous published results and for which two new ensembles of random matrices useful for the nonparametric models are introduced. In a second part, the nonparametric probabilistic approach of random uncertainties is presented for linear dynamical systems and for nonlinear dynamical systems constituted of a linear part with additional localized nonlinearities. In a third part, a new method is proposed for estimating the parameters of the nonparametric approach from experiments. Finally, examples with experimental comparisons are given.     

Consistency in dataflow graphs

Analytical properties of programming languages with dataflow graph semantics are discussed. It is shown that one of the most serious problems with these languages is that subtle inconsistencies between parts of the dataflow graph can be inadvertently created. These inconsistencies can lead to deadlock, or in the case of nonterminating programs, to unbounded memory requirements. Consistency is defined to mean that the same number of tokens is consumed as produced on any arc, in the long run. A token-flow model is developed for testing for inconsistency. The method is a generalization of consistency checks for synchronous dataflow (SDF) graphs. The token-flow model is compared to similar tests applied to hybrid dynamical systems. It is argued that dataflow semantics make steady-state analysis possible, leading to a simpler method in most cases     

Applications of artificial neural nets in structural mechanics

First the fundamentals of neurologically motivated computing are briefly discussed. This is followed by presenting two of the many possible applications in structural mechanics. Both of these are oriented towards structural optimization. In the first mode a neural net model of the structural response is created and then attached to any conventional optimization algorithm. In the second mode a neural net model of an experienced designer is created knowledgeable within a narrow class of structural concepts.Presented at the CISM Course Shape and Layout Optimization in Structural Design, Udine, Italy, July 1990     

Detection of cracks using neural networks and computational mechanics

An inverse analysis method is proposed to simulate the A-scan ultrasonic nondestructive testing by means of back-propagation neural networks and computational mechanics. Both direct problem and inverse problem are considered in this study. In the direct problem, the frequency responses of a cracked medium subjected to an impact loading are calculated by the computational mechanics combining the finite element method with the boundary integral equation. The transient responses are obtained using fast Fourier transform. In the inverse problem, the back-propagation neural networks are trained by the characteristic parameters extracted from the various surface responses obtained from the direct problem. These surface responses carry a great deal of information about the structure of the medium with or without cracks. The trained neural networks are then utilized for the classification and identification of the crack in the medium to determine the type, location, and length of the crack.     

Performance issues in dataflow machines

Issues affecting the performance of dataflow computers at the machine and language levels are explored. It is suggested that performance is dictated by the nature and the means of identification, distribution and control of workload in the hardware system. Dataflow is an asynchronous concurrent notation based on fine-grain message-passing in graphical programs. Dataflow machines comprise multiple processing elements and structure store modules connected together via a packet-based switching network. Workload is in the form of finegrain data packets which trigger instruction-level activity in the various components of the hardware architecture. Workload is identified by a compiler for a high-level, single-assignment language, and is distributed across the hardware components dynamically at run-time. The amount of work at any instant can be controlled by a parallelism “throttle”. The paper studies the performance of one example of a dataflow computer, the Manchester Dataflow Machine (MDFM).     

Nonsmooth computational mechanics algorithms, quasidifferentiability and related topics

Several extensions of smooth computational mechanics algorithms for the treatment of nonsmooth and possible nonconvex problems are briefly discussed in this paper. A potential or dissipation energy minimization problem approach is used for the structural analysis problem, so as to make the link with mathematical optimization techniques straightforward. Variational inequality problems, hemivariational inequality problems and systems of variational inequalities can be treated by the methods reviewed in this paper. The use of quasidifferentiable and codifferentiable optimization techniques is proposed for the solution of the more general class of nonconvex, possibly nonsmooth problems. Established and new directions in path-following techniques are discussed and are linked with nonsmooth mechanics algorithms.