coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a non-standard way in which the right hand side of the coarse grid equations involves unknown parameters to be solved for on the coarse grid. This in particular leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem demonstrate the effectiveness of the method proposed. Using an FMG algorithm solution to the level of discretization errors is obtained in just a few work units (less than 10), where a work unit is the work involved in one Jacobi relization on the finest level. Author N89-27421# International Centre for Theoretical Physics, Trieste (Italy). USE OF THE FOX DERIVATIVES IN THE SOLUTION OF THE WORD PROBLEM FOR GROUPS Subrata Majumdar (Rajahahi Univ., Bangladesh ) Sep. 1988 6 p Submitted for publication (DE88-705978; IC-88/242) Avail: NTIS (US Sales Only) HC A02/MF A01 Applying Fox's free partial derivative, the word problem of a finitely presented group has been reduced to the problem of finding an algorithm for determining the existence of a root of a system of linear equations over the integral group ring. The solubility of the word problem for torsion-free one-relator groups and DOE torsion-free polycyclic-by-finite groups has been deduced. N89-27422# Keuring van Electrotechnische Materialen N.V., ANALYSIS OF HUMAN-ERROR SEQUENCES WITH FAULT G. Heslinga 1988 88 p (PB89-147631; ISSN-0167-8590; ISBN-90-353-0070-X) Avail: NTIS HC A05/MF A01 CSCL 12A It was investigated whether the event-tree technique, which is frequently used to analyze technical failures, can also be used for the analysis of human errors. The study was limited to errors that can occur during performance of procedural actions and to their possible consequences. The event-tree technique was modified for the purpose and is referred to as the Technique for Human-Error-Sequence Identification and Signification (THESIS). It appeared that the THESIS event trees raise problems if applied to human performance instead of technical systems. The influence of these problems on the applicability of THESIS was assessed by means of mathematical analyses, field studies and laboratory experiments. The main conclusion is that, with certain limitations, event trees can be used to predict sequences of human errors if procedural actions are performed. The limitations are related to the nature of the process that has to be controlled, the existence of several procedures to achieve the same goal and the knowledge of all kinds of data, such as dependence between human errors, human-error probabilities and recovery-attempt probabilities. Author N89-27423# Stanford Univ., CA. Information Systems Lab. (Contract N00014-86-K-0112) (AD-A206073) Avail: NTIS HC A02/MF A01 CSCL 12/2 A detailed study of the the problem of low crest-factor signals was made based on the techniques used in harmonic probing of nonlinear systems. Particularly interesting here is the numerical evidence suggesting that the phases used originally exceed the performance achievable with the Shapiro-Rudin phases, which can be proved to yield bounded crest factor for multitone signals containing an arbitrarily large number of tones. The crest factor problem relates two norms, L-sq and L at infinity, of a signal; comparing the gains of an operator with respect to two norms is much harder. A new computational method for the design of linear controllers was developed. A new method of computational stability analysis of systems is derived. Many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of x-dot = Ax for some appropriate A. The existence of such Lyapunov function can be determined by solving a non-differentiable convex program. GRA N89-27424# Army Research Office, Research Triangle Park, NC. TRANSACTIONS OF THE 6TH ARMY CONFERENCE ON (AD-A207252; AD-E801886; ARO-89-1) Avail: NTIS HC This year the planned program of the conference consisted of three parts, namely: seven one hour invited addresses; thirty-two half hour solicited talks covering the following topics: Computational Solid and Structural Mechanics, Reactive and Compressible Flows, Symbolic Computing and Applications, and Parallel Computing; and thirty-two contributed papers. Most of the latter were presented by Army scientists and covered topics directly related to problems they face in their laboratories. During the course of the conference, these Army scientists had an opportunity to discuss problems with nationally known scientists. Topics addressed include: Nonlinear Elasto-Plastic Finite Element Analysis of the Thin Shell of Revolution; Aspects of Edge Constraints in Shear-Deformable Plate and Shell Elements; Anomalous Waves in Shock Wave-Fluid Interface Interactions; Mathematical Modeling of Sound Propagation in the Atmosphere Using the Parabolic Approximation; Time-Dependent Shear Flow of a Non-Newtonian Fluid; and On the Positive Roots of an Equation Involving a Bessel Function. GRA N89-27426# Naval Ship Research and Development Center, (AD-A207279; DTRC/TM-27-88-56) Avail: NTIS HC A04/MF A01 CSCL 20/11 Galilean transformations between the absolute and moving frame impose a crypto-steady state relation between time derivations of a thermodynamic function in the absolute frame and their gradients in the moving frame. These crypto steady relationships are inherently contained within the Navier-Stokes equations for the absolute and moving frames. The substantial total enthalpy derivative coupled with the substantial entropic energy derivative may be written solely in terms of the flow field of the moving frame. In the moving frame the relative total enthalpy, known as the rothalpy, yields a vanishing substantial derivative. Therefore, the substantial entropic energy derivative is uncoupled and explicit in the moving frames and may be used to obtain an uncoupled explicit substantial total enthalpy derivative. GRA (AD-A207572; MD89-09-RCM-IB-1; TR89-09-1; BN-1094-1) Avail: NTIS HC A03/MF A01 CSCL 12/1 An approach is presented which allows us to derive a family of homogenization approaches and assess the accuracy of any homogenization in the relation of given input data. The study of periodic media is one application of partial differential equations that have highly oscillatory, periodic coefficients. Essentially, the problem is to solve a elliptic differential equation. One of the main applications of this differential equation is in the field of composite materials. Here the aim is to replace the composite by homogeneous materials with the bulk material properties. GRA AN APPROACH FOR CONSTRUCTING FAMILIES OF R. C. Morgan and Ivo Babuska Feb. 1989 36 p (AD-A207573; MD89-10-RCM-IB-2; TR89-10-2; BN-1095-2) Avail: NTIS HC A03/MF A01 CSCL 12/1 The paper is the second in the series devoted to the study of constructions of families of homogenizations. In the first paper the properties of the kernel Phi were utilized. In this paper these properties are established. An integral representation of the solution to a differential equation is developed that models the equations that arise in the study of periodic media (e.g., composite materials). GRA N89-27429# Maryland Univ., College Park. Inst. for Physical Science and Technology. Ivo Babuska and Tadeusz Janik Feb. 1989 46 p The paper is the second in the series addressing the h-p version of the finite element method for parabolic equations. The present paper addresses the case where in both variables, (spatial and time) the h-p version is used. Error estimation is given and numerical computations are presented. In both cases we used the same p and q in all time intervals. The results show that the flexibility of the method, when properly employed, leads to the large increase of computational effectivity. Various adaptive approaches here will be very effective tools for such an optimal choice. GRA implementable second-order models of functions to be optimized. A particular area of work suggested as a major topic of investigation was the development of a computationally implementable and GRA efficient Newton-type algorithm for nonsmooth problems. N89-27431# Technische Univ., Delft (Netherlands). Faculty of LOCAL MODE SMOOTHING ANALYSIS OF VARIOUS ITERATIVE METHODS M. Khalil 1988 19 p (Rept-88-67; ISSN-0922-5641; ETN-89-94898) Copyright Avail: NTIS HC A03/MF A01 Local mode analysis on a finite domain with periodic boundary conditions is used to assess the smoothing efficiency of iterative methods based on incomplete factorizations. The analysis consists of an analytic and numerical study of a simple 2-D problem discretized by finite differences. This analysis is done for pointwise and blockwise incomplete factorizations. Results show how this analysis is helpful to obtain simple expressions for the smoothing factors and to introduce new smoothers. It gives also a good prediction of the multigrid convergence rate. ESA N89-27432# Technische Univ., Delft (Netherlands). Faculty of Technical Mathematics and Informatics. ROW-ORIENTED DIRECT SOLVING OF LINEAR ALGEBRAIC EQUATIONS. INVERSE PROJECTION METHOD E. Dekker and L. Dekker 1988 21 p (Rept-88-81; ISSN-0922-5641; ETN-89-94910) Copyright Avail: NTIS HC A03/MF A01 Serial and parallel algorithms are discussed, which were derived from a direct solution method for linear algebraic equations based on row-oriented matrix claculus: the inverse-projection method. In this method no elimination of unknowns is applied. The matrix equation is considered to be a set of inner product equations that are solved by means of orthogonalization techniques. This orthogonalization requires extensive inner product calculus. Pipelined as well as parallel processing can be applied, resulting in parallel algorithms with a large speed-up and which can easily and efficiently be implemented onto MIMD supercomputers provided with local memories and designed to perform both parallel and pipelined processing. An example of a structured sparse matrix is used to show that by taking the structural characteristics into account, inverse projection algorithms can be designed which take considerably less computing time than is necessary in the case of full matrices. ESA N89-27433*# National Aeronautics and Space Administration. Ames Research Center, Moffett Field, CA. A DIRECT PROCEDURE FOR INTERPOLATION ON A (NASA-TM-102213; A-89210; NAS 1.15:102213) Avail: NTIS A direct procedure is presented for locally bicubic interpolation on a structured, curvilinear, two-dimensional grid. The physical (Cartesian) space is transformed to a computational space in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. Required partial derivative information is obtained by finite differences in the computational space. The partial derivatives in physical space are determined by repeated application of the chain rule for partial differentiation. A bilinear transformation is used to analytically transform the individual quadrilateral cells in physical space into unit squares. The interpolation is performed within each unit square using a piecewise bicubic spline. Author (Contract NCC2-515) (NASA-CR-185034; NAS 1.26:185034) Avail: NTIS HC A07/MF A01 CSCL 12A Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a rapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs. N89-27435# Sandia National Labs., Albuquerque, NM. USING CONJOINT MESHING PRIMITIVES TO GENERATE QUADRILATERAL AND HEXAHEDRAL ELEMENTS IN IRREGULAR REGIONS Author Michael B. Stephenson (Brigham Young Univ., Provo, UT.) and (Contract DE-AC04-76DP-00789) The parameter-space mapping technique used in most finite element mesh generation programs requires that the geometry be subdivided into either rectangular areas in 2-D or rectilinear volumes in 3-D to produce, respectively, quadrilateral or hexahedral elements. Since subdivision occurs in parameter space, the edges bounding the areas and volumes need not be straight or parallel lines. Simple geometries may be subdivided easily while irregular features challenge the analyst. This paper presents the formulation and application of conjoint meshing primitives that assist the analyst in meshing in and around irregular features. The term conjoint is applied to these primitives because each is composed of several rectangular areas or rectilinear volumes. Interval assignments may vary from side to side, within a set of constraints, for each primitive. Thus, all of them are useful for transitions between other regular areas or volumes. In 2-D, the primitive areas are the triangle, pentagon, semi-circle, circle, and rectangular transition. These primitives are implemented in the Sandia meshing program FASTQ and are used in regular production work. They are also the basis for decomposition regions in the developing artificial intelligence Automated Meshing Knowledge System, AMEKS. N89-27436# Lawrence Livermore National Lab., CA. DOE Theodore H. Einwohner and Richard J. Fateman 19 Apr. 1989 14 P Presented at the International Symposium on Symbolic and Algebraic Computing, Portland, OR, 17-19 Jul. 1989 (Contract W-7405-eng-48) (DE89-011404; UCRL-100959; CONF-890779-1) Avail: NTIS HC A03/MF A01 Techniques for a MACSYMA package for expanding an arbitrary univariate expression as a truncated series in Chebyshev polynomials and manipulating such expansions is described. A data structure is introduced to represent a truncated expansion in a set of orthogonal polynomials. The data structure contains the independent variable, the name of the orthogonal polynomial set, the number of terms retained, and a list of the expansion coefficients. Although we restrict attention here to the set of Chebyshev polynomials as the orthogonal set, extension to other orthogonal polynomials will be done later. A data structure for truncated power series is provided as an alternative. The principal function of the package converts a given expression into the aforementioned data structure. Special cases are the conversion of sums, products, the ratio, or the composition of truncated DOE Chebyshev expansions. N89-27437# Illinois Univ., Urbana. Dept. of Computer Science. (DE89-014812; DOE/ER-25026/29; UILU-ENG-89-1737; The traditional approach for solving large dynamical systems is time consuming. Waveform relaxation, an iterative technique for solving systems of differential equations, can be used to reduce the processing time. It has been shown to converge superlinearly on finite intervals. In this paper, the order of accuracy of solutions generated by a relaxation approach, the waveform Gauss-Seidel method, is discussed. In this approach, a directed graph, called a dependency graph, is used to indicate the coupling relations among all components. The relation between the accuracy increase after each Gauss-Seidel iteration and the lengths of ascending chains (simple directed paths) in cycles in the dependency graph is discussed. It is proved that the cycle in the dependency graph which has the minimum ratio of its length to its number of ascending chains, determines the average accuracy increase. Effective use of the waveform Gauss-Seidel method depends on the ordering of the components. The result in this paper provides a basis for selecting the ordering. DOE N89-27438# Illinois Univ., Urbana. Dept. of Computer Science. SAFETY IN NUMBERS: THE BOUNDLESS ERRORS OF NUMERICAL COMPUTATION Robert D. Skeel Jun. 1989 (Contract DE-FG02-87ER-25026) (DE89-014813; DOE/ER-25026/30; NCG-89-3) Avail: NTIS HC A03/MF A01 13 p Perhaps the greatest unresolved question in numerical computing is how to cope with the issue of uncertainty in the accuracy of computed numerical quantities. The problem is not so much the errors in the answers, but the lack of a correct error bound or a confidence interval. The problem arises because of the failure to keep track of known errors and because of unknown errors due to finite sampling techniques. Several approaches to this question are discussed, principally interval analysis and probabilistic techniques. Reasons for the neglect of the uncertainty issue are suggested, and the benefits of providing consistently correct answers are considered. DOE N89-27439# Universiteit Twente, Enschede (Netherlands). Dept. of Computer Science. A QUALITATIVE WAY OF SOLVING THE POLE BALANCING PROBLEM A. Makarovic 4 Nov. 1988 37 p (MEMO-INF-88-44; UT-KBS-88-03; ISBN-90-365-0220-9; ETN-89-94762) Avail: NTIS HC A03/MF A01 A method for designing a control rule for the pole-cart system is presented. Conventional techniques are used to model the system by a set of differential equations. The high complexity of the model is simplified by restructuring and approximating the equations. Ultimately a very simple model results. It is shown that designing a control rule for this model is an easy task. Even small changes in complexity may have a great influence on the search space of potential solutions. ESA N89-27441# Rome Univ. (Italy). Dipartimento di Fisica. F. Calogero and S. DeLillo (Salerno Univ., Italy) 31 May 1988 N89-27442# Rome Univ. (Italy). Dipartimento di Fisica. UNIVERSALITY AND INTEGRABILITY OF THE NONLINEAR EVOLUTION PDES DESCRIBING N-WAVE INTERACTIONS F. Calogero 7 Jul. 1988 36 p Submitted for publication (Preprint-603; ETN-89-94692) Avail: NTIS HC A03/MF A01 The universality of the equations describing N-wave interactions is demonstrated by deriving them from a very large class of nonlinear evolution equations (essentially all those whose linea part is dispersive). Various forms of these equations are displayed. The fact that these universal nonlinear evolution equations are obtained by an appropriate asymptotic limit from such a large class of nonlinear evolution equations, suggests that they should be integrable, since for this it is sufficient that the large class from which they are obtainable contains just one integrable equation. This expectation is validated in several cases, by deriving the equations from known integrable equations. In this manner an explanation may be provided of the (already known) integrable nature of certain equations; and integrable equations may be obtained. Both S-integrable and C-integrable equations are discussed, namely both equations integrable via an appropriate spectral transform and solvable via an appropriate change of variables. The treatment is limited to equations in 1+1 dimensions. N89-27443# Rome Univ. (Italy). Dipartimento di Fisica. NONLINEAR WAVE EQUATIONS SOLVABLE BY THE SPECTRAL TRANSFORM N89-27444 National Physical Lab., Teddington (England). Div. of Information Technology and Computing. THE LEAST SQUARES SOLUTION OF LINEAR EQUATIONS WITH BLOCK-ANGULAR OBSERVATION MATRIX M. G. Cox Apr. 1989 18 p Presented at the NPL Conference on Advances in Reliable Numerical Computation, Teddington, United Kingdom, 8-10 Jul. 1987 (NPL-DITC-139/89; ISSN-0262-5369; ETN-89-94964) Copyright Avail: National Physical Laboratory, Teddington, Middlesex, TW11 OLW, United Kingdom The least-squares solution of a system of overdetermined linear equations whose observation matrix is block angular is considered. A structure-exploiting method of solution based on the use of orthogonal transformations is described. The algorithm requires considerably less storage space than other direct methods and, unlike otherwise competitive iterative techniques, permits accurate statistics (variances, covariances) associated with the solution to be provided. ESA ESA Statistics. A. Degasperis 30 Jan. 1989 91 p Presented at the International School of Physics E. Fermi Lectures on Nonlinear Topics in Ocean Physics, Varenna, Italy, 26 Jul. 5 Aug. 1988 publication Submitted for (Preprint-957; ETN-89-94730) Avail: NTIS HC A05/MF A01 The main mathematical tools which prove to be essential to the spectral analysis of (special classes of) solutions of nonlinear wave equations are introduced. The two basic ingredients of the spectral analysis are a linear differential equation containing a complex (spectral) parameter, and a linear Riemann-Hilbert boundary value problem or, more generally, a linear D-bar problem in the complex plane of this parameter. ESA North Carolina Univ., Chapel Hill. Dept. of An upper bound B sub f is given for the information capacity of the Poisson channel with marginally stationary random noise intensity and causal feedback. The capacity is shown to converge to B sub f in the limit of longer and longer communication intervals for a class of random noise intensities including the case in which the noise intensity is nontime-varying. An upper bound B sub nf on the capacity is also established for the Poisson channel with marginally stationary noise and no feedback. In this case also, for a class of random noise intensities including nontime-varying noise intensity, B sub nf is found to be the capacity of the channel without feedback in the limit of longer and long communication intervals. The fractional difference between B sub f and B sub nf is considered as a means to quantify the improvement afforded by feedback. Also, certain nonstandard encoder constraints are addressed and the importance of the encoder intensity peak constraint to the channel capacity problem is explored. GRA N89-27448# Naval Postgraduate School, Monterey, CA. CONSTANT ACCESS SYSTEMS: A GENERAL FRAMEWORK FOR GREEDY OPTIMIZATION ON STOCHASTIC NETWORKS Michael P. Bailey Mar. 1989 39 p (AD-A207525; NPS55-89-02) Avail: NTIS HC A03/MF A01 CSCL 12/3 We consider network optimization problems in which the weights of the edges are random variables. We develop conditions on the combinatorial structure of the problem which guarantee that the objective function value is a first passage time in an appropriately constructed Markov process. The arc weights must be exponentially distributed, the method of solution of the deterministic problem must be greedy in a general sense, and the accumulation of objective function value during the greedy procedure must occur at a constant rate. We call these structures constant access systems after the third property. Examples of constant access systems include the shortest path system, time until disconnection in a network of failing components, and some bottleneck optimization problems. For each system, we give the distribution of the objective function, the distribution of the solution of the problem, and the probability that a given arc is a member of the optimal solution. We also provide easily implementable formulae for the moments of these quantities. N89-27449# Rome Univ. (Italy). Dipartimento di Fisica. DIFFERENTIAL STOCHASTIC EQUATIONS [EQUAZIONI DIFFERENZIALI STOCASTICHE] GRA Francesco Guerra 24 Oct. 1988 47 p In ITALIAN Submitted for publication (Preprint-635; ETN-89-94715) Avail: NTIS NC A03/MF A01 Stochastic differential equations and their physical interpretation are explained. Deterministic evolutions subjected to stochastic perturbations are discussed. The applications to quantum mechanics, astrophysics, and in general dynamic systems are explained. Transformations under time inversion are discussed. The equations presented include Fokker-Plank, Ito-Girsanov and Feynman-Kac. ESA N89-27450# Office National d'Etudes et de Recherches Aerospatiales, Paris (France). SOLUTION OF DETERMINISTIC DIFFERENTIAL GAMES: THE C. Marchal 1987 28 p In FRENCH; ENGLISH summary Deterministic differential games are described and strategies are discussed. The interest of the appoximate strategy method is that it reduces the game to a succesion of ordinary problems of optimization and allows a systematic step by step improvement of the strategies. Two good opposing strategies give close upper and lower bounds of the value of the game. If the Hamiltonian of the game is either convex or concave with respect to the adjunct vector, the game is equivalent to a problem of optimization. ESA N89-27451# Stanford Univ., CA. Dept. of Statistics. SAMPLING BASED APPROACHES TO CALCULATING MARGINAL DENSITIES Technical Report No. 415 Alan E. Gelfand and Adrian F. M. Smith 11 Apr. 1989 26 p (Contract N00014-86-K-0156; NR Proj. 042-267) (AD-A208388; SU-TR-415) Avail: NTIS HC A03/MF A01 CSCL 12/3 Stochastic substitution, the Gibbs sampler and the sampling-importance-resampling algorithm can be viewed as three alternative sampling, or Monte Carlo, based approaches to the calculation of numerical estimates of marginal probability distributions. The three approaches will be reviewed, and compared and contrasted, in relation to various joint probability structures P. E. Sokol, R. N. Silver, and J. W. Clark (Washington Univ., Saint Louis, MO.) Presented at the Workshop on 36 p Momentum Distributions, Argonne, IL, 24 Oct. 1988 (Contracts W-7405-eng-36; W-31-109-eng-38) (DE89-012617; LA-UR-89-1604; CONF-8810118-7) Avail: NTIS HC A03/MF A01 There have been several excellent reviews of momentumdistribution research in particular subject areas of physics such as electronic systems and nuclear systems. However, it is the commonality of interests, difficulties, and prospects across all of physics, along with certain pivotal advances, which led to the organization of an interdisciplinary Workshop on Momentum 24 and 26 October 1988. The purpose of this overview is to explain why scientists with such diverse backgrounds were brought together at this meeting, to introduce and discuss the common elements of momentum-distribution studies, and to establish a common language. We hope to facilitate an appreciation of the more specialized articles which follow in these proceedings. We begin by summarizing the general properties of momentum distributions. Differences and similarities of atomic, electronic, and nuclear many-body systems are examined, in terms of characteristic lengths and energies, relative importance of exchange, and the nature of the two-particle interactions. We continue with a brief commentary on the microscopic methods used to calculate n(p) from first principles. DOE |