Static Analysis Numerical Algorithms
2016-04-01
abstract domain provides (1) an abstract type to represent concrete program states, and (2) abstract functions to represent the effect of concrete ...state-changing actions. Rather than simulate the concrete program, abstract interpretation uses abstract domains to construct and simulate an...On the other hand, the abstraction does allow us to cheaply compute some kinds of information about the concrete program. In the example, we can
Stochastic Formal Correctness of Numerical Algorithms
NASA Technical Reports Server (NTRS)
Daumas, Marc; Lester, David; Martin-Dorel, Erik; Truffert, Annick
2009-01-01
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.
Numerical Algorithms and Parallel Tasking.
1984-07-01
34 Principal Investigator, Virginia Klema, Research Staff, George Cybenko and Elizabeth Ducot . During the period, May 15, 1983 through May 14, 1984...Virginia Klema and Elizabeth Ducot have been supported for four months, and George Cybenko has been supported for one month. During this time system...algorithms or applications is the responsibility of the user. Virginia Klema and Elizabeth Ducot presented a description of the concurrent computing
Trees, bialgebras and intrinsic numerical algorithms
NASA Technical Reports Server (NTRS)
Crouch, Peter; Grossman, Robert; Larson, Richard
1990-01-01
Preliminary work about intrinsic numerical integrators evolving on groups is described. Fix a finite dimensional Lie group G; let g denote its Lie algebra, and let Y(sub 1),...,Y(sub N) denote a basis of g. A class of numerical algorithms is presented that approximate solutions to differential equations evolving on G of the form: dot-x(t) = F(x(t)), x(0) = p is an element of G. The algorithms depend upon constants c(sub i) and c(sub ij), for i = 1,...,k and j is less than i. The algorithms have the property that if the algorithm starts on the group, then it remains on the group. In addition, they also have the property that if G is the abelian group R(N), then the algorithm becomes the classical Runge-Kutta algorithm. The Cayley algebra generated by labeled, ordered trees is used to generate the equations that the coefficients c(sub i) and c(sub ij) must satisfy in order for the algorithm to yield an rth order numerical integrator and to analyze the resulting algorithms.
Numerical linear algebra algorithms and software
NASA Astrophysics Data System (ADS)
Dongarra, Jack J.; Eijkhout, Victor
2000-11-01
The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.
Numerical Algorithms Based on Biorthogonal Wavelets
NASA Technical Reports Server (NTRS)
Ponenti, Pj.; Liandrat, J.
1996-01-01
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.
Simplification of multiple Fourier series - An example of algorithmic approach
NASA Technical Reports Server (NTRS)
Ng, E. W.
1981-01-01
This paper describes one example of multiple Fourier series which originate from a problem of spectral analysis of time series data. The example is exercised here with an algorithmic approach which can be generalized for other series manipulation on a computer. The generalized approach is presently pursued towards applications to a variety of multiple series and towards a general purpose algorithm for computer algebra implementation.
Adaptive Numerical Algorithms in Space Weather Modeling
NASA Technical Reports Server (NTRS)
Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav
2010-01-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical
Adaptive numerical algorithms in space weather modeling
NASA Astrophysics Data System (ADS)
Tóth, Gábor; van der Holst, Bart; Sokolov, Igor V.; De Zeeuw, Darren L.; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Najib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav
2012-02-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit
Aquarius RFI Detection and Mitigation Algorithm: Assessment and Examples
NASA Technical Reports Server (NTRS)
Le Vine, David M.; De Matthaeis, P.; Ruf, Christopher S.; Chen, D. D.
2013-01-01
Aquarius is an L-band radiometer system designed to map sea surface salinity from space. This is a sensitive measurement, and protection from radio frequency interference (RFI) is important for success. An initial look at the performance of the Aquarius RFI detection and mitigation algorithm is reported together with examples of the global distribution of RFI at the L-band. To protect against RFI, Aquarius employs rapid sampling (10 ms) and a "glitch" detection algorithm that looks for outliers among the samples. Samples identified as RFI are removed, and the remainder is averaged to produce an RFI-free signal for the salinity retrieval algorithm. The RFI detection algorithm appears to work well over the ocean with modest rates for false alarms (5%) and missed detection. The global distribution of RFI coincides well with population centers and is consistent with observations reported by the Soil Moisture and Ocean Salinity mission.
Research on numerical algorithms for large space structures
NASA Technical Reports Server (NTRS)
Denman, E. D.
1982-01-01
Numerical algorithms for large space structures were investigated with particular emphasis on decoupling method for analysis and design. Numerous aspects of the analysis of large systems ranging from the algebraic theory to lambda matrices to identification algorithms were considered. A general treatment of the algebraic theory of lambda matrices is presented and the theory is applied to second order lambda matrices.
Numerical Algorithm for Delta of Asian Option.
Zhang, Boxiang; Yu, Yang; Wang, Weiguo
2015-01-01
We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.
A Polynomial Time, Numerically Stable Integer Relation Algorithm
NASA Technical Reports Server (NTRS)
Ferguson, Helaman R. P.; Bailey, Daivd H.; Kutler, Paul (Technical Monitor)
1998-01-01
Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.
Numerical comparison of Kalman filter algorithms - Orbit determination case study
NASA Technical Reports Server (NTRS)
Bierman, G. J.; Thornton, C. L.
1977-01-01
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
A Numerical Instability in an ADI Algorithm for Gyrokinetics
E.A. Belli; G.W. Hammett
2004-12-17
We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.
Experiences with an adaptive mesh refinement algorithm in numerical relativity.
NASA Astrophysics Data System (ADS)
Choptuik, M. W.
An implementation of the Berger/Oliger mesh refinement algorithm for a model problem in numerical relativity is described. The principles of operation of the method are reviewed and its use in conjunction with leap-frog schemes is considered. The performance of the algorithm is illustrated with results from a study of the Einstein/massless scalar field equations in spherical symmetry.
Research on numerical algorithms for large space structures
NASA Technical Reports Server (NTRS)
Denman, E. D.
1981-01-01
Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.
An efficient algorithm for numerical airfoil optimization
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.
1979-01-01
A new optimization algorithm is presented. The method is based on sequential application of a second-order Taylor's series approximation to the airfoil characteristics. Compared to previous methods, design efficiency improvements of more than a factor of 2 are demonstrated. If multiple optimizations are performed, the efficiency improvements are more dramatic due to the ability of the technique to utilize existing data. The method is demonstrated by application to subsonic and transonic airfoil design but is a general optimization technique and is not limited to a particular application or aerodynamic analysis.
A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials
Dorr, M R; Fattebert, J; Wickett, M E; Belak, J F; Turchi, P A
2008-12-04
We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.
Technical Report: Scalable Parallel Algorithms for High Dimensional Numerical Integration
Masalma, Yahya; Jiao, Yu
2010-10-01
We implemented a scalable parallel quasi-Monte Carlo numerical high-dimensional integration for tera-scale data points. The implemented algorithm uses the Sobol s quasi-sequences to generate random samples. Sobol s sequence was used to avoid clustering effects in the generated random samples and to produce low-discrepancy random samples which cover the entire integration domain. The performance of the algorithm was tested. Obtained results prove the scalability and accuracy of the implemented algorithms. The implemented algorithm could be used in different applications where a huge data volume is generated and numerical integration is required. We suggest using the hyprid MPI and OpenMP programming model to improve the performance of the algorithms. If the mixed model is used, attention should be paid to the scalability and accuracy.
Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows
NASA Technical Reports Server (NTRS)
Moitra, Stuti; Gatski, Thomas B.
1997-01-01
A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.
A hybrid artificial bee colony algorithm for numerical function optimization
NASA Astrophysics Data System (ADS)
Alqattan, Zakaria N.; Abdullah, Rosni
2015-02-01
Artificial Bee Colony (ABC) algorithm is one of the swarm intelligence algorithms; it has been introduced by Karaboga in 2005. It is a meta-heuristic optimization search algorithm inspired from the intelligent foraging behavior of the honey bees in nature. Its unique search process made it as one of the most competitive algorithm with some other search algorithms in the area of optimization, such as Genetic algorithm (GA) and Particle Swarm Optimization (PSO). However, the ABC performance of the local search process and the bee movement or the solution improvement equation still has some weaknesses. The ABC is good in avoiding trapping at the local optimum but it spends its time searching around unpromising random selected solutions. Inspired by the PSO, we propose a Hybrid Particle-movement ABC algorithm called HPABC, which adapts the particle movement process to improve the exploration of the original ABC algorithm. Numerical benchmark functions were used in order to experimentally test the HPABC algorithm. The results illustrate that the HPABC algorithm can outperform the ABC algorithm in most of the experiments (75% better in accuracy and over 3 times faster).
A novel wavefront-based algorithm for numerical simulation of quasi-optical systems
NASA Astrophysics Data System (ADS)
Zhang, Xiaoling; Lou, Zheng; Hu, Jie; Zhou, Kangmin; Zuo, Yingxi; Shi, Shengcai
2016-11-01
A novel wavefront-based algorithm for the beam simulation of both reflective and refractive optics in a complicated quasi-optical system is proposed. The algorithm can be regarded as the extension to the conventional Physical Optics algorithm to handle dielectrics. Internal reflections are modeled in an accurate fashion, and coating and flossy materials can be treated in a straightforward manner. A parallel implementation of the algorithm has been developed and numerical examples show that the algorithm yields sufficient accuracy by comparing with experimental results, while the computational complexity is much less than the full-wave methods. The algorithm offers an alternative approach to the modeling of quasi-optical systems in addition to the Geometrical Optics modeling and full-wave methods.
An efficient cuckoo search algorithm for numerical function optimization
NASA Astrophysics Data System (ADS)
Ong, Pauline; Zainuddin, Zarita
2013-04-01
Cuckoo search algorithm which reproduces the breeding strategy of the best known brood parasitic bird, the cuckoos has demonstrated its superiority in obtaining the global solution for numerical optimization problems. However, the involvement of fixed step approach in its exploration and exploitation behavior might slow down the search process considerably. In this regards, an improved cuckoo search algorithm with adaptive step size adjustment is introduced and its feasibility on a variety of benchmarks is validated. The obtained results show that the proposed scheme outperforms the standard cuckoo search algorithm in terms of convergence characteristic while preserving the fascinating features of the original method.
Multiresolution representation and numerical algorithms: A brief review
NASA Technical Reports Server (NTRS)
Harten, Amiram
1994-01-01
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.
Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes
NASA Technical Reports Server (NTRS)
Abrams, D.; Williams, C.
1999-01-01
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
A novel bee swarm optimization algorithm for numerical function optimization
NASA Astrophysics Data System (ADS)
Akbari, Reza; Mohammadi, Alireza; Ziarati, Koorush
2010-10-01
The optimization algorithms which are inspired from intelligent behavior of honey bees are among the most recently introduced population based techniques. In this paper, a novel algorithm called bee swarm optimization, or BSO, and its two extensions for improving its performance are presented. The BSO is a population based optimization technique which is inspired from foraging behavior of honey bees. The proposed approach provides different patterns which are used by the bees to adjust their flying trajectories. As the first extension, the BSO algorithm introduces different approaches such as repulsion factor and penalizing fitness (RP) to mitigate the stagnation problem. Second, to maintain efficiently the balance between exploration and exploitation, time-varying weights (TVW) are introduced into the BSO algorithm. The proposed algorithm (BSO) and its two extensions (BSO-RP and BSO-RPTVW) are compared with existing algorithms which are based on intelligent behavior of honey bees, on a set of well known numerical test functions. The experimental results show that the BSO algorithms are effective and robust; produce excellent results, and outperform other algorithms investigated in this consideration.
Finite elasto-plastic deformation. I - Theory and numerical examples
NASA Technical Reports Server (NTRS)
Osias, J. R.; Swedlow, J. L.
1974-01-01
It is demonstrated that the problem of elasto-plastic finite deformation is governed by a quasi-linear model irrespective of deformation magnitude. This feature follows from the adoption of a rate viewpoint toward finite deformation analysis in an Eulerian reference frame. Objectivity of the formulation is preserved by introduction of a frame-invariant stress rate. Equations for piece-wise linear incremental finite element analysis are developed by application of the Galerkin method to the instantaneously linear governing differential equations of the quasi-linear model. Numerical solution capability has been established for problems of plane strain and plane stress. The accuracy of the numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation admitting comparative analytic solution. It is shown that accurate, objective numerical solutions can be obtained for problems involving dimensional changes of an order of magnitude and rotations of a full radian.
Numerical Laplace Transform Inversion Employing the Gaver-Stehfest Algorithm.
ERIC Educational Resources Information Center
Jacquot, Raymond G.; And Others
1985-01-01
Presents a technique for the numerical inversion of Laplace Transforms and several examples employing this technique. Limitations of the method in terms of available computer word length and the effects of these limitations on approximate inverse functions are also discussed. (JN)
Numerical algorithms for the atomistic dopant profiling of semiconductor materials
NASA Astrophysics Data System (ADS)
Aghaei Anvigh, Samira
In this dissertation, we investigate the possibility to use scanning microscopy such as scanning capacitance microscopy (SCM) and scanning spreading resistance microscopy (SSRM) for the "atomistic" dopant profiling of semiconductor materials. For this purpose, we first analyze the discrete effects of random dopant fluctuations (RDF) on SCM and SSRM measurements with nanoscale probes and show that RDF significantly affects the differential capacitance and spreading resistance of the SCM and SSRM measurements if the dimension of the probe is below 50 nm. Then, we develop a mathematical algorithm to compute the spatial coordinates of the ionized impurities in the depletion region using a set of scanning microscopy measurements. The proposed numerical algorithm is then applied to extract the (x, y, z) coordinates of ionized impurities in the depletion region in the case of a few semiconductor materials with different doping configuration. The numerical algorithm developed to solve the above inverse problem is based on the evaluation of doping sensitivity functions of the differential capacitance, which show how sensitive the differential capacitance is to doping variations at different locations. To develop the numerical algorithm we first express the doping sensitivity functions in terms of the Gâteaux derivative of the differential capacitance, use Riesz representation theorem, and then apply a gradient optimization approach to compute the locations of the dopants. The algorithm is verified numerically using 2-D simulations, in which the C-V curves are measured at 3 different locations on the surface of the semiconductor. Although the cases studied in this dissertation are much idealized and, in reality, the C-V measurements are subject to noise and other experimental errors, it is shown that if the differential capacitance is measured precisely, SCM measurements can be potentially used for the "atomistic" profiling of ionized impurities in doped semiconductors.
Evaluation of a new parallel numerical parameter optimization algorithm for a dynamical system
NASA Astrophysics Data System (ADS)
Duran, Ahmet; Tuncel, Mehmet
2016-10-01
It is important to have a scalable parallel numerical parameter optimization algorithm for a dynamical system used in financial applications where time limitation is crucial. We use Message Passing Interface parallel programming and present such a new parallel algorithm for parameter estimation. For example, we apply the algorithm to the asset flow differential equations that have been developed and analyzed since 1989 (see [3-6] and references contained therein). We achieved speed-up for some time series to run up to 512 cores (see [10]). Unlike [10], we consider more extensive financial market situations, for example, in presence of low volatility, high volatility and stock market price at a discount/premium to its net asset value with varying magnitude, in this work. Moreover, we evaluated the convergence of the model parameter vector, the nonlinear least squares error and maximum improvement factor to quantify the success of the optimization process depending on the number of initial parameter vectors.
Determining the Numerical Stability of Quantum Chemistry Algorithms.
Knizia, Gerald; Li, Wenbin; Simon, Sven; Werner, Hans-Joachim
2011-08-09
We present a simple, broadly applicable method for determining the numerical properties of quantum chemistry algorithms. The method deliberately introduces random numerical noise into computations, which is of the same order of magnitude as the floating point precision. Accordingly, repeated runs of an algorithm give slightly different results, which can be analyzed statistically to obtain precise estimates of its numerical stability. This noise is produced by automatic code injection into regular compiler output, so that no substantial programming effort is required, only a recompilation of the affected program sections. The method is applied to investigate: (i) the numerical stability of the three-center Obara-Saika integral evaluation scheme for high angular momenta, (ii) if coupled cluster perturbative triples can be evaluated with single precision arithmetic, (iii) how to implement the density fitting approximation in Møller-Plesset perturbation theory (MP2) most accurately, and (iv) which parts of density fitted MP2 can be safely evaluated with single precision arithmetic. In the integral case, we find a numerical instability in an equation that is used in almost all integral programs. Due to the results of (ii) and (iv), we conjecture that single precision arithmetic can be applied whenever a calculation is done in an orthogonal basis set and excessively long linear sums are avoided.
An algorithm for the numerical solution of linear differential games
Polovinkin, E S; Ivanov, G E; Balashov, M V; Konstantinov, R V; Khorev, A V
2001-10-31
A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented and estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.
Computational Fluid Dynamics. [numerical methods and algorithm development
NASA Technical Reports Server (NTRS)
1992-01-01
This collection of papers was presented at the Computational Fluid Dynamics (CFD) Conference held at Ames Research Center in California on March 12 through 14, 1991. It is an overview of CFD activities at NASA Lewis Research Center. The main thrust of computational work at Lewis is aimed at propulsion systems. Specific issues related to propulsion CFD and associated modeling will also be presented. Examples of results obtained with the most recent algorithm development will also be presented.
Algorithms for the Fractional Calculus: A Selection of Numerical Methods
NASA Technical Reports Server (NTRS)
Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.
2003-01-01
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.
Canonical algorithms for numerical integration of charged particle motion equations
NASA Astrophysics Data System (ADS)
Efimov, I. N.; Morozov, E. A.; Morozova, A. R.
2017-02-01
A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.
The development and evaluation of numerical algorithms for MIMD computers
NASA Technical Reports Server (NTRS)
Voigt, Robert G.
1990-01-01
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 to 29, 1989. The workshop is summarized in attachments. Attachment D - Workshop Summary; and Attachment E - List of Workshop Participants.
Numerical simulation of groundwater flooding: An example from the UK.
NASA Astrophysics Data System (ADS)
Hughes, A. G.; Jackson, C. R.; Vounaki, T.; Peach, D. W.; Wheater, H. S.
2008-12-01
The numerical simulation of groundwater flooding is increasingly necessary as the problem is gaining recognition from government bodies and climate change may bring more extreme events. However producing a suitable simulation of groundwater flooding involves many technical challenges. The timescale of the development of the flood can be short, recharge must be calculated correctly, the unsaturated zone must be considered as well as the "usual" suitable simulation of the saturated zone. The latter requires good simulation of absolute as well as relative values, since the timing and extent of the water table reaching the ground surface must be simulated well. All these factors combined with data scarcity makes simulation of groundwater flooding difficult. The Natural Environmental Research Council, in the UK, is funding a consortium to examine the problem of groundwater flooding in the Chalk, a micro-porous fractured limestone, which is an important aquifer for water supply in South-East England. This consortium, consisting of the British Geological Survey, Imperial College and the Centre for Ecology and Hydrology are studying groundwater flooding in the Pang and Lambourn catchments, located 50 kilometres to the west of London. A modelling system is currently under development of simulate the groundwater flooding which occurred in winter 2000/1, winter 2002/3 and summer 2007. The project has taken an existing groundwater flow model to simulate the groundwater flooding that occurred in winter 2000/1. The groundwater flow model, originally developed for another part of the catchment, has been run with daily stress periods as opposed to monthly in the original model. This reduction in the length of the stress period has resulted in a much improved simulation of the groundwater and river baseflow hydrographs during the flooding. Analysis of the time lag between recharge and groundwater rise using the model shows that there is a spatial and a temporal distribution in time
Predictive Lateral Logic for Numerical Entry Guidance Algorithms
NASA Technical Reports Server (NTRS)
Smith, Kelly M.
2016-01-01
Recent entry guidance algorithm development123 has tended to focus on numerical integration of trajectories onboard in order to evaluate candidate bank profiles. Such methods enjoy benefits such as flexibility to varying mission profiles and improved robustness to large dispersions. A common element across many of these modern entry guidance algorithms is a reliance upon the concept of Apollo heritage lateral error (or azimuth error) deadbands in which the number of bank reversals to be performed is non-deterministic. This paper presents a closed-loop bank reversal method that operates with a fixed number of bank reversals defined prior to flight. However, this number of bank reversals can be modified at any point, including in flight, based on contingencies such as fuel leaks where propellant usage must be minimized.
The Structure-Mapping Engine: Algorithm and Examples.
ERIC Educational Resources Information Center
Falkenhainer, Brian; And Others
This description of the Structure-Mapping Engine (SME), a flexible, cognitive simulation program for studying analogical processing which is based on Gentner's Structure-Mapping theory of analogy, points out that the SME provides a "tool kit" for constructing matching algorithms consistent with this theory. This report provides: (1) a…
A numerical algorithm for endochronic plasticity and comparison with experiment
NASA Technical Reports Server (NTRS)
Valanis, K. C.; Fan, J.
1985-01-01
A numerical algorithm based on the finite element method of analysis of the boundary value problem in a continuum is presented, in the case where the plastic response of the material is given in the context of endochronic plasticity. The relevant constitutive equation is expressed in incremental form and plastic effects are accounted for by the method of an induced pseudo-force in the matrix equations. The results of the analysis are compared with observed values in the case of a plate with two symmetric notches and loaded longitudinally in its own plane. The agreement between theory and experiment is excellent.
Algorithm-Based Fault Tolerance for Numerical Subroutines
NASA Technical Reports Server (NTRS)
Tumon, Michael; Granat, Robert; Lou, John
2007-01-01
A software library implements a new methodology of detecting faults in numerical subroutines, thus enabling application programs that contain the subroutines to recover transparently from single-event upsets. The software library in question is fault-detecting middleware that is wrapped around the numericalsubroutines. Conventional serial versions (based on LAPACK and FFTW) and a parallel version (based on ScaLAPACK) exist. The source code of the application program that contains the numerical subroutines is not modified, and the middleware is transparent to the user. The methodology used is a type of algorithm- based fault tolerance (ABFT). In ABFT, a checksum is computed before a computation and compared with the checksum of the computational result; an error is declared if the difference between the checksums exceeds some threshold. Novel normalization methods are used in the checksum comparison to ensure correct fault detections independent of algorithm inputs. In tests of this software reported in the peer-reviewed literature, this library was shown to enable detection of 99.9 percent of significant faults while generating no false alarms.
Particle-In-Cell Multi-Algorithm Numerical Test-Bed
NASA Astrophysics Data System (ADS)
Meyers, M. D.; Yu, P.; Tableman, A.; Decyk, V. K.; Mori, W. B.
2015-11-01
We describe a numerical test-bed that allows for the direct comparison of different numerical simulation schemes using only a single code. It is built from the UPIC Framework, which is a set of codes and modules for constructing parallel PIC codes. In this test-bed code, Maxwell's equations are solved in Fourier space in two dimensions. One can readily examine the numerical properties of a real space finite difference scheme by including its operators' Fourier space representations in the Maxwell solver. The fields can be defined at the same location in a simulation cell or can be offset appropriately by half-cells, as in the Yee finite difference time domain scheme. This allows for the accurate comparison of numerical properties (dispersion relations, numerical stability, etc.) across finite difference schemes, or against the original spectral scheme. We have also included different options for the charge and current deposits, including a strict charge conserving current deposit. The test-bed also includes options for studying the analytic time domain scheme, which eliminates numerical dispersion errors in vacuum. We will show examples from the test-bed that illustrate how the properties of some numerical instabilities vary between different PIC algorithms. Work supported by the NSF grant ACI 1339893 and DOE grant DE-SC0008491.
Wide Area Persistent Scatterer Interferometry: Algorithms and Examples
NASA Astrophysics Data System (ADS)
Adam, Nico; Rodriguez-Gonzalez, Fernando; Parizzi, Alessandro; Liebhart, Werner
2012-01-01
The persistent scatterer interferometry (PSI) is a well established monitoring technique for urban areas. It has been updated in order to process wide areas with the accepted characteristics in precision and resolution. Of course, the covered processing area now includes rural areas with a low persistent scatterer (PS) density. In order to bridge forested areas and water bodies, low quality and more distant PSs need to be included into the reference network. The development of the wide area product (WAP) succeeded to cope with the resulting difficulties resulting in spatial error propagation. In this paper, the developed WAP system is described and a processing example is presented.
Verifying Algorithms for Autonomous Aircraft by Simulation Generalities and Example
NASA Technical Reports Server (NTRS)
White, Allan L.
2010-01-01
An open question in Air Traffic Management is what procedures can be validated by simulation where the simulation shows that the probability of undesirable events is below the required level at some confidence level. The problem is including enough realism to be convincing while retaining enough efficiency to run the large number of trials needed for high confidence. The paper first examines the probabilistic interpretation of a typical requirement by a regulatory agency and computes the number of trials needed to establish the requirement at an equivalent confidence level. Since any simulation is likely to consider only one type of event and there are several types of events, the paper examines under what conditions this separate consideration is valid. The paper establishes a separation algorithm at the required confidence level where the aircraft operates under feedback control as is subject to perturbations. There is a discussion where it is shown that a scenario three of four orders of magnitude more complex is feasible. The question of what can be validated by simulation remains open, but there is reason to be optimistic.
Understanding disordered systems through numerical simulation and algorithm development
NASA Astrophysics Data System (ADS)
Sweeney, Sean Michael
Disordered systems arise in many physical contexts. Not all matter is uniform, and impurities or heterogeneities can be modeled by fixed random disorder. Numerous complex networks also possess fixed disorder, leading to applications in transportation systems, telecommunications, social networks, and epidemic modeling, to name a few. Due to their random nature and power law critical behavior, disordered systems are difficult to study analytically. Numerical simulation can help overcome this hurdle by allowing for the rapid computation of system states. In order to get precise statistics and extrapolate to the thermodynamic limit, large systems must be studied over many realizations. Thus, innovative algorithm development is essential in order reduce memory or running time requirements of simulations. This thesis presents a review of disordered systems, as well as a thorough study of two particular systems through numerical simulation, algorithm development and optimization, and careful statistical analysis of scaling properties. Chapter 1 provides a thorough overview of disordered systems, the history of their study in the physics community, and the development of techniques used to study them. Topics of quenched disorder, phase transitions, the renormalization group, criticality, and scale invariance are discussed. Several prominent models of disordered systems are also explained. Lastly, analysis techniques used in studying disordered systems are covered. In Chapter 2, minimal spanning trees on critical percolation clusters are studied, motivated in part by an analytic perturbation expansion by Jackson and Read that I check against numerical calculations. This system has a direct mapping to the ground state of the strongly disordered spin glass. We compute the path length fractal dimension of these trees in dimensions d = {2, 3, 4, 5} and find our results to be compatible with the analytic results suggested by Jackson and Read. In Chapter 3, the random bond Ising
Numerical algorithms for computations of feedback laws arising in control of flexible systems
NASA Technical Reports Server (NTRS)
Lasiecka, Irena
1989-01-01
Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.
Linsen, Sarah; Torbeyns, Joke; Verschaffel, Lieven; Reynvoet, Bert; De Smedt, Bert
2016-03-01
There are two well-known computation methods for solving multi-digit subtraction items, namely mental and algorithmic computation. It has been contended that mental and algorithmic computation differentially rely on numerical magnitude processing, an assumption that has already been examined in children, but not yet in adults. Therefore, in this study, we examined how numerical magnitude processing was associated with mental and algorithmic computation, and whether this association with numerical magnitude processing was different for mental versus algorithmic computation. We also investigated whether the association between numerical magnitude processing and mental and algorithmic computation differed for measures of symbolic versus nonsymbolic numerical magnitude processing. Results showed that symbolic, and not nonsymbolic, numerical magnitude processing was associated with mental computation, but not with algorithmic computation. Additional analyses showed, however, that the size of this association with symbolic numerical magnitude processing was not significantly different for mental and algorithmic computation. We also tried to further clarify the association between numerical magnitude processing and complex calculation by also including relevant arithmetical subskills, i.e. arithmetic facts, needed for complex calculation that are also known to be dependent on numerical magnitude processing. Results showed that the associations between symbolic numerical magnitude processing and mental and algorithmic computation were fully explained by individual differences in elementary arithmetic fact knowledge.
A stable and efficient numerical algorithm for unconfined aquifer analysis
Keating, Elizabeth; Zyvoloski, George
2008-01-01
The non-linearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of forward model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency, and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to solution of Richard's Equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem, as well.
A stable and efficient numerical algorithm for unconfined aquifer analysis.
Keating, Elizabeth; Zyvoloski, George
2009-01-01
The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well.
2007-12-06
problems studied in this project involve numerically solving partial differential equations with either discontinuous or rapidly changing solutions ...REPORT Algorithm Development and Application of High Order Numerical Methods for Shocked and Rapid Changing Solutions 14. ABSTRACT 16. SECURITY...discontinuous Galerkin finite element methods, for solving partial differential equations with discontinuous or rapidly changing solutions . Algorithm
NASA Astrophysics Data System (ADS)
He, Jianbin; Yu, Simin; Cai, Jianping
2016-12-01
Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.
A fast algorithm for numerical solutions to Fortet's equation
NASA Astrophysics Data System (ADS)
Brumen, Gorazd
2008-10-01
A fast algorithm for computation of default times of multiple firms in a structural model is presented. The algorithm uses a multivariate extension of the Fortet's equation and the structure of Toeplitz matrices to significantly improve the computation time. In a financial market consisting of M[not double greater-than sign]1 firms and N discretization points in every dimension the algorithm uses O(nlogn·M·M!·NM(M-1)/2) operations, where n is the number of discretization points in the time domain. The algorithm is applied to firm survival probability computation and zero coupon bond pricing.
Numerical algorithms for highly oscillatory dynamic system based on commutator-free method
NASA Astrophysics Data System (ADS)
Li, Wencheng; Deng, Zichen; Zhang, Suying
2007-04-01
In the present paper, an efficiently improved modified Magnus integrator algorithm based on commutator-free method is proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the second-order dynamic systems are transferred to the frame of reference by introducing new variable so that highly oscillatory behaviour inherited from the entries. Then the modified Magnus integrator method based on local linearization is appropriately designed for solving the above new form. And some optimized strategies for reducing the number of function evaluations and matrix operations are also suggested. Finally, several numerical examples for highly oscillatory dynamic systems, such as Airy equation, Bessel equation, Mathieu equation, are presented to demonstrate the validity and effectiveness of the proposed method.
A numerical comparison of discrete Kalman filtering algorithms: An orbit determination case study
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1976-01-01
The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.
An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization
Choi, Tae Jong; Ahn, Chang Wook; An, Jinung
2013-01-01
Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems. PMID:23935445
An adaptive Cauchy differential evolution algorithm for global numerical optimization.
Choi, Tae Jong; Ahn, Chang Wook; An, Jinung
2013-01-01
Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems.
Numerical Algorithms and Mathematical Software for Linear Control and Estimation Theory.
1985-05-30
RD -R157 525 NUMERICAL ALGORITHMS AND MATHEMATICAL SOFTWJARE FOR i/i LINEAR CONTROL AND EST..U) MASSACHUSETTS INST OF TECH CAMBRIDGE STATISTICS...PERIOD COVERED"~~ "ia--Dec. 14, 1981-- LD Numerical Algorithms and Mathematical Dec. 13, 1984*Software for Linear Control and 1.0 Estimation Theory...THIS PAGE (Wten Date Entered) .. :..0 70 FINAL REPORT--ARO Grant DAAG29-82-K-0028,"Numerical Algorithms and Mathematical Software for Linear Control and
NASA Astrophysics Data System (ADS)
Mattei, D.; Smith, I.; Ferrari, A.; Carbillet, M.
2010-10-01
Post-processing for exoplanet detection using direct imaging requires large data cubes and/or sophisticated signal processing technics. For alt-azimuthal mounts, a projection effect called field rotation makes the potential planet rotate in a known manner on the set of images. For ground based telescopes that use extreme adaptive optics and advanced coronagraphy, technics based on field rotation are already broadly used and still under progress. In most such technics, for a given initial position of the planet the planet intensity estimate is a linear function of the set of images. However, due to field rotation the modified instrumental response applied is not shift invariant like usual linear filters. Testing all possible initial positions is therefore very time-consuming. To reduce the time process, we propose to deal with each subset of initial positions computed on a different machine using parallelization programming. In particular, the MOODS algorithm dedicated to the VLT-SPHERE instrument, that estimates jointly the light contributions of the star and the potential exoplanet, is parallelized on the Observatoire de la Cote d'Azur cluster. Different parallelization methods (OpenMP, MPI, Jobs Array) have been elaborated for the initial MOODS code and compared to each other. The one finally chosen splits the initial positions on the processors available by accounting at best for the different constraints of the cluster structure: memory, job submission queues, number of available CPUs, cluster average load. At the end, a standard set of images is satisfactorily processed in a few hours instead of a few days.
Numerical Optimization Algorithms and Software for Systems Biology
Saunders, Michael
2013-02-02
The basic aims of this work are: to develop reliable algorithms for solving optimization problems involving large stoi- chiometric matrices; to investigate cyclic dependency between metabolic and macromolecular biosynthetic networks; and to quantify the significance of thermodynamic constraints on prokaryotic metabolism.
An application of fast algorithms to numerical electromagnetic modeling
Bezvoda, V.; Segeth, K.
1987-03-01
Numerical electromagnetic modeling by the finite-difference or finite-element methods leads to a large sparse system of linear algebraic equations. Fast direct methods, requiring an order of at most q log q arithmetic operations to solve a system of q equations, cannot easily be applied to such a system. This paper describes the iterative application of a fast method, namely cyclic reduction, to the numerical solution of the Helmholtz equation with a piecewise constant imaginary coefficient of the absolute term in a plane domain. By means of numerical tests the advantages and limitations of the method compared with classical direct methods are discussed. The iterative application of the cyclic reduction method is very efficient if one can exploit a known solution of a similar (e.g., simpler) problem as the initial approximation. This makes cyclic reduction a powerful tool in solving the inverse problem by trial-and-error.
An efficient numerical algorithm for transverse impact problems
NASA Technical Reports Server (NTRS)
Sankar, B. V.; Sun, C. T.
1985-01-01
Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.
Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm
Godfrey, Brendan B.; Vay, Jean-Luc; Haber, Irving
2014-02-01
The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell's equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper derives and solves the numerical dispersion relation for the PSATD algorithm and compares the results with corresponding behavior of the more conventional pseudo-spectral time-domain (PSTD) and finite difference time-domain (FDTD) algorithms. In general, PSATD offers superior stability properties over a reasonable range of time steps. More importantly, one version of the PSATD algorithm, when combined with digital filtering, is almost completely free of the numerical Cherenkov instability for time steps (scaled to the speed of light) comparable to or smaller than the axial cell size.
Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study
NASA Technical Reports Server (NTRS)
Bierman, G. J.; Thornton, C. L.
1976-01-01
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
A numeric comparison of variable selection algorithms for supervised learning
NASA Astrophysics Data System (ADS)
Palombo, G.; Narsky, I.
2009-12-01
Datasets in modern High Energy Physics (HEP) experiments are often described by dozens or even hundreds of input variables. Reducing a full variable set to a subset that most completely represents information about data is therefore an important task in analysis of HEP data. We compare various variable selection algorithms for supervised learning using several datasets such as, for instance, imaging gamma-ray Cherenkov telescope (MAGIC) data found at the UCI repository. We use classifiers and variable selection methods implemented in the statistical package StatPatternRecognition (SPR), a free open-source C++ package developed in the HEP community ( http://sourceforge.net/projects/statpatrec/). For each dataset, we select a powerful classifier and estimate its learning accuracy on variable subsets obtained by various selection algorithms. When possible, we also estimate the CPU time needed for the variable subset selection. The results of this analysis are compared with those published previously for these datasets using other statistical packages such as R and Weka. We show that the most accurate, yet slowest, method is a wrapper algorithm known as generalized sequential forward selection ("Add N Remove R") implemented in SPR.
A bibliography on parallel and vector numerical algorithms
NASA Technical Reports Server (NTRS)
Ortega, James M.; Voigt, Robert G.; Romine, Charles H.
1988-01-01
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.
A bibliography on parallel and vector numerical algorithms
NASA Technical Reports Server (NTRS)
Ortega, J. M.; Voigt, R. G.
1987-01-01
This is a bibliography of 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 listed also.
An Example-Based Super-Resolution Algorithm for Selfie Images.
William, Jino Hans; Venkateswaran, N; Narayanan, Srinath; Ramachandran, Sandeep
2016-01-01
A selfie is typically a self-portrait captured using the front camera of a smartphone. Most state-of-the-art smartphones are equipped with a high-resolution (HR) rear camera and a low-resolution (LR) front camera. As selfies are captured by front camera with limited pixel resolution, the fine details in it are explicitly missed. This paper aims to improve the resolution of selfies by exploiting the fine details in HR images captured by rear camera using an example-based super-resolution (SR) algorithm. HR images captured by rear camera carry significant fine details and are used as an exemplar to train an optimal matrix-value regression (MVR) operator. The MVR operator serves as an image-pair priori which learns the correspondence between the LR-HR patch-pairs and is effectively used to super-resolve LR selfie images. The proposed MVR algorithm avoids vectorization of image patch-pairs and preserves image-level information during both learning and recovering process. The proposed algorithm is evaluated for its efficiency and effectiveness both qualitatively and quantitatively with other state-of-the-art SR algorithms. The results validate that the proposed algorithm is efficient as it requires less than 3 seconds to super-resolve LR selfie and is effective as it preserves sharp details without introducing any counterfeit fine details.
An Example-Based Super-Resolution Algorithm for Selfie Images
William, Jino Hans; Venkateswaran, N.; Narayanan, Srinath; Ramachandran, Sandeep
2016-01-01
A selfie is typically a self-portrait captured using the front camera of a smartphone. Most state-of-the-art smartphones are equipped with a high-resolution (HR) rear camera and a low-resolution (LR) front camera. As selfies are captured by front camera with limited pixel resolution, the fine details in it are explicitly missed. This paper aims to improve the resolution of selfies by exploiting the fine details in HR images captured by rear camera using an example-based super-resolution (SR) algorithm. HR images captured by rear camera carry significant fine details and are used as an exemplar to train an optimal matrix-value regression (MVR) operator. The MVR operator serves as an image-pair priori which learns the correspondence between the LR-HR patch-pairs and is effectively used to super-resolve LR selfie images. The proposed MVR algorithm avoids vectorization of image patch-pairs and preserves image-level information during both learning and recovering process. The proposed algorithm is evaluated for its efficiency and effectiveness both qualitatively and quantitatively with other state-of-the-art SR algorithms. The results validate that the proposed algorithm is efficient as it requires less than 3 seconds to super-resolve LR selfie and is effective as it preserves sharp details without introducing any counterfeit fine details. PMID:27064500
Fourier analysis of numerical algorithms for the Maxwell equations
NASA Technical Reports Server (NTRS)
Liu, Yen
1993-01-01
The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial and time discretizations applied to the Maxwell equations on multi-dimensional grids. Both Cartesian grids and non-Cartesian grids based on hexagons and tetradecahedra are studied and compared. The numerical errors are quantitatively determined in terms of phase speed, wave number, propagation direction, gridspacings, and CFL number. The study shows that centered schemes are more efficient than upwind schemes. The non-Cartesian grids yield superior isotropy and higher accuracy than the Cartesian ones. For the centered schemes, the staggered grids produce less errors than the unstaggered ones. A new unstaggered scheme which has all the best properties is introduced. The study also demonstrates that a proper choice of time discretization can reduce the overall numerical errors due to the spatial discretization.
Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm
NASA Astrophysics Data System (ADS)
Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.
2008-07-01
The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.
A direct numerical reconstruction algorithm for the 3D Calderón problem
NASA Astrophysics Data System (ADS)
Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim
2011-04-01
In three dimensions Calderón's problem was addressed and solved in theory in the 1980s in a series of papers, but only recently the numerical implementation of the algorithm was initiated. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conductivity equation and a (non-physical) scattering transform. The resulting reconstruction algorithm is in principle direct and addresses the full non-linear problem immediately. In this paper we will outline the theoretical reconstruction method and describe how the method can be implemented numerically. We will give three different implementations, and compare their performance on a numerical phantom.
NASA Technical Reports Server (NTRS)
Scheid, R. E.; Milman, M. H.; Salama, M.; Bruno, R.; Gibson, J. S.
1990-01-01
This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objectives of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to assist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further considerations, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose. Analytical and numerical examples are also presented.
Structural algorithm to reservoir reconstruction using passive seismic data (synthetic example)
Smaglichenko, Tatyana A.; Volodin, Igor A.; Lukyanitsa, Andrei A.; Smaglichenko, Alexander V.; Sayankina, Maria K.
2012-09-26
Using of passive seismic observations to detect a reservoir is a new direction of prospecting and exploration of hydrocarbons. In order to identify thin reservoir model we applied the modification of Gaussian elimination method in conditions of incomplete synthetic data. Because of the singularity of a matrix conventional method does not work. Therefore structural algorithm has been developed by analyzing the given model as a complex model. Numerical results demonstrate of its advantage compared with usual way of solution. We conclude that the gas reservoir is reconstructed by retrieving of the image of encasing shale beneath it.
Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning
NASA Astrophysics Data System (ADS)
Bradley, Ben K.
Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and
NASA Astrophysics Data System (ADS)
Chen, Jiaoxuan; Zhang, Maomao; Liu, Yinyan; Chen, Jiaoliao; Li, Yi
2017-03-01
Electrical capacitance tomography (ECT) is a promising technique applied in many fields. However, the solutions for ECT are not unique and highly sensitive to the measurement noise. To remain a good shape of reconstructed object and endure a noisy data, a Rudin–Osher–Fatemi (ROF) model with total variation regularization is applied to image reconstruction in ECT. Two numerical methods, which are simplified augmented Lagrangian (SAL) and accelerated alternating direction method of multipliers (AADMM), are innovatively introduced to try to solve the above mentioned problems in ECT. The effect of the parameters and the number of iterations for different algorithms, and the noise level in capacitance data are discussed. Both simulation and experimental tests were carried out to validate the feasibility of the proposed algorithms, compared to the Landweber iteration (LI) algorithm. The results show that the SAL and AADMM algorithms can handle a high level of noise and the AADMM algorithm outperforms other algorithms in identifying the object from its background.
Variationally consistent discretization schemes and numerical algorithms for contact problems
NASA Astrophysics Data System (ADS)
Wohlmuth, Barbara
We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of
NASA Astrophysics Data System (ADS)
Kim, J.; Sonnenthal, E. L.; Rutqvist, J.
2011-12-01
Rigorous modeling of coupling between fluid, heat, and geomechanics (thermo-poro-mechanics), in fractured porous media is one of the important and difficult topics in geothermal reservoir simulation, because the physics are highly nonlinear and strongly coupled. Coupled fluid/heat flow and geomechanics are investigated using the multiple interacting continua (MINC) method as applied to naturally fractured media. In this study, we generalize constitutive relations for the isothermal elastic dual porosity model proposed by Berryman (2002) to those for the non-isothermal elastic/elastoplastic multiple porosity model, and derive the coupling coefficients of coupled fluid/heat flow and geomechanics and constraints of the coefficients. When the off-diagonal terms of the total compressibility matrix for the flow problem are zero, the upscaled drained bulk modulus for geomechanics becomes the harmonic average of drained bulk moduli of the multiple continua. In this case, the drained elastic/elastoplastic moduli for mechanics are determined by a combination of the drained moduli and volume fractions in multiple porosity materials. We also determine a relation between local strains of all multiple porosity materials in a gridblock and the global strain of the gridblock, from which we can track local and global elastic/plastic variables. For elastoplasticity, the return mapping is performed for all multiple porosity materials in the gridblock. For numerical implementation, we employ and extend the fixed-stress sequential method of the single porosity model to coupled fluid/heat flow and geomechanics in multiple porosity systems, because it provides numerical stability and high accuracy. This sequential scheme can be easily implemented by using a porosity function and its corresponding porosity correction, making use of the existing robust flow and geomechanics simulators. We implemented the proposed modeling and numerical algorithm to the reaction transport simulator
Chen, Deng-kai; Gu, Rong; Gu, Yu-feng; Yu, Sui-huai
2016-01-01
Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design. PMID:27630709
Yang, Yan-Pu; Chen, Deng-Kai; Gu, Rong; Gu, Yu-Feng; Yu, Sui-Huai
2016-01-01
Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design.
A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study
NASA Technical Reports Server (NTRS)
Thornton, C. L.; Bierman, G. J.
1976-01-01
An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.
Numerical optimization algorithm for rotationally invariant multi-orbital slave-boson method
NASA Astrophysics Data System (ADS)
Quan, Ya-Min; Wang, Qing-wei; Liu, Da-Yong; Yu, Xiang-Long; Zou, Liang-Jian
2015-06-01
We develop a generalized numerical optimization algorithm for the rotationally invariant multi-orbital slave boson approach, which is applicable for arbitrary boundary constraints of high-dimensional objective function by combining several classical optimization techniques. After constructing the calculation architecture of rotationally invariant multi-orbital slave boson model, we apply this optimization algorithm to find the stable ground state and magnetic configuration of two-orbital Hubbard models. The numerical results are consistent with available solutions, confirming the correctness and accuracy of our present algorithm. Furthermore, we utilize it to explore the effects of the transverse Hund's coupling terms on metal-insulator transition, orbital selective Mott phase and magnetism. These results show the quick convergency and robust stable character of our algorithm in searching the optimized solution of strongly correlated electron systems.
Mikesell, T. Dylan; Malcolm, Alison E.; Yang, Di; Haney, Matthew M.
2015-01-01
Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here, we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We illustrate the differences of all three methods compared to one another using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has better time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements. DTW is a new tool that may find new applications in seismology and other geophysical methods (e.g., as a waveform inversion misfit function).
Wacker, C; Schröder, R R
2015-04-01
For a long time, the high-energy approximation was sufficient for any image simulation in electron microscopy. This changed with the advent of aberration correctors that allow high-resolution imaging at low electron energies. To deal with this fact, we present a numerical solution of the exact Schrödinger equation that is novel in the field of electron microscopy. Furthermore, we investigate systematically the advantages and problems of several multislice algorithms, especially the real-space algorithms.
NASA Astrophysics Data System (ADS)
Penenko, Alexey; Antokhin, Pavel
2016-11-01
The performance of a variational data assimilation algorithm for a transport and transformation model of atmospheric chemical composition is studied numerically in the case where the emission inventories are missing while there are additional in situ indirect concentration measurements. The algorithm is based on decomposition and splitting methods with a direct solution of the data assimilation problems at the splitting stages. This design allows avoiding iterative processes and working in real-time. In numerical experiments we study the sensitivity of data assimilation to measurement data quantity and quality.
Buet, C.; Cordier; Degond, P.; Lemou, M.
1997-05-15
We present fast numerical algorithms to solve the nonlinear Fokker-Planck-Landau equation in 3D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the Fokker-Planck-Landau equation, such as the conservation of mass, momentum, and energy, the decay of the entropy, and the fact that the steady states are Maxwellians. At the end of this paper, we give numerical results illustrating the efficiency of these fast algorithms in terms of accuracy and CPU time. 20 refs., 7 figs.
On the impact of communication complexity in the design of parallel numerical algorithms
NASA Technical Reports Server (NTRS)
Gannon, D.; Vanrosendale, J.
1984-01-01
This paper describes two models of the cost of data movement in parallel numerical algorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In the second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm independent upper bounds on system performance are derived for several problems that are important to scientific computation.
Errors, correlations and fidelity for noisy Hamilton flows. Theory and numerical examples
NASA Astrophysics Data System (ADS)
Turchetti, G.; Sinigardi, S.; Servizi, G.; Panichi, F.; Vaienti, S.
2017-02-01
We analyse the asymptotic growth of the error for Hamiltonian flows due to small random perturbations. We compare the forward error with the reversibility error, showing their equivalence for linear flows on a compact phase space. The forward error, given by the root mean square deviation σ (t) of the noisy flow, grows according to a power law if the system is integrable and according to an exponential law if it is chaotic. The autocorrelation and the fidelity, defined as the correlation of the perturbed flow with respect to the unperturbed one, exhibit an exponential decay as \\exp ≤ft(-2{π2}{σ2}(t)\\right) . Some numerical examples such as the anharmonic oscillator and the Hénon Heiles model confirm these results. We finally consider the effect of the observational noise on an integrable system, and show that the decay of correlations can only be observed after a sequence of measurements and that the multiplicative noise is more effective if the delay between two measurements is large.
A Parallel Compact Multi-Dimensional Numerical Algorithm with Aeroacoustics Applications
NASA Technical Reports Server (NTRS)
Povitsky, Alex; Morris, Philip J.
1999-01-01
In this study we propose a novel method to parallelize high-order compact numerical algorithms for the solution of three-dimensional PDEs (Partial Differential Equations) in a space-time domain. For this numerical integration most of the computer time is spent in computation of spatial derivatives at each stage of the Runge-Kutta temporal update. The most efficient direct method to compute spatial derivatives on a serial computer is a version of Gaussian elimination for narrow linear banded systems known as the Thomas algorithm. In a straightforward pipelined implementation of the Thomas algorithm processors are idle due to the forward and backward recurrences of the Thomas algorithm. To utilize processors during this time, we propose to use them for either non-local data independent computations, solving lines in the next spatial direction, or local data-dependent computations by the Runge-Kutta method. To achieve this goal, control of processor communication and computations by a static schedule is adopted. Thus, our parallel code is driven by a communication and computation schedule instead of the usual "creative, programming" approach. The obtained parallelization speed-up of the novel algorithm is about twice as much as that for the standard pipelined algorithm and close to that for the explicit DRP algorithm.
Numerical convergence and interpretation of the fuzzy c-shells clustering algorithm.
Bezdek, J C; Hathaway, R J
1992-01-01
R. N. Dave's (1990) version of fuzzy c-shells is an iterative clustering algorithm which requires the application of Newton's method or a similar general optimization technique at each half step in any sequence of iterates for minimizing the associated objective function. An important computational question concerns the accuracy of the solution required at each half step within the overall iteration. The general convergence theory for grouped coordination minimization is applied to this question to show that numerically exact solution of the half-step subproblems in Dave's algorithm is not necessary. One iteration of Newton's method in each coordinate minimization half step yields a sequence obtained using the fuzzy c-shells algorithm with numerically exact coordinate minimization at each half step. It is shown that fuzzy c-shells generates hyperspherical prototypes to the clusters it finds for certain special cases of the measure of dissimilarity used.
NASA Astrophysics Data System (ADS)
Wichert, Viktoria; Arkenberg, Mario; Hauschildt, Peter H.
2016-10-01
Highly resolved state-of-the-art 3D atmosphere simulations will remain computationally extremely expensive for years to come. In addition to the need for more computing power, rethinking coding practices is necessary. We take a dual approach by introducing especially adapted, parallel numerical methods and correspondingly parallelizing critical code passages. In the following, we present our respective work on PHOENIX/3D. With new parallel numerical algorithms, there is a big opportunity for improvement when iteratively solving the system of equations emerging from the operator splitting of the radiative transfer equation J = ΛS. The narrow-banded approximate Λ-operator Λ* , which is used in PHOENIX/3D, occurs in each iteration step. By implementing a numerical algorithm which takes advantage of its characteristic traits, the parallel code's efficiency is further increased and a speed-up in computational time can be achieved.
NASA Astrophysics Data System (ADS)
Gharsalli, Leila; Mohammad-Djafari, Ali; Fraysse, Aurélia; Rodet, Thomas
2013-08-01
Our aim is to solve a linear inverse problem using various methods based on the Variational Bayesian Approximation (VBA). We choose to take sparsity into account via a scale mixture prior, more precisely a student-t model. The joint posterior of the unknown and hidden variable of the mixtures is approximated via the VBA. To do this approximation, classically the alternate algorithm is used. But this method is not the most efficient. Recently other optimization algorithms have been proposed; indeed classical iterative algorithms of optimization such as the steepest descent method and the conjugate gradient have been studied in the space of the probability densities involved in the Bayesian methodology to treat this problem. The main object of this work is to present these three algorithms and a numerical comparison of their performances.
PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release
NASA Astrophysics Data System (ADS)
Pizzocri, D.; Rabiti, C.; Luzzi, L.; Barani, T.; Van Uffelen, P.; Pastore, G.
2016-09-01
The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of the corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this paper, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, combined with polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of PolyPole-1 is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.
Stochastic models and numerical algorithms for a class of regulatory gene networks.
Fournier, Thomas; Gabriel, Jean-Pierre; Pasquier, Jerôme; Mazza, Christian; Galbete, José; Mermod, Nicolas
2009-08-01
Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.
A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
Alex, Arne; Delft, Jan von; Kalus, Matthias; Huckleberry, Alan
2011-02-15
We present an algorithm for the explicit numerical calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients, based on the Gelfand-Tsetlin pattern calculus. Our algorithm is well suited for numerical implementation; we include a computer code in an appendix. Our exposition presumes only familiarity with the representation theory of SU(2).
François, Marianne M.
2015-05-28
A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented. The volume tracking method, also known as the volume-of-fluid method has become an established numerical approach to model and simulate interfacial flows. Its advantage is its strict mass conservation. However, because the interface is not explicitly tracked but captured via the material volume fraction on a fixed mesh, accurate estimation of the interface position, its geometric properties and modeling of interfacial physics in the volume tracking framework remain difficult. Several improvements have been made over the last decade to address these challenges.more » In this study, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted.« less
Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature
Bramble, J.H. . Dept. of Mathematics); Goldstein, C.I.; Pasciak, J.E. . Applied Mathematics Dept.)
1994-05-01
The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in R[sup 2] with a crack.
NASA Astrophysics Data System (ADS)
Fedoseyev, A.; Kansa, E. J.; Tsynkov, S.; Petropavlovskiy, S.; Osintcev, M.; Shumlak, U.; Henshaw, W. D.
2016-10-01
We present the implementation of the Lacuna method, that removes a key diffculty that currently hampers many existing methods for computing unsteady electromagnetic waves on unbounded regions. Numerical accuracy and/or stability may deterio-rate over long times due to the treatment of artificial outer boundaries. We describe a developed universal algorithm and software that correct this problem by employing the Huygens' principle and lacunae of Maxwell's equations. The algorithm provides a temporally uniform guaranteed error bound (no deterioration at all), and the software will enable robust electromagnetic simulations in a high-performance computing environment. The methodology applies to any geometry, any scheme, and any boundary condition. It eliminates the long-time deterioration regardless of its origin and how it manifests itself. In retrospect, the lacunae method was first proposed by V. Ryaben'kii and subsequently developed by S. Tsynkov. We have completed development of an innovative numerical methodology for high fidelity error-controlled modeling of a broad variety of electromagnetic and other wave phenomena. Proof-of-concept 3D computations have been conducted that con-vincingly demonstrate the feasibility and effciency of the proposed approach. Our algorithms are being implemented as robust commercial software tools in a standalone module to be combined with existing numerical schemes in several widely used computational electromagnetic codes.
Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Hafez, Mohammed; Dacles, Jennifer
1989-01-01
The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.
NASA Astrophysics Data System (ADS)
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-11-11
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-01-01
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted “useful” data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency. PMID:26569247
NASA Technical Reports Server (NTRS)
Daso, E. O.
1986-01-01
An implicit approximate factorization algorithm is employed to quantify the parametric effects of Courant number and artificial smoothing on numerical solutions of the unsteady 3-D Euler equations for a windmilling propeller (low speed) flow field. The results show that propeller global or performance chracteristics vary strongly with Courant number and artificial dissipation parameters, though the variation is such less severe at high Courant numbers. Candidate sets of Courant number and dissipation parameters could result in parameter-dependent solutions. Parameter-independent numerical solutions can be obtained if low values of the dissipation parameter-time step ratio are used in the computations. Furthermore, it is realized that too much artificial damping can degrade numerical stability. Finally, it is demonstrated that highly resolved meshes may, in some cases, delay convergence, thereby suggesting some optimum cell size for a given flow solution. It is suspected that improper boundary treatment may account for the cell size constraint.
NASA Astrophysics Data System (ADS)
Degtyarev, Alexander; Khramushin, Vasily
2016-02-01
The paper deals with the computer implementation of direct computational experiments in fluid mechanics, constructed on the basis of the approach developed by the authors. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the effciency of the algorithms developed by numerical procedures with natural parallelism. The paper examines the main objects and operations that let you manage computational experiments and monitor the status of the computation process. Special attention is given to a) realization of tensor representations of numerical schemes for direct simulation; b) realization of representation of large particles of a continuous medium motion in two coordinate systems (global and mobile); c) computing operations in the projections of coordinate systems, direct and inverse transformation in these systems. Particular attention is paid to the use of hardware and software of modern computer systems.
Obuchowski, Nancy A; Barnhart, Huiman X; Buckler, Andrew J; Pennello, Gene; Wang, Xiao-Feng; Kalpathy-Cramer, Jayashree; Kim, Hyun J Grace; Reeves, Anthony P
2015-02-01
Quantitative imaging biomarkers are being used increasingly in medicine to diagnose and monitor patients' disease. The computer algorithms that measure quantitative imaging biomarkers have different technical performance characteristics. In this paper we illustrate the appropriate statistical methods for assessing and comparing the bias, precision, and agreement of computer algorithms. We use data from three studies of pulmonary nodules. The first study is a small phantom study used to illustrate metrics for assessing repeatability. The second study is a large phantom study allowing assessment of four algorithms' bias and reproducibility for measuring tumor volume and the change in tumor volume. The third study is a small clinical study of patients whose tumors were measured on two occasions. This study allows a direct assessment of six algorithms' performance for measuring tumor change. With these three examples we compare and contrast study designs and performance metrics, and we illustrate the advantages and limitations of various common statistical methods for quantitative imaging biomarker studies.
Godfrey, Brendan B.; Vay, Jean-Luc
2013-09-01
Rapidly growing numerical instabilities routinely occur in multidimensional particle-in-cell computer simulations of plasma-based particle accelerators, astrophysical phenomena, and relativistic charged particle beams. Reducing instability growth to acceptable levels has necessitated higher resolution grids, high-order field solvers, current filtering, etc. except for certain ratios of the time step to the axial cell size, for which numerical growth rates and saturation levels are reduced substantially. This paper derives and solves the cold beam dispersion relation for numerical instabilities in multidimensional, relativistic, electromagnetic particle-in-cell programs employing either the standard or the Cole–Karkkainnen finite difference field solver on a staggered mesh and the common Esirkepov current-gathering algorithm. Good overall agreement is achieved with previously reported results of the WARP code. In particular, the existence of select time steps for which instabilities are minimized is explained. Additionally, an alternative field interpolation algorithm is proposed for which instabilities are almost completely eliminated for a particular time step in ultra-relativistic simulations.
A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization.
Zhu, Binglian; Zhu, Wenyong; Liu, Zijuan; Duan, Qingyan; Cao, Long
2016-01-01
This paper proposes a novel quantum-behaved bat algorithm with the direction of mean best position (QMBA). In QMBA, the position of each bat is mainly updated by the current optimal solution in the early stage of searching and in the late search it also depends on the mean best position which can enhance the convergence speed of the algorithm. During the process of searching, quantum behavior of bats is introduced which is beneficial to jump out of local optimal solution and make the quantum-behaved bats not easily fall into local optimal solution, and it has better ability to adapt complex environment. Meanwhile, QMBA makes good use of statistical information of best position which bats had experienced to generate better quality solutions. This approach not only inherits the characteristic of quick convergence, simplicity, and easy implementation of original bat algorithm, but also increases the diversity of population and improves the accuracy of solution. Twenty-four benchmark test functions are tested and compared with other variant bat algorithms for numerical optimization the simulation results show that this approach is simple and efficient and can achieve a more accurate solution.
A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization
Zhu, Wenyong; Liu, Zijuan; Duan, Qingyan; Cao, Long
2016-01-01
This paper proposes a novel quantum-behaved bat algorithm with the direction of mean best position (QMBA). In QMBA, the position of each bat is mainly updated by the current optimal solution in the early stage of searching and in the late search it also depends on the mean best position which can enhance the convergence speed of the algorithm. During the process of searching, quantum behavior of bats is introduced which is beneficial to jump out of local optimal solution and make the quantum-behaved bats not easily fall into local optimal solution, and it has better ability to adapt complex environment. Meanwhile, QMBA makes good use of statistical information of best position which bats had experienced to generate better quality solutions. This approach not only inherits the characteristic of quick convergence, simplicity, and easy implementation of original bat algorithm, but also increases the diversity of population and improves the accuracy of solution. Twenty-four benchmark test functions are tested and compared with other variant bat algorithms for numerical optimization the simulation results show that this approach is simple and efficient and can achieve a more accurate solution. PMID:27293424
Samaan, Michael A; Weinhandl, Joshua T; Bawab, Sebastian Y; Ringleb, Stacie I
2016-12-01
Musculoskeletal modeling allows for the determination of various parameters during dynamic maneuvers by using in vivo kinematic and ground reaction force (GRF) data as inputs. Differences between experimental and model marker data and inconsistencies in the GRFs applied to these musculoskeletal models may not produce accurate simulations. Therefore, residual forces and moments are applied to these models in order to reduce these differences. Numerical optimization techniques can be used to determine optimal tracking weights of each degree of freedom of a musculoskeletal model in order to reduce differences between the experimental and model marker data as well as residual forces and moments. In this study, the particle swarm optimization (PSO) and simplex simulated annealing (SIMPSA) algorithms were used to determine optimal tracking weights for the simulation of a sidestep cut. The PSO and SIMPSA algorithms were able to produce model kinematics that were within 1.4° of experimental kinematics with residual forces and moments of less than 10 N and 18 Nm, respectively. The PSO algorithm was able to replicate the experimental kinematic data more closely and produce more dynamically consistent kinematic data for a sidestep cut compared to the SIMPSA algorithm. Future studies should use external optimization routines to determine dynamically consistent kinematic data and report the differences between experimental and model data for these musculoskeletal simulations.
NASA Astrophysics Data System (ADS)
Lin, K.-M.; Hu, M.-H.; Hung, C.-T.; Wu, J.-S.; Hwang, F.-N.; Chen, Y.-S.; Cheng, G.
2012-12-01
Development of a hybrid numerical algorithm which couples weakly with the gas flow model (GFM) and the plasma fluid model (PFM) for simulating an atmospheric-pressure plasma jet (APPJ) and its acceleration by two approaches is presented. The weak coupling between gas flow and discharge is introduced by transferring between the results obtained from the steady-state solution of the GFM and cycle-averaged solution of the PFM respectively. Approaches of reducing the overall runtime include parallel computing of the GFM and the PFM solvers, and employing a temporal multi-scale method (TMSM) for PFM. Parallel computing of both solvers is realized using the domain decomposition method with the message passing interface (MPI) on distributed-memory machines. The TMSM considers only chemical reactions by ignoring the transport terms when integrating temporally the continuity equations of heavy species at each time step, and then the transport terms are restored only at an interval of time marching steps. The total reduction of runtime is 47% by applying the TMSM to the APPJ example presented in this study. Application of the proposed hybrid algorithm is demonstrated by simulating a parallel-plate helium APPJ impinging onto a substrate, which the cycle-averaged properties of the 200th cycle are presented. The distribution patterns of species densities are strongly correlated by the background gas flow pattern, which shows that consideration of gas flow in APPJ simulations is critical.
Comparative Study of Algorithms for the Numerical Simulation of Lattice QCD
Luz, Fernando H. P.; Mendes, Tereza
2010-11-12
Large-scale numerical simulations are the prime method for a nonperturbative study of QCD from first principles. Although the lattice simulation of the pure-gauge (or quenched-QCD) case may be performed very efficiently on parallel machines, there are several additional difficulties in the simulation of the full-QCD case, i.e. when dynamical quark effects are taken into account. We discuss the main aspects of full-QCD simulations, describing the most common algorithms. We present a comparative analysis of performance for two versions of the hybrid Monte Carlo method (the so-called R and RHMC algorithms), as provided in the MILC software package. We consider two degenerate flavors of light quarks in the staggered formulation, having in mind the case of finite-temperature QCD.
A semi-numerical algorithm for instability of compressible multilayered structures
NASA Astrophysics Data System (ADS)
Tang, Shan; Yang, Yang; Peng, Xiang He; Liu, Wing Kam; Huang, Xiao Xu; Elkhodary, Khalil
2015-07-01
A computational method is proposed for the analysis and prediction of instability (wrinkling or necking) of multilayered compressible plates and sheets made by metals or polymers under plane strain conditions. In previous works, a basic assumption (or a physical argument) that has been frequently made is that materials are incompressible to simplify mathematical derivations. To account for the compressibility of metals and polymers (the lower Poisson's ratio leads to the more compressible material), we propose a combined semi-numerical algorithm and finite element method for instability analysis. Our proposed algorithm is herein verified by comparing its predictions with published results in literature for thin films with polymer/metal substrates and for polymer/metal systems. The new combined method is then used to predict the effects of compressibility on instability behaviors. Results suggest potential utility for compressibility in the design of multilayered structures.
Bu Sunyoung Huang Jingfang Boyer, Treavor H. Miller, Cass T.
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H; Miller, Cass T
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-01-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications. PMID:20577570
New Concepts in Breast Cancer Emerge from Analyzing Clinical Data Using Numerical Algorithms
Retsky, Michael
2009-01-01
A small international group has recently challenged fundamental concepts in breast cancer. As a guiding principle in therapy, it has long been assumed that breast cancer growth is continuous. However, this group suggests tumor growth commonly includes extended periods of quasi-stable dormancy. Furthermore, surgery to remove the primary tumor often awakens distant dormant micrometastases. Accordingly, over half of all relapses in breast cancer are accelerated in this manner. This paper describes how a numerical algorithm was used to come to these conclusions. Based on these findings, a dormancy preservation therapy is proposed. PMID:19440287
NASA Technical Reports Server (NTRS)
Whyte, W. A.; Heyward, A. O.; Ponchak, D. S.; Spence, R. L.; Zuzek, J. E.
1988-01-01
A detailed description of a Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software package for communication satellite systems planning is presented. This software provides a method of generating predetermined arc segments for use in the development of an allotment planning procedure to be carried out at the 1988 World Administrative Radio Conference (WARC - 88) on the use of the GEO and the planning of space services utilizing GEO. The features of the NASARC software package are described, and detailed information is given about the function of each of the four NASARC program modules. The results of a sample world scenario are presented and discussed.
NASA Technical Reports Server (NTRS)
Gatski, T. B.; Grosch, C. E.; Rose, M. E.; Spall, R. E.
1987-01-01
A numerical algorithm is presented which is used to solve the unsteady, fully three-dimensional, incompressible Navier-Stokes equations in vorticity-velocity variables. A discussion of the discrete approximation scheme is presented as well as the solution method used to solve the resulting algebraic set of difference equations. Second order spatial and temporal accuracy is verified through solution comparisons with exact results obtained for steady three-dimensional stagnation point flow and unsteady axisymmetric vortex spin-up. In addition, results are presented for the problem of unsteady bubble-type vortex breakdown with emphasis on internal bubble dynamics and structure.
NASA Astrophysics Data System (ADS)
Zemlyanaya, E. V.; Bashashin, M. V.; Rahmonov, I. R.; Shukrinov, Yu. M.; Atanasova, P. Kh.; Volokhova, A. V.
2016-10-01
We consider a model of system of long Josephson junctions (LJJ) with inductive and capacitive coupling. Corresponding system of nonlinear partial differential equations is solved by means of the standard three-point finite-difference approximation in the spatial coordinate and utilizing the Runge-Kutta method for solution of the resulting Cauchy problem. A parallel algorithm is developed and implemented on a basis of the MPI (Message Passing Interface) technology. Effect of the coupling between the JJs on the properties of LJJ system is demonstrated. Numerical results are discussed from the viewpoint of effectiveness of parallel implementation.
Recent examples of mesoscale numerical forecasts of severe weather events along the east coast
NASA Technical Reports Server (NTRS)
Kocin, P. J.; Uccellini, L. W.; Zack, J. W.; Kaplan, M. L.
1984-01-01
Mesoscale numerical forecasts utilizing the Mesoscale Atmospheric Simulation System (MASS) are documented for two East Coast severe weather events. The two events are the thunderstorm and heavy snow bursts in the Washington, D.C. - Baltimore, MD region on 8 March 1984 and the devastating tornado outbreak across North and South Carolina on 28 March 1984. The forecasts are presented to demonstrate the ability of the model to simulate dynamical interactions and diabatic processes and to note some of the problems encountered when using mesoscale models for day-to-day forecasting.
NASA Technical Reports Server (NTRS)
Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.
1990-01-01
Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.
A Numerical Algorithm for Complex Biological Flow in Irregular Microdevice Geometries
Nonaka, A; Miller, G H; Marshall, T; Liepmann, D; Gulati, S; Trebotich, D; Colella, P
2003-12-15
We present a numerical algorithm to simulate non-Newtonian flow in complex microdevice components. The model consists of continuum viscoelastic incompressible flow in irregular microscale geometries. Our numerical approach is the projection method of Bell, Colella and Glaz (BCG) to impose the incompressibility constraint coupled with the polymeric stress splitting discretization of Trebotich, Colella and Miller (TCM). In this approach we exploit the hyperbolic structure of the equations of motion to achieve higher resolution in the presence of strong gradients and to gain an order of magnitude in the timestep. We also extend BCG and TCM to an embedded boundary method to treat irregular domain geometries which exist in microdevices. Our method allows for particle representation in a continuum fluid. We present preliminary results for incompressible viscous flow with comparison to flow of DNA and simulants in microchannels and other components used in chem/bio microdevices.
González, J M; Whitman, W B; Hodson, R E; Moran, M A
1996-01-01
Culturable bacteria that were numerically important members of a marine enrichment community were identified and characterized phylogenetically. Selective and nonselective isolation methods were used to obtain 133 culturable bacterial isolates from model marine communities enriched with the high-molecular-weight (lignin-rich) fraction of pulp mill effluent. The culture collection was screened against community DNA from the lignin enrichments by whole-genome hybridization methods, and three marine bacterial isolates were identified as being numerically important in the communities. One isolate was in the alpha-subclass of Proteobacteria, and the other two were in the gamma-subclass of Proteobacteria. Isolate-specific 16S rRNA oligonucleotide probes designed to precisely quantify the isolates in the lignin enrichment communities indicated contributions ranging from 2 to 32% of enrichment DNA, values nearly identical to those originally obtained by the simpler whole-genome hybridization method. Two 16S rRNA sequences closely related to that of one of the isolates, although not identical, were amplified via PCR from the seawater sample originally used to inoculate the enrichment medium. Partial sequences of 14 other isolates revealed significant phylogenetic diversity and unusual sequences among the culturable lignin enrichment bacteria, with the Proteobacteria, Cytophaga-Flavobacterium, and gram-positive groups represented. PMID:8953714
Cloud classification from satellite data using a fuzzy sets algorithm: A polar example
NASA Technical Reports Server (NTRS)
Key, J. R.; Maslanik, J. A.; Barry, R. G.
1988-01-01
Where spatial boundaries between phenomena are diffuse, classification methods which construct mutually exclusive clusters seem inappropriate. The Fuzzy c-means (FCM) algorithm assigns each observation to all clusters, with membership values as a function of distance to the cluster center. The FCM algorithm is applied to AVHRR data for the purpose of classifying polar clouds and surfaces. Careful analysis of the fuzzy sets can provide information on which spectral channels are best suited to the classification of particular features, and can help determine likely areas of misclassification. General agreement in the resulting classes and cloud fraction was found between the FCM algorithm, a manual classification, and an unsupervised maximum likelihood classifier.
Cloud classification from satellite data using a fuzzy sets algorithm - A polar example
NASA Technical Reports Server (NTRS)
Key, J. R.; Maslanik, J. A.; Barry, R. G.
1989-01-01
Where spatial boundaries between phenomena are diffuse, classification methods which construct mutually exclusive clusters seem inappropriate. The Fuzzy c-means (FCM) algorithm assigns each observation to all clusters, with membership values as a function of distance to the cluster center. The FCM algorithm is applied to AVHRR data for the purpose of classifying polar clouds and surfaces. Careful analysis of the fuzzy sets can provide information on which spectral channels are best suited to the classification of particular features, and can help determine like areas of misclassification. General agreement in the resulting classes and cloud fraction was found between the FCM algorithm, a manual classification, and an unsupervised maximum likelihood classifier.
NASA Astrophysics Data System (ADS)
García, Hermes A.; Guerrero-Bolaño, Francisco J.; Obregón-Neira, Nelson
2010-05-01
Due to both mathematical tractability and efficiency on computational resources, it is very common to find in the realm of numerical modeling in hydro-engineering that regular linearization techniques have been applied to nonlinear partial differential equations properly obtained in environmental flow studies. Sometimes this simplification is also made along with omission of nonlinear terms involved in such equations which in turn diminishes the performance of any implemented approach. This is the case for example, for contaminant transport modeling in streams. Nowadays, a traditional and one of the most common used water quality model such as QUAL2k, preserves its original algorithm, which omits nonlinear terms through linearization techniques, in spite of the continuous algorithmic development and computer power enhancement. For that reason, the main objective of this research was to generate a flexible tool for non-linear water quality modeling. The solution implemented here was based on two genetic algorithms, used in a nested way in order to find two different types of solutions sets: the first set is composed by the concentrations of the physical-chemical variables used in the modeling approach (16 variables), which satisfies the non-linear equation system. The second set, is the typical solution of the inverse problem, the parameters and constants values for the model when it is applied to a particular stream. From a total of sixteen (16) variables, thirteen (13) was modeled by using non-linear coupled equation systems and three (3) was modeled in an independent way. The model used here had a requirement of fifty (50) parameters. The nested genetic algorithm used for the numerical solution of a non-linear equation system proved to serve as a flexible tool to handle with the intrinsic non-linearity that emerges from the interactions occurring between multiple variables involved in water quality studies. However because there is a strong data limitation in
NASA Astrophysics Data System (ADS)
Rajashekararadhya, S. V.; Ranjan, P. Vanaja
India is a multi-lingual multi script country, where eighteen official scripts are accepted and have over hundred regional languages. In this paper we propose a zone based hybrid feature extraction algorithm scheme towards the recognition of off-line handwritten numerals of south Indian scripts. The character centroid is computed and the image (character/numeral) is further divided in to n equal zones. Average distance and Average angle from the character centroid to the pixels present in the zone are computed (two features). Similarly zone centroid is computed (two features). This procedure is repeated sequentially for all the zones/grids/boxes present in the numeral image. There could be some zones that are empty, and then the value of that particular zone image value in the feature vector is zero. Finally 4*n such features are extracted. Nearest neighbor classifier is used for subsequent classification and recognition purpose. We obtained 97.55 %, 94 %, 92.5% and 95.2 % recognition rate for Kannada, Telugu, Tamil and Malayalam numerals respectively.
Path dependence of J in three numerical examples. [J integral in three crack propagation problems
NASA Technical Reports Server (NTRS)
Karabin, M. E., Jr.; Swedlow, J. L.
1979-01-01
Three cracked geometries are studied with the aid of a new finite element model. The procedure employs a variable singularity at the crack tip that tracks changes in the material response during the loading process. Two of the problems are tension-loaded center-crack panels and the other is a three-point bend specimen. Results usually agree with other numerical and analytical analyses, except the finding that J is path dependent as a substantial plastic zone develops. Credible J values are obtained near the crack tip and J shows a significant increase as the radius of J path increases over two orders of magnitude. Incremental and deformation theories are identical provided the stresses exhibit proportionality found in the far field stresses but not near the tip.
Ghose, K.B.; Adamowicz, L.
1995-12-01
The present work represents the first attempt to utilize the idea of recursively generated intermediates (RGI) in the framework of the state-selective multi-reference coupled-cluster method truncated at triple excitations [SS CCSD(T)]. The expressions for stepwise generation of intermediates are so structured that the spin and point symmetry simplifications can be easily applied during computation. Suitable modifications in SS CCSD(T) equations are introduced to allow for optional quasilinearization of nonlinear terms in difficult convergence situations. The computational code is, as expected, much faster than the SS CCSD(T) code without RGI adaptation. This has been numerically demonstrated by potential energy surface (PES) calculation of the HF molecule using a double zeta basis. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
NASA Astrophysics Data System (ADS)
Cioni, Raffaello; Longo, Antonella; Macedonio, Giovanni; Santacroce, Roberto; Sbrana, Alessandro; Sulpizio, Roberto; Andronico, Daniele
2003-02-01
A general methodology of pyroclastic fall hazard assessment is proposed on the basis of integrated results of field studies and numerical simulations. These approaches result in two different methods of assessing hazard: (1) the "field frequency," based on the thickness and distribution of past deposits and (2) the "simulated probability," based on the numerical modeling of tephra transport and fallout. The proposed methodology mostly applies to volcanoes that, by showing a clear correlation between the repose time and the magnitude of the following eruptions, allows the definition of a reference "maximum expected event" (MEE). The application to Vesuvius is shown in detail. Using the field frequency method, stratigraphic data of 24 explosive events in the 3-6 volcanic explosivity index range in the last 18,000 years of activity are extrapolated to a regular grid in order to obtain the frequency of exceedance in the past of a certain threshold value of mass loading (100, 200, 300, and 400 kg/m2). Using the simulated probability method, the mass loading related to the MEE is calculated based on the expected erupted mass (5 × 1011 kg), the wind velocity profiles recorded during 14 years, and various column heights and grain-size populations. The role of these factors was parametrically studied performing ˜160,000 simulations, and the probability that mass loading exceeded the chosen threshold at each node was evaluated. As a general rule, the field frequency method results are more reliable in proximal regions, provided that an accurate database of field measurements is available. On the other hand, the simulated probability method better describes events in middle distal areas, provided that the MEE magnitude can be reliably assumed. In the Vesuvius case, the integration of the two methods results in a new fallout hazard map, here presented for a mass loading value of 200 kg/m2.
Belič, Aleš; Pompon, Denis; Monostory, Katalin; Kelly, Diane; Kelly, Steven; Rozman, Damjana
2013-06-01
Alternative pathways of metabolic networks represent the escape routes that can reduce drug efficacy and can cause severe adverse effects. In this paper we introduce a mathematical algorithm and a coding system for rapid computational construction of metabolic networks. The initial data for the algorithm are the source substrate code and the enzyme/metabolite interaction tables. The major strength of the algorithm is the adaptive coding system of the enzyme-substrate interactions. A reverse application of the algorithm is also possible, when optimisation algorithm is used to compute the enzyme/metabolite rules from the reference network structure. The coding system is user-defined and must be adapted to the studied problem. The algorithm is most effective for computation of networks that consist of metabolites with similar molecular structures. The computation of the cholesterol biosynthesis metabolic network suggests that 89 intermediates can theoretically be formed between lanosterol and cholesterol, only 20 are presently considered as cholesterol intermediates. Alternative metabolites may represent links with other metabolic networks both as precursors and metabolites of cholesterol. A possible cholesterol-by-pass pathway to bile acids metabolism through cholestanol is suggested.
A numerical algorithm with preference statements to evaluate the performance of scientists.
Ricker, Martin
Academic evaluation committees have been increasingly receptive for using the number of published indexed articles, as well as citations, to evaluate the performance of scientists. It is, however, impossible to develop a stand-alone, objective numerical algorithm for the evaluation of academic activities, because any evaluation necessarily includes subjective preference statements. In a market, the market prices represent preference statements, but scientists work largely in a non-market context. I propose a numerical algorithm that serves to determine the distribution of reward money in Mexico's evaluation system, which uses relative prices of scientific goods and services as input. The relative prices would be determined by an evaluation committee. In this way, large evaluation systems (like Mexico's Sistema Nacional de Investigadores) could work semi-automatically, but not arbitrarily or superficially, to determine quantitatively the academic performance of scientists every few years. Data of 73 scientists from the Biology Institute of Mexico's National University are analyzed, and it is shown that the reward assignation and academic priorities depend heavily on those preferences. A maximum number of products or activities to be evaluated is recommended, to encourage quality over quantity.
Source-structure trade-offs in ambient noise correlations: Theory and numerical examples
NASA Astrophysics Data System (ADS)
Fichtner, A.; Sager, K.; Ermert, L. A.
2015-12-01
We analyse the physics and geometry of trade-offs between Earth structure and noise sources in inter-station noise correlations. Our approach is based on the computation of off-diagonal Hessian elements that describe the extent to which variations in noise sources can compensate for variations in Earth structure without changing the misfit beyond the measurement uncertainty. Despite the fact that all ambient noise inverse problems are special in terms of their receiver configuration and data, some general statements concerning source-structure trade-offs can be made: (i) While source-structure trade-offs may be reduced to some extent by clever measurement design, there are inherent trade-offs that can generally not be avoided. These inherent trade-offs may lead to a mispositioning of structural heterogeneities when the noise source distribution is unknown. (ii) When attenuation is weak, source-structure trade-offs in ambient noise correlations are a global phenomenon, meaning that there is no noise source perturbation that does not trade-off with some Earth structure, and vice versa. (iii) The most significant source-structure trade-offs occur within two elliptically shaped regions connecting a potential noise source perturbation to each one of the receivers. (iv) Far from these elliptical regions, only small-scale structure can trade off against changes in the noise source. (v) While source-structure trade-offs mostly decay with increasing attenuation, they are nearly unaffected by attenuation when the noise source perturbation is located near the receiver-receiver line. We complement these theoretical considerations by numerical experiments where we model ambient noise correlations for arbitrary source geometries. The experiments illustrate how and to which extent unknown noise sources may map into spurious Earth structure. This work is intended to contribute to the development of joint source-structure inversions of ambient noise correlations, and in particular
Transient dynamics of terrestrial carbon storage: Mathematical foundation and numeric examples
Luo, Yiqi; Shi, Zheng; Lu, Xingjie; ...
2016-09-16
Terrestrial ecosystems absorb roughly 30% of anthropogenic CO2 emissions since preindustrial era, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling, experimental, and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under climate change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP)more » and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Furthermore, this and our other studies have demonstrated that one matrix equation can exactly replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. Moreover, the emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C
Transient dynamics of terrestrial carbon storage: Mathematical foundation and numeric examples
Luo, Yiqi; Shi, Zheng; Lu, Xingjie; Xia, Jianyang; Liang, Junyi; Wang, Ying; Smith, Matthew J.; Jiang, Lifen; Ahlstrom, Anders; Chen, Benito; Hararuk, Oleksandra; Hastings, Alan; Hoffman, Forrest; Medlyn, Belinda; Niu, Shuli; Rasmussen, Martin; Todd-Brown, Katherine; Wang, Ying -Ping
2016-09-16
Terrestrial ecosystems absorb roughly 30% of anthropogenic CO_{2} emissions since preindustrial era, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling, experimental, and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under climate change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times.
Furthermore, this and our other studies have demonstrated that one matrix equation can exactly replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. Moreover, the emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of
Numerical linked-cluster algorithms. I. Spin systems on square, triangular, and kagomé lattices.
Rigol, Marcos; Bryant, Tyler; Singh, Rajiv R P
2007-06-01
We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We present studies of thermodynamic observables for spin models on square, triangular, and kagomé lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLCs, are presented. We also include a comparison of NLC results with those obtained from exact analytical expressions (where available), high-temperature expansions (HTE), exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo simulations. For many models and properties NLC results are substantially more accurate than HTE and ED.
A numerical algorithm for optimal feedback gains in high dimensional LQR problems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Ito, K.
1986-01-01
A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.
NASA Technical Reports Server (NTRS)
Russell, William S.; Roberts, William W., Jr.
1993-01-01
An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.
NASA Astrophysics Data System (ADS)
Li, Yiming
2007-12-01
This symposium is an open forum for discussion on the current trends and future directions of physical modeling, mathematical theory, and numerical algorithm in electrical and electronic engineering. The goal is for computational scientists and engineers, computer scientists, applied mathematicians, physicists, and researchers to present their recent advances and exchange experience. We welcome contributions from researchers of academia and industry. All papers to be presented in this symposium have carefully been reviewed and selected. They include semiconductor devices, circuit theory, statistical signal processing, design optimization, network design, intelligent transportation system, and wireless communication. Welcome to this interdisciplinary symposium in International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2007). Look forward to seeing you in Corfu, Greece!
A new free-surface stabilization algorithm for geodynamical modelling: Theory and numerical tests
NASA Astrophysics Data System (ADS)
Andrés-Martínez, Miguel; Morgan, Jason P.; Pérez-Gussinyé, Marta; Rüpke, Lars
2015-09-01
The surface of the solid Earth is effectively stress free in its subaerial portions, and hydrostatic beneath the oceans. Unfortunately, this type of boundary condition is difficult to treat computationally, and for computational convenience, numerical models have often used simpler approximations that do not involve a normal stress-loaded, shear-stress free top surface that is free to move. Viscous flow models with a computational free surface typically confront stability problems when the time step is bigger than the viscous relaxation time. The small time step required for stability (< 2 Kyr) makes this type of model computationally intensive, so there remains a need to develop strategies that mitigate the stability problem by making larger (at least ∼10 Kyr) time steps stable and accurate. Here we present a new free-surface stabilization algorithm for finite element codes which solves the stability problem by adding to the Stokes formulation an intrinsic penalization term equivalent to a portion of the future load at the surface nodes. Our algorithm is straightforward to implement and can be used with both Eulerian or Lagrangian grids. It includes α and β parameters to respectively control both the vertical and the horizontal slope-dependent penalization terms, and uses Uzawa-like iterations to solve the resulting system at a cost comparable to a non-stress free surface formulation. Four tests were carried out in order to study the accuracy and the stability of the algorithm: (1) a decaying first-order sinusoidal topography test, (2) a decaying high-order sinusoidal topography test, (3) a Rayleigh-Taylor instability test, and (4) a steep-slope test. For these tests, we investigate which α and β parameters give the best results in terms of both accuracy and stability. We also compare the accuracy and the stability of our algorithm with a similar implicit approach recently developed by Kaus et al. (2010). We find that our algorithm is slightly more accurate
Dong, S.
2015-02-15
We present a family of physical formulations, and a numerical algorithm, based on a class of general order parameters for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids with given densities, dynamic viscosities, and pairwise surface tensions. The N-phase formulations stem from a phase field model we developed in a recent work based on the conservations of mass/momentum, and the second law of thermodynamics. The introduction of general order parameters leads to an extremely strongly-coupled system of (N−1) phase field equations. On the other hand, the general form enables one to compute the N-phase mixing energy density coefficients in an explicit fashion in terms of the pairwise surface tensions. We show that the increased complexity in the form of the phase field equations associated with general order parameters in actuality does not cause essential computational difficulties. Our numerical algorithm reformulates the (N−1) strongly-coupled phase field equations for general order parameters into 2(N−1) Helmholtz-type equations that are completely de-coupled from one another. This leads to a computational complexity comparable to that for the simplified phase field equations associated with certain special choice of the order parameters. We demonstrate the capabilities of the method developed herein using several test problems involving multiple fluid phases and large contrasts in densities and viscosities among the multitude of fluids. In particular, by comparing simulation results with the Langmuir–de Gennes theory of floating liquid lenses we show that the method using general order parameters produces physically accurate results for multiple fluid phases.
NASA Astrophysics Data System (ADS)
Chernyavskiy, Andrey; Khamitov, Kamil; Teplov, Alexey; Voevodin, Vadim; Voevodin, Vladimir
2016-10-01
In recent years, quantum information technologies (QIT) showed great development, although, the way of the implementation of QIT faces the serious difficulties, some of which are challenging computational tasks. This work is devoted to the deep and broad analysis of the parallel algorithmic properties of such tasks. As an example we take one- and two-qubit transformations of a many-qubit quantum state, which are the most critical kernels of many important QIT applications. The analysis of the algorithms uses the methodology of the AlgoWiki project (algowiki-project.org) and consists of two parts: theoretical and experimental. Theoretical part includes features like sequential and parallel complexity, macro structure, and visual information graph. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia) and includes the analysis of locality and memory access, scalability and the set of more specific dynamic characteristics of realization. This approach allowed us to obtain bottlenecks and generate ideas of efficiency improvement.
Numerical Arc Segmentation Algorithm for a Radio Conference-NASARC, Version 2.0: User's Manual
NASA Technical Reports Server (NTRS)
Whyte, Wayne A., Jr.; Heyward, Ann O.; Ponchak, Denise S.; Spence, Rodney L.; Zuzek, John E.
1987-01-01
The information contained in the NASARC (Version 2.0) Technical Manual (NASA TM-100160) and the NASARC (Version 2.0) User's Manual (NASA TM-100161) relates to the state of the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through October 16, 1987. The technical manual describes the NASARC concept and the algorithms which are used to implement it. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions have been incorporated in the Version 2.0 software over prior versions. These revisions have enhanced the modeling capabilities of the NASARC procedure while greatly reducing the computer run time and memory requirements. Array dimensions within the software have been structured to fit into the currently available 6-megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 2.0) allows worldwide scenarios to be accommodated within these memory constraints while at the same time reducing computer run time.
Numerical arc segmentation algorithm for a radio conference-NASARC (version 2.0) technical manual
NASA Technical Reports Server (NTRS)
Whyte, Wayne A., Jr.; Heyward, Ann O.; Ponchak, Denise S.; Spence, Rodney L.; Zuzek, John E.
1987-01-01
The information contained in the NASARC (Version 2.0) Technical Manual (NASA TM-100160) and NASARC (Version 2.0) User's Manual (NASA TM-100161) relates to the state of NASARC software development through October 16, 1987. The Technical Manual describes the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operating instructions. Significant revisions have been incorporated in the Version 2.0 software. These revisions have enhanced the modeling capabilities of the NASARC procedure while greatly reducing the computer run time and memory requirements. Array dimensions within the software have been structured to fit within the currently available 6-megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 2.0) allows worldwide scenarios to be accommodated within these memory constraints while at the same time effecting an overall reduction in computer run time.
Numerical Arc Segmentation Algorithm for a Radio Conference-NASARC (version 4.0) technical manual
NASA Technical Reports Server (NTRS)
Whyte, Wayne A., Jr.; Heyward, Ann O.; Ponchak, Denise S.; Spence, Rodney L.; Zuzek, John E.
1988-01-01
The information contained in the NASARC (Version 4.0) Technical Manual and NASARC (Version 4.0) User's Manual relates to the Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through November 1, 1988. The Technical Manual describes the NASARC concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions were incorporated in the Version 4.0 software over prior versions. These revisions have further enhanced the modeling capabilities of the NASARC procedure and provide improved arrangements of predetermined arcs within the geostationary orbits. Array dimensions within the software were structured to fit within the currently available 12 megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 4.0) allows worldwide planning problem scenarios to be accommodated within computer run time and memory constraints with enhanced likelihood and ease of solution.
Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC), version 4.0: User's manual
NASA Technical Reports Server (NTRS)
Whyte, Wayne A., Jr.; Heyward, Ann O.; Ponchak, Denise S.; Spence, Rodney L.; Zuzek, John E.
1988-01-01
The information in the NASARC (Version 4.0) Technical Manual (NASA-TM-101453) and NASARC (Version 4.0) User's Manual (NASA-TM-101454) relates to the state of Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) software development through November 1, 1988. The Technical Manual describes the NASARC concept and the algorithms used to implement the concept. The User's Manual provides information on computer system considerations, installation instructions, description of input files, and program operation instructions. Significant revisions were incorporated in the Version 4.0 software over prior versions. These revisions have further enhanced the modeling capabilities of the NASARC procedure and provide improved arrangements of predetermined arcs within the geostationary orbit. Array dimensions within the software were structured to fit within the currently available 12-megabyte memory capacity of the International Frequency Registration Board (IFRB) computer facility. A piecewise approach to predetermined arc generation in NASARC (Version 4.) allows worldwide planning problem scenarios to be accommodated within computer run time and memory constraints with enhanced likelihood and ease of solution.
2014-01-01
Quantitative imaging biomarkers (QIBs) are being used increasingly in medicine to diagnose and monitor patients’ disease. The computer algorithms that measure QIBs have different technical performance characteristics. In this paper we illustrate the appropriate statistical methods for assessing and comparing the bias, precision, and agreement of computer algorithms. We use data from three studies of pulmonary nodules. The first study is a small phantom study used to illustrate metrics for assessing repeatability. The second study is a large phantom study allowing assessment of four algorithms’ bias and reproducibility for measuring tumor volume and the change in tumor volume. The third study is a small clinical study of patients whose tumors were measured on two occasions. This study allows a direct assessment of six algorithms’ performance for measuring tumor change. With these three examples we compare and contrast study designs and performance metrics, and we illustrate the advantages and limitations of various common statistical methods for QIB studies. PMID:24919828
An Implicit Algorithm for the Numerical Simulation of Shape-Memory Alloys
Becker, R; Stolken, J; Jannetti, C; Bassani, J
2003-10-16
Shape-memory alloys (SMA) have the potential to be used in a variety of interesting applications due to their unique properties of pseudoelasticity and the shape-memory effect. However, in order to design SMA devices efficiently, a physics-based constitutive model is required to accurately simulate the behavior of shape-memory alloys. The scope of this work is to extend the numerical capabilities of the SMA constitutive model developed by Jannetti et. al. (2003), to handle large-scale polycrystalline simulations. The constitutive model is implemented within the finite-element software ABAQUS/Standard using a user defined material subroutine, or UMAT. To improve the efficiency of the numerical simulations, so that polycrystalline specimens of shape-memory alloys can be modeled, a fully implicit algorithm has been implemented to integrate the constitutive equations. Using an implicit integration scheme increases the efficiency of the UMAT over the previously implemented explicit integration method by a factor of more than 100 for single crystal simulations.
Anor, Tomer; Madsen, Joseph R; Dupont, Pierre
2011-05-09
We propose a novel systematic approach to optimizing the design of concentric tube robots for neurosurgical procedures. These procedures require that the robot approach specified target sites while navigating and operating within an anatomically constrained work space. The availability of preoperative imaging makes our approach particularly suited for neurosurgery, and we illustrate the method with the example of endoscopic choroid plexus ablation. A novel parameterization of the robot characteristics is used in conjunction with a global pattern search optimization method. The formulation returns the design of the least-complex robot capable of reaching single or multiple target points in a confined space with constrained optimization metrics. A particular advantage of this approach is that it identifies the need for either fixed-curvature versus variable-curvature sections. We demonstrate the performance of the method in four clinically relevant examples.
NASA Astrophysics Data System (ADS)
Kitaura, F. S.; Enßlin, T. A.
2008-09-01
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior, data likelihood and numerical inverse extraregularization schemes are derived and classified. The Bayesian methodology presented in this paper tries to unify and extend the following methods: Wiener filtering, Tikhonov regularization, ridge regression, maximum entropy and inverse regularization techniques. The inverse techniques considered here are the asymptotic regularization, the Jacobi, Steepest Descent, Newton-Raphson, Landweber-Fridman and both linear and non-linear Krylov methods based on Fletcher-Reeves, Polak-Ribière and Hestenes-Stiefel conjugate gradients. The structures of the up-to-date highest performing algorithms are presented, based on an operator scheme, which permits one to exploit the power of fast Fourier transforms. Using such an implementation of the generalized Wiener filter in the novel ARGO software package, the different numerical schemes are benchmarked with one-, two- and three-dimensional problems including structured white and Poissonian noise, data windowing and blurring effects. A novel numerical Krylov scheme is shown to be superior in terms of performance and fidelity. These fast inverse methods ultimately will enable the application of sampling techniques to explore complex joint posterior distributions. We outline how the space of the dark matter density field, the peculiar velocity field and the power spectrum can jointly be investigated by a Gibbs-sampling process. Such a method can be applied for the redshift distortions correction of the observed galaxies and for time-reversal reconstructions of the initial density field.
NASA Astrophysics Data System (ADS)
Alahyane, M.; Hakim, A.; Raghay, S.
2017-01-01
In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large category of problems this could be understood from its stability and convergence, which depends strongly on the parameter of relaxation, in some cases this algorithm could have an unexpected behavior. Therefore, in our work we focus on this particular point to overcome this respected choice of relaxation parameter and to find a sufficient condition for the convergence of the algorithm in general cases. This will be followed by numerical applications in image processing variety of fluid flow problems described by incompressible Navier-Stokes equations.
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Lomax, Harvard
1987-01-01
The past decade has seen considerable activity in algorithm development for the Navier-Stokes equations. This has resulted in a wide variety of useful new techniques. Some examples for the numerical solution of the Navier-Stokes equations are presented, divided into two parts. One is devoted to the incompressible Navier-Stokes equations, and the other to the compressible form.
From bicycle chain ring shape to gear ratio: algorithm and examples.
van Soest, A J
2014-01-03
A simple model of the bicycle drive system with a non-circular front chain ring is proposed and an algorithm is devised for calculation of the corresponding Gear Ratio As a Function Of Crank Angle (GRAFOCA). It is shown that the true effective radius of the chain ring is always the perpendicular distance between the crank axis and the line through the chain segment between the chain ring and the cog. It is illustrated that the true effective radius of the chain ring at any crank angle may differ substantially from the maximum vertical distance between the crank axis and the chain ring circumference that is used as a proxy for the effective chain ring radius in several studies; in particular, the crank angle at which the effective chain ring radius is maximal as predicted from the latter approach may deviate by as much as 0.30 rad from the true value. The algorithm proposed may help in designing chain rings that achieve the desired GRAFOCA.
NASA Technical Reports Server (NTRS)
Platnick, Steven; Wind, Galina; Zhang, Zhibo; Ackerman, Steven A.; Maddux, Brent
2012-01-01
The optical and microphysical structure of warm boundary layer marine clouds is of fundamental importance for understanding a variety of cloud radiation and precipitation processes. With the advent of MODIS (Moderate Resolution Imaging Spectroradiometer) on the NASA EOS Terra and Aqua platforms, simultaneous global/daily 1km retrievals of cloud optical thickness and effective particle size are provided, as well as the derived water path. In addition, the cloud product (MOD06/MYD06 for MODIS Terra and Aqua, respectively) provides separate effective radii results using the l.6, 2.1, and 3.7 m spectral channels. Cloud retrieval statistics are highly sensitive to how a pixel identified as being "notclear" by a cloud mask (e.g., the MOD35/MYD35 product) is determined to be useful for an optical retrieval based on a 1-D cloud model. The Collection 5 MODIS retrieval algorithm removed pixels associated with cloud'edges as well as ocean pixels with partly cloudy elements in the 250m MODIS cloud mask - part of the so-called Clear Sky Restoral (CSR) algorithm. Collection 6 attempts retrievals for those two pixel populations, but allows a user to isolate or filter out the populations via CSR pixel-level Quality Assessment (QA) assignments. In this paper, using the preliminary Collection 6 MOD06 product, we present global and regional statistical results of marine warm cloud retrieval sensitivities to the cloud edge and 250m partly cloudy pixel populations. As expected, retrievals for these pixels are generally consistent with a breakdown of the ID cloud model. While optical thickness for these suspect pixel populations may have some utility for radiative studies, the retrievals should be used with extreme caution for process and microphysical studies.
NASA Astrophysics Data System (ADS)
Harmon, Michael; Gamba, Irene M.; Ren, Kui
2016-12-01
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.
Algorithm for direct numerical simulation of emulsion flow through a granular material
NASA Astrophysics Data System (ADS)
Zinchenko, Alexander Z.; Davis, Robert H.
2008-08-01
A multipole-accelerated 3D boundary-integral algorithm capable of modelling an emulsion flow through a granular material by direct multiparticle-multidrop simulations in a periodic box is developed and tested. The particles form a random arrangement at high volume fraction rigidly held in space (including the case of an equilibrium packing in mechanical contact). Deformable drops (with non-deformed diameter comparable with the particle size) squeeze between the particles under a specified average pressure gradient. The algorithm includes recent boundary-integral desingularization tools especially important for drop-solid and drop-drop interactions, the Hebeker representation for solid particle contributions, and unstructured surface triangulations with fixed topology. Multipole acceleration, with two levels of mesh node decomposition (entire drop/solid surfaces and "patches"), is a significant improvement over schemes used in previous, purely multidrop simulations; it remains efficient at very high resolutions ( 104- 105 triangular elements per surface) and has no lower limitation on the number of particles or drops. Such resolutions are necessary in the problem to alleviate lubrication difficulties, especially for near-critical squeezing conditions, as well as using ˜104 time steps and an iterative solution at each step, both for contrast and matching viscosities. Examples are shown for squeezing of 25-40 drops through an array of 9-14 solids, with the total volume fraction of 70% for particles and drops. The flow rates for the drop and continuous phases are calculated. Extensive convergence testing with respect to program parameters (triangulation, multipole truncation, etc.) is made.
NASA Astrophysics Data System (ADS)
Jackson, T. J.; Le Vine, David E.
1996-10-01
Microwave remote sensing at L-band (21 cm wavelength) can provide a direct measurement of the surface soil moisture for a range of cover conditions and within reasonable error bounds. Surface soil moisture observations are rare and, therefore, the use of these data in hydrology and other disciplines has not been fully explored or developed. Without satellite-based observing systems, the only way to collect these data in large-scale studies is with an aircraft platform. Recently, aircraft systems such as the push broom microwave radiometer (PBMR) and the electronically scanned thinned array radiometer (ESTAR) have been developed to facilitate such investigations. In addition, field experiments have attempted to collect the passive microwave data as part of an integrated set of hydrologic data. One of the most ambitious of these investigations was the Washita'92 experiment. Preliminary analysis of these data has shown that the microwave observations are indicative of deterministic spatial and temporal variations in the surface soil moisture. Users of these data should be aware of a number of issues related to using aircraft-based systems and practical approaches to applying soil moisture estimation algorithms to large data sets. This paper outlines the process of mapping surface soil moisture from an aircraft-based passive microwave radiometer system for the Washita'92 experiment.
Dehghani, Hamid; Eames, Matthew E.; Yalavarthy, Phaneendra K.; Davis, Scott C.; Srinivasan, Subhadra; Carpenter, Colin M.; Pogue, Brian W.; Paulsen, Keith D.
2009-01-01
SUMMARY Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package. PMID:20182646
NASA Technical Reports Server (NTRS)
Whyte, W. A.; Heyward, A. O.; Ponchak, D. S.; Spence, R. L.; Zuzek, J. E.
1988-01-01
The Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) provides a method of generating predetermined arc segments for use in the development of an allotment planning procedure to be carried out at the 1988 World Administrative Radio Conference (WARC) on the Use of the Geostationary Satellite Orbit and the Planning of Space Services Utilizing It. Through careful selection of the predetermined arc (PDA) for each administration, flexibility can be increased in terms of choice of system technical characteristics and specific orbit location while reducing the need for coordination among administrations. The NASARC software determines pairwise compatibility between all possible service areas at discrete arc locations. NASARC then exhaustively enumerates groups of administrations whose satellites can be closely located in orbit, and finds the arc segment over which each such compatible group exists. From the set of all possible compatible groupings, groups and their associated arc segments are selected using a heuristic procedure such that a PDA is identified for each administration. Various aspects of the NASARC concept and how the software accomplishes specific features of allotment planning are discussed.
Numerical nonwavefront-guided algorithm for expansion or recentration of the optical zone
NASA Astrophysics Data System (ADS)
Arba Mosquera, Samuel; Verma, Shwetabh
2014-08-01
Complications may arise due to the decentered ablations during refractive surgery, resulting from human or mechanical errors. Decentration may cause over-/under-corrections, with patients complaining about seeing glares and halos after the procedure. Customized wavefront-guided treatments are often used to design retreatment procedures. However, due to the limitations of wavefront sensors in precisely measuring very large aberrations, some extreme cases may suffer when retreated with wavefront-guided treatments. We propose a simple and inexpensive numerical (nonwavefront-guided) algorithm to recenter the optical zone (OZ) and to correct the refractive error with minimal tissue removal. Due to its tissue-saving capabilities, this method can benefit patients with critical residual corneal thickness. Based on the reconstruction of ablation achieved in the first surgical procedure, we calculate a target ablation (by manipulating the achieved OZ) with adequate centration and an OZ sufficient enough to envelope the achieved ablation. The net ablation map for the retreatment procedure is calculated from the achieved and target ablations and is suitable to expand, recenter, and modulate the lower-order refractive components in a retreatment procedure. The results of our simulations suggest minimal tissue removal with OZ centration and expansion. Enlarging the OZ implies correcting spherical aberrations, whereas inducing centration implies correcting coma. This method shows the potential to improve visual outcomes in extreme cases of retreatment, possibly serving as an uncomplicated and inexpensive alternative to wavefront-guided retreatments.
NASA Astrophysics Data System (ADS)
Whyte, W. A.; Heyward, A. O.; Ponchak, D. S.; Spence, R. L.; Zuzek, J. E.
The Numerical Arc Segmentation Algorithm for a Radio Conference (NASARC) provides a method of generating predetermined arc segments for use in the development of an allotment planning procedure to be carried out at the 1988 World Administrative Radio Conference (WARC) on the Use of the Geostationary Satellite Orbit and the Planning of Space Services Utilizing It. Through careful selection of the predetermined arc (PDA) for each administration, flexibility can be increased in terms of choice of system technical characteristics and specific orbit location while reducing the need for coordination among administrations. The NASARC software determines pairwise compatibility between all possible service areas at discrete arc locations. NASARC then exhaustively enumerates groups of administrations whose satellites can be closely located in orbit, and finds the arc segment over which each such compatible group exists. From the set of all possible compatible groupings, groups and their associated arc segments are selected using a heuristic procedure such that a PDA is identified for each administration. Various aspects of the NASARC concept and how the software accomplishes specific features of allotment planning are discussed.
Cell light scattering characteristic numerical simulation research based on FDTD algorithm
NASA Astrophysics Data System (ADS)
Lin, Xiaogang; Wan, Nan; Zhu, Hao; Weng, Lingdong
2017-01-01
In this study, finite-difference time-domain (FDTD) algorithm has been used to work out the cell light scattering problem. Before beginning to do the simulation contrast, finding out the changes or the differences between normal cells and abnormal cells which may be cancerous or maldevelopment is necessary. The preparation of simulation are building up the simple cell model of cell which consists of organelles, nucleus and cytoplasm and setting up the suitable precision of mesh. Meanwhile, setting up the total field scattering field source as the excitation source and far field projection analysis group is also important. Every step need to be explained by the principles of mathematic such as the numerical dispersion, perfect matched layer boundary condition and near-far field extrapolation. The consequences of simulation indicated that the position of nucleus changed will increase the back scattering intensity and the significant difference on the peak value of scattering intensity may result from the changes of the size of cytoplasm. The study may help us find out the regulations based on the simulation consequences and the regulations can be meaningful for early diagnosis of cancers.
ERIC Educational Resources Information Center
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
NASA Astrophysics Data System (ADS)
Eaves, Nick A.; Zhang, Qingan; Liu, Fengshan; Guo, Hongsheng; Dworkin, Seth B.; Thomson, Murray J.
2016-10-01
Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene-air and methane-air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated.
NASA Technical Reports Server (NTRS)
Spratlin, Kenneth Milton
1987-01-01
An adaptive numeric predictor-corrector guidance is developed for atmospheric entry vehicles which utilize lift to achieve maximum footprint capability. Applicability of the guidance design to vehicles with a wide range of performance capabilities is desired so as to reduce the need for algorithm redesign with each new vehicle. Adaptability is desired to minimize mission-specific analysis and planning. The guidance algorithm motivation and design are presented. Performance is assessed for application of the algorithm to the NASA Entry Research Vehicle (ERV). The dispersions the guidance must be designed to handle are presented. The achievable operational footprint for expected worst-case dispersions is presented. The algorithm performs excellently for the expected dispersions and captures most of the achievable footprint.
NASA Technical Reports Server (NTRS)
Powell, Richard W.
1998-01-01
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.
Zhu, Xinjun; Chen, Zhanqing; Tang, Chen; Mi, Qinghua; Yan, Xiusheng
2013-03-20
In this paper, we are concerned with denoising in experimentally obtained electronic speckle pattern interferometry (ESPI) speckle fringe patterns with poor quality. We extend the application of two existing oriented partial differential equation (PDE) filters, including the second-order single oriented PDE filter and the double oriented PDE filter, to two experimentally obtained ESPI speckle fringe patterns with very poor quality, and compare them with other efficient filtering methods, including the adaptive weighted filter, the improved nonlinear complex diffusion PDE, and the windowed Fourier transform method. All of the five filters have been illustrated to be efficient denoising methods through previous comparative analyses in published papers. The experimental results have demonstrated that the two oriented PDE models are applicable to low-quality ESPI speckle fringe patterns. Then for solving the main shortcoming of the two oriented PDE models, we develop the numerically fast algorithms based on Gauss-Seidel strategy for the two oriented PDE models. The proposed numerical algorithms are capable of accelerating the convergence greatly, and perform significantly better in terms of computational efficiency. Our numerically fast algorithms are extended automatically to some other PDE filtering models.
Shi, Mingren; Renton, Michael
2011-10-01
Computational simulation models can provide a way of understanding and predicting insect population dynamics and evolution of resistance, but the usefulness of such models depends on generating or estimating the values of key parameters. In this paper, we describe four numerical algorithms generating or estimating key parameters for simulating four different processes within such models. First, we describe a novel method to generate an offspring genotype table for one- or two-locus genetic models for simulating evolution of resistance, and how this method can be extended to create offspring genotype tables for models with more than two loci. Second, we describe how we use a generalized inverse matrix to find a least-squares solution to an over-determined linear system for estimation of parameters in probit models of kill rates. This algorithm can also be used for the estimation of parameters of Freundlich adsorption isotherms. Third, we describe a simple algorithm to randomly select initial frequencies of genotypes either without any special constraints or with some pre-selected frequencies. Also we give a simple method to calculate the "stable" Hardy-Weinberg equilibrium proportions that would result from these initial frequencies. Fourth we describe how the problem of estimating the intrinsic rate of natural increase of a population can be converted to a root-finding problem and how the bisection algorithm can then be used to find the rate. We implemented all these algorithms using MATLAB and Python code; the key statements in both codes consist of only a few commands and are given in the appendices. The results of numerical experiments are also provided to demonstrate that our algorithms are valid and efficient.
Numerical simulation study of the dynamical behavior of the Niedermayer algorithm
NASA Astrophysics Data System (ADS)
Girardi, D.; Branco, N. S.
2010-04-01
We calculate the dynamic critical exponent for the Niedermayer algorithm applied to the two-dimensional Ising and XY models, for various values of the free parameter E0. For E0 = - 1 we regain the Metropolis algorithm and for E0 = 1 we regain the Wolff algorithm. For - 1 < E0 < 1, we show that the mean size of the clusters of (possibly) turned spins initially grows with the linear size of the lattice, L, but eventually saturates at a given lattice size \\widetilde {L} , which depends on E0. For L\\gt \\widetilde {L} , the Niedermayer algorithm is equivalent to the Metropolis one, i.e., they have the same dynamic exponent. For E0 > 1, the autocorrelation time is always greater than for E0 = 1 (Wolff) and, more important, it also grows faster than a power of L. Therefore, we show that the best choice of cluster algorithm is the Wolff one, when comparing against the Niedermayer generalization. We also obtain the dynamic behavior of the Wolff algorithm: although not conclusively, we propose a scaling law for the dependence of the autocorrelation time on L.
NASA Astrophysics Data System (ADS)
Tang, Yu-Hang; Karniadakis, George Em
2014-11-01
We present a scalable dissipative particle dynamics simulation code, fully implemented on the Graphics Processing Units (GPUs) using a hybrid CUDA/MPI programming model, which achieves 10-30 times speedup on a single GPU over 16 CPU cores and almost linear weak scaling across a thousand nodes. A unified framework is developed within which the efficient generation of the neighbor list and maintaining particle data locality are addressed. Our algorithm generates strictly ordered neighbor lists in parallel, while the construction is deterministic and makes no use of atomic operations or sorting. Such neighbor list leads to optimal data loading efficiency when combined with a two-level particle reordering scheme. A faster in situ generation scheme for Gaussian random numbers is proposed using precomputed binary signatures. We designed custom transcendental functions that are fast and accurate for evaluating the pairwise interaction. The correctness and accuracy of the code is verified through a set of test cases simulating Poiseuille flow and spontaneous vesicle formation. Computer benchmarks demonstrate the speedup of our implementation over the CPU implementation as well as strong and weak scalability. A large-scale simulation of spontaneous vesicle formation consisting of 128 million particles was conducted to further illustrate the practicality of our code in real-world applications. Catalogue identifier: AETN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETN_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 1 602 716 No. of bytes in distributed program, including test data, etc.: 26 489 166 Distribution format: tar.gz Programming language: C/C++, CUDA C/C++, MPI. Computer: Any computers having nVidia GPGPUs with compute capability 3.0. Operating system: Linux. Has the code been
NASA Astrophysics Data System (ADS)
Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.
2015-12-01
Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly
Bor, E; Turduev, M; Kurt, H
2016-08-01
Photonic structure designs based on optimization algorithms provide superior properties compared to those using intuition-based approaches. In the present study, we numerically and experimentally demonstrate subwavelength focusing of light using wavelength scale absorption-free dielectric scattering objects embedded in an air background. An optimization algorithm based on differential evolution integrated into the finite-difference time-domain method was applied to determine the locations of each circular dielectric object with a constant radius and refractive index. The multiobjective cost function defined inside the algorithm ensures strong focusing of light with low intensity side lobes. The temporal and spectral responses of the designed compact photonic structure provided a beam spot size in air with a full width at half maximum value of 0.19λ, where λ is the wavelength of light. The experiments were carried out in the microwave region to verify numerical findings, and very good agreement between the two approaches was found. The subwavelength light focusing is associated with a strong interference effect due to nonuniformly arranged scatterers and an irregular index gradient. Improving the focusing capability of optical elements by surpassing the diffraction limit of light is of paramount importance in optical imaging, lithography, data storage, and strong light-matter interaction.
Bor, E.; Turduev, M.; Kurt, H.
2016-01-01
Photonic structure designs based on optimization algorithms provide superior properties compared to those using intuition-based approaches. In the present study, we numerically and experimentally demonstrate subwavelength focusing of light using wavelength scale absorption-free dielectric scattering objects embedded in an air background. An optimization algorithm based on differential evolution integrated into the finite-difference time-domain method was applied to determine the locations of each circular dielectric object with a constant radius and refractive index. The multiobjective cost function defined inside the algorithm ensures strong focusing of light with low intensity side lobes. The temporal and spectral responses of the designed compact photonic structure provided a beam spot size in air with a full width at half maximum value of 0.19λ, where λ is the wavelength of light. The experiments were carried out in the microwave region to verify numerical findings, and very good agreement between the two approaches was found. The subwavelength light focusing is associated with a strong interference effect due to nonuniformly arranged scatterers and an irregular index gradient. Improving the focusing capability of optical elements by surpassing the diffraction limit of light is of paramount importance in optical imaging, lithography, data storage, and strong light-matter interaction. PMID:27477060
NASA Astrophysics Data System (ADS)
Bor, E.; Turduev, M.; Kurt, H.
2016-08-01
Photonic structure designs based on optimization algorithms provide superior properties compared to those using intuition-based approaches. In the present study, we numerically and experimentally demonstrate subwavelength focusing of light using wavelength scale absorption-free dielectric scattering objects embedded in an air background. An optimization algorithm based on differential evolution integrated into the finite-difference time-domain method was applied to determine the locations of each circular dielectric object with a constant radius and refractive index. The multiobjective cost function defined inside the algorithm ensures strong focusing of light with low intensity side lobes. The temporal and spectral responses of the designed compact photonic structure provided a beam spot size in air with a full width at half maximum value of 0.19λ, where λ is the wavelength of light. The experiments were carried out in the microwave region to verify numerical findings, and very good agreement between the two approaches was found. The subwavelength light focusing is associated with a strong interference effect due to nonuniformly arranged scatterers and an irregular index gradient. Improving the focusing capability of optical elements by surpassing the diffraction limit of light is of paramount importance in optical imaging, lithography, data storage, and strong light-matter interaction.
NASA Astrophysics Data System (ADS)
Mehrmann, Volker; Xu, Hongguo
2000-11-01
We study classical control problems like pole assignment, stabilization, linear quadratic control and H[infinity] control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches.
Artificial algae algorithm with multi-light source for numerical optimization and applications.
Uymaz, Sait Ali; Tezel, Gulay; Yel, Esra
2015-12-01
Artificial algae algorithm (AAA), which is one of the recently developed bio-inspired optimization algorithms, has been introduced by inspiration from living behaviors of microalgae. In AAA, the modification of the algal colonies, i.e. exploration and exploitation is provided with a helical movement. In this study, AAA was modified by implementing multi-light source movement and artificial algae algorithm with multi-light source (AAAML) version was established. In this new version, we propose the selection of a different light source for each dimension that is modified with the helical movement for stronger balance between exploration and exploitation. These light sources have been selected by tournament method and each light source are different from each other. This gives different solutions in the search space. The best of these three light sources provides orientation to the better region of search space. Furthermore, the diversity in the source space is obtained with the worst light source. In addition, the other light source improves the balance. To indicate the performance of AAA with new proposed operators (AAAML), experiments were performed on two different sets. Firstly, the performance of AAA and AAAML was evaluated on the IEEE-CEC'13 benchmark set. The second set was real-world optimization problems used in the IEEE-CEC'11. To verify the effectiveness and efficiency of the proposed algorithm, the results were compared with other state-of-the-art hybrid and modified algorithms. Experimental results showed that the multi-light source movement (MLS) increases the success of the AAA.
NASA Astrophysics Data System (ADS)
Li, Tiexiang; Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Jenn-Nan
2017-03-01
We propose an efficient eigensolver for computing densely distributed spectra of the two-dimensional transmission eigenvalue problem (TEP), which is derived from Maxwell’s equations with Tellegen media and the transverse magnetic mode. The governing equations, when discretized by the standard piecewise linear finite element method, give rise to a large-scale quadratic eigenvalue problem (QEP). Our numerical simulation shows that half of the positive eigenvalues of the QEP are densely distributed in some interval near the origin. The quadratic Jacobi–Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Extensive numerical simulations show that our proposed method processes the convergence efficiently, even when it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by nonlinear functions, which can be applied to estimate the denseness of the eigenvalues for the TEP.
1979-09-01
ithm for Computational Fluid Dynamics," Ph.D. Dissertation, Univ. of Tennessee, Report ESM 78-1, 1978. 18. Thames, F. C., Thompson , J . F ., and Mastin...C. W., "Numerical Solution of the Navier-Stokes Equations for Arbitrary Two-Dimensional Air- foils," NASA SP-347, 1975. 19. Thompson , J . F ., Thames...Number of Arbitrary Two-Dimensional Bodies," NASA CR-2729, 1976. 20. Thames, F. C., Thompson , J . F ., Mastin, C. W., and Walker, R. L., "Numerical
Scanning of wind turbine upwind conditions: numerical algorithm and first applications
NASA Astrophysics Data System (ADS)
Calaf, Marc; Cortina, Gerard; Sharma, Varun; Parlange, Marc B.
2014-11-01
Wind turbines still obtain in-situ meteorological information by means of traditional wind vane and cup anemometers installed at the turbine's nacelle, right behind the blades. This has two important drawbacks: 1-turbine misalignment with the mean wind direction is common and energy losses are experienced; 2-the near-blade monitoring does not provide any time to readjust the profile of the wind turbine to incoming turbulence gusts. A solution is to install wind Lidar devices on the turbine's nacelle. This technique is currently under development as an alternative to traditional in-situ wind anemometry because it can measure the wind vector at substantial distances upwind. However, at what upwind distance should they interrogate the atmosphere? A new flexible wind turbine algorithm for large eddy simulations of wind farms that allows answering this question, will be presented. The new wind turbine algorithm timely corrects the turbines' yaw misalignment with the changing wind. The upwind scanning flexibility of the algorithm also allows to track the wind vector and turbulent kinetic energy as they approach the wind turbine's rotor blades. Results will illustrate the spatiotemporal evolution of the wind vector and the turbulent kinetic energy as the incoming flow approaches the wind turbine under different atmospheric stability conditions. Results will also show that the available atmospheric wind power is larger during daytime periods at the cost of an increased variance.
1989-03-01
by Colorado State University, Fort Collins, CO, for US Army Engineer Waterways Experiment Station, Vicksburg, MS. Thompson , J . F . 1983 (Mar). "A...Waterways Experiment Station, Vicksburg, MS. Thompson , J . F ., and Bernard, R. S. 1985 (Aug). "WESSEL: Code for Numerical Simulation of Two-Dimensional Time
AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)
A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...
Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm
NASA Technical Reports Server (NTRS)
Hwang, Chyi; Lu, Ming-Jeng; Shieh, Leang S.
1991-01-01
The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.
NASA Astrophysics Data System (ADS)
Zhang, Lisha
We present fast and robust numerical algorithms for 3-D scattering from perfectly electrical conducting (PEC) and dielectric random rough surfaces in microwave remote sensing. The Coifman wavelets or Coiflets are employed to implement Galerkin's procedure in the method of moments (MoM). Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N2) to O( N). The orthogonality and Riesz basis of the Coiflets generate well conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. The resulting impedance matrix is further sparsified by the matrix-formed standard fast wavelet transform (SFWT). By properly selecting multiresolution levels of the total transformation matrix, the solution precision can be enhanced while matrix sparsity and memory consumption have not been noticeably sacrificed. The unified fast scattering algorithm for dielectric random rough surfaces can asymptotically reduce to the PEC case when the loss tangent grows extremely large. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems. Compared with previous publications and laboratory measurements, good agreement is observed.
Fischer, Martin H.; Brugger, Peter
2011-01-01
Spatial–numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific, and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Implications of this “manumerical cognition” stance for the distinction between grounded, embodied, and situated cognition are discussed. PMID:22028696
NASA Technical Reports Server (NTRS)
Carter, Richard G.
1989-01-01
For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.
Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs
Javadi, H. H. S.; Navidi, H. R.
2014-01-01
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. PMID:25485295
NASA Technical Reports Server (NTRS)
Durisen, Richard H.; Murphy, Brian W.; Cramer, Nichael Lynn; Cuzzi, Jeffrey N.; Mullikin, Thomas L.
1989-01-01
Ballistic transport, defined as the net radial transport of mass and angular momentum due to exchanges of meteoroid hypersonic-impact ejecta by neighboring planetary ring regions on time-scales orders-of-magnitude shorter than the age of the solar system, is presently considered as a problem in mathematical physics. The preliminary results of a numerical scheme for following the combined effects of ballistic transport and viscous diffusion demonstrate that ballistic transport generates structure near sharp edges already present in the ring-mass distribution; the entire ring system ultimately develops an undulatory structure whose length scale is typically of the order of the radial excursion of the impact ejecta.
An efficient algorithm for numerical computations of continuous densities of states
NASA Astrophysics Data System (ADS)
Langfeld, K.; Lucini, B.; Pellegrini, R.; Rago, A.
2016-06-01
In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard integration. In this work, our recently introduced method in this class (the LLR approach) is analysed and further developed. Our approach is a histogram free method particularly suited for systems with continuous degrees of freedom giving rise to a continuum density of states, as it is commonly found in lattice gauge theories and in some statistical mechanics systems. We show that the method possesses an exponential error suppression that allows us to estimate the density of states over several orders of magnitude with nearly constant relative precision. We explain how ergodicity issues can be avoided and how expectation values of arbitrary observables can be obtained within this framework. We then demonstrate the method using compact U(1) lattice gauge theory as a show case. A thorough study of the algorithm parameter dependence of the results is performed and compared with the analytically expected behaviour. We obtain high precision values for the critical coupling for the phase transition and for the peak value of the specific heat for lattice sizes ranging from 8^4 to 20^4. Our results perfectly agree with the reference values reported in the literature, which covers lattice sizes up to 18^4. Robust results for the 20^4 volume are obtained for the first time. This latter investigation, which, due to strong metastabilities developed at the pseudo-critical coupling of the system, so far has been out of reach even on supercomputers with importance sampling approaches, has been performed to high accuracy with modest computational resources. This shows the potential of the method for studies of first order phase transitions. Other situations where the method is expected to be superior to importance sampling techniques are pointed
NASA Astrophysics Data System (ADS)
Angeli, D.; Stalio, E.; Corticelli, M. A.; Barozzi, G. S.
2015-11-01
A parallel algorithm is presented for the Direct Numerical Simulation of buoyancy- induced flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. A semi-implicit scheme is employed for the diffusive terms, which are treated implicitly on the periodic plane and explicitly along the homogeneous direction, while all convective terms are explicit, via the second-order Adams-Bashfort scheme. The contemporary solution of velocity and pressure fields is achieved by means of a projection method. The numerical resolution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for the case of flow around an array of heated cylindrical rods arranged in a square lattice. Grid independence is assessed in laminar flow conditions, and DNS results in turbulent conditions are presented for two different grids and compared to available literature data, thus confirming the favorable qualities of the method.
Wan, Hui; Rasch, Philip J.; Zhang, Kai; Kazil, Jan; Leung, Lai-Yung R.
2013-06-26
The purpose of this paper is to draw attention to the need for appropriate numerical techniques to represent process interactions in climate models. In two versions of the ECHAM-HAM model, different time integration methods are used to solve the sulfuric acid (H2SO4) gas evolution equation, which lead to substantially different results in the H2SO4 gas concentration and the aerosol nucleation rate. Using convergence tests and sensitivity simulations performed with various time stepping schemes, it is confirmed that numerical errors in the second model version are significantly smaller than those in version one. The use of sequential operator splitting in combination with long time step is identified as the main reason for the large systematic biases in the old model. The remaining errors in version two in the nucleation rate, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei in the lower troposphere. These errors can be significantly reduced by employing an implicit solver that handles production, condensation and nucleation at the same time. Lessons learned in this work underline the need for more caution when treating multi-time-scale problems involving compensating and competing processes, a common occurrence in current climate models.
NASA Technical Reports Server (NTRS)
Weir, Kent A.; Wells, Eugene M.
1990-01-01
The design and operation of a Strapdown Navigation Analysis Program (SNAP) developed to perform covariance analysis on spacecraft inertial-measurement-unit (IMU) navigation errors are described and demonstrated. Consideration is given to the IMU modeling subroutine (with user-specified sensor characteristics), the data input procedures, state updates and the simulation of instrument failures, the determination of the nominal trajectory, the mapping-matrix and Monte Carlo covariance-matrix propagation methods, and aided-navigation simulation. Numerical results are presented in tables for sample applications involving (1) the Galileo/IUS spacecraft from its deployment from the Space Shuttle to a point 10 to the 8th ft from the center of the earth and (2) the TDRS-C/IUS spacecraft from Space Shuttle liftoff to a point about 2 h before IUS deployment. SNAP is shown to give reliable results for both cases, with good general agreement between the mapping-matrix and Monte Carlo predictions.
NASA Astrophysics Data System (ADS)
Katsuro-Hopkins, Oksana; Sabbagh, S. A.; Bialek, J. M.; Park, H. K.; Kim, J. Y.; You, K.-I.; Glasser, A. H.; Lao, L. L.
2007-11-01
Stability to ideal MHD kink/ballooning modes and the resistive wall mode (RWM) is investigated for the KSTAR tokamak. Free-boundary equilibria that comply with magnetic field coil current constraints are computed for monotonic and reversed shear safety factor profiles and H-mode tokamak pressure profiles. Advanced tokamak operation at moderate to low plasma internal inductance shows that a factor of two improvement in the plasma beta limit over the no-wall beta limit is possible for toroidal mode number of unity. The KSTAR conducting structure, passive stabilizers, and in-vessel control coils are modeled by the VALEN-3D code and the active RWM stabilization performance of the device is evaluated using both standard and advanced feedback algorithms. Steady-state power and voltage requirements for the system are estimated based on the expected noise on the RWM sensor signals. Using NSTX experimental RWM sensors noise data as input, a reduced VALEN state-space LQG controller is designed to realistically assess KSTAR stabilization system performance.
Mouton, S.; Ledoux, Y.; Teissandier, D.; Sebastian, P.
2010-06-15
A key challenge for the future is to reduce drastically the human impact on the environment. In the aeronautic field, this challenge aims at optimizing the design of the aircraft to decrease the global mass. This reduction leads to the optimization of every part constitutive of the plane. This operation is even more delicate when the used material is composite material. In this case, it is necessary to find a compromise between the strength, the mass and the manufacturing cost of the component. Due to these different kinds of design constraints it is necessary to assist engineer with decision support system to determine feasible solutions. In this paper, an approach is proposed based on the coupling of the different key characteristics of the design process and on the consideration of the failure risk of the component. The originality of this work is that the manufacturing deviations due to the RTM process are integrated in the simulation of the assembly process. Two kinds of deviations are identified: volume impregnation (injection phase of RTM process) and geometrical deviations (curing and cooling phases). The quantification of these deviations and the related failure risk calculation is based on finite element simulations (Pam RTM registered and Samcef registered softwares). The use of genetic algorithm allows to estimate the impact of the design choices and their consequences on the failure risk of the component. The main focus of the paper is the optimization of tool design. In the framework of decision support systems, the failure risk calculation is used for making the comparison of possible industrialization alternatives. It is proposed to apply this method on a particular part of the airplane structure: a spar unit made of carbon fiber/epoxy composite.
NASA Astrophysics Data System (ADS)
Audet, Pascal
2016-06-01
The expanding fleet of broad-band ocean-bottom seismograph (OBS) stations is facilitating the study of the structure and seismicity of oceanic plates at regional scales. For continental studies, an important tool to characterize continental crust and mantle structure is the analysis of teleseismic P receiver functions. In the oceans, however, receiver functions potentially suffer from several limiting factors that are unique to ocean sites and plate structures. In this study, we model receiver functions for a variety of oceanic lithospheric structures to investigate the possibilities and limitations of receiver functions using OBS data. Several potentially contaminating effects are examined, including pressure reverberations from the water column for various ocean-floor depths and the effects of a layer of low-velocity marine sediments. These modelling results indicate that receiver functions from OBS data are difficult to interpret in the presence of marine sediments, but shallow-water sites in subduction zone forearcs may be suitable for constraining various crustal elements around the locked megathrust fault. We propose using a complementary approach based on transfer function modelling combined with a grid search approach that bypasses receiver functions altogether and estimates model properties directly from minimally processed waveforms. Using real data examples from the Cascadia Initiative, we show how receiver and transfer functions can be used to infer seismic properties of the oceanic plate in both shallow (Cascadia forearc) and deep (Juan de Fuca Ridge) ocean settings.
Real-space, mean-field algorithm to numerically calculate long-range interactions
NASA Astrophysics Data System (ADS)
Cadilhe, A.; Costa, B. V.
2016-02-01
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
Numerical Algorithms & Parallel Tasking.
1985-09-12
senior personnel have been supported under this contract: Virginia Klema, principal investigator (3.5 months), Elizabeth Ducot (2.25 months), and George...CONCURRENT ENVIRONMENT Elizabeth R. Ducot The purpose of this note is twofold. The first is to present the mechanisms by which a user activates and describes
Baez, M L; Borzi, R A
2017-02-08
We study the three-dimensional Kasteleyn transition in both nearest neighbours and dipolar spin ice models using an algorithm that conserves the number of excitations. We first limit the interactions range to nearest neighbours to test the method in the presence of a field applied along [Formula: see text], and then focus on the dipolar spin ice model. The effect of dipolar interactions, which is known to be greatly self screened at zero field, is particularly strong near full polarization. It shifts the Kasteleyn transition to lower temperatures, which decreases ≈0.4 K for the parameters corresponding to the best known spin ice materials, [Formula: see text] and [Formula: see text]. This shift implies effective dipolar fields as big as 0.05 T opposing the applied field, and thus favouring the creation of 'strings' of reversed spins. We compare the reduction in the transition temperature with results in previous experiments, and study the phenomenon quantitatively using a simple molecular field approach. Finally, we relate the presence of the effective residual field to the appearance of string-ordered phases at low fields and temperatures, and we check numerically that for fields applied along [Formula: see text] there are only three different stable phases at zero temperature.
NASA Astrophysics Data System (ADS)
Baez, M. L.; Borzi, R. A.
2017-02-01
We study the three-dimensional Kasteleyn transition in both nearest neighbours and dipolar spin ice models using an algorithm that conserves the number of excitations. We first limit the interactions range to nearest neighbours to test the method in the presence of a field applied along ≤ft[1 0 0\\right] , and then focus on the dipolar spin ice model. The effect of dipolar interactions, which is known to be greatly self screened at zero field, is particularly strong near full polarization. It shifts the Kasteleyn transition to lower temperatures, which decreases ≈0.4 K for the parameters corresponding to the best known spin ice materials, \\text{D}{{\\text{y}}2}\\text{T}{{\\text{i}}2}{{\\text{O}}7} and \\text{H}{{\\text{o}}2}\\text{T}{{\\text{i}}2}{{\\text{O}}7} . This shift implies effective dipolar fields as big as 0.05 T opposing the applied field, and thus favouring the creation of ‘strings’ of reversed spins. We compare the reduction in the transition temperature with results in previous experiments, and study the phenomenon quantitatively using a simple molecular field approach. Finally, we relate the presence of the effective residual field to the appearance of string-ordered phases at low fields and temperatures, and we check numerically that for fields applied along ≤ft[1 0 0\\right] there are only three different stable phases at zero temperature.
NASA Astrophysics Data System (ADS)
Gasparini, N. M.; Whipple, K. X.; Willenbring, J.; Crosby, B. T.; Brocard, G. Y.
2013-12-01
Numerical landscape evolution models (LEMs) offer us the unique opportunity to watch a landscape evolve under any set of environmental forcings that we can quantify. The possibilities for using LEMs are infinite, but complications arise when trying to model a real landscape. Specifically, numerical models cannot recreate every aspect of a real landscape because exact initial conditions are unknown, there will always be gaps in the known tectonic and climatic history, and the geomorphic transport laws that govern redistribution of mass due to surface processes will always be a simplified representation of the actual process. Yet, even with these constraints, numerical models remain the only tool that offers us the potential to explore a limitless range of evolutionary scenarios, allowing us to, at the very least, identify possible drivers responsible for the morphology of the current landscape, and just as importantly, rule out others. Here we highlight two examples in which we use a numerical model to explore the signature of different forcings on landscape morphology and erosion patterns. In the first landscape, the Northern Bolivian Andes, the relative imprint of rock uplift and precipitation patterns on landscape morphology is widely contested. We use the CHILD LEM to systematically vary climate and tectonics and quantify their fingerprints on channel profiles across a steep mountain front. We find that rock uplift and precipitation patterns in this landscape and others can be teased out by examining channel profiles of variably sized catchments that drain different parts of the topography. In the second landscape, the South Fork Eel River (SFER), northern California, USA, the tectonic history is relatively well known; a wave of rock uplift swept through the watershed from headwaters to outlet, perturbing the landscape and sending a wave of bedrock incision upstream. Nine millennial-scale erosion rates from along the mainstem of the river illustrate a pattern of
Mallick, S.
1999-03-01
In this paper, a prestack inversion method using a genetic algorithm (GA) is presented, and issues relating to the implementation of prestack GA inversion in practice are discussed. GA is a Monte-Carlo type inversion, using a natural analogy to the biological evolution process. When GA is cast into a Bayesian framework, a priori information of the model parameters and the physics of the forward problem are used to compute synthetic data. These synthetic data can then be matched with observations to obtain approximate estimates of the marginal a posteriori probability density (PPD) functions in the model space. Plots of these PPD functions allow an interpreter to choose models which best describe the specific geologic setting and lead to an accurate prediction of seismic lithology. Poststack inversion and prestack GA inversion were applied to a Woodbine gas sand data set from East Texas. A comparison of prestack inversion with poststack inversion demonstrates that prestack inversion shows detailed stratigraphic features of the subsurface which are not visible on the poststack inversion.
New pole placement algorithm - Polynomial matrix approach
NASA Technical Reports Server (NTRS)
Shafai, B.; Keel, L. H.
1990-01-01
A simple and direct pole-placement algorithm is introduced for dynamical systems having a block companion matrix A. The algorithm utilizes well-established properties of matrix polynomials. Pole placement is achieved by appropriately assigning coefficient matrices of the corresponding matrix polynomial. This involves only matrix additions and multiplications without requiring matrix inversion. A numerical example is given for the purpose of illustration.
Zhu, Xin-Guang; de Sturler, Eric; Long, Stephen P
2007-10-01
The distribution of resources between enzymes of photosynthetic carbon metabolism might be assumed to have been optimized by natural selection. However, natural selection for survival and fecundity does not necessarily select for maximal photosynthetic productivity. Further, the concentration of a key substrate, atmospheric CO(2), has changed more over the past 100 years than the past 25 million years, with the likelihood that natural selection has had inadequate time to reoptimize resource partitioning for this change. Could photosynthetic rate be increased by altered partitioning of resources among the enzymes of carbon metabolism? This question is addressed using an "evolutionary" algorithm to progressively search for multiple alterations in partitioning that increase photosynthetic rate. To do this, we extended existing metabolic models of C(3) photosynthesis by including the photorespiratory pathway (PCOP) and metabolism to starch and sucrose to develop a complete dynamic model of photosynthetic carbon metabolism. The model consists of linked differential equations, each representing the change of concentration of one metabolite. Initial concentrations of metabolites and maximal activities of enzymes were extracted from the literature. The dynamics of CO(2) fixation and metabolite concentrations were realistically simulated by numerical integration, such that the model could mimic well-established physiological phenomena. For example, a realistic steady-state rate of CO(2) uptake was attained and then reattained after perturbing O(2) concentration. Using an evolutionary algorithm, partitioning of a fixed total amount of protein-nitrogen between enzymes was allowed to vary. The individual with the higher light-saturated photosynthetic rate was selected and used to seed the next generation. After 1,500 generations, photosynthesis was increased substantially. This suggests that the "typical" partitioning in C(3) leaves might be suboptimal for maximizing the light
A Food Chain Algorithm for Capacitated Vehicle Routing Problem with Recycling in Reverse Logistics
NASA Astrophysics Data System (ADS)
Song, Qiang; Gao, Xuexia; Santos, Emmanuel T.
2015-12-01
This paper introduces the capacitated vehicle routing problem with recycling in reverse logistics, and designs a food chain algorithm for it. Some illustrative examples are selected to conduct simulation and comparison. Numerical results show that the performance of the food chain algorithm is better than the genetic algorithm, particle swarm optimization as well as quantum evolutionary algorithm.
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1995-01-01
Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.
NASA Astrophysics Data System (ADS)
Gasparini, N. M.; Hobley, D. E. J.; Tucker, G. E.; Istanbulluoglu, E.; Adams, J. M.; Nudurupati, S. S.; Hutton, E. W. H.
2014-12-01
Computational models are important tools that can be used to quantitatively understand the evolution of real landscapes. Commonalities exist among most landscape evolution models, although they are also idiosyncratic, in that they are coded in different languages, require different input values, and are designed to tackle a unique set of questions. These differences can make applying a landscape evolution model challenging, especially for novice programmers. In this study, we compare and contrast two landscape evolution models that are designed to tackle similar questions, but the actual model designs are quite different. The first model, CHILD, is over a decade-old and is relatively well-tested, well-developed and well-used. It is coded in C++, operates on an irregular grid and was designed more with function rather than user-experience in mind. In contrast, the second model, Landlab, is relatively new and was designed to be accessible to a wide range of scientists, including those who have not previously used or developed a numerical model. Landlab is coded in Python, a relatively easy language for the non-proficient programmer, and has the ability to model landscapes described on both regular and irregular grids. We present landscape simulations from both modeling platforms. Our goal is to illustrate best practices for implementing a new process module in a landscape evolution model, and therefore the simulations are applicable regardless of the modeling platform. We contrast differences and highlight similarities between the use of the two models, including setting-up the model and input file for different evolutionary scenarios, computational time, and model output. Whenever possible, we compare model output with analytical solutions and illustrate the effects, or lack thereof, of a uniform vs. non-uniform grid. Our simulations focus on implementing a single process, including detachment-limited or transport-limited fluvial bedrock incision and linear or non
Performance-Based Seismic Design of Steel Frames Utilizing Colliding Bodies Algorithm
Veladi, H.
2014-01-01
A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm. PMID:25202717
Performance-based seismic design of steel frames utilizing colliding bodies algorithm.
Veladi, H
2014-01-01
A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm.
Numerical anomalies mimicking physical effects
Menikoff, R.
1995-09-01
Numerical simulations of flows with shock waves typically use finite-difference shock-capturing algorithms. These algorithms give a shock a numerical width in order to generate the entropy increase that must occur across a shock wave. For algorithms in conservation form, steady-state shock waves are insensitive to the numerical dissipation because of the Hugoniot jump conditions. However, localized numerical errors occur when shock waves interact. Examples are the ``excess wall heating`` in the Noh problem (shock reflected from rigid wall), errors when a shock impacts a material interface or an abrupt change in mesh spacing, and the start-up error from initializing a shock as a discontinuity. This class of anomalies can be explained by the entropy generation that occurs in the transient flow when a shock profile is formed or changed. The entropy error is localized spatially but under mesh refinement does not decrease in magnitude. Similar effects have been observed in shock tube experiments with partly dispersed shock waves. In this case, the shock has a physical width due to a relaxation process. An entropy anomaly from a transient shock interaction is inherent in the structure of the conservation equations for fluid flow. The anomaly can be expected to occur whenever heat conduction can be neglected and a shock wave has a non-zero width, whether the width is physical or numerical. Thus, the numerical anomaly from an artificial shock width mimics a real physical effect.
NASA Astrophysics Data System (ADS)
Motheau, E.; Abraham, J.
2016-05-01
A novel and efficient algorithm is presented in this paper to deal with DNS of turbulent reacting flows under the low-Mach-number assumption, with detailed chemistry and a quasi-spectral accuracy. The temporal integration of the equations relies on an operating-split strategy, where chemical reactions are solved implicitly with a stiff solver and the convection-diffusion operators are solved with a Runge-Kutta-Chebyshev method. The spatial discretisation is performed with high-order compact schemes, and a FFT based constant-coefficient spectral solver is employed to solve a variable-coefficient Poisson equation. The numerical implementation takes advantage of the 2DECOMP&FFT libraries developed by [1], which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient. An enhanced pressure-correction method is proposed to speed up the achievement of machine precision accuracy. It is demonstrated that a second-order accuracy is reached in time, while the spatial accuracy ranges from fourth-order to sixth-order depending on the set of imposed boundary conditions. The software developed to implement the present algorithm is called HOLOMAC, and its numerical efficiency opens the way to deal with DNS of reacting flows to understand complex turbulent and chemical phenomena in flames.
NASA Astrophysics Data System (ADS)
Sheng, I. C.; Kuan, C. K.; Chen, Y. T.; Yang, J. Y.; Hsiung, G. Y.; Chen, J. R.
2010-06-01
The pressure distribution is an important aspect of a UHV subsystem in either a storage ring or a front end. The design of the 3-GeV, 400-mA Taiwan Photon Source (TPS) foresees outgassing induced by photons and due to a bending magnet and an insertion device. An algorithm to calculate the photon-stimulated absorption (PSD) due to highly energetic radiation from a synchrotron source is presented. Several results using undulator sources such as IU20 are also presented, and the pressure distribution is illustrated.
NASA Technical Reports Server (NTRS)
Wehrbein, W. M.; Leovy, C. B.
1981-01-01
A Curtis matrix is used to compute cooling by the 15 micron and 10 micron bands of carbon dioxide. Escape of radiation to space and exchange the lower boundary are used for the 9.6 micron band of ozone. Voigt line shape, vibrational relaxation, line overlap, and the temperature dependence of line strength distributions and transmission functions are incorporated into the Curtis matrices. The distributions of the atmospheric constituents included in the algorithm, and the method used to compute the Curtis matrices are discussed as well as cooling or heating by the 9.6 micron band of ozone. The FORTRAN programs and subroutines that were developed are described and listed.
NASA Astrophysics Data System (ADS)
Kirk, N. P.; Connor, J. N. L.; Curtis, P. R.; Hobbs, C. A.
2000-07-01
A numerical procedure for the evaluation of the Bessoid canonical integral J({x,y}) is described. J({x,y}) is defined, for x and y real, by eq1 where J0(·) is a Bessel function of order zero. J({x,y}) plays an important role in the description of cusped focusing when there is axial symmetry present. It arises in the diffraction theory of aberrations, in the design of optical instruments and of highly directional microwave antennas and in the theory of image formation for high-resolution electron microscopes. The numerical procedure replaces the integration path along the real t axis with a more convenient contour in the complex t plane, thereby rendering the oscillatory integrand more amenable to numerical quadrature. The computations use a modified version of the CUSPINT computer code (Kirk et al 2000 Comput. Phys. Commun. at press), which evaluates the cuspoid canonical integrals and their first-order partial derivatives. Plots and tables of J({x,y}) and its zeros are presented for the grid -8.0≤x≤8.0 and -8.0≤y≤8.0. Some useful series expansions of J({x,y}) are also derived.
Fukuda, Ikuo; Nakamura, Haruki
2006-02-01
For an arbitrary ordinary differential equation (ODE), a scheme for constructing an extended ODE endowed with a time-invariant function is here proposed. This scheme enables us to examine the accuracy of the numerical integration of an ODE that may itself have had no invariant. These quantities are constructed by referring to the Nosé-Hoover molecular dynamics equation and its related conserved quantity. By applying this procedure to several molecular dynamics equations, the conventional conserved quantity individually defined in each dynamics can be reproduced in a uniform, generalized way; our concept allows a transparent outlook underlying these quantities and ideas. Developing the technique, for a certain class of ODEs we construct a numerical integrator that is not only explicit and symmetric, but preserves a unit Jacobian for a suitably defined extended ODE, which also provides an invariant. Our concept is thus to simply build a divergence-free extended ODE whose solution is just a lift-up of the original ODE, and to constitute an efficient integrator that preserves the phase-space volume on the extended system. We present precise discussions about the general mathematical properties of the integrator and provide specific conditions that should be incorporated for practical applications.
Nourgaliev R.; Knoll D.; Mousseau V.; Berry R.
2007-04-01
The state-of-the-art for Direct Numerical Simulation (DNS) of boiling multiphase flows is reviewed, focussing on potential of available computational techniques, the level of current success for their applications to model several basic flow regimes (film, pool-nucleate and wall-nucleate boiling -- FB, PNB and WNB, respectively). Then, we discuss multiphysics and multiscale nature of practical boiling flows in LWR reactors, requiring high-fidelity treatment of interfacial dynamics, phase-change, hydrodynamics, compressibility, heat transfer, and non-equilibrium thermodynamics and chemistry of liquid/vapor and fluid/solid-wall interfaces. Finally, we outline the framework for the {\\sf Fervent} code, being developed at INL for DNS of reactor-relevant boiling multiphase flows, with the purpose of gaining insight into the physics of multiphase flow regimes, and generating a basis for effective-field modeling in terms of its formulation and closure laws.
Teramoto, Elias Hideo; Chang, Hung Kiang
2017-03-01
Mass transfer of light non-aqueous phase liquids (LNAPLs) trapped in porous media is a complex phenomenon. Water table fluctuations have been identified as responsible for generating significant variations in the concentration of dissolved hydrocarbons. Based on field evidence, this work presents a conceptual model and a numerical solution for mass transfer from entrapped LNAPL to groundwater controlled by both LNAPL saturation and seasonal water table fluctuations within the LNAPL smear zone. The numerical approach is capable of reproducing aqueous BTEX concentration trends under three different scenarios - water table fluctuating within smear zone, above the smear zone and partially within smear zone, resulting in in-phase, out-of-phase and alternating in-phase and out-of-phase BTEX concentration trend with respect to water table oscillation, respectively. The results demonstrate the model's applicability under observed field conditions and its ability to predict source zone depletion.
NASA Astrophysics Data System (ADS)
Hwang, Feng-Nan; Cai, Shang-Rong; Shao, Yun-Long; Wu, Jong-Shinn
2010-09-01
We investigate fully parallel Newton-Krylov-Schwarz (NKS) algorithms for solving the large sparse nonlinear systems of equations arising from the finite element discretization of the three-dimensional Poisson-Boltzmann equation (PBE), which is often used to describe the colloidal phenomena of an electric double layer around charged objects in colloidal and interfacial science. The NKS algorithm employs an inexact Newton method with backtracking (INB) as the nonlinear solver in conjunction with a Krylov subspace method as the linear solver for the corresponding Jacobian system. An overlapping Schwarz method as a preconditioner to accelerate the convergence of the linear solver. Two test cases including two isolated charged particles and two colloidal particles in a cylindrical pore are used as benchmark problems to validate the correctness of our parallel NKS-based PBE solver. In addition, a truly three-dimensional case, which models the interaction between two charged spherical particles within a rough charged micro-capillary, is simulated to demonstrate the applicability of our PBE solver to handle a problem with complex geometry. Finally, based on the result obtained from a PC cluster of parallel machines, we show numerically that NKS is quite suitable for the numerical simulation of interaction between colloidal particles, since NKS is robust in the sense that INB is able to converge within a small number of iterations regardless of the geometry, the mesh size, the number of processors. With help of an additive preconditioned Krylov subspace method NKS achieves parallel efficiency of 71% or better on up to a hundred processors for a 3D problem with 5 million unknowns.
LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; ...
2015-12-14
Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification ofmore » uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.« less
LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; Bulik, Ireneusz W.; Chan, Garnet Kin-Lic; Chung, Chia -Min; Deng, Youjin; Ferrero, Michel; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A.; Kozik, E.; Liu, Xuan -Wen; Millis, Andrew J.; Prokof’ev, N. V.; Qin, Mingpu; Scuseria, Gustavo E.; Shi, Hao; Svistunov, B. V.; Tocchio, Luca F.; Tupitsyn, I. S.; White, Steven R.; Zhang, Shiwei; Zheng, Bo -Xiao; Zhu, Zhenyue; Gull, Emanuel
2015-12-14
Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
NASA Astrophysics Data System (ADS)
Kindrachuk, Vitaliy M.; Galanov, Boris A.
2014-02-01
A computationally efficient solution scheme is presented for the mechanical problems whose formulations include the Kuhn-Tucker or Signorini-Fichera conditions. It is proposed to reformulate these problems replacing inequalities in these conditions by equations with respect to new unknowns. The solutions of the modified problems have simple physical meanings and determine uniquely the unknowns of the original problems. The approach avoids application of multi-valued operators (inclusions or inequalities) in formulation of the problems. Hence, the modified formulations are suitable for numerical analysis using established powerful mathematical methods and corresponding solvers developed for solving systems of non-linear equations.
NASA Astrophysics Data System (ADS)
Wachowicz-Pyzik, A.; Sowiżdżał, A.; Pająk, L.
2016-09-01
The numerical modeling enables us to reduce the risk related to the selection of best localization of wells. Moreover, at the stage of production, modeling is a suitable tool for optimization of well operational parameters, which guarantees the long life of doublets. The thorough selection of software together with relevant methodology applied to generation of numerical models significantly improve the quality of obtained results. In the following paper, we discuss the impact of density of calculation grid on the results of geothermal doublet simulation with the TOUGH2 code, which applies the finite-difference method. The study area is located between the Szczecin Trough and the Fore-sudetic Monocline, where the Choszczno IG-1 well has been completed. Our research was divided into the two stages. At the first stage, we examined the changes of density of polygon calculation grids used in computations of operational parameters of geothermal doublets. At the second stage, we analyzed the influence of distance between the production and the injection wells on variability in time of operational parameters. The results demonstrated that in both studied cases, the largest differences occurred in pressures measured in production and injection wells whereas the differences in temperatures were less pronounced.
Farquhar, J.; Chacko, T. . Dept. of Geology); Frost, B.R. )
1992-01-01
The Sybille Pit is a late-stage magnetite-ilmenite-plagioclase-bearing differentiate of the Laramie Anorthosite with a wide range of grain sizes and modal mineralogy. This variability makes Sybille an ideal locality in which to study the factors that affect isotopic thermometry in plutonic environments. The authors have developed a numerical model based on isotope exchange trajectories that retrieves close to magmatic temperatures for samples from Sybille. This method is based on the premise that hand sample-scale sub-systems close to exchange with each other at temperatures that exceed those of the constituent minerals. The temperature of hand-sample scale closure is retrieved by back calculating the isotope exchange trajectories to the temperature at which two samples with widely different model compositions are in isotopic equilibrium. Application of these methods to samples from Sybille provides promising results. Whereas conventional isotopic thermometry of individual samples yields a wide range of temperatures ([approximately]600 to > 1000 C) depending on the mineral-pair chosen, application of this numerical model to multiple samples yields temperatures of 1,070 [+-] 100 C which corresponds closely to the inferred solidus for these rocks.
NASA Astrophysics Data System (ADS)
Lebreton, Carole; Stelzer, Kerstin; Brockmann, Carsten; Bertels, Luc; Pringle, Nicholas; Paperin, Michael; Danne, Olaf; Knaeps, Els; Ruddick, Kevin
2016-08-01
Image processing for satellite water quality products requires reliable cloud and cloud shadow detection and cloud classification before atmospheric correction. Within the FP7/HIGHROC ("HIGH spatial and temporal Resolution Ocean Colour") Project, it was necessary to improve cloud detection and the cloud classification algorithms for the spatial high resolution sensors, aiming at Sentinel 2 and using Landsat 8 as a precursor. We present a comparison of three different algorithms, AFAR developed by RBINS; ACCAm created by VITO, and IDEPIX developed by Brockmann Consult. We show image comparisons and the results of the comparison using a pixel identification database (PixBox); FMASK results are also presented as reference.
Vanhille, Christian
2017-01-01
This work deals with a theoretical analysis about the possibility of using linear and nonlinear acoustic properties to modify ultrasound by adding gas bubbles of determined sizes in a liquid. We use a two-dimensional numerical model to evaluate the effect that one and several monodisperse bubble populations confined in restricted areas of a liquid have on ultrasound by calculating their nonlinear interaction. The filtering of an input ultrasonic pulse performed by a net of bubbly-liquid cells is analyzed. The generation of a low-frequency component from a single cell impinged by a two-frequency harmonic wave is also studied. These effects rely on the particular dispersive character of attenuation and nonlinearity of such bubbly fluids, which can be extremely high near bubble resonance. They allow us to observe how gas bubbles can change acoustic signals. Variations of the bubbly medium parameters induce alterations of the effects undergone by ultrasound. Results suggest that acoustic signals can be manipulated by bubbles. This capacity to achieve the modification and control of sound with oscillating gas bubbles introduces the concept of bubbly-liquid-based acoustic metamaterials (BLAMMs). PMID:28106748
NASA Astrophysics Data System (ADS)
Cebriá, J. M.; Martín-Escorza, C.; López-Ruiz, J.; Morán-Zenteno, D. J.; Martiny, B. M.
2011-04-01
Identification of geological lineaments using numerical methods is a useful tool to reveal structures that may not be evident to the naked eye. In this sense, monogenetic volcanic fields represent an especially suitable case for the application of such techniques, since eruptive vents can be considered as point-like features. Application of a two-point azimuth method to the Michoacán-Guanajuato Volcanic Field (Mexico) and the Calatrava Volcanic Province (Spain) demonstrates that the main lineaments controlling the distributions of volcanic vents (~ 322° in Calatrava and ~ 30° in Michoacán) approach the respective main compressional axes that dominate in the area (i.e. the Cocos-North America plates convergence and the main Betics compressional direction, respectively). Considering the stress fields that are present in each volcanic area and their respective geodynamic history, it seems that although volcanism may be a consequence of contemporaneous extensional regimes, the distribution of the volcanic vents in these kinds of monogenetic fields is actually controlled by reactivation of older fractures which then become more favourable for producing space for magma ascent at near-surface levels.
NASA Astrophysics Data System (ADS)
Benaïchouche, Abed; Stab, Olivier; Tessier, Bruno; Cojan, Isabelle
2016-01-01
In landscapes dominated by fluvial erosion, the landscape morphology is closely related to the hydrographic network system. In this paper, we investigate the hydrographic network reorganization caused by a headward piracy mechanism between two drainage basins in France, the Meuse and the Moselle. Several piracies occurred in the Meuse basin during the past one million years, and the basin's current characteristics are favorable to new piracies by the Moselle river network. This study evaluates the consequences over the next several million years of a relative lowering of the Moselle River (and thus of its basin) with respect to the Meuse River. The problem is addressed with a numerical modeling approach (landscape evolution model, hereafter LEM) that requires empirical determinations of parameters and threshold values. Classically, fitting of the parameters is based on analysis of the relationship between the slope and the drainage area and is conducted under the hypothesis of equilibrium. Application of this conventional approach to the capture issue yields incomplete results that have been consolidated by a parametric sensitivity analysis. The LEM equations give a six-dimensional parameter space that was explored with over 15,000 simulations using the landscape evolution model GOLEM. The results demonstrate that stream piracies occur in only four locations in the studied reach near the city of Toul. The locations are mainly controlled by the local topography and are model-independent. Nevertheless, the chronology of the captures depends on two parameters: the river concavity (given by the fluvial advection equation) and the hillslope erosion factor. Thus, the simulations lead to three different scenarios that are explained by a phenomenon of exclusion or a string of events.
Numerical methods for control optimization in linear systems
NASA Astrophysics Data System (ADS)
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
NASA Astrophysics Data System (ADS)
Carlino, Stefano; Troiano, Antonio; Giulia Di Giuseppe, Maria; Tramelli, Anna; Troise, Claudia; Somma, Renato; De Natale, Giuseppe
2015-04-01
The active volcanic area of Campi Flegrei caldera has been the site of many geothermal investigations, since the early XX century. This caldera is characterised by high heat flow, with maximum value > 150 mWm-2, geothermal gradients larger than 200°Ckm-1 and diffuse magmatic gases discharge at the surface. These features encouraged an extensive campaign for geothermal investigation, started in 1939, with many drillings performed at Campanian volcanoes (Campi Flegrei and Ischia) and later at Vesuvius. Several wells aimed to the exploitation of high enthalpy geothermal energy, were drilled in the Campi Flegrei caldera, down to a maximum depth of ~3 km involving mainly two sites (Mofete and S.Vito geothermal fields) located in western and northern sector of caldera respectively. The most interesting site for geothermal exploitation was the Mofete zone, where a number of 4 productive wells were drilled and tested to produce electrical power. Based on data inferred from the productive tests it was established a potential electrical extractable power from Mofete field of at least 10MWe. More recently an empirical evaluation of the whole geothermal potential of the caldera provides a value of more than 1 GWe. The results of AGIP-ENEL exploration at Campi Flegrei highlighted the feasibility of geothermal exploitation. Here, we show for the first time the results of numerical simulations (TOUGH2 code ®) of fluids extraction and reinjection from the Mofete geothermal field, in order to produce at least 5MWe from zero emission power plant (Organic Rankine Cycle type). The simulation is aimed to understand the perturbation of the geothermal reservoir in terms of temperature, pressure change, and possible related seismicity, after different simulated time of exploitation. The modeling is mainly constrained by the data derived from geothermal exploration and productive tests performed since 1979 by AGIP-ENEL Companies. A general assessment of the maximum potential magnitude
Alibés, Andreu; Nadra, Alejandro D; De Masi, Federico; Bulyk, Martha L; Serrano, Luis; Stricher, François
2010-11-01
Quite often a single or a combination of protein mutations is linked to specific diseases. However, distinguishing from sequence information which mutations have real effects in the protein's function is not trivial. Protein design tools are commonly used to explain mutations that affect protein stability, or protein-protein interaction, but not for mutations that could affect protein-DNA binding. Here, we used the protein design algorithm FoldX to model all known missense mutations in the paired box domain of Pax6, a highly conserved transcription factor involved in eye development and in several diseases such as aniridia. The validity of FoldX to deal with protein-DNA interactions was demonstrated by showing that high levels of accuracy can be achieved for mutations affecting these interactions. Also we showed that protein-design algorithms can accurately reproduce experimental DNA-binding logos. We conclude that 88% of the Pax6 mutations can be linked to changes in intrinsic stability (77%) and/or to its capabilities to bind DNA (30%). Our study emphasizes the importance of structure-based analysis to understand the molecular basis of diseases and shows that protein-DNA interactions can be analyzed to the same level of accuracy as protein stability, or protein-protein interactions.
Logistics distribution centers location problem and algorithm under fuzzy environment
NASA Astrophysics Data System (ADS)
Yang, Lixing; Ji, Xiaoyu; Gao, Ziyou; Li, Keping
2007-11-01
Distribution centers location problem is concerned with how to select distribution centers from the potential set so that the total relevant cost is minimized. This paper mainly investigates this problem under fuzzy environment. Consequentially, chance-constrained programming model for the problem is designed and some properties of the model are investigated. Tabu search algorithm, genetic algorithm and fuzzy simulation algorithm are integrated to seek the approximate best solution of the model. A numerical example is also given to show the application of the algorithm.
Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations
NASA Astrophysics Data System (ADS)
Li, Yu-Jia; Jin, Jian-Ming
2009-05-01
A parallel implementation of the electromagnetic dual-primal finite element tearing and interconnecting algorithm (FETI-DPEM) is designed for general three-dimensional (3D) electromagnetic large-scale simulations. As a domain decomposition implementation of the finite element method, the FETI-DPEM algorithm provides fully decoupled subdomain problems and an excellent numerical scalability, and thus is well suited for parallel computation. The parallel implementation of the FETI-DPEM algorithm on a distributed-memory system using the message passing interface (MPI) is discussed in detail along with a few practical guidelines obtained from numerical experiments. Numerical examples are provided to demonstrate the efficiency of the parallel implementation.
Local multiplicative Schwarz algorithms for convection-diffusion equations
NASA Technical Reports Server (NTRS)
Cai, Xiao-Chuan; Sarkis, Marcus
1995-01-01
We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.
Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm
NASA Astrophysics Data System (ADS)
Xiao, Wei-Lin; Zhang, Wei-Guo; Zhang, Xili; Zhang, Xiaoli
2012-12-01
This paper deals with the problem of pricing equity warrants in a mixed fractional Brownian environment. Based on the quasi-conditional expectation and the Fourier transform, we present the pricing model for equity warrants. Moreover, a hybrid intelligent algorithm, which is based on the Genetic Algorithm, is employed to solve the nonlinear optimization problem. The performance of our model and the proposed algorithm have been illustrated with some numerical examples.
A hybrid algorithm for Caputo fractional differential equations
NASA Astrophysics Data System (ADS)
Salgado, G. H. O.; Aguirre, L. A.
2016-04-01
This paper is concerned with the numerical solution of fractional initial value problems (FIVP) in sense of Caputo's definition for dynamical systems. Unlike for integer-order derivatives that have a single definition, there is more than one definition of non integer-order derivatives and the solution of an FIVP is definition-dependent. In this paper, the chief differences of the main definitions of fractional derivatives are revisited and a numerical algorithm to solve an FIVP for Caputo derivative is proposed. The main advantages of the algorithm are twofold: it can be initialized with integer-order derivatives, and it is faster than the corresponding standard algorithm. The performance of the proposed algorithm is illustrated with examples which suggest that it requires about half the computation time to achieve the same accuracy than the standard algorithm.
Analysis of data mining classification by comparison of C4.5 and ID algorithms
NASA Astrophysics Data System (ADS)
Sudrajat, R.; Irianingsih, I.; Krisnawan, D.
2017-01-01
The rapid development of information technology, triggered by the intensive use of information technology. For example, data mining widely used in investment. Many techniques that can be used assisting in investment, the method that used for classification is decision tree. Decision tree has a variety of algorithms, such as C4.5 and ID3. Both algorithms can generate different models for similar data sets and different accuracy. C4.5 and ID3 algorithms with discrete data provide accuracy are 87.16% and 99.83% and C4.5 algorithm with numerical data is 89.69%. C4.5 and ID3 algorithms with discrete data provides 520 and 598 customers and C4.5 algorithm with numerical data is 546 customers. From the analysis of the both algorithm it can classified quite well because error rate less than 15%.
Geist, G.A.; Howell, G.W.; Watkins, D.S.
1997-11-01
The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.
Symbalisty, E.M.D.; Zinn, J.; Whitaker, R.W.
1995-09-01
This paper describes the history, physics, and algorithms of the computer code RADFLO and its extension HYCHEM. RADFLO is a one-dimensional, radiation-transport hydrodynamics code that is used to compute early-time fireball behavior for low-altitude nuclear bursts. The primary use of the code is the prediction of optical signals produced by nuclear explosions. It has also been used to predict thermal and hydrodynamic effects that are used for vulnerability and lethality applications. Another closely related code, HYCHEM, is an extension of RADFLO which includes the effects of nonequilibrium chemistry. Some examples of numerical results will be shown, along with scaling expressions derived from those results. We describe new computations of the structures and luminosities of steady-state shock waves and radiative thermal waves, which have been extended to cover a range of ambient air densities for high-altitude applications. We also describe recent modifications of the codes to use a one-dimensional analog of the CAVEAT fluid-dynamics algorithm in place of the former standard Richtmyer-von Neumann algorithm.
Algorithms and Algorithmic Languages.
ERIC Educational Resources Information Center
Veselov, V. M.; Koprov, V. M.
This paper is intended as an introduction to a number of problems connected with the description of algorithms and algorithmic languages, particularly the syntaxes and semantics of algorithmic languages. The terms "letter, word, alphabet" are defined and described. The concept of the algorithm is defined and the relation between the algorithm and…
Fast algorithm for relaxation processes in big-data systems
NASA Astrophysics Data System (ADS)
Hwang, S.; Lee, D.-S.; Kahng, B.
2014-10-01
Relaxation processes driven by a Laplacian matrix can be found in many real-world big-data systems, for example, in search engines on the World Wide Web and the dynamic load-balancing protocols in mesh networks. To numerically implement such processes, a fast-running algorithm for the calculation of the pseudoinverse of the Laplacian matrix is essential. Here we propose an algorithm which computes quickly and efficiently the pseudoinverse of Markov chain generator matrices satisfying the detailed-balance condition, a general class of matrices including the Laplacian. The algorithm utilizes the renormalization of the Gaussian integral. In addition to its applicability to a wide range of problems, the algorithm outperforms other algorithms in its ability to compute within a manageable computing time arbitrary elements of the pseudoinverse of a matrix of size millions by millions. Therefore our algorithm can be used very widely in analyzing the relaxation processes occurring on large-scale networked systems.
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Markov chain Monte Carlo methods: an introductory example
NASA Astrophysics Data System (ADS)
Klauenberg, Katy; Elster, Clemens
2016-02-01
When the Guide to the Expression of Uncertainty in Measurement (GUM) and methods from its supplements are not applicable, the Bayesian approach may be a valid and welcome alternative. Evaluating the posterior distribution, estimates or uncertainties involved in Bayesian inferences often requires numerical methods to avoid high-dimensional integrations. Markov chain Monte Carlo (MCMC) sampling is such a method—powerful, flexible and widely applied. Here, a concise introduction is given, illustrated by a simple, typical example from metrology. The Metropolis-Hastings algorithm is the most basic and yet flexible MCMC method. Its underlying concepts are explained and the algorithm is given step by step. The few lines of software code required for its implementation invite interested readers to get started. Diagnostics to evaluate the performance and common algorithmic choices are illustrated to calibrate the Metropolis-Hastings algorithm for efficiency. Routine application of MCMC algorithms may be hindered currently by the difficulty to assess the convergence of MCMC output and thus to assure the validity of results. An example points to the importance of convergence and initiates discussion about advantages as well as areas of research. Available software tools are mentioned throughout.
NASA Astrophysics Data System (ADS)
Razali, Azhani Mohd; Abdullah, Jaafar
2015-04-01
Single Photon Emission Computed Tomography (SPECT) is a well-known imaging technique used in medical application, and it is part of medical imaging modalities that made the diagnosis and treatment of disease possible. However, SPECT technique is not only limited to the medical sector. Many works are carried out to adapt the same concept by using high-energy photon emission to diagnose process malfunctions in critical industrial systems such as in chemical reaction engineering research laboratories, as well as in oil and gas, petrochemical and petrochemical refining industries. Motivated by vast applications of SPECT technique, this work attempts to study the application of SPECT on a Pebble Bed Reactor (PBR) using numerical phantom of pebbles inside the PBR core. From the cross-sectional images obtained from SPECT, the behavior of pebbles inside the core can be analyzed for further improvement of the PBR design. As the quality of the reconstructed image is largely dependent on the algorithm used, this work aims to compare two image reconstruction algorithms for SPECT, namely the Expectation Maximization Algorithm and the Exact Inversion Formula. The results obtained from the Exact Inversion Formula showed better image contrast and sharpness, and shorter computational time compared to the Expectation Maximization Algorithm.
Razali, Azhani Mohd Abdullah, Jaafar
2015-04-29
Single Photon Emission Computed Tomography (SPECT) is a well-known imaging technique used in medical application, and it is part of medical imaging modalities that made the diagnosis and treatment of disease possible. However, SPECT technique is not only limited to the medical sector. Many works are carried out to adapt the same concept by using high-energy photon emission to diagnose process malfunctions in critical industrial systems such as in chemical reaction engineering research laboratories, as well as in oil and gas, petrochemical and petrochemical refining industries. Motivated by vast applications of SPECT technique, this work attempts to study the application of SPECT on a Pebble Bed Reactor (PBR) using numerical phantom of pebbles inside the PBR core. From the cross-sectional images obtained from SPECT, the behavior of pebbles inside the core can be analyzed for further improvement of the PBR design. As the quality of the reconstructed image is largely dependent on the algorithm used, this work aims to compare two image reconstruction algorithms for SPECT, namely the Expectation Maximization Algorithm and the Exact Inversion Formula. The results obtained from the Exact Inversion Formula showed better image contrast and sharpness, and shorter computational time compared to the Expectation Maximization Algorithm.
Accurate Finite Difference Algorithms
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1996-01-01
Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.
NASA Technical Reports Server (NTRS)
Kleinman, D. L.
1976-01-01
A numerical technique is given for solving the matrix quadratic equation that arises in the optimal stationary control of linear systems with state (and/or control) dependent noise. The technique exploits fully existing, efficient algorithms for the matrix Lyapunov and Ricatti equations. The computational requirements are discussed, with an associated example.
Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations
NASA Technical Reports Server (NTRS)
Dey, S. K.
1982-01-01
Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.
Boundary acquisition for setup of numerical simulation
Diegert, C.
1997-12-31
The author presents a work flow diagram that includes a path that begins with taking experimental measurements, and ends with obtaining insight from results produced by numerical simulation. Two examples illustrate this path: (1) Three-dimensional imaging measurement at micron scale, using X-ray tomography, provides information on the boundaries of irregularly-shaped alumina oxide particles held in an epoxy matrix. A subsequent numerical simulation predicts the electrical field concentrations that would occur in the observed particle configurations. (2) Three-dimensional imaging measurement at meter scale, again using X-ray tomography, provides information on the boundaries fossilized bone fragments in a Parasaurolophus crest recently discovered in New Mexico. A subsequent numerical simulation predicts acoustic response of the elaborate internal structure of nasal passageways defined by the fossil record. The author must both add value, and must change the format of the three-dimensional imaging measurements before the define the geometric boundary initial conditions for the automatic mesh generation, and subsequent numerical simulation. The author applies a variety of filters and statistical classification algorithms to estimate the extents of the structures relevant to the subsequent numerical simulation, and capture these extents as faceted geometries. The author will describe the particular combination of manual and automatic methods used in the above two examples.
Gao, Wei; Chen, Dongliang; Wang, Xu
2016-01-01
To compute the stability of underground engineering, a constitutive model of surrounding rock must be identified. Many constitutive models for rock mass have been proposed. In this model identification study, a generalized constitutive law for an elastic-plastic constitutive model is applied. Using the generalized constitutive law, the problem of model identification is transformed to a problem of parameter identification, which is a typical and complicated optimization. To improve the efficiency of the traditional optimization method, an immunized genetic algorithm that is proposed by the author is applied in this study. In this new algorithm, the principle of artificial immune algorithm is combined with the genetic algorithm. Therefore, the entire computation efficiency of model identification will be improved. Using this new model identification method, a numerical example and an engineering example are used to verify the computing ability of the algorithm. The results show that this new model identification algorithm can significantly improve the computation efficiency and the computation effect.
Advances in Numerical Boundary Conditions for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.
1997-01-01
Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.
NASA Astrophysics Data System (ADS)
Pei, Chengquan; Tian, Jinshou; Wu, Shengli; He, Jiai; Liu, Zhen
2016-10-01
The transient response is of great influence on the electromagnetic compatibility of synchronous scanning streak cameras (SSSCs). In this paper we propose a numerical method to evaluate the transient response of the scanning deflection plate (SDP). First, we created a simplified circuit model for the SDP used in an SSSC, and then derived the Baum-Liu-Tesche (BLT) equation in the frequency domain. From the frequency-domain BLT equation, its transient counterpart was derived. These parameters, together with the transient-BLT equation, were used to compute the transient load voltage and load current, and then a novel numerical method to fulfill the continuity equation was used. Several numerical simulations were conducted to verify this proposed method. The computed results were then compared with transient responses obtained by a frequency-domain/fast Fourier transform (FFT) method, and the accordance was excellent for highly conducting cables. The benefit of deriving the BLT equation in the time domain is that it may be used with slight modifications to calculate the transient response and the error can be controlled by a computer program. The result showed that the transient voltage was up to 1000 V and the transient current was approximately 10 A, so some protective measures should be taken to improve the electromagnetic compatibility.
A frictional sliding algorithm for liquid droplets
NASA Astrophysics Data System (ADS)
Sauer, Roger A.
2016-12-01
This work presents a new frictional sliding algorithm for liquid menisci in contact with solid substrates. In contrast to solid-solid contact, the liquid-solid contact behavior is governed by the contact line, where a contact angle forms and undergoes hysteresis. The new algorithm admits arbitrary meniscus shapes and arbitrary substrate roughness, heterogeneity and compliance. It is discussed and analyzed in the context of droplet contact, but it also applies to liquid films and solids with surface tension. The droplet is modeled as a stabilized membrane enclosing an incompressible medium. The contact formulation is considered rate-independent such that hydrostatic conditions apply. Three distinct contact algorithms are needed to describe the cases of frictionless surface contact, frictionless line contact and frictional line contact. For the latter, a predictor-corrector algorithm is proposed in order to enforce the contact conditions at the contact line and thus distinguish between the cases of advancing, pinning and receding. The algorithms are discretized within a monolithic finite element formulation. Several numerical examples are presented to illustrate the numerical and physical behavior of sliding droplets.
Introduction to Numerical Methods
Schoonover, Joseph A.
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis
ERIC Educational Resources Information Center
Bernaards, Coen A.; Jennrich, Robert I.
2005-01-01
Almost all modern rotation of factor loadings is based on optimizing a criterion, for example, the quartimax criterion for quartimax rotation. Recent advancements in numerical methods have led to general orthogonal and oblique algorithms for optimizing essentially any rotation criterion. All that is required for a specific application is a…
NASA Astrophysics Data System (ADS)
Ryaben'kii, V. S.; Turchaninov, V. I.; Epshteyn, Ye. Yu.
2006-10-01
An algorithm composition scheme for the numerical solution of boundary value problems in composite domains is proposed and illustrated using an example. The scheme requires neither difference approximations of the boundary conditions nor matching conditions on the boundary between the subdomains. The scheme is suited for multiprocessor computers.
Cryer, S A; van Wesenbeeck, I J; Knuteson, J A
2003-05-21
Soil fumigants, used to control nematodes and crop disease, can volatilize from the soil application zone and into the atmosphere to create the potential for human inhalation exposure. An objective for this work is to illustrate the ability of simple numerical models to correctly predict pesticide volatilization rates from agricultural fields and to expand emission predictions to nearby air concentrations for use in the exposure component of a risk assessment. This work focuses on a numerical system using two U.S. EPA models (PRZM3 and ISCST3) to predict regional volatilization and nearby air concentrations for the soil fumigant 1,3-dichloropropene. New approaches deal with links to regional databases, seamless coupling of emission and dispersion models, incorporation of Monte Carlo sampling techniques to account for parametric uncertainty, and model input sensitivity analysis. Predicted volatility flux profiles of 1,3-dichloropropene (1,3-D) from soil for tarped and untarped fields were compared against field data and used as source terms for ISCST3. PRZM3 can successfully estimate correct order of magnitude regional soil volatilization losses of 1,3-D when representative regional input parameters are used (soil, weather, chemical, and management practices). Estimated 1,3-D emission losses and resulting air concentrations were investigated for five geographically diverse regions. Air concentrations (15-day averages) are compared with the current U.S. EPA's criteria for human exposure and risk assessment to determine appropriate setback distances from treated fields. Sensitive input parameters for volatility losses were functions of the region being simulated.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Yu, Zhi
2013-10-15
Smoothing functions are commonly used to reduce numerical noise arising from coarse sampling of particles in particle-in-cell (PIC) plasma simulations. When applying smoothing functions to symplectic algorithms, the conservation of symplectic structure should be guaranteed to preserve good conservation properties. In this paper, we show how to construct a variational multi-symplectic PIC algorithm with smoothing functions for the Vlasov-Maxwell system. The conservation of the multi-symplectic structure and the reduction of numerical noise make this algorithm specifically suitable for simulating long-term dynamics of plasmas, such as those in the steady-state operation or long-pulse discharge of a super-conducting tokamak. The algorithm has been implemented in a 6D large scale PIC code. Numerical examples are given to demonstrate the good conservation properties of the multi-symplectic algorithm and the reduction of the noise due to the application of smoothing function.
NASA Astrophysics Data System (ADS)
Kim, Jung-Gon; Shin, Won-Ho; Hwang, Hyun-Woo; Jeong, Jun; Park, Kyoung-Su; Park, No-Cheol; Yang, Hyunseok; Park, Young-Pil; Moo Park, Jin; Son, Do Hyeon; Kyo Seo, Jeong; Choi, In Ho
2010-08-01
A near-field storage system using a solid immersion lens (SIL) has been studied as a high-density optical disc drive system. The major goal of this research is to improve the robustness of the air-gap controller for a SIL-based near-field recording (NFR) system against dynamic disturbances, such as external shocks. The servo system is essential in near-field (NF) technology because the nanogap distance between the SIL and the disc is 50 nm or less. Also, the air-gap distance must be maintained without collision between the SIL and the disc to detect a stable gap error and read-out signals when an external shock is applied. Therefore, we propose an improved air-gap control algorithm using only an acceleration feedforward controller (AFC) to maintain the air-gap distance without contact for a 4.48 G at 10 ms shock. Thus, the antishock control performance for the SIL-based NF storage system in the presence of external shocks is markedly improved. Furthermore, to enhance the performance of the antishock air-gap control, we use the AFC with a double disturbance observer and a dead-zone nonlinear controller. As a result, the air-gap distance is maintained without contact for a 6.56 G@10 ms shock.
Active Learning with Irrelevant Examples
NASA Technical Reports Server (NTRS)
Wagstaff, Kiri; Mazzoni, Dominic
2009-01-01
An improved active learning method has been devised for training data classifiers. One example of a data classifier is the algorithm used by the United States Postal Service since the 1960s to recognize scans of handwritten digits for processing zip codes. Active learning algorithms enable rapid training with minimal investment of time on the part of human experts to provide training examples consisting of correctly classified (labeled) input data. They function by identifying which examples would be most profitable for a human expert to label. The goal is to maximize classifier accuracy while minimizing the number of examples the expert must label. Although there are several well-established methods for active learning, they may not operate well when irrelevant examples are present in the data set. That is, they may select an item for labeling that the expert simply cannot assign to any of the valid classes. In the context of classifying handwritten digits, the irrelevant items may include stray marks, smudges, and mis-scans. Querying the expert about these items results in wasted time or erroneous labels, if the expert is forced to assign the item to one of the valid classes. In contrast, the new algorithm provides a specific mechanism for avoiding querying the irrelevant items. This algorithm has two components: an active learner (which could be a conventional active learning algorithm) and a relevance classifier. The combination of these components yields a method, denoted Relevance Bias, that enables the active learner to avoid querying irrelevant data so as to increase its learning rate and efficiency when irrelevant items are present. The algorithm collects irrelevant data in a set of rejected examples, then trains the relevance classifier to distinguish between labeled (relevant) training examples and the rejected ones. The active learner combines its ranking of the items with the probability that they are relevant to yield a final decision about which item
NASA Astrophysics Data System (ADS)
Maglevanny, I. I.; Smolar, V. A.
2016-01-01
We introduce a new technique of interpolation of the energy-loss function (ELF) in solids sampled by empirical optical spectra. Finding appropriate interpolation methods for ELFs poses several challenges. The sampled ELFs are usually very heterogeneous, can originate from various sources thus so called "data gaps" can appear, and significant discontinuities and multiple high outliers can be present. As a result an interpolation based on those data may not perform well at predicting reasonable physical results. Reliable interpolation tools, suitable for ELF applications, should therefore satisfy several important demands: accuracy and predictive power, robustness and computational efficiency, and ease of use. We examined the effect on the fitting quality due to different interpolation schemes with emphasis on ELF mesh optimization procedures and we argue that the optimal fitting should be based on preliminary log-log scaling data transforms by which the non-uniformity of sampled data distribution may be considerably reduced. The transformed data are then interpolated by local monotonicity preserving Steffen spline. The result is a piece-wise smooth fitting curve with continuous first-order derivatives that passes through all data points without spurious oscillations. Local extrema can occur only at grid points where they are given by the data, but not in between two adjacent grid points. It is found that proposed technique gives the most accurate results and also that its computational time is short. Thus, it is feasible using this simple method to address practical problems associated with interaction between a bulk material and a moving electron. A compact C++ implementation of our algorithm is also presented.
Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised
NASA Technical Reports Server (NTRS)
Yee, Helen C.; Sweby, Peter K.
1997-01-01
The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.
Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories
NASA Astrophysics Data System (ADS)
Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.
2010-06-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Numeric Databases in the Sciences.
ERIC Educational Resources Information Center
Meschel, S. V.
1984-01-01
Provides exploration into types of numeric databases available (also known as source databases, nonbibliographic databases, data-files, data-banks, fact banks); examines differences and similarities between bibliographic and numeric databases; identifies disciplines that utilize numeric databases; and surveys representative examples in the…
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
NASA Astrophysics Data System (ADS)
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Acceleration of quantum optimal control theory algorithms with mixing strategies.
Castro, Alberto; Gross, E K U
2009-05-01
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in quantum optimal control theory (QOCT). We show how the nonlinear equations of QOCT can be viewed as a "fixed-point" nonlinear problem. The iterative algorithms for this class of problems may benefit from mixing strategies, as it happens, e.g., in the quest for the ground-state density in Kohn-Sham density-functional theory. We demonstrate, with some numerical examples, how the same mixing schemes utilized in this latter nonlinear problem may significantly accelerate the QOCT iterative procedures.
Thermoluminescence curves simulation using genetic algorithm with factorial design
NASA Astrophysics Data System (ADS)
Popko, E. A.; Weinstein, I. A.
2016-05-01
The evolutionary approach is an effective optimization tool for numeric analysis of thermoluminescence (TL) processes to assess the microparameters of kinetic models and to determine its effects on the shape of TL peaks. In this paper, the procedure for tuning of genetic algorithm (GA) is presented. This approach is based on multifactorial experiment and allows choosing intrinsic mechanisms of evolutionary operators which provide the most efficient algorithm performance. The proposed method is tested by considering the “one trap-one recombination center” (OTOR) model as an example and advantages for approximation of experimental TL curves are shown.
Efficient sequential and parallel algorithms for record linkage
Mamun, Abdullah-Al; Mi, Tian; Aseltine, Robert; Rajasekaran, Sanguthevar
2014-01-01
Background and objective Integrating data from multiple sources is a crucial and challenging problem. Even though there exist numerous algorithms for record linkage or deduplication, they suffer from either large time needs or restrictions on the number of datasets that they can integrate. In this paper we report efficient sequential and parallel algorithms for record linkage which handle any number of datasets and outperform previous algorithms. Methods Our algorithms employ hierarchical clustering algorithms as the basis. A key idea that we use is radix sorting on certain attributes to eliminate identical records before any further processing. Another novel idea is to form a graph that links similar records and find the connected components. Results Our sequential and parallel algorithms have been tested on a real dataset of 1 083 878 records and synthetic datasets ranging in size from 50 000 to 9 000 000 records. Our sequential algorithm runs at least two times faster, for any dataset, than the previous best-known algorithm, the two-phase algorithm using faster computation of the edit distance (TPA (FCED)). The speedups obtained by our parallel algorithm are almost linear. For example, we get a speedup of 7.5 with 8 cores (residing in a single node), 14.1 with 16 cores (residing in two nodes), and 26.4 with 32 cores (residing in four nodes). Conclusions We have compared the performance of our sequential algorithm with TPA (FCED) and found that our algorithm outperforms the previous one. The accuracy is the same as that of this previous best-known algorithm. PMID:24154837
Verifying a Computer Algorithm Mathematically.
ERIC Educational Resources Information Center
Olson, Alton T.
1986-01-01
Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)
Randomized Algorithms for Matrices and Data
NASA Astrophysics Data System (ADS)
Mahoney, Michael W.
2012-03-01
This chapter reviews recent work on randomized matrix algorithms. By “randomized matrix algorithms,” we refer to a class of recently developed random sampling and random projection algorithms for ubiquitous linear algebra problems such as least-squares (LS) regression and low-rank matrix approximation. These developments have been driven by applications in large-scale data analysis—applications which place very different demands on matrices than traditional scientific computing applications. Thus, in this review, we will focus on highlighting the simplicity and generality of several core ideas that underlie the usefulness of these randomized algorithms in scientific applications such as genetics (where these algorithms have already been applied) and astronomy (where, hopefully, in part due to this review they will soon be applied). The work we will review here had its origins within theoretical computer science (TCS). An important feature in the use of randomized algorithms in TCS more generally is that one must identify and then algorithmically deal with relevant “nonuniformity structure” in the data. For the randomized matrix algorithms to be reviewed here and that have proven useful recently in numerical linear algebra (NLA) and large-scale data analysis applications, the relevant nonuniformity structure is defined by the so-called statistical leverage scores. Defined more precisely below, these leverage scores are basically the diagonal elements of the projection matrix onto the dominant part of the spectrum of the input matrix. As such, they have a long history in statistical data analysis, where they have been used for outlier detection in regression diagnostics. More generally, these scores often have a very natural interpretation in terms of the data and processes generating the data. For example, they can be interpreted in terms of the leverage or influence that a given data point has on, say, the best low-rank matrix approximation; and this
A general-purpose contact detection algorithm for nonlinear structural analysis codes
Heinstein, M.W.; Attaway, S.W.; Swegle, J.W.; Mello, F.J.
1993-05-01
A new contact detection algorithm has been developed to address difficulties associated with the numerical simulation of contact in nonlinear finite element structural analysis codes. Problems including accurate and efficient detection of contact for self-contacting surfaces, tearing and eroding surfaces, and multi-body impact are addressed. The proposed algorithm is portable between dynamic and quasi-static codes and can efficiently model contact between a variety of finite element types including shells, bricks, beams and particles. The algorithm is composed of (1) a location strategy that uses a global search to decide which slave nodes are in proximity to a master surface and (2) an accurate detailed contact check that uses the projected motions of both master surface and slave node. In this report, currently used contact detection algorithms and their associated difficulties are discussed. Then the proposed algorithm and how it addresses these problems is described. Finally, the capability of the new algorithm is illustrated with several example problems.
Fast Numerical Methods for Stochastic Partial Differential Equations
2016-04-15
uncertainty quantification. In the last decade much progress has been made in the construction of numerical algorithms to efficiently solve SPDES with...applicable SPDES with efficient numerical methods. This project is intended to address the numerical analysis as well as algorithm aspects of SPDES. Three...differential equations. Our work contains algorithm constructions, rigorous error analysis, and extensive numerical experiments to demonstrate our algorithm
A hybrid Gerchberg-Saxton-like algorithm for DOE and CGH calculation
NASA Astrophysics Data System (ADS)
Wang, Haichao; Yue, Weirui; Song, Qiang; Liu, Jingdan; Situ, Guohai
2017-02-01
The Gerchberg-Saxton (GS) algorithm is widely used in various disciplines of modern sciences and technologies where phase retrieval is required. However, this legendary algorithm most likely stagnates after a few iterations. Many efforts have been taken to improve this situation. Here we propose to introduce the strategy of gradient descent and weighting technique to the GS algorithm, and demonstrate it using two examples: design of a diffractive optical element (DOE) to achieve off-axis illumination in lithographic tools, and design of a computer generated hologram (CGH) for holographic display. Both numerical simulation and optical experiments are carried out for demonstration.
NASA Astrophysics Data System (ADS)
Lim, Gerald
2005-03-01
I have implemented a simple and robust numerical technique for calculating axisymmetric equilibrium shapes of one-component lipid bilayer vesicles. This so-called Tethered Infinitesimal Tori and Spheres (TITS) Algorithm gives shapes that are automatically stable with respect to axisymmetric perturbations. The latest version of this algorithm can, but is not restricted to, impose constraints on any of three geometrical quantities: the area, volume and pole-to-pole distance (in the case of tether formation). In this talk, I will introduce the basic principles of the TITS Algorithm and demonstrate its versatility through a few example shape calculations involving the Helfrich and Area Difference Elasticity bending free energies.
Structure and structure-preserving algorithms for plasma physics
NASA Astrophysics Data System (ADS)
Morrison, P. J.
2016-10-01
Conventional simulation studies of plasma physics are based on numerically solving the underpinning differential (or integro-differential) equations. Usual algorithms in general do not preserve known geometric structure of the physical systems, such as the local energy-momentum conservation law, Casimir invariants, and the symplectic structure (Poincaré invariants). As a consequence, numerical errors may accumulate coherently with time and long-term simulation results may be unreliable. Recently, a series of geometric algorithms that preserve the geometric structures resulting from the Hamiltonian and action principle (HAP) form of theoretical models in plasma physics have been developed by several authors. The superiority of these geometric algorithms has been demonstrated with many test cases. For example, symplectic integrators for guiding-center dynamics have been constructed to preserve the noncanonical symplectic structures and bound the energy-momentum errors for all simulation time-steps; variational and symplectic algorithms have been discovered and successfully applied to the Vlasov-Maxwell system, MHD, and other magnetofluid equations as well. Hamiltonian truncations of the full Vlasov-Maxwell system have opened the field of discrete gyrokinetics and led to the GEMPIC algorithm. The vision that future numerical capabilities in plasma physics should be based on structure-preserving geometric algorithms will be presented. It will be argued that the geometric consequences of HAP form and resulting geometric algorithms suitable for plasma physics studies cannot be adapted from existing mathematical literature but, rather, need to be discovered and worked out by theoretical plasma physicists. The talk will review existing HAP structures of plasma physics for a variety of models, and how they have been adapted for numerical implementation. Supported by DOE DE-FG02-04ER-54742.
REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination
NASA Technical Reports Server (NTRS)
Bar-Itzhack, Itzhack Y.
1996-01-01
In order to find the attitude of a spacecraft with respect to a reference coordinate system, vector measurements are taken. The vectors are pairs of measurements of the same generalized vector, taken in the spacecraft body coordinates, as well as in the reference coordinate system. We are interested in finding the best estimate of the transformation between these coordinate system.s The algorithm called QUEST yields that estimate where attitude is expressed by a quarternion. Quest is an efficient algorithm which provides a least squares fit of the quaternion of rotation to the vector measurements. Quest however, is a single time point (single frame) batch algorithm, thus measurements that were taken at previous time points are discarded. The algorithm presented in this work provides a recursive routine which considers all past measurements. The algorithm is based on on the fact that the, so called, K matrix, one of whose eigenvectors is the sought quaternion, is linerly related to the measured pairs, and on the ability to propagate K. The extraction of the appropriate eigenvector is done according to the classical QUEST algorithm. This stage, however, can be eliminated, and the computation simplified, if a standard eigenvalue-eigenvector solver algorithm is used. The development of the recursive algorithm is presented and illustrated via a numerical example.
NASA Astrophysics Data System (ADS)
Mehanee, Salah A.; Essa, Khalid S.
2015-08-01
A new two-and-a-half dimensional (2.5D) regularized inversion scheme has been developed for the interpretation of residual gravity data by a dipping thin-sheet model. This scheme solves for the characteristic inverse parameters (depth to top z, dip angle θ, extension in depth L, strike length 2 Y, and amplitude coefficient A) of a model in the space of logarithms of these parameters (log( z), log( θ), log( L), log( Y), and log(| A|)). The developed method has been successfully verified on synthetic examples without noise. The method is found stable and can estimate the inverse parameters of the buried target with acceptable accuracy when applied to data contaminated with various noise levels. However, some of the inverse parameters encountered some inaccuracy when the method was applied to synthetic data distorted by significant neighboring gravity effects/interferences. The validity of this method for practical applications has been successfully illustrated on two field examples with diverse geologic settings from mineral exploration. The estimated inverse parameters of the real data investigated are found to generally conform well with those yielded from drilling. The method is shown to be highly applicable for mineral prospecting and reconnaissance studies. It is capable of extracting the various characteristic inverse parameters that are of geologic and economic significance, and is of particular value in cases where the residual gravity data set is due to an isolated thin-sheet type buried target. The sensitivity analysis carried out on the Jacobian matrices of the field examples investigated here has shown that the parameter that can be determined with the superior accuracy is θ (as confirmed from drilling information). The parameters z, L, Y, and A can be estimated with acceptable accuracy, especially the parameters z and A. This inverse problem is non-unique. The non-uniqueness analysis and the tabulated inverse results presented here have shown that the
Parallel algorithms for boundary value problems
NASA Technical Reports Server (NTRS)
Lin, Avi
1991-01-01
A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.
Parallel algorithms for boundary value problems
NASA Technical Reports Server (NTRS)
Lin, Avi
1990-01-01
A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.
"Recognizing Numerical Constants"
NASA Technical Reports Server (NTRS)
Bailey, David H.; Craw, James M. (Technical Monitor)
1995-01-01
The advent of inexpensive, high performance computer and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining, within certain limits, whether a computed real or complex number can be written as a simple expression involving the classical constants of mathematics. In this presentation, some of the recently discovered techniques for constant recognition, notably integer relation detection algorithms, will be presented. As an application of these methods, the author's recent work in recognizing "Euler sums" will be described in some detail.
A split finite element algorithm for the compressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Baker, A. J.
1979-01-01
An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.
Concurrent Computing: Numerical Algorithms and Some Applications.
1986-07-15
determinant of the harmonic frequencies This result was obtained via a combination of relationships using classical trigonometric moment theory and...component, the out put management subsystem, is the most problem dependent. Current plans call for the design of basic tools for displaying results which...will be augmented as particular applications are tried. During this same time period, we plan to establish a network linking the project’s concurrent
Implementation of Parallel Algorithms
1993-06-30
their socia ’ relations or to achieve some goals. For example, we define a pair-wise force law of i epulsion and attraction for a group of identical...quantization based compression schemes. Photo-refractive crystals, which provide high density recording in real time, are used as our holographic media . The...of Parallel Algorithms (J. Reif, ed.). Kluwer Academic Pu’ ishers, 1993. (4) "A Dynamic Separator Algorithm", D. Armon and J. Reif. To appear in
Parallel Algorithms and Patterns
Robey, Robert W.
2016-06-16
This is a powerpoint presentation on parallel algorithms and patterns. A parallel algorithm is a well-defined, step-by-step computational procedure that emphasizes concurrency to solve a problem. Examples of problems include: Sorting, searching, optimization, matrix operations. A parallel pattern is a computational step in a sequence of independent, potentially concurrent operations that occurs in diverse scenarios with some frequency. Examples are: Reductions, prefix scans, ghost cell updates. We only touch on parallel patterns in this presentation. It really deserves its own detailed discussion which Gabe Rockefeller would like to develop.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Haq, Ihsanul
2014-01-01
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Haq, Ihsanul
2014-01-01
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions. PMID:24672381
NASA Astrophysics Data System (ADS)
Jaunat, J.; Dupuy, A.; Huneau, F.; Celle-Jeanton, H.; Le Coustumer, P.
2016-09-01
A numerical groundwater model of the weathered crystalline aquifer of Ursuya (a major water source for the north-western Pyrenees region, south-western France) has been computed based on monitoring of hydrological, hydrodynamic and meteorological parameters over 3 years. The equivalent porous media model was used to simulate groundwater flow in the different layers of the weathered profile: from surface to depth, the weathered layer (5 · 10-8 ≤ K ≤ 5 · 10-7 m s-1), the transition layer (7 · 10-8 ≤ K ≤ 1 · 10-5 m s-1, the highest values being along major discontinuities), two fissured layers (3.5 · 10-8 ≤ K ≤ 5 · 10-4 m s-1, depending on weathering profile conditions and on the existence of active fractures), and the hard-rock basement simulated with a negligible hydraulic conductivity ( K = 1 10 -9 ). Hydrodynamic properties of these five calculation layers demonstrate both the impact of the weathering degree and of the discontinuities on the groundwater flow. The great agreement between simulated and observed hydraulic conditions allowed for validation of the methodology and its proposed use for application on analogous aquifers. With the aim of long-term management of this strategic aquifer, the model was then used to evaluate the impact of climate change on the groundwater resource. The simulations performed according to the most pessimistic climatic scenario until 2050 show a low sensitivity of the aquifer. The decreasing trend of the natural discharge is estimated at about -360 m3 y-1 for recharge decreasing at about -5.6 mm y-1 (0.8 % of annual recharge).
Numerical methods used in fusion science numerical modeling
NASA Astrophysics Data System (ADS)
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
Numerical simulation of dusty plasmas
Winske, D.
1995-09-01
The numerical simulation of physical processes in dusty plasmas is reviewed, with emphasis on recent results and unresolved issues. Three areas of research are discussed: grain charging, weak dust-plasma interactions, and strong dust-plasma interactions. For each area, we review the basic concepts that are tested by simulations, present some appropriate examples, and examine numerical issues associated with extending present work.
Numerical Approaches to Spacetime Singularities.
Berger, Beverly K
1998-01-01
This review updates a previous review article [22]. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G.E.
2016-01-15
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Methods of information theory and algorithmic complexity for network biology.
Zenil, Hector; Kiani, Narsis A; Tegnér, Jesper
2016-03-01
We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdös-Rényi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data. We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs, characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.
Algorithms for verbal autopsies: a validation study in Kenyan children.
Quigley, M. A.; Armstrong Schellenberg, J. R.; Snow, R. W.
1996-01-01
The verbal autopsy (VA) questionnaire is a widely used method for collecting information on cause-specific mortality where the medical certification of deaths in childhood is incomplete. This paper discusses review by physicians and expert algorithms as approaches to ascribing cause of deaths from the VA questionnaire and proposes an alternative, data-derived approach. In this validation study, the relatives of 295 children who had died in hospital were interviewed using a VA questionnaire. The children were assigned causes of death using data-derived algorithms obtained under logistic regression and using expert algorithms. For most causes of death, the data-derived algorithms and expert algorithms yielded similar levels of diagnostic accuracy. However, a data-derived algorithm for malaria gave a sensitivity of 71% (95% Cl: 58-84%), which was significantly higher than the sensitivity of 47% obtained under an expert algorithm. The need for exploring this and other ways in which the VA technique can be improved are discussed. The implications of less-than-perfect sensitivity and specificity are explored using numerical examples. Misclassification bias should be taken into consideration when planning and evaluating epidemiological studies. PMID:8706229
NASA Astrophysics Data System (ADS)
FENG, Xiaojun; Gerbault, Muriel; Martin, Roland; Ganne, Jérôme; Jessell, Mark
2015-04-01
High strain zones appear to play a significant role in feeding the upper crust with fluids and partially molten material from lower crust sources. The Bole-Bulenga terrain (North-Western Ghana) is located in between two subvertical shear zones, and mainly consists of high-grade orthogneisses, paragneisses and metabasites intruded by partially molten lower crustal material with monzogranites and orthogneisses (Eburnean orogeny, around 2.1 Ga). In order to understand the location of these high grade rocks at the edges and in between these two shear zones, a three dimensional numerical model was built to test the influence of different orientations of a system of branched strike-slip faults on visco-plastic deformation, under compressional and simple shear boundary conditions. Our models indicate domains of tensile vs. compressional strain as well as shear zones, and show that not only internal fault zones but also the host rock in between the faults behave relatively softer than external regions. Under both applied compressive and simple shear boundary conditions, these softened domains constitute preferential zones of tensile strain accommodation (dilation) in the upper crust, which may favor infilling by deeper partially molten rocks. Our modeled pre-existing faults zones are assumed to have formed during an early D1 stage of deformation, and they are shown to passively migrate and rotate together with the solid matrix under applied external boundary conditions (corresponding to a post D1 - early D2 phase of deformation). We suggest that in the Bole-Bulenga terrain, fluids or partially molten material stored in deeper crustal domains, preferentially intruded the upper crust within these highly (shear and tensile) strained domains, thanks to this D2 shearing deformation phase. Building relief at the surface is primarily controlled by fault orientations, together with mechanical parameters and external boundary conditions. In particular, greatest magnitudes of relief
ERIC Educational Resources Information Center
Siegler, Robert S.; Braithwaite, David W.
2016-01-01
In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…
ERIC Educational Resources Information Center
Bright, William
In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…
NASA Technical Reports Server (NTRS)
Martin, E. D.; Lomax, H.
1977-01-01
Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.
Numerical modeling of ocean hydrodynamics with variational assimilation of observational data
NASA Astrophysics Data System (ADS)
Zalesny, V. B.; Agoshkov, V. I.; Shutyaev, V. P.; Le Dimet, F.; Ivchenko, B. O.
2016-07-01
Models and methods of the numerical modeling of ocean hydrodynamics dating back to the pioneering works of A.S. Sarkisyan are considered, with emphasis on the formulation of problems and algorithms of mathematical modeling and the four-dimensional variational assimilation of observational data. An algorithm is proposed for studying the sensitivity of the optimal solution to observational data errors in a seasurface temperature assimilation problem in order to retrieve heat fluxes on the surface. An example of a solution of the optimal problem of the World Ocean hydrodynamics with the assimilation of climatic temperature and salinity observations is offered.
NASA Astrophysics Data System (ADS)
Amisigo, B. A.; van de Giesen, N. C.
2005-04-01
A spatio-temporal linear dynamic model has been developed for patching short gaps in daily river runoff series. The model was cast in a state-space form in which the state variable was estimated using the Kalman smoother (RTS smoother). The EM algorithm was used to concurrently estimate both parameter and missing runoff values. Application of the model to daily runoff series in the Volta Basin of West Africa showed that the model was capable of providing good estimates of missing runoff values at a gauging station from the remaining series at the station and at spatially correlated stations in the same sub-basin.
NASA Astrophysics Data System (ADS)
Chierici, Francesco; Beranzoli, Laura; Best, Mairi; Embriaco, Davide; Favali, Paolo; Galbraith, Nan; Heeseman, Martin; Kelly, Deborah; Pignagnoli, Luca; Pirenne, Benoit; Scofield, Oscar; Weller, Robert; Zitellini, Nevio
2015-04-01
The development of Tsunami modeling and Tsunami Early Warning Systems able to operate in near-source areas is a common need for many coastal regions like Mediterranean, Juan de Fuca/NE Pacific Coast of North America, Indian Ocean archipelagos and Japan. These regions with the important exception of Mediterranean and North East Atlantic are presently covered by Tsunami Warning Systems and Ocean Bottom Observatories, in the frame of EMSO, OOI and ONC ocean networks equipped with a varieties of sensors, using different technologies, data formats and detection procedures. A significant improvement in efficiency, cost saving and detection reliability can be achieved by exchanging technologies and data and by harmonizing sensors metadata and instrument settings. To undertake a step in this direction we propose to apply the Tsunami Detection Algorithm, which was developed in the framework of NEAREST EU project for open ocean data in near source areas and is presently used by NEMO-SN1 EMSO abyssal observatory, to the tide gauge data of Arena Cove, CA and Cordova, AK. We show the first results of the application of the algorithm.
On the numeric integration of dynamic attitude equations
NASA Technical Reports Server (NTRS)
Crouch, P. E.; Yan, Y.; Grossman, Robert
1992-01-01
We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.
Frontiers in Numerical Relativity
NASA Astrophysics Data System (ADS)
Evans, Charles R.; Finn, Lee S.; Hobill, David W.
2011-06-01
Preface; Participants; Introduction; 1. Supercomputing and numerical relativity: a look at the past, present and future David W. Hobill and Larry L. Smarr; 2. Computational relativity in two and three dimensions Stuart L. Shapiro and Saul A. Teukolsky; 3. Slowly moving maximally charged black holes Robert C. Ferrell and Douglas M. Eardley; 4. Kepler's third law in general relativity Steven Detweiler; 5. Black hole spacetimes: testing numerical relativity David H. Bernstein, David W. Hobill and Larry L. Smarr; 6. Three dimensional initial data of numerical relativity Ken-ichi Oohara and Takashi Nakamura; 7. Initial data for collisions of black holes and other gravitational miscellany James W. York, Jr.; 8. Analytic-numerical matching for gravitational waveform extraction Andrew M. Abrahams; 9. Supernovae, gravitational radiation and the quadrupole formula L. S. Finn; 10. Gravitational radiation from perturbations of stellar core collapse models Edward Seidel and Thomas Moore; 11. General relativistic implicit radiation hydrodynamics in polar sliced space-time Paul J. Schinder; 12. General relativistic radiation hydrodynamics in spherically symmetric spacetimes A. Mezzacappa and R. A. Matzner; 13. Constraint preserving transport for magnetohydrodynamics John F. Hawley and Charles R. Evans; 14. Enforcing the momentum constraints during axisymmetric spacelike simulations Charles R. Evans; 15. Experiences with an adaptive mesh refinement algorithm in numerical relativity Matthew W. Choptuik; 16. The multigrid technique Gregory B. Cook; 17. Finite element methods in numerical relativity P. J. Mann; 18. Pseudo-spectral methods applied to gravitational collapse Silvano Bonazzola and Jean-Alain Marck; 19. Methods in 3D numerical relativity Takashi Nakamura and Ken-ichi Oohara; 20. Nonaxisymmetric rotating gravitational collapse and gravitational radiation Richard F. Stark; 21. Nonaxisymmetric neutron star collisions: initial results using smooth particle hydrodynamics
NASA Technical Reports Server (NTRS)
Wang, Lui; Bayer, Steven E.
1991-01-01
Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.
An algorithm for the solution of dynamic linear programs
NASA Technical Reports Server (NTRS)
Psiaki, Mark L.
1989-01-01
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation
NASA Astrophysics Data System (ADS)
Mohsen Mousavi, Seyed; Niaki, Seyed Taghi Akhavan; Mehdizadeh, Esmaeil; Tavarroth, Mohammad Reza
2013-10-01
A new mathematical model for the capacitated multi-facility location-allocation problem with probabilistic customers' locations and demands is developed in this article. The model is formulated into the frameworks of the expected value model (EVM) and the chance-constrained programming (CCP) based on two different distance measures. In order to solve the model, two hybrid intelligent algorithms are proposed, where the simplex algorithm and stochastic simulation are the bases for both algorithms. However, in the first algorithm, named SSGA, a special type of genetic algorithm is combined and in the second, SSVDO, a vibration-damping optimisation (VDO) algorithm is united. The Taguchi method is employed to tune the parameters of the two proposed algorithms. Finally, some numerical examples are given to illustrate the applications of the proposed methodologies and to compare their performances.
Numerical Relativistic Quantum Optics
2013-11-08
Introduction 1 II. Relativistic Wave Equations 2 III. Stationary States 4 A. Analytical Solutions for Coulomb Potentials 4 B. Numerical Solutions...C. Relativistic Ionization Example 15 V. Computational Performance 18 VI. Conclusions 21 VII. Acknowledgements 22 References 23 1 I. INTRODUCTION ...peculiar result that B0 = 1 TG is a weak field. At present, such fields are observed only in connection with astrophysical phenomena [14]. The highest
Wang-Landau integration --- The application of Wang-Landau sampling in numerical integration
NASA Astrophysics Data System (ADS)
Li, Ying Wai; Wuest, Thomas; Landau, David P.; Qing Lin, Hai
2007-03-01
Wang-Landau sampling was first introduced to simulate the density of states in energy space for various physical systems. This technique can be extended to numerical integrations due to certain similarities in nature of these two problems. It can be further applied to study quantum many-body systems. We report the feasibility of this application by discussing the correspondence between Wang-Landau integration and Wang-Landau sampling for Ising model. Numerical results for 1D and 2D integrations are shown. In particular, the utilization of this algorithm in the periodic lattice Anderson model is discussed as an illustrative example.
Parallel algorithms for unconstrained optimizations by multisplitting
He, Qing
1994-12-31
In this paper a new parallel iterative algorithm for unconstrained optimization using the idea of multisplitting is proposed. This algorithm uses the existing sequential algorithms without any parallelization. Some convergence and numerical results for this algorithm are presented. The experiments are performed on an Intel iPSC/860 Hyper Cube with 64 nodes. It is interesting that the sequential implementation on one node shows that if the problem is split properly, the algorithm converges much faster than one without splitting.
Implementation of a partitioned algorithm for simulation of large CSI problems
NASA Technical Reports Server (NTRS)
Alvin, Kenneth F.; Park, K. C.
1991-01-01
The implementation of a partitioned numerical algorithm for determining the dynamic response of coupled structure/controller/estimator finite-dimensional systems is reviewed. The partitioned approach leads to a set of coupled first and second-order linear differential equations which are numerically integrated with extrapolation and implicit step methods. The present software implementation, ACSIS, utilizes parallel processing techniques at various levels to optimize performance on a shared-memory concurrent/vector processing system. A general procedure for the design of controller and filter gains is also implemented, which utilizes the vibration characteristics of the structure to be solved. Also presented are: example problems; a user's guide to the software; the procedures and algorithm scripts; a stability analysis for the algorithm; and the source code for the parallel implementation.
Probabilistic numerics and uncertainty in computations
Hennig, Philipp; Osborne, Michael A.; Girolami, Mark
2015-01-01
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations. PMID:26346321
Probabilistic numerics and uncertainty in computations.
Hennig, Philipp; Osborne, Michael A; Girolami, Mark
2015-07-08
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.
SToRM: A numerical model for environmental surface flows
Simoes, Francisco J.
2009-01-01
SToRM (System for Transport and River Modeling) is a numerical model developed to simulate free surface flows in complex environmental domains. It is based on the depth-averaged St. Venant equations, which are discretized using unstructured upwind finite volume methods, and contains both steady and unsteady solution techniques. This article provides a brief description of the numerical approach selected to discretize the governing equations in space and time, including important aspects of solving natural environmental flows, such as the wetting and drying algorithm. The presentation is illustrated with several application examples, covering both laboratory and natural river flow cases, which show the model’s ability to solve complex flow phenomena.
NASA Astrophysics Data System (ADS)
Rahneshin, Vahid; Chierichetti, Maria
2016-09-01
In this paper, a combined numerical and experimental method, called Extended Load Confluence Algorithm, is presented to accurately predict the dynamic response of non-periodic structures when little or no information about the applied loads is available. This approach, which falls into the category of Shape Sensing methods, inputs limited experimental information acquired from sensors to a mapping algorithm that predicts the response at unmeasured locations. The proposed algorithm consists of three major cores: an experimental core for data acquisition, a numerical core based on Finite Element Method for modeling the structure, and a mapping algorithm that improves the numerical model based on a modal approach in the frequency domain. The robustness and precision of the proposed algorithm are verified through numerical and experimental examples. The results of this paper demonstrate that without a precise knowledge of the loads acting on the structure, the dynamic behavior of the system can be predicted in an effective and precise manner after just a few iterations.
The Superior Lambert Algorithm
NASA Astrophysics Data System (ADS)
der, G.
2011-09-01
Lambert algorithms are used extensively for initial orbit determination, mission planning, space debris correlation, and missile targeting, just to name a few applications. Due to the significance of the Lambert problem in Astrodynamics, Gauss, Battin, Godal, Lancaster, Gooding, Sun and many others (References 1 to 15) have provided numerous formulations leading to various analytic solutions and iterative methods. Most Lambert algorithms and their computer programs can only work within one revolution, break down or converge slowly when the transfer angle is near zero or 180 degrees, and their multi-revolution limitations are either ignored or barely addressed. Despite claims of robustness, many Lambert algorithms fail without notice, and the users seldom have a clue why. The DerAstrodynamics lambert2 algorithm, which is based on the analytic solution formulated by Sun, works for any number of revolutions and converges rapidly at any transfer angle. It provides significant capability enhancements over every other Lambert algorithm in use today. These include improved speed, accuracy, robustness, and multirevolution capabilities as well as implementation simplicity. Additionally, the lambert2 algorithm provides a powerful tool for solving the angles-only problem without artificial singularities (pointed out by Gooding in Reference 16), which involves 3 lines of sight captured by optical sensors, or systems such as the Air Force Space Surveillance System (AFSSS). The analytic solution is derived from the extended Godal’s time equation by Sun, while the iterative method of solution is that of Laguerre, modified for robustness. The Keplerian solution of a Lambert algorithm can be extended to include the non-Keplerian terms of the Vinti algorithm via a simple targeting technique (References 17 to 19). Accurate analytic non-Keplerian trajectories can be predicted for satellites and ballistic missiles, while performing at least 100 times faster in speed than most
Hybrid particle swarm global optimization algorithm for phase diversity phase retrieval.
Zhang, P G; Yang, C L; Xu, Z H; Cao, Z L; Mu, Q Q; Xuan, L
2016-10-31
The core problem of phase diversity phase retrieval (PDPR) is to find suitable optimization algorithms for wave-front sensing of different scales, especially for large-scale wavefront sensing. When dealing with large-scale wave-front sensing, existing gradient-based local optimization algorithms used in PDPR are easily trapped in local minimums near initial positions, and available global optimization algorithms possess low convergence efficiency. We construct a practicable optimization algorithm used in PDPR for large-scale wave-front sensing. This algorithm, named EPSO-BFGS, is a two-step hybrid global optimization algorithm based on the combination of evolutionary particle swarm optimization (EPSO) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Firstly, EPSO provides global search and obtains a rough global minimum position in limited search steps. Then, BFGS initialized by the rough global minimum position approaches the global minimum with high accuracy and fast convergence speed. Numerical examples testify to the feasibility and reliability of EPSO-BFGS for wave-front sensing of different scales. Two numerical cases also validate the ability of EPSO-BFGS for large-scale wave-front sensing. The effectiveness of EPSO-BFGS is further affirmed by performing a verification experiment.
NASA Technical Reports Server (NTRS)
Chen, Y. S.
1986-01-01
In the present paper, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BEC) systems has been developed and evaluated. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme and a central differencing plus artificial dissipation scheme are used to approximate the convection terms in the governing equations. Effects of these two schemes on the accuracy of numerical predictions are studied. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm, SIMPLE-C. Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present numerical method.
ERIC Educational Resources Information Center
Sozio, Gerry
2009-01-01
Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that…
NASA Technical Reports Server (NTRS)
Baker, John G.
2009-01-01
Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.
An example-based face relighting
NASA Astrophysics Data System (ADS)
Shim, Hyunjung; Chen, Tsuhan
2012-03-01
In this paper, we propose a new face relighting algorithm powered by a large database of face images captured under various known lighting conditions (a Multi-PIE database). Key insight of our algorithm is that a face can be represented by an assemble of patches from many other faces. The algorithm finds the most similar face patches in the database in terms of the lighting and the appearance. By assembling the matched patches, we can visualize the input face under various lighting conditions. Unlike existing face relighting algorithms, we neither use any kinds of face model nor make a physical assumption. Instead, our algorithm is a data-driven approach, synthesizing the appearance of the image patch using the appearance of the example patch. Using a data-driven approach, we can account for various intrinsic facial features including the non-Lambertian skin properties as well as the hair. Also, our algorithm is insensitive to the face misalignment. We demonstrate the performance of our algorithm by face relighting and face recognition experiments. Especially, the synthesized results show that the proposed algorithm can successfully handle various intrinsic features of an input face. Also, from the face recognition experiment, we show that our method is comparable to the most recent face relighting work.
Optimal control of switched linear systems based on Migrant Particle Swarm Optimization algorithm
NASA Astrophysics Data System (ADS)
Xie, Fuqiang; Wang, Yongji; Zheng, Zongzhun; Li, Chuanfeng
2009-10-01
The optimal control problem for switched linear systems with internally forced switching has more constraints than with externally forced switching. Heavy computations and slow convergence in solving this problem is a major obstacle. In this paper we describe a new approach for solving this problem, which is called Migrant Particle Swarm Optimization (Migrant PSO). Imitating the behavior of a flock of migrant birds, the Migrant PSO applies naturally to both continuous and discrete spaces, in which definitive optimization algorithm and stochastic search method are combined. The efficacy of the proposed algorithm is illustrated via a numerical example.
The minimal residual QR-factorization algorithm for reliably solving subset regression problems
NASA Technical Reports Server (NTRS)
Verhaegen, M. H.
1987-01-01
A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.
NASA Technical Reports Server (NTRS)
Abrams, D.; Williams, C.
1999-01-01
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.
Numerical Polynomial Homotopy Continuation Method and String Vacua
Mehta, Dhagash
2011-01-01
Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less
NASA Astrophysics Data System (ADS)
Kumar, Sunil
2013-12-01
The main aim of the present work is to propose a new and simple algorithm to obtain a quick and accurate analytical solution of the time fractional Fokker-Plank equation which arises in various fields in natural science, including solid-state physics, quantum optics, chemical physics, theoretical biology, and circuit theory. This new and simple algorithm is an innovative adjustment in Laplace transform algorithm which makes the calculations much simpler and applicable to several practical problems in science and engineering. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore reduces the numerical computations to a great extent. Furthermore, several numerical examples are presented to illustrate the accuracy and the stability of the method.
Multidisciplinary Optimization of Airborne Radome Using Genetic Algorithm
NASA Astrophysics Data System (ADS)
Tang, Xinggang; Zhang, Weihong; Zhu, Jihong
A multidisciplinary optimization scheme of airborne radome is proposed. The optimization procedure takes into account the structural and the electromagnetic responses simultaneously. The structural analysis is performed with the finite element method using Patran/Nastran, while the electromagnetic analysis is carried out using the Plane Wave Spectrum and Surface Integration technique. The genetic algorithm is employed for the multidisciplinary optimization process. The thicknesses of multilayer radome wall are optimized to maximize the overall transmission coefficient of the antenna-radome system under the constraint of the structural failure criteria. The proposed scheme and the optimization approach are successfully assessed with an illustrative numerical example.
Efficient computer algebra algorithms for polynomial matrices in control design
NASA Technical Reports Server (NTRS)
Baras, J. S.; Macenany, D. C.; Munach, R.
1989-01-01
The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.
NASA Technical Reports Server (NTRS)
Dongarra, Jack
1998-01-01
This exploratory study initiated our inquiry into algorithms and applications that would benefit by latency tolerant approach to algorithm building, including the construction of new algorithms where appropriate. In a multithreaded execution, when a processor reaches a point where remote memory access is necessary, the request is sent out on the network and a context--switch occurs to a new thread of computation. This effectively masks a long and unpredictable latency due to remote loads, thereby providing tolerance to remote access latency. We began to develop standards to profile various algorithm and application parameters, such as the degree of parallelism, granularity, precision, instruction set mix, interprocessor communication, latency etc. These tools will continue to develop and evolve as the Information Power Grid environment matures. To provide a richer context for this research, the project also focused on issues of fault-tolerance and computation migration of numerical algorithms and software. During the initial phase we tried to increase our understanding of the bottlenecks in single processor performance. Our work began by developing an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. Based on the results we achieved in this study we are planning to study other architectures of interest, including development of cost models, and developing code generators appropriate to these architectures.
NASA Astrophysics Data System (ADS)
Hu, Zixi; Yao, Zhewei; Li, Jinglai
2017-03-01
Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.
1992-12-01
fisica matematica . ABSTRACT - We consider a new method for the numerical solution both of non- linear systems of equations and of cornplementauity... Matematica , Serie V11 Volume 9 , Roma (1989), 521-543 An Inexact Continuous Method for the Solution of Large Systems of Equations and Complementarity...34 - 00185 Roma - Italy APPENDIX 2 A Quadratically Convergent Method for Unear Programming’ Stefano Herzel Dipartimento di Matematica -G. Castelnuovo
Numerical Approaches to Spacetime Singularities.
Berger, Beverly K
2002-01-01
This Living Review updates a previous version [25] which is itself an update of a review article [31]. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity.
Learning from examples in large neural networks
NASA Astrophysics Data System (ADS)
Sompolinsky, H.; Tishby, N.; Seung, H. S.
1990-09-01
A statistical-mechanical theory of learning from examples in layered networks at finite temperature is studied. When the training error is a smooth function of continuously varying weights, the generalization error falls off asymptotically as the inverse number of examples. By analytical and numerical studies of single-layer perceptrons, we show that when the weights are discrete, the generalization error can exhibit a discontinuous transition to perfect generalization. For intermediate sizes of the example set, the state of perfect generalization coexists with a metastable spin-glass state.
Xie, Jiaquan; Huang, Qingxue; Yang, Xia
2016-01-01
In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.
NASA Astrophysics Data System (ADS)
Begue, C.; Periaux, J.; Perrier, P.; Pouletty, C.
1985-11-01
A self-adaptive finite-element method, coupled to a homogenization model of turbulence, is presented for the numerical simulation of unsteady turbulent flow of viscous fluids in air intakes. The nonlinear subproblem due to the convection is solved by an iterative algorithm, and the linear Stokes subproblem due to the diffusion is solved by a Hood-Taylor type iterative algorithm. An efficient and precise minielement approximation is used, and the adaptive mesh procedure is automatic in the calculation, using the physical criteria of rotation and divergence to determine the submeshing zones. The numerical method is demonstrated for the example of three-dimensional laminar flow around and in air intake at a Reynolds number of 200.
High-order algorithms for compressible reacting flow with complex chemistry
NASA Astrophysics Data System (ADS)
Emmett, Matthew; Zhang, Weiqun; Bell, John B.
2014-05-01
In this paper we describe a numerical algorithm for integrating the multicomponent, reacting, compressible Navier-Stokes equations, targeted for direct numerical simulation of combustion phenomena. The algorithm addresses two shortcomings of previous methods. First, it incorporates an eighth-order narrow stencil approximation of diffusive terms that reduces the communication compared to existing methods and removes the need to use a filtering algorithm to remove Nyquist frequency oscillations that are not damped with traditional approaches. The methodology also incorporates a multirate temporal integration strategy that provides an efficient mechanism for treating chemical mechanisms that are stiff relative to fluid dynamical time-scales. The overall methodology is eighth order in space with options for fourth order to eighth order in time. The implementation uses a hybrid programming model designed for effective utilisation of many-core architectures. We present numerical results demonstrating the convergence properties of the algorithm with realistic chemical kinetics and illustrating its performance characteristics. We also present a validation example showing that the algorithm matches detailed results obtained with an established low Mach number solver.
Numerical inversion of finite Toeplitz matrices and vector Toeplitz matrices
NASA Technical Reports Server (NTRS)
Bareiss, E. H.
1969-01-01
Numerical technique increases the efficiencies of the numerical methods involving Toeplitz matrices by reducing the number of multiplications required by an N-order Toeplitz matrix from N-cubed to N-squared multiplications. Some efficient algorithms are given.
Algorithmic Complexity. Volume II.
1982-06-01
works, give an example, and discuss the inherent weaknesses and their causes. Electrical Network Analysis Knuth mentions the applicability of...of these 3 products of 2-coefficient 2 1 polynomials can be found by a repeated application of the 3 multiplication W Ascheme, only 3.3-9 scalar...see another application of this paradigm later. We now investigate the efficiency of the divide-and-conquer polynomial multiplication algorithm. Let M(n
ARPANET Routing Algorithm Improvements
1978-10-01
IMPROVEMENTS . .PFOnINI ORG. REPORT MUNDER -- ) _ .. .... 3940 7, AUT(c) .. .. .. CONTRACT Of GRANT NUMSlet e) SJ. M. /Mc~uillan E. C./Rosen I...8217), this problem may persist for a very long time, causing extremely bad performance throughout the whole network (for instance, if w’ reports that one of...algorithm may naturally tend to oscillate between bad routing paths and become itself a major contributor to network congestion. These examples show
Reproducibility of Research Algorithms in GOES-R Operational Software
NASA Astrophysics Data System (ADS)
Kennelly, E.; Botos, C.; Snell, H. E.; Steinfelt, E.; Khanna, R.; Zaccheo, T.
2012-12-01
The research to operations transition for satellite observations is an area of active interest as identified by The National Research Council Committee on NASA-NOAA Transition from Research to Operations. Their report recommends improved transitional processes for bridging technology from research to operations. Assuring the accuracy of operational algorithm results as compared to research baselines, called reproducibility in this paper, is a critical step in the GOES-R transition process. This paper defines reproducibility methods and measurements for verifying that operationally implemented algorithms conform to research baselines, demonstrated with examples from GOES-R software development. The approach defines reproducibility for implemented algorithms that produce continuous data in terms of a traditional goodness-of-fit measure (i.e., correlation coefficient), while the reproducibility for discrete categorical data is measured using a classification matrix. These reproducibility metrics have been incorporated in a set of Test Tools developed for GOES-R and the software processes have been developed to include these metrics to validate both the scientific and numerical implementation of the GOES-R algorithms. In this work, we outline the test and validation processes and summarize the current results for GOES-R Level 2+ algorithms.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
NASA Technical Reports Server (NTRS)
Smelyanskiy, V. N.; Toussaint, U. V.; Timucin, D. A.
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
New knowledge-based genetic algorithm for excavator boom structural optimization
NASA Astrophysics Data System (ADS)
Hua, Haiyan; Lin, Shuwen
2014-03-01
Due to the insufficiency of utilizing knowledge to guide the complex optimal searching, existing genetic algorithms fail to effectively solve excavator boom structural optimization problem. To improve the optimization efficiency and quality, a new knowledge-based real-coded genetic algorithm is proposed. A dual evolution mechanism combining knowledge evolution with genetic algorithm is established to extract, handle and utilize the shallow and deep implicit constraint knowledge to guide the optimal searching of genetic algorithm circularly. Based on this dual evolution mechanism, knowledge evolution and population evolution can be connected by knowledge influence operators to improve the configurability of knowledge and genetic operators. Then, the new knowledge-based selection operator, crossover operator and mutation operator are proposed to integrate the optimal process knowledge and domain culture to guide the excavator boom structural optimization. Eight kinds of testing algorithms, which include different genetic operators, are taken as examples to solve the structural optimization of a medium-sized excavator boom. By comparing the results of optimization, it is shown that the algorithm including all the new knowledge-based genetic operators can more remarkably improve the evolutionary rate and searching ability than other testing algorithms, which demonstrates the effectiveness of knowledge for guiding optimal searching. The proposed knowledge-based genetic algorithm by combining multi-level knowledge evolution with numerical optimization provides a new effective method for solving the complex engineering optimization problem.
Synthesis of Greedy Algorithms Using Dominance Relations
NASA Technical Reports Server (NTRS)
Nedunuri, Srinivas; Smith, Douglas R.; Cook, William R.
2010-01-01
Greedy algorithms exploit problem structure and constraints to achieve linear-time performance. Yet there is still no completely satisfactory way of constructing greedy algorithms. For example, the Greedy Algorithm of Edmonds depends upon translating a problem into an algebraic structure called a matroid, but the existence of such a translation can be as hard to determine as the existence of a greedy algorithm itself. An alternative characterization of greedy algorithms is in terms of dominance relations, a well-known algorithmic technique used to prune search spaces. We demonstrate a process by which dominance relations can be methodically derived for a number of greedy algorithms, including activity selection, and prefix-free codes. By incorporating our approach into an existing framework for algorithm synthesis, we demonstrate that it could be the basis for an effective engineering method for greedy algorithms. We also compare our approach with other characterizations of greedy algorithms.
The Cartan algorithm in five dimensions
NASA Astrophysics Data System (ADS)
McNutt, D. D.; Coley, A. A.; Forget, A.
2017-03-01
In this paper, we introduce an algorithm to determine the equivalence of five dimensional spacetimes, which generalizes the Karlhede algorithm for four dimensional general relativity. As an alternative to the Petrov type classification, we employ the alignment classification to algebraically classify the Weyl tensor. To illustrate the algorithm, we discuss three examples: the singly rotating Myers-Perry solution, the Kerr (Anti-) de Sitter solution, and the rotating black ring solution. We briefly discuss some applications of the Cartan algorithm in five dimensions.
Kalos, M.
2006-05-09
The Monte Carlo example programs VARHATOM and DMCATOM are two small, simple FORTRAN programs that illustrate the use of the Monte Carlo Mathematical technique for calculating the ground state energy of the hydrogen atom.
An artificial bee colony algorithm for uncertain portfolio selection.
Chen, Wei
2014-01-01
Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm.
An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection
Chen, Wei
2014-01-01
Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm. PMID:25089292
NASA Astrophysics Data System (ADS)
Kang, I. S.; Leal, L. G.
1987-07-01
A numerical technique for solving axisymmetric, unsteady free-boundary problems in fluid mechanics is presented. This finite-difference method is a generalization of the steady algorithm reported by Ryskin and Leal (1984). In this scheme, all boundary surfaces of the solution domain at any time coincide exactly with a coordinate line of a numerically generated orthogonal coordinate system. Thus, unreasonable grid deformation during calculation is not a problem. A transient algorithm for applying the orthogonal mapping technique to unsteady free-boundary problems is developed. The unsteady deformation of a bubble in a uniaxial extensional flow for Reynolds numbers between 0.1 and 100 is considered as an example.
Conditional Convergence of Numerical Series
ERIC Educational Resources Information Center
Gomez, E.; Plaza, A.
2002-01-01
One of the most astonishing properties when studying numerical series is that the sum is not commutative, that is the sum may change when the order of its elements is altered. In this note an example is given of such a series. A well-known mathematical proof is given and a MATLAB[C] program used for different rearrangements of the series…
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1991-01-01
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1990-01-01
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
A simple suboptimal least-squares algorithm for attitude determination with multiple sensors
NASA Technical Reports Server (NTRS)
Brozenec, Thomas F.; Bender, Douglas J.
1994-01-01
Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is
PSLQ: An Algorithm to Discover Integer Relations
Bailey, David H.; Borwein, J. M.
2009-04-03
Let x = (x{sub 1}, x{sub 2} {hor_ellipsis}, x{sub n}) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers a{sub i}, not all zero, such that a{sub 1}x{sub 1} + a{sub 2}x{sub 2} + {hor_ellipsis} + a{sub n}x{sub n} = 0. By an integer relation algorithm, we mean a practical computational scheme that can recover the vector of integers ai, if it exists, or can produce bounds within which no integer relation exists. As we will see in the examples below, an integer relation algorithm can be used to recognize a computed constant in terms of a formula involving known constants, or to discover an underlying relation between quantities that can be computed to high precision. At the present time, the most effective algorithm for integer relation detection is the 'PSLQ' algorithm of mathematician-sculptor Helaman Ferguson [10, 4]. Some efficient 'multi-level' implementations of PSLQ, as well as a variant of PSLQ that is well-suited for highly parallel computer systems, are given in [4]. PSLQ constructs a sequence of integer-valued matrices B{sub n} that reduces the vector y = xB{sub n}, until either the relation is found (as one of the columns of B{sub n}), or else precision is exhausted. At the same time, PSLQ generates a steadily growing bound on the size of any possible relation. When a relation is found, the size of smallest entry of the vector y abruptly drops to roughly 'epsilon' (i.e. 10{sup -p}, where p is the number of digits of precision). The size of this drop can be viewed as a 'confidence level' that the relation is real and not merely a numerical artifact - a drop of 20 or more orders of magnitude almost always indicates a real relation. Very high precision arithmetic must be used in PSLQ. If one wishes to recover a relation of length n, with coefficients of maximum size d digits, then the input vector x must be specified to at least nd digits, and one must employ nd-digit floating-point arithmetic. Maple and
Learning about Functions through Learner-Generated Examples
ERIC Educational Resources Information Center
Dinkelman, Martha O.; Cavey, Laurie O.
2015-01-01
In many mathematics classrooms, the teacher provides "worked examples" to demonstrate how students should perform certain algorithms or processes. Some students find it difficult to generalize from the examples that teachers provide and cannot apply what they have learned in new situations (Watson and Mason 2002). Instead, teachers might…
Revised numerical wrapper for PIES code
NASA Astrophysics Data System (ADS)
Raburn, Daniel; Reiman, Allan; Monticello, Donald
2015-11-01
A revised external numerical wrapper has been developed for the Princeton Iterative Equilibrium Solver (PIES code), which is capable of calculating 3D MHD equilibria with islands. The numerical wrapper has been demonstrated to greatly improve the rate of convergence in numerous cases corresponding to equilibria in the TFTR device where magnetic islands are present. The numerical wrapper makes use of a Jacobian-free Newton-Krylov solver along with adaptive preconditioning and a sophisticated subspace-restricted Levenberg-Marquardt backtracking algorithm. The details of the numerical wrapper and several sample results are presented.
An overview of SuperLU: Algorithms, implementation, and userinterface
Li, Xiaoye S.
2003-09-30
We give an overview of the algorithms, design philosophy,and implementation techniques in the software SuperLU, for solving sparseunsymmetric linear systems. In particular, we highlight the differencesbetween the sequential SuperLU (including its multithreaded extension)and parallel SuperLU_DIST. These include the numerical pivoting strategy,the ordering strategy for preserving sparsity, the ordering in which theupdating tasks are performed, the numerical kernel, and theparallelization strategy. Because of the scalability concern, theparallel code is drastically different from the sequential one. Wedescribe the user interfaces ofthe libraries, and illustrate how to usethe libraries most efficiently depending on some matrix characteristics.Finally, we give some examples of how the solver has been used inlarge-scale scientific applications, and the performance.
Mapping quantitative traits in unselected families: algorithms and examples.
Dupuis, Josée; Shi, Jianxin; Manning, Alisa K; Benjamin, Emelia J; Meigs, James B; Cupples, L Adrienne; Siegmund, David
2009-11-01
Linkage analysis has been widely used to identify from family data genetic variants influencing quantitative traits. Common approaches have both strengths and limitations. Likelihood ratio tests typically computed in variance component analysis can accommodate large families but are highly sensitive to departure from normality assumptions. Regression-based approaches are more robust but their use has primarily been restricted to nuclear families. In this paper, we develop methods for mapping quantitative traits in moderately large pedigrees. Our methods are based on the score statistic, which in contrast to the likelihood ratio statistic can use nonparametric estimators of variability to achieve robustness of the false-positive rate against departures from the hypothesized phenotypic model. Because the score statistic is easier to calculate than the likelihood ratio statistic, our basic mapping methods utilize relatively simple computer code that performs statistical analysis on output from any program that computes estimates of identity by descent. This simplicity also permits development and evaluation of methods to deal with multivariate and ordinal phenotypes, and with gene-gene and gene-environment interaction. We demonstrate our methods on simulated data and on fasting insulin, a quantitative trait measured in the Framingham Heart Study.
The Structure-Mapping Engine: Algorithm and Examples.
1987-07-01
08540 Ann Arbor. MI 48109 Dr Sherrie Gott AFHRL MODJ Dr Wayne Harvey Ms Julia S Hough BrooKs AFB TX 78235 SRI International Lawrence Eribaum Associates...Performance Lanoratory Department of Psychology Catholic University of Evanston IL 60201 Amer~ca Dr Wayne Gray Wasnington. DC 20064 Army Research Institute...22333 Norcross, GA 30092 Dr Sylvia A S Shafto Department of Computer Science Dr Lynne Recer Dr David Rumelhart Towson State University Department of
Algorithms for propagating uncertainty across heterogeneous domains
Cho, Heyrim; Yang, Xiu; Venturi, D.; Karniadakis, George E.
2015-12-30
We address an important research area in stochastic multi-scale modeling, namely the propagation of uncertainty across heterogeneous domains characterized by partially correlated processes with vastly different correlation lengths. This class of problems arise very often when computing stochastic PDEs and particle models with stochastic/stochastic domain interaction but also with stochastic/deterministic coupling. The domains may be fully embedded, adjacent or partially overlapping. The fundamental open question we address is the construction of proper transmission boundary conditions that preserve global statistical properties of the solution across different subdomains. Often, the codes that model different parts of the domains are black-box and hence a domain decomposition technique is required. No rigorous theory or even effective empirical algorithms have yet been developed for this purpose, although interfaces defined in terms of functionals of random fields (e.g., multi-point cumulants) can overcome the computationally prohibitive problem of preserving sample-path continuity across domains. The key idea of the different methods we propose relies on combining local reduced-order representations of random fields with multi-level domain decomposition. Specifically, we propose two new algorithms: The first one enforces the continuity of the conditional mean and variance of the solution across adjacent subdomains by using Schwarz iterations. The second algorithm is based on PDE-constrained multi-objective optimization, and it allows us to set more general interface conditions. The effectiveness of these new algorithms is demonstrated in numerical examples involving elliptic problems with random diffusion coefficients, stochastically advected scalar fields, and nonlinear advection-reaction problems with random reaction rates.
A retrodictive stochastic simulation algorithm
Vaughan, T.G. Drummond, P.D.; Drummond, A.J.
2010-05-20
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
Numerical recipes, The art of scientific computing
Press, W.H.; Flannery, B.P.; Teukolsky, S.; Vetterling, W.T.
1986-01-01
Seventeen chapter are divided into 130 sections provide a self-contained treatment that derives, critically discusses, and actually implements over 200 of the most important numerical algorithms for scientific work. Each algorithm is presented both in FORTRAN and Pascal, with the source programs printed in the book itself. The scope of Numerical Recipes ranges from standard areas of numerical analysis (linear algebra, differential equations, roots) through subjects useful to signal processing (Fourier methods, filtering), data analysis (least squares, robust fitting, statistical functions), simulation (random deviates and Monte Carlo). The routines themselves are available for a wide variety of different computers, from personal computers to mainframes, and are largely portable among different machines.
A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva
2016-12-01
There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.
Programming the gradient projection algorithm
NASA Technical Reports Server (NTRS)
Hargrove, A.
1983-01-01
The gradient projection method of numerical optimization which is applied to problems having linear constraints but nonlinear objective functions is described and analyzed. The algorithm is found to be efficient and thorough for small systems, but requires the addition of auxiliary methods and programming for large scale systems with severe nonlinearities. In order to verify the theoretical results a digital computer is used to simulate the algorithm.
NASA Astrophysics Data System (ADS)
Vaucouleur, Sebastien
2011-02-01
We introduce code query by example for customisation of evolvable software products in general and of enterprise resource planning systems (ERPs) in particular. The concept is based on an initial empirical study on practices around ERP systems. We motivate our design choices based on those empirical results, and we show how the proposed solution helps with respect to the infamous upgrade problem: the conflict between the need for customisation and the need for upgrade of ERP systems. We further show how code query by example can be used as a form of lightweight static analysis, to detect automatically potential defects in large software products. Code query by example as a form of lightweight static analysis is particularly interesting in the context of ERP systems: it is often the case that programmers working in this field are not computer science specialists but more of domain experts. Hence, they require a simple language to express custom rules.
NASA Astrophysics Data System (ADS)
Wolfe, William J.; Wood, David; Sorensen, Stephen E.
1996-12-01
This paper discusses automated scheduling as it applies to complex domains such as factories, transportation, and communications systems. The window-constrained-packing problem is introduced as an ideal model of the scheduling trade offs. Specific algorithms are compared in terms of simplicity, speed, and accuracy. In particular, dispatch, look-ahead, and genetic algorithms are statistically compared on randomly generated job sets. The conclusion is that dispatch methods are fast and fairly accurate; while modern algorithms, such as genetic and simulate annealing, have excessive run times, and are too complex to be practical.
Sobel, E.; Lange, K.; O`Connell, J.R.
1996-12-31
Haplotyping is the logical process of inferring gene flow in a pedigree based on phenotyping results at a small number of genetic loci. This paper formalizes the haplotyping problem and suggests four algorithms for haplotype reconstruction. These algorithms range from exhaustive enumeration of all haplotype vectors to combinatorial optimization by simulated annealing. Application of the algorithms to published genetic analyses shows that manual haplotyping is often erroneous. Haplotyping is employed in screening pedigrees for phenotyping errors and in positional cloning of disease genes from conserved haplotypes in population isolates. 26 refs., 6 figs., 3 tabs.
NASA Technical Reports Server (NTRS)
Pinsky, P. M.; Ortiz, M.; Taylor, R. L.
1982-01-01
The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into elastic and plastic parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stabiity properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.
Discovering Substructure in Examples
1988-05-01
the gestalt motivation for the previouslv discussed heuristics, gestalt theory suggests many additional 16 %0 [ ’ , factors identified in human...to substructure discovery. Gestalt theory motivates several of the ideas behind the substructure discovery algorithm. In the area of machine learning...5.1. Gestalt Psychology Many of the ideas in this thesis originated from work in gestalt psychology [Kohler47]. Gestalt theory identifies several
Teaching Responsibility through Example
ERIC Educational Resources Information Center
Notar, Toni A.
2008-01-01
As Literacy Outreach Coordinator for Opportunity to Read (OTR), the Watsonville (CA) Public Library literacy program, this author has recognized the concept of responsibility through example. Adult learners incorporate concepts easily when these concepts are specifically demonstrated for them by someone similar to them. Sounds simple, but putting…
A Unifying Probability Example.
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.
2002-01-01
Presents an example from probability and statistics that ties together several topics including the mean and variance of a discrete random variable, the binomial distribution and its particular mean and variance, the sum of independent random variables, the mean and variance of the sum, and the central limit theorem. Uses Excel to illustrate these…
Example-based segmentation for breast mass images
NASA Astrophysics Data System (ADS)
Huang, Qingying; Xu, Songhua; Luo, Xiaonan
2013-03-01
A new example-based mass segmentation algorithm is proposed for breast mass images. The training examples used in the new algorithm are prepared by three medical imaging professionals who manually outlined mass contours of 45 sample breast mass images. These manually segmented mass images are then partitioned into small regular grid cells, which are used as reference samples by the algorithm. Each time when the algorithm is applied to segment a previously unseen breast mass image, it first detects grid cell regions in the image that likely overlap with the underlying mass region. Upon identifying such candidate regions, the algorithm then locates the exact mass contour through an example based segmentation procedure where the algorithm retrieves, transfers, and re-applies the human expert knowledge regarding mass segmentation as encoded in the reference samples. The key advantage of our approach lies in its adaptability in tailoring to the skills and preferences of multiple experts through simply switching to a different corpus of human segmentation samples. To explore the effectiveness of the new approach, we comparatively evaluated the accuracy of the algorithm for mass segmentation against segmentation results both manually produced by several medical imaging professionals and automatically by a state-of-the-art level set based method. The comparison results demonstrate that the new algorithm achieves a higher accuracy than the level set based peer method with statistical significance.2
NASA Astrophysics Data System (ADS)
Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.
2014-09-01
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach
NASA Astrophysics Data System (ADS)
Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M.
2017-02-01
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.
Dynamical Approach Study of Spurious Numerics in Nonlinear Computations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Mansour, Nagi (Technical Monitor)
2002-01-01
The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.
Cuba: Multidimensional numerical integration library
NASA Astrophysics Data System (ADS)
Hahn, Thomas
2016-08-01
The Cuba library offers four independent routines for multidimensional numerical integration: Vegas, Suave, Divonne, and Cuhre. The four algorithms work by very different methods, and can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces. Their invocation is very similar, making it easy to cross-check by substituting one method by another. For further safeguarding, the output is supplemented by a chi-square probability which quantifies the reliability of the error estimate.
Tutorial examples for uncertainty quantification methods.
De Bord, Sarah
2015-08-01
This report details the work accomplished during my 2015 SULI summer internship at Sandia National Laboratories in Livermore, CA. During this internship, I worked on multiple tasks with the common goal of making uncertainty quantification (UQ) methods more accessible to the general scientific community. As part of my work, I created a comprehensive numerical integration example to incorporate into the user manual of a UQ software package. Further, I developed examples involving heat transfer through a window to incorporate into tutorial lectures that serve as an introduction to UQ methods.
NASA Astrophysics Data System (ADS)
Renouf, Mathieu; Dubois, Frederic; Alart, Pierre
2004-07-01
The NSCD method has shown its efficiency in the simulation of granular media. Since the number of particles and contact increases, the shape of the discrete elements becomes more complicated and the simulated problems becomes more complex, the numerical tools need to be improved in order to preserve reasonable elapsed CPU time. In this paper we present a parallelization approach of the NSCD algorithm and we investigate its influence on the numerical behaviour of the method. We illustrate the efficiency on an example made of hard disks: a free surface compaction.
A Simple Two Aircraft Conflict Resolution Algorithm
NASA Technical Reports Server (NTRS)
Chatterji, Gano B.
2006-01-01
Conflict detection and resolution methods are crucial for distributed air-ground traffic management in which the crew in, the cockpit, dispatchers in operation control centers sad and traffic controllers in the ground-based air traffic management facilities share information and participate in the traffic flow and traffic control functions. This paper describes a conflict detection, and a conflict resolution method. The conflict detection method predicts the minimum separation and the time-to-go to the closest point of approach by assuming that both the aircraft will continue to fly at their current speeds along their current headings. The conflict resolution method described here is motivated by the proportional navigation algorithm, which is often used for missile guidance during the terminal phase. It generates speed and heading commands to rotate the line-of-sight either clockwise or counter-clockwise for conflict resolution. Once the aircraft achieve a positive range-rate and no further conflict is predicted, the algorithm generates heading commands to turn back the aircraft to their nominal trajectories. The speed commands are set to the optimal pre-resolution speeds. Six numerical examples are presented to demonstrate the conflict detection, and the conflict resolution methods.
A Simple Two Aircraft Conflict Resolution Algorithm
NASA Technical Reports Server (NTRS)
Chatterji, Gano B.
1999-01-01
Conflict detection and resolution methods are crucial for distributed air-ground traffic management in which the crew in the cockpit, dispatchers in operation control centers and air traffic controllers in the ground-based air traffic management facilities share information and participate in the traffic flow and traffic control imctions.This paper describes a conflict detection and a conflict resolution method. The conflict detection method predicts the minimum separation and the time-to-go to the closest point of approach by assuming that both the aircraft will continue to fly at their current speeds along their current headings. The conflict resolution method described here is motivated by the proportional navigation algorithm. It generates speed and heading commands to rotate the line-of-sight either clockwise or counter-clockwise for conflict resolution. Once the aircraft achieve a positive range-rate and no further conflict is predicted, the algorithm generates heading commands to turn back the aircraft to their nominal trajectories. The speed commands are set to the optimal pre-resolution speeds. Six numerical examples are presented to demonstrate the conflict detection and resolution method.
Simulation and design of high precision unit processes via numerical methods
NASA Astrophysics Data System (ADS)
Stafford, Roger
1988-08-01
SDRC has developed new computer codes specifically tailored for precise and fist simulations of manufacturing processes. Critical aspects of unit processes involve nonlinear transient heat transfer coupled with slow creeping flow. Finite element methods are chosen. Numerical algorithms are adopted which are specifically suited to the problem. Key elements of these simulations are outlined. SDRC has integrated unit process simulations with CAD/CAM design systems, analysis graphics systems, automated inspection, and data base. An example will illustrate data flow, simulation results, and how engineers are using these tools to design new processes for large complex parts.
Improved delay-leaping simulation algorithm for biochemical reaction systems with delays
NASA Astrophysics Data System (ADS)
Yi, Na; Zhuang, Gang; Da, Liang; Wang, Yifei
2012-04-01
In biochemical reaction systems dominated by delays, the simulation speed of the stochastic simulation algorithm depends on the size of the wait queue. As a result, it is important to control the size of the wait queue to improve the efficiency of the simulation. An improved accelerated delay stochastic simulation algorithm for biochemical reaction systems with delays, termed the improved delay-leaping algorithm, is proposed in this paper. The update method for the wait queue is effective in reducing the size of the queue as well as shortening the storage and access time, thereby accelerating the simulation speed. Numerical simulation on two examples indicates that this method not only obtains a more significant efficiency compared with the existing methods, but also can be widely applied in biochemical reaction systems with delays.
Nonlinear algorithm for navigation of a moving object in magnetic field
NASA Astrophysics Data System (ADS)
Tkhorenko, M. Yu.; Karshakov, E. V.; Shevchenko, A. M.
2017-01-01
Consideration was given to the problem of relative positioning with the use of alternating magnetic field. The problem was shown to be solvable using a system of three magnetic dipoles emitting magnetic field at different frequencies. Ambiguity of its solution was discussed, and ways to resolve it were proposed. An algorithm for relative positioning based on the solution of this problem was proposed. Error equations of the positioning algorithm and the results of their analysis were presented. Calibration procedures, improving accuracy of relative positioning, are also considered. One of these procedures, based on nonlinear optimization techniques, was presented in greater details. The paper was supplied with several numerical examples demonstrating effectiveness of proposed algorithms in relative positioning.
A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas
Xiong, Z; Cohen, R H; Rognlien, T D; Xu, X Q
2007-04-18
A high-order finite volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm is based on a general fourth-order reconstruction scheme for an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. The method provides density conservation and high-order-accurate evaluation of the FPO independent of the choice of the velocity coordinates. As an example, a linearized FPO in constant-of-motion coordinates, i.e. the total energy and the magnetic moment, is developed using the present algorithm combined with a cut-cell merging procedure. Numerical tests include the Spitzer thermalization problem and the return to isotropy for distributions initialized with velocity space loss cones. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Rosenbluth potentials.
An Algorithm for the Mixed Transportation Network Design Problem.
Liu, Xinyu; Chen, Qun
2016-01-01
This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.
DC Algorithm for Extended Robust Support Vector Machine.
Fujiwara, Shuhei; Takeda, Akiko; Kanamori, Takafumi
2017-03-23
Nonconvex variants of support vector machines (SVMs) have been developed for various purposes. For example, robust SVMs attain robustness to outliers by using a nonconvex loss function, while extended [Formula: see text]-SVM (E[Formula: see text]-SVM) extends the range of the hyperparameter by introducing a nonconvex constraint. Here, we consider an extended robust support vector machine (ER-SVM), a robust variant of E[Formula: see text]-SVM. ER-SVM combines two types of nonconvexity from robust SVMs and E[Formula: see text]-SVM. Because of the two nonconvexities, the existing algorithm we proposed needs to be divided into two parts depending on whether the hyperparameter value is in the extended range or not. The algorithm also heuristically solves the nonconvex problem in the extended range. In this letter, we propose a new, efficient algorithm for ER-SVM. The algorithm deals with two types of nonconvexity while never entailing more computations than either E[Formula: see text]-SVM or robust SVM, and it finds a critical point of ER-SVM. Furthermore, we show that ER-SVM includes the existing robust SVMs as special cases. Numerical experiments confirm the effectiveness of integrating the two nonconvexities.
Locomotive assignment problem with train precedence using genetic algorithm
NASA Astrophysics Data System (ADS)
Noori, Siamak; Ghannadpour, Seyed Farid
2012-07-01
This paper aims to study the locomotive assignment problem which is very important for railway companies, in view of high cost of operating locomotives. This problem is to determine the minimum cost assignment of homogeneous locomotives located in some central depots to a set of pre-scheduled trains in order to provide sufficient power to pull the trains from their origins to their destinations. These trains have different degrees of priority for servicing, and the high class of trains should be serviced earlier than others. This problem is modeled using vehicle routing and scheduling problem where trains representing the customers are supposed to be serviced in pre-specified hard/soft fuzzy time windows. A two-phase approach is used which, in the first phase, the multi-depot locomotive assignment is converted to a set of single depot problems, and after that, each single depot problem is solved heuristically by a hybrid genetic algorithm. In the genetic algorithm, various heuristics and efficient operators are used in the evolutionary search. The suggested algorithm is applied to solve the medium sized numerical example to check capabilities of the model and algorithm. Moreover, some of the results are compared with those solutions produced by branch-and-bound technique to determine validity and quality of the model. Results show that suggested approach is rather effective in respect of quality and time.
An Algorithm for the Mixed Transportation Network Design Problem
Liu, Xinyu; Chen, Qun
2016-01-01
This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. PMID:27626803
Nonclassicality thresholds for multiqubit states: Numerical analysis
Gruca, Jacek; Zukowski, Marek; Laskowski, Wieslaw; Kiesel, Nikolai; Wieczorek, Witlef; Weinfurter, Harald; Schmid, Christian
2010-07-15
States that strongly violate Bell's inequalities are required in many quantum-informational protocols as, for example, in cryptography, secret sharing, and the reduction of communication complexity. We investigate families of such states with a numerical method which allows us to reveal nonclassicality even without direct knowledge of Bell's inequalities for the given problem. An extensive set of numerical results is presented and discussed.
Systematic reviews. Some examples.
Knipschild, P.
1994-01-01
Reviewing the literature is a scientific inquiry that needs a clear design to preclude bias. It is a real enterprise if one aims at completeness of the literature on a certain subject. Going through refereed English language journals is not enough. On line databases are helpful, but mainly as a starting point. This article gives examples of systematic reviews on vitamin C and the common cold, pyridoxine against the premenstrual syndrome, homeopathy, and physiotherapy. Images p720-a PMID:7950526
Numerical analysis of a quasistatic piezoelectric problem with damage*
NASA Astrophysics Data System (ADS)
Fernández, José R.; Martínez, Rebeca; Stavroulakis, Georgios E.
2008-07-01
The quasistatic evolution of the mechanical state of a piezoelectric body with damage is numerically studied in this paper. Both damage and piezoelectric effects are included into the model. The variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential, and a nonlinear parabolic variational equation for the damage field. The existence of a unique weak solution is stated. Then, a fully discrete scheme is introduced by using a finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, a two-dimensional example is presented to demonstrate the behaviour of the solution. To cite this article: J.R. Fernández et al., C. R. Mecanique 336 (2008).
Algorithm for reaction classification.
Kraut, Hans; Eiblmaier, Josef; Grethe, Guenter; Löw, Peter; Matuszczyk, Heinz; Saller, Heinz
2013-11-25
Reaction classification has important applications, and many approaches to classification have been applied. Our own algorithm tests all maximum common substructures (MCS) between all reactant and product molecules in order to find an atom mapping containing the minimum chemical distance (MCD). Recent publications have concluded that new MCS algorithms need to be compared with existing methods in a reproducible environment, preferably on a generalized test set, yet the number of test sets available is small, and they are not truly representative of the range of reactions that occur in real reaction databases. We have designed a challenging test set of reactions and are making it publicly available and usable with InfoChem's software or other classification algorithms. We supply a representative set of example reactions, grouped into different levels of difficulty, from a large number of reaction databases that chemists actually encounter in practice, in order to demonstrate the basic requirements for a mapping algorithm to detect the reaction centers in a consistent way. We invite the scientific community to contribute to the future extension and improvement of this data set, to achieve the goal of a common standard.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
Tomasz Plawski, J. Hovater
2010-09-01
A digital low level radio frequency (RF) system typically incorporates either a heterodyne or direct sampling technique, followed by fast ADCs, then an FPGA, and finally a transmitting DAC. This universal platform opens up the possibilities for a variety of control algorithm implementations. The foremost concern for an RF control system is cavity field stability, and to meet the required quality of regulation, the chosen control system needs to have sufficient feedback gain. In this paper we will investigate the effectiveness of the regulation for three basic control system algorithms: I&Q (In-phase and Quadrature), Amplitude & Phase and digital SEL (Self Exciting Loop) along with the example of the Jefferson Lab 12 GeV cavity field control system.
Comprehensive eye evaluation algorithm
NASA Astrophysics Data System (ADS)
Agurto, C.; Nemeth, S.; Zamora, G.; Vahtel, M.; Soliz, P.; Barriga, S.
2016-03-01
In recent years, several research groups have developed automatic algorithms to detect diabetic retinopathy (DR) in individuals with diabetes (DM), using digital retinal images. Studies have indicated that diabetics have 1.5 times the annual risk of developing primary open angle glaucoma (POAG) as do people without DM. Moreover, DM patients have 1.8 times the risk for age-related macular degeneration (AMD). Although numerous investigators are developing automatic DR detection algorithms, there have been few successful efforts to create an automatic algorithm that can detect other ocular diseases, such as POAG and AMD. Consequently, our aim in the current study was to develop a comprehensive eye evaluation algorithm that not only detects DR in retinal images, but also automatically identifies glaucoma suspects and AMD by integrating other personal medical information with the retinal features. The proposed system is fully automatic and provides the likelihood of each of the three eye disease. The system was evaluated in two datasets of 104 and 88 diabetic cases. For each eye, we used two non-mydriatic digital color fundus photographs (macula and optic disc centered) and, when available, information about age, duration of diabetes, cataracts, hypertension, gender, and laboratory data. Our results show that the combination of multimodal features can increase the AUC by up to 5%, 7%, and 8% in the detection of AMD, DR, and glaucoma respectively. Marked improvement was achieved when laboratory results were combined with retinal image features.
Paradigms: examples from the bacterium Xylella fastidiosa.
Purcell, Alexander
2013-01-01
The history of advances in research on Xylella fastidiosa provides excellent examples of how paradigms both advance and limit our scientific understanding of plant pathogens and the plant diseases they cause. I describe this from a personal perspective, having been directly involved with many persons who made paradigm-changing discoveries, beginning with the discovery that a bacterium, not a virus, causes Pierce's disease of grape and other plant diseases in numerous plant species, including important crop and forest species.
Effects of Worked Examples, Example-Problem, and Problem-Example Pairs on Novices' Learning
ERIC Educational Resources Information Center
van Gog, Tamara; Kester, Liesbeth; Paas, Fred
2011-01-01
Research has demonstrated that instruction that relies more heavily on example study is more effective for novices' learning than instruction consisting of problem solving. However, "a heavier reliance on example study" has been implemented in different ways. For example, worked examples only (WE), example-problem pairs (WE-PS), or problem-example…
Parallel algorithm development
Adams, T.F.
1996-06-01
Rapid changes in parallel computing technology are causing significant changes in the strategies being used for parallel algorithm development. One approach is simply to write computer code in a standard language like FORTRAN 77 or with the expectation that the compiler will produce executable code that will run in parallel. The alternatives are: (1) to build explicit message passing directly into the source code; or (2) to write source code without explicit reference to message passing or parallelism, but use a general communications library to provide efficient parallel execution. Application of these strategies is illustrated with examples of codes currently under development.
NASA Astrophysics Data System (ADS)
Krasnikov, S. D.; Kuznetsov, E. B.
2016-09-01
Numerical continuation of solution through certain singular points of the curve of the set of solutions to a system of nonlinear algebraic or transcendental equations with a parameter is considered. Bifurcation points of codimension two and three are investigated. Algorithms and computer programs are developed that implement the procedure of discrete parametric continuation of the solution and find all branches at simple bifurcation points of codimension two and three. Corresponding theorems are proved, and each algorithm is rigorously justified. A novel algorithm for the estimation of errors of tangential vectors at simple bifurcation points of a finite codimension m is proposed. The operation of the computer programs is demonstrated by test examples, which allows one to estimate their efficiency and confirm the theoretical results.
Numerical Propulsion System Simulation
NASA Technical Reports Server (NTRS)
Naiman, Cynthia
2006-01-01
The NASA Glenn Research Center, in partnership with the aerospace industry, other government agencies, and academia, is leading the effort to develop an advanced multidisciplinary analysis environment for aerospace propulsion systems called the Numerical Propulsion System Simulation (NPSS). NPSS is a framework for performing analysis of complex systems. The initial development of NPSS focused on the analysis and design of airbreathing aircraft engines, but the resulting NPSS framework may be applied to any system, for example: aerospace, rockets, hypersonics, power and propulsion, fuel cells, ground based power, and even human system modeling. NPSS provides increased flexibility for the user, which reduces the total development time and cost. It is currently being extended to support the NASA Aeronautics Research Mission Directorate Fundamental Aeronautics Program and the Advanced Virtual Engine Test Cell (AVETeC). NPSS focuses on the integration of multiple disciplines such as aerodynamics, structure, and heat transfer with numerical zooming on component codes. Zooming is the coupling of analyses at various levels of detail. NPSS development includes capabilities to facilitate collaborative engineering. The NPSS will provide improved tools to develop custom components and to use capability for zooming to higher fidelity codes, coupling to multidiscipline codes, transmitting secure data, and distributing simulations across different platforms. These powerful capabilities extend NPSS from a zero-dimensional simulation tool to a multi-fidelity, multidiscipline system-level simulation tool for the full development life cycle.
Procedure and Program Examples
NASA Astrophysics Data System (ADS)
Britz, Dieter
Here some modules, procedures and whole programs are described, that may be useful to the reader, as they have been, to the author. They are all in Fortran 90/95 and start with a generally useful module, that will be used in most procedures and programs in the examples, and another module useful for programs using a Rosenbrock variant. The source texts (except for the two modules) are not reproduced here, but can be downloaded from the web site www.springerlink.com/openurl.asp?genre=issue &issn=1616-6361&volume=666 (the two lines form one contiguous URL!).
Schulz, Andreas S.; Shmoys, David B.; Williamson, David P.
1997-01-01
Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525
Alocomotino Control Algorithm for Robotic Linkage Systems
Dohner, Jeffrey L.
2016-10-01
This dissertation describes the development of a control algorithm that transitions a robotic linkage system between stabilized states producing responsive locomotion. The developed algorithm is demonstrated using a simple robotic construction consisting of a few links with actuation and sensing at each joint. Numerical and experimental validation is presented.
Evolving evolutionary algorithms using linear genetic programming.
Oltean, Mihai
2005-01-01
A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.
Numerical Continuation of Hamiltonian Relative Periodic Orbits
NASA Astrophysics Data System (ADS)
Wulff, Claudia; Schebesch, Andreas
2008-08-01
The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years, there has been rapid progress in the development of a bifurcation theory for dynamical systems with structure, such as symmetry or symplecticity. But as yet, there are few results on the numerical computation of those bifurcations. The methods we present in this paper are a first step toward a systematic numerical analysis of generic bifurcations of Hamiltonian symmetric periodic orbits and relative periodic orbits (RPOs). First, we show how to numerically exploit spatio-temporal symmetries of Hamiltonian periodic orbits. Then we describe a general method for the numerical computation of RPOs persisting from periodic orbits in a symmetry breaking bifurcation. Finally, we present an algorithm for the numerical continuation of non-degenerate Hamiltonian relative periodic orbits with regular drift-momentum pair. Our path following algorithm is based on a multiple shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincaré section and a tangential continuation method with implicit reparametrization. We apply our methods to continue the famous figure eight choreography of the three-body system. We find a relative period doubling bifurcation of the planar rotating eight family and compute the rotating choreographies bifurcating from it.
Reliable numerical computation in an optimal output-feedback design
NASA Technical Reports Server (NTRS)
Vansteenwyk, Brett; Ly, Uy-Loi
1991-01-01
A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.
Development and application of unified algorithms for problems in computational science
NASA Technical Reports Server (NTRS)
Shankar, Vijaya; Chakravarthy, Sukumar
1987-01-01
A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.
APL simulation of Grover's algorithm
NASA Astrophysics Data System (ADS)
Lipovaca, Samir
2012-02-01
Grover's algorithm is a fast quantum search algorithm. Classically, to solve the search problem for a search space of size N we need approximately N operations. Grover's algorithm offers a quadratic speedup. Since present quantum computers are not robust enough for code writing and execution, to experiment with Grover's algorithm, we will simulate it using the APL programming language. The APL programming language is especially suited for this task. For example, to compute Walsh-Hadamard transformation matrix for N quantum states via a tensor product of N Hadamard matrices we need to iterate N-1 times only one line of the code. Initial study indicates the quantum mechanical amplitude of the solution is almost independent of the search space size and rapidly reaches 0.999 values with slight variations at higher decimal places.
Numerical taxonomy on data: Experimental results
Cohen, J.; Farach, M.
1997-12-01
The numerical taxonomy problems associated with most of the optimization criteria described above are NP - hard [3, 5, 1, 4]. In, the first positive result for numerical taxonomy was presented. They showed that if e is the distance to the closest tree metric under the L{sub {infinity}} norm. i.e., e = min{sub T} [L{sub {infinity}} (T-D)], then it is possible to construct a tree T such that L{sub {infinity}} (T-D) {le} 3e, that is, they gave a 3-approximation algorithm for this problem. We will refer to this algorithm as the Single Pivot (SP) heuristic.
Recent advances in numerical PDEs
NASA Astrophysics Data System (ADS)
Zuev, Julia Michelle
In this thesis, we investigate four neighboring topics, all in the general area of numerical methods for solving Partial Differential Equations (PDEs). Topic 1. Radial Basis Functions (RBF) are widely used for multi-dimensional interpolation of scattered data. This methodology offers smooth and accurate interpolants, which can be further refined, if necessary, by clustering nodes in select areas. We show, however, that local refinements with RBF (in a constant shape parameter [varepsilon] regime) may lead to the oscillatory errors associated with the Runge phenomenon (RP). RP is best known in the case of high-order polynomial interpolation, where its effects can be accurately predicted via Lebesgue constant L (which is based solely on the node distribution). We study the RP and the applicability of Lebesgue constant (as well as other error measures) in RBF interpolation. Mainly, we allow for a spatially variable shape parameter, and demonstrate how it can be used to suppress RP-like edge effects and to improve the overall stability and accuracy. Topic 2. Although not as versatile as RBFs, cubic splines are useful for interpolating grid-based data. In 2-D, we consider a patch representation via Hermite basis functions s i,j ( u, v ) = [Special characters omitted.] h mn H m ( u ) H n ( v ), as opposed to the standard bicubic representation. Stitching requirements for the rectangular non-equispaced grid yield a 2-D tridiagonal linear system AX = B, where X represents the unknown first derivatives. We discover that the standard methods for solving this NxM system do not take advantage of the spline-specific format of the matrix B. We develop an alternative approach using this specialization of the RHS, which allows us to pre-compute coefficients only once, instead of N times. MATLAB implementation of our fast 2-D cubic spline algorithm is provided. We confirm analytically and numerically that for large N ( N > 200), our method is at least 3 times faster than the
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Rankin, Charles C.
2006-01-01
This document summarizes the STructural Analysis of General Shells (STAGS) development effort, STAGS performance for selected demonstration problems, and STAGS application problems illustrating selected advanced features available in the STAGS Version 5.0. Each problem is discussed including selected background information and reference solutions when available. The modeling and solution approach for each problem is described and illustrated. Numerical results are presented and compared with reference solutions, test data, and/or results obtained from mesh refinement studies. These solutions provide an indication of the overall capabilities of the STAGS nonlinear finite element analysis tool and provide users with representative cases, including input files, to explore these capabilities that may then be tailored to other applications.
Asynchronous Event-Driven Particle Algorithms
Donev, A
2007-02-28
We present in a unifying way the main components of three examples of asynchronous event-driven algorithms for simulating physical systems of interacting particles. The first example, hard-particle molecular dynamics (MD), is well-known. We also present a recently-developed diffusion kinetic Monte Carlo (DKMC) algorithm, as well as a novel event-driven algorithm for Direct Simulation Monte Carlo (DSMC). Finally, we describe how to combine MD with DSMC in an event-driven framework, and discuss some promises and challenges for event-driven simulation of realistic physical systems.
NASA Astrophysics Data System (ADS)
Chen, Peijun; Huang, Jianguo; Zhang, Xiaoqun
2013-02-01
Recently, the minimization of a sum of two convex functions has received considerable interest in a variational image restoration model. In this paper, we propose a general algorithmic framework for solving a separable convex minimization problem from the point of view of fixed point algorithms based on proximity operators (Moreau 1962 C. R. Acad. Sci., Paris I 255 2897-99). Motivated by proximal forward-backward splitting proposed in Combettes and Wajs (2005 Multiscale Model. Simul. 4 1168-200) and fixed point algorithms based on the proximity operator (FP2O) for image denoising (Micchelli et al 2011 Inverse Problems 27 45009-38), we design a primal-dual fixed point algorithm based on the proximity operator (PDFP2Oκ for κ ∈ [0, 1)) and obtain a scheme with a closed-form solution for each iteration. Using the firmly nonexpansive properties of the proximity operator and with the help of a special norm over a product space, we achieve the convergence of the proposed PDFP2Oκ algorithm. Moreover, under some stronger assumptions, we can prove the global linear convergence of the proposed algorithm. We also give the connection of the proposed algorithm with other existing first-order methods. Finally, we illustrate the efficiency of PDFP2Oκ through some numerical examples on image supper-resolution, computerized tomographic reconstruction and parallel magnetic resonance imaging. Generally speaking, our method PDFP2O (κ = 0) is comparable with other state-of-the-art methods in numerical performance, while it has some advantages on parameter selection in real applications.
Nonlinear dynamics and numerical uncertainties in CFD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.
1996-01-01
The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.
In Praise of Numerical Computation
NASA Astrophysics Data System (ADS)
Yap, Chee K.
Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms’ design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name “numerical computational geometry” for such activities.
Optimal Multistage Algorithm for Adjoint Computation
Aupy, Guillaume; Herrmann, Julien; Hovland, Paul; Robert, Yves
2016-01-01
We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.
Large scale tracking algorithms
Hansen, Ross L.; Love, Joshua Alan; Melgaard, David Kennett; Karelitz, David B.; Pitts, Todd Alan; Zollweg, Joshua David; Anderson, Dylan Z.; Nandy, Prabal; Whitlow, Gary L.; Bender, Daniel A.; Byrne, Raymond Harry
2015-01-01
Low signal-to-noise data processing algorithms for improved detection, tracking, discrimination and situational threat assessment are a key research challenge. As sensor technologies progress, the number of pixels will increase signi cantly. This will result in increased resolution, which could improve object discrimination, but unfortunately, will also result in a significant increase in the number of potential targets to track. Many tracking techniques, like multi-hypothesis trackers, suffer from a combinatorial explosion as the number of potential targets increase. As the resolution increases, the phenomenology applied towards detection algorithms also changes. For low resolution sensors, "blob" tracking is the norm. For higher resolution data, additional information may be employed in the detection and classfication steps. The most challenging scenarios are those where the targets cannot be fully resolved, yet must be tracked and distinguished for neighboring closely spaced objects. Tracking vehicles in an urban environment is an example of such a challenging scenario. This report evaluates several potential tracking algorithms for large-scale tracking in an urban environment.
Evaluation of Algorithms for Automatic Data Extraction from Digital Holographic Images of Particles
NASA Astrophysics Data System (ADS)
Dyomin, V. V.; Kamenev, D. V.
2016-02-01
The procedures and algorithms providing a numerical implementation of the physical process of image reconstruction from in-line particle holograms are discussed. The methods are proposed which allow functioning of this process in an automatic mode and ensure data processing and extraction from digital particle holograms in a form convenient for subsequent physical interpretation. The experimental results on realization of these methods are presented, using digital holograms of plankton particles, air bubbles in water, and sand particles, obtained under laboratory conditions as examples.
An algorithm for solving the fractional convection diffusion equation with nonlinear source term
NASA Astrophysics Data System (ADS)
Momani, Shaher
2007-10-01
In this paper an algorithm based on Adomian's decomposition method is developed to approximate the solution of the nonlinear fractional convection-diffusion equation {∂αu}/{∂tα}={∂2u}/{∂x2}-c{∂u}/{∂x}+Ψ(u)+f(x,t),0
Optimizing the Point-In-Box Search Algorithm for the Cray Y-MP(TM) Supercomputer
Attaway, S.W.; Davis, M.E.; Heinstein, M.W.; Swegle, J.S.
1998-12-23
Determining the subset of points (particles) in a problem domain that are contained within certain spatial regions of interest can be one of the most time-consuming parts of some computer simulations. Examples where this 'point-in-box' search can dominate the computation time include (1) finite element contact problems; (2) molecular dynamics simulations; and (3) interactions between particles in numerical methods, such as discrete particle methods or smooth particle hydrodynamics. This paper describes methods to optimize a point-in-box search algorithm developed by Swegle that make optimal use of the architectural features of the Cray Y-MP Supercomputer.
The Application of Imperialist Competitive Algorithm for Fuzzy Random Portfolio Selection Problem
NASA Astrophysics Data System (ADS)
EhsanHesamSadati, Mir; Bagherzadeh Mohasefi, Jamshid
2013-10-01
This paper presents an implementation of the Imperialist Competitive Algorithm (ICA) for solving the fuzzy random portfolio selection problem where the asset returns are represented by fuzzy random variables. Portfolio Optimization is an important research field in modern finance. By using the necessity-based model, fuzzy random variables reformulate to the linear programming and ICA will be designed to find the optimum solution. To show the efficiency of the proposed method, a numerical example illustrates the whole idea on implementation of ICA for fuzzy random portfolio selection problem.
Enghauser, Michael
2015-02-01
The goal of the Domestic Nuclear Detection Office (DNDO) Algorithm Improvement Program (AIP) is to facilitate gamma-radiation detector nuclide identification algorithm development, improvement, and validation. Accordingly, scoring criteria have been developed to objectively assess the performance of nuclide identification algorithms. In addition, a Microsoft Excel spreadsheet application for automated nuclide identification scoring has been developed. This report provides an overview of the equations, nuclide weighting factors, nuclide equivalencies, and configuration weighting factors used by the application for scoring nuclide identification algorithm performance. Furthermore, this report presents a general overview of the nuclide identification algorithm scoring application including illustrative examples.
Example based lesion segmentation
NASA Astrophysics Data System (ADS)
Roy, Snehashis; He, Qing; Carass, Aaron; Jog, Amod; Cuzzocreo, Jennifer L.; Reich, Daniel S.; Prince, Jerry; Pham, Dzung
2014-03-01
Automatic and accurate detection of white matter lesions is a significant step toward understanding the progression of many diseases, like Alzheimer's disease or multiple sclerosis. Multi-modal MR images are often used to segment T2 white matter lesions that can represent regions of demyelination or ischemia. Some automated lesion segmentation methods describe the lesion intensities using generative models, and then classify the lesions with some combination of heuristics and cost minimization. In contrast, we propose a patch-based method, in which lesions are found using examples from an atlas containing multi-modal MR images and corresponding manual delineations of lesions. Patches from subject MR images are matched to patches from the atlas and lesion memberships are found based on patch similarity weights. We experiment on 43 subjects with MS, whose scans show various levels of lesion-load. We demonstrate significant improvement in Dice coefficient and total lesion volume compared to a state of the art model-based lesion segmentation method, indicating more accurate delineation of lesions.
Chen, Ying-ping; Chen, Chao-Hong
2010-01-01
An adaptive discretization method, called split-on-demand (SoD), enables estimation of distribution algorithms (EDAs) for discrete variables to solve continuous optimization problems. SoD randomly splits a continuous interval if the number of search points within the interval exceeds a threshold, which is decreased at every iteration. After the split operation, the nonempty intervals are assigned integer codes, and the search points are discretized accordingly. As an example of using SoD with EDAs, the integration of SoD and the extended compact genetic algorithm (ECGA) is presented and numerically examined. In this integration, we adopt a local search mechanism as an optional component of our back end optimization engine. As a result, the proposed framework can be considered as a memetic algorithm, and SoD can potentially be applied to other memetic algorithms. The numerical experiments consist of two parts: (1) a set of benchmark functions on which ECGA with SoD and ECGA with two well-known discretization methods: the fixed-height histogram (FHH) and the fixed-width histogram (FWH) are compared; (2) a real-world application, the economic dispatch problem, on which ECGA with SoD is compared to other methods. The experimental results indicate that SoD is a better discretization method to work with ECGA. Moreover, ECGA with SoD works quite well on the economic dispatch problem and delivers solutions better than the best known results obtained by other methods in existence.
Multiresolution strategies for the numerical solution of optimal control problems
NASA Astrophysics Data System (ADS)
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
A generalized memory test algorithm
NASA Technical Reports Server (NTRS)
Milner, E. J.
1982-01-01
A general algorithm for testing digital computer memory is presented. The test checks that (1) every bit can be cleared and set in each memory work, and (2) bits are not erroneously cleared and/or set elsewhere in memory at the same time. The algorithm can be applied to any size memory block and any size memory word. It is concise and efficient, requiring the very few cycles through memory. For example, a test of 16-bit-word-size memory requries only 384 cycles through memory. Approximately 15 seconds were required to test a 32K block of such memory, using a microcomputer having a cycle time of 133 nanoseconds.
NASA Technical Reports Server (NTRS)
Reed, K. W.; Atluri, S. N.
1983-01-01
A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is base upon a generalization of de Veubeke's complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and thg resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.
Thermostat algorithm for generating target ensembles.
Bravetti, A; Tapias, D
2016-02-01
We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nosé and Hoover, our algorithm is based on a non-Hamiltonian system in an extended phase space. However, the equations of motion in our case follow from contact geometry and we show that in general they have a similar form to those of the so-called density dynamics algorithm. As a prototypical example, we apply our algorithm to produce a Gibbs canonical distribution for a one-dimensional harmonic oscillator.
Introduction to Cluster Monte Carlo Algorithms
NASA Astrophysics Data System (ADS)
Luijten, E.
This chapter provides an introduction to cluster Monte Carlo algorithms for classical statistical-mechanical systems. A brief review of the conventional Metropolis algorithm is given, followed by a detailed discussion of the lattice cluster algorithm developed by Swendsen and Wang and the single-cluster variant introduced by Wolff. For continuum systems, the geometric cluster algorithm of Dress and Krauth is described. It is shown how their geometric approach can be generalized to incorporate particle interactions beyond hardcore repulsions, thus forging a connection between the lattice and continuum approaches. Several illustrative examples are discussed.
An improved sink particle algorithm for SPH simulations
NASA Astrophysics Data System (ADS)
Hubber, D. A.; Walch, S.; Whitworth, A. P.
2013-04-01
Numerical simulations of star formation frequently rely on the implementation of sink particles: (a) to avoid expending computational resource on the detailed internal physics of individual collapsing protostars, (b) to derive mass functions, binary statistics and clustering kinematics (and hence to make comparisons with observation), and (c) to model radiative and mechanical feedback; sink particles are also used in other contexts, for example to represent accreting black holes in galactic nuclei. We present a new algorithm for creating and evolving sink particles in smoothed particle hydrodynamic (SPH) simulations, which appears to represent a significant improvement over existing algorithms - particularly in situations where sinks are introduced after the gas has become optically thick to its own cooling radiation and started to heat up by adiabatic compression. (i) It avoids spurious creation of sinks. (ii) It regulates the accretion of matter on to a sink so as to mitigate non-physical perturbations in the vicinity of the sink. (iii) Sinks accrete matter, but the associated angular momentum is transferred back to the surrounding medium. With the new algorithm - and modulo the need to invoke sufficient resolution to capture the physics preceding sink formation - the properties of sinks formed in simulations are essentially independent of the user-defined parameters of sink creation, or the number of SPH particles used.
A multiscale hybrid algorithm for fluctuating hydrodynamics
NASA Astrophysics Data System (ADS)
Williams, Sarah Anne
We develop an algorithmic hybrid for simulating multiscale fluid flow with microscopic fluctuations. Random fluctuations occur in fluids at microscopic scales, and these microscopic fluctuations can lead to macroscopic system effects. For example, in the Rayleigh-Taylor problem, where a relatively heavy gas sits on top of a relatively light gas, spontaneous microscopic fluctuation at the interface of the gases leads to turbulent mixing. Given near-term computational power, the physical and temporal domain on which these systems can be studied using traditional particle simulations is extremely limited. Therefore, we seek algorithmic solutions to increase the effective computing power available to study such problems. We develop an explicit numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics via stochastic; fluxes. A major goal is to correctly preserve the influence of the microscopic fluctuations on the behavior of the system. We show that several classical approaches fail to accurately reproduce fluctuations in energy or density, and we introduce a customized conservative centered scheme with a third-order Runge-Kutta temporal integrator that is specficially designed to produce correct fluctuations in all conserved quantities. We then use the adaptive mesh and algorithm refinement (AMAR) paradigm to create a multiscale hybrid method by coupling our LLNS solver with the direct simulation Monte Carlo (DSMC) particle method. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically at non-hydrodynamic time scales. As an extension of
Disruptive Innovation in Numerical Hydrodynamics
Waltz, Jacob I.
2012-09-06
We propose the research and development of a high-fidelity hydrodynamic algorithm for tetrahedral meshes that will lead to a disruptive innovation in the numerical modeling of Laboratory problems. Our proposed innovation has the potential to reduce turnaround time by orders of magnitude relative to Advanced Simulation and Computing (ASC) codes; reduce simulation setup costs by millions of dollars per year; and effectively leverage Graphics Processing Unit (GPU) and future Exascale computing hardware. If successful, this work will lead to a dramatic leap forward in the Laboratory's quest for a predictive simulation capability.
Development of Improved Algorithms and Multiscale Modeling Capability with SUNTANS
2015-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Development of Improved Algorithms and Multiscale...a wide range of scales through use of accurate numerical methods and high- performance computational algorithms . The tool will be applied to study...dissipation. OBJECTIVES The primary objective is to enhance the capabilities of the SUNTANS model through development of algorithms to study
An algorithm for the automatic synchronization of Omega receivers
NASA Technical Reports Server (NTRS)
Stonestreet, W. M.; Marzetta, T. L.
1977-01-01
The Omega navigation system and the requirement for receiver synchronization are discussed. A description of the synchronization algorithm is provided. The numerical simulation and its associated assumptions were examined and results of the simulation are presented. The suggested form of the synchronization algorithm and the suggested receiver design values were surveyed. A Fortran of the synchronization algorithm used in the simulation was also included.
Approximate learning algorithm in Boltzmann machines.
Yasuda, Muneki; Tanaka, Kazuyuki
2009-11-01
Boltzmann machines can be regarded as Markov random fields. For binary cases, they are equivalent to the Ising spin model in statistical mechanics. Learning systems in Boltzmann machines are one of the NP-hard problems. Thus, in general we have to use approximate methods to construct practical learning algorithms in this context. In this letter, we propose new and practical learning algorithms for Boltzmann machines by using the belief propagation algorithm and the linear response approximation, which are often referred as advanced mean field methods. Finally, we show the validity of our algorithm using numerical experiments.
A MEDLINE categorization algorithm
Darmoni, Stefan J; Névéol, Aurelie; Renard, Jean-Marie; Gehanno, Jean-Francois; Soualmia, Lina F; Dahamna, Badisse; Thirion, Benoit
2006-01-01
Background Categorization is designed to enhance resource description by organizing content description so as to enable the reader to grasp quickly and easily what are the main topics discussed in it. The objective of this work is to propose a categorization algorithm to classify a set of scientific articles indexed with the MeSH thesaurus, and in particular those of the MEDLINE bibliographic database. In a large bibliographic database such as MEDLINE, finding materials of particular interest to a specialty group, or relevant to a particular audience, can be difficult. The categorization refines the retrieval of indexed material. In the CISMeF terminology, metaterms can be considered as super-concepts. They were primarily conceived to improve recall in the CISMeF quality-controlled health gateway. Methods The MEDLINE categorization algorithm (MCA) is based on semantic links existing between MeSH terms and metaterms on the one hand and between MeSH subheadings and metaterms on the other hand. These links are used to automatically infer a list of metaterms from any MeSH term/subheading indexing. Medical librarians manually select the semantic links. Results The MEDLINE categorization algorithm lists the medical specialties relevant to a MEDLINE file by decreasing order of their importance. The MEDLINE categorization algorithm is available on a Web site. It can run on any MEDLINE file in a batch mode. As an example, the top 3 medical specialties for the set of 60 articles published in BioMed Central Medical Informatics & Decision Making, which are currently indexed in MEDLINE are: information science, organization and administration and medical informatics. Conclusion We have presented a MEDLINE categorization algorithm in order to classify the medical specialties addressed in any MEDLINE file in the form of a ranked list of relevant specialties. The categorization method introduced in this paper is based on the manual indexing of resources with MeSH (terms
Reactive Collision Avoidance Algorithm
NASA Technical Reports Server (NTRS)
Scharf, Daniel; Acikmese, Behcet; Ploen, Scott; Hadaegh, Fred
2010-01-01
The reactive collision avoidance (RCA) algorithm allows a spacecraft to find a fuel-optimal trajectory for avoiding an arbitrary number of colliding spacecraft in real time while accounting for acceleration limits. In addition to spacecraft, the technology can be used for vehicles that can accelerate in any direction, such as helicopters and submersibles. In contrast to existing, passive algorithms that simultaneously design trajectories for a cluster of vehicles working to achieve a common goal, RCA is implemented onboard spacecraft only when an imminent collision is detected, and then plans a collision avoidance maneuver for only that host vehicle, thus preventing a collision in an off-nominal situation for which passive algorithms cannot. An example scenario for such a situation might be when a spacecraft in the cluster is approaching another one, but enters safe mode and begins to drift. Functionally, the RCA detects colliding spacecraft, plans an evasion trajectory by solving the Evasion Trajectory Problem (ETP), and then recovers after the collision is avoided. A direct optimization approach was used to develop the algorithm so it can run in real time. In this innovation, a parameterized class of avoidance trajectories is specified, and then the optimal trajectory is found by searching over the parameters. The class of trajectories is selected as bang-off-bang as motivated by optimal control theory. That is, an avoiding spacecraft first applies full acceleration in a constant direction, then coasts, and finally applies full acceleration to stop. The parameter optimization problem can be solved offline and stored as a look-up table of values. Using a look-up table allows the algorithm to run in real time. Given a colliding spacecraft, the properties of the collision geometry serve as indices of the look-up table that gives the optimal trajectory. For multiple colliding spacecraft, the set of trajectories that avoid all spacecraft is rapidly searched on
Zhang, Huaguang; Jiang, He; Luo, Chaomin; Xiao, Geyang
2016-10-03
In this paper, we investigate the nonzero-sum games for a class of discrete-time (DT) nonlinear systems by using a novel policy iteration (PI) adaptive dynamic programming (ADP) method. The main idea of our proposed PI scheme is to utilize the iterative ADP algorithm to obtain the iterative control policies, which not only ensure the system to achieve stability but also minimize the performance index function for each player. This paper integrates game theory, optimal control theory, and reinforcement learning technique to formulate and handle the DT nonzero-sum games for multiplayer. First, we design three actor-critic algorithms, an offline one and two online ones, for the PI scheme. Subsequently, neural networks are employed to implement these algorithms and the corresponding stability analysis is also provided via the Lyapunov theory. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.
NASA Astrophysics Data System (ADS)
Trifunović, Jovan
2012-12-01
Various backfill materials are used with the aim to reduce grounding resistance of grounding systems to the desired values. The algorithm for determination of a proper combination of features a backfill material needs to possess in order to successfully perform this task is developed and presented. It is based on the numerical analysis of the results obtained with finite-element method modelling of the considered grounding system, surrounding soil, backfill material and imperfect contact. As an example, the developed algorithm is applied on two grounding loops (one conventional and the other backfilled with bentonite suspension) embedded in a two-layer soil. The results obtained with the application of the proposed algorithm can be used as guidance for the researchers who are looking for new suitable low cost backfill materials.
Numerical Relativity's Contributions to Theoretical Astrophysics, and Its Path Forward
NASA Astrophysics Data System (ADS)
Etienne, Zachariah
2015-04-01
In the extreme violence of merger and mass accretion, compact objects like black holes, neutron stars, and white dwarfs are thought to launch some of the most luminous outbursts of electromagnetic, neutrino, and gravitational wave energy in the Universe. Modeling these systems realistically remains a central problem in theoretical astrophysics, due to two key challenges. First, the emission mechanisms often stem from magnetized flows and dynamical gravitational fields spanning many orders of magnitude in lengthscale and timescale, from the strong-field region near compact objects, to the often magnetically-dominated, weak-field regions far away. Second, the equations governing the dynamics are highly complex and nonlinear, including the full general relativistic field equations as coupled to the equations of radiation general relativistic magnetohydrodynamics. I will review some of the current progress in developing numerical relativity codes that robustly and efficiently solve these equations (or some subset thereof) on non-uniform numerical grids to capture the multi-scale nature of compact object merger and mass accretion. Some key results from such codes will also be explored, providing examples of how numerical relativity has advanced theoretical astrophysics. Though these results are highly interesting, they often rely on extremely computationally expensive simulations that lack the accuracy and physical realism required for complete theoretical models. Thus, although numerical relativity simulations have begun to address key astrophysical questions, large gaps in our understanding remain. Bridging these gaps will require a continued focus on adding more physics to our simulations, as well as development of more computationally-efficient formulations of the equations and the algorithms for solving them.
A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics
Franceschini, Andrea; Ferronato, Massimiliano Janna, Carlo; Teatini, Pietro
2016-06-01
The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.
NASA Technical Reports Server (NTRS)
Korkin, S.; Lyapustin, A.
2012-01-01
The Levenberg-Marquardt algorithm [1, 2] provides a numerical iterative solution to the problem of minimization of a function over a space of its parameters. In our work, the Levenberg-Marquardt algorithm retrieves optical parameters of a thin (single scattering) plane parallel atmosphere irradiated by collimated infinitely wide monochromatic beam of light. Black ground surface is assumed. Computational accuracy, sensitivity to the initial guess and the presence of noise in the signal, and other properties of the algorithm are investigated in scalar (using intensity only) and vector (including polarization) modes. We consider an atmosphere that contains a mixture of coarse and fine fractions. Following [3], the fractions are simulated using Henyey-Greenstein model. Though not realistic, this assumption is very convenient for tests [4, p.354]. In our case it yields analytical evaluation of Jacobian matrix. Assuming the MISR geometry of observation [5] as an example, the average scattering cosines and the ratio of coarse and fine fractions, the atmosphere optical depth, and the single scattering albedo, are the five parameters to be determined numerically. In our implementation of the algorithm, the system of five linear equations is solved using the fast Cramer s rule [6]. A simple subroutine developed by the authors, makes the algorithm independent from external libraries. All Fortran 90/95 codes discussed in the presentation will be available immediately after the meeting from sergey.v.korkin@nasa.gov by request.
Numerical pole assignment by eigenvalue Jacobian inversion
NASA Technical Reports Server (NTRS)
Sevaston, George E.
1986-01-01
A numerical procedure for solving the linear pole placement problem is developed which operates by the inversion of an analytically determined eigenvalue Jacobian matrix. Attention is given to convergence characteristics and pathological situations. It is not concluded that the algorithm developed is suitable for computer-aided control system design with particular reference to the scan platform pointing control system for the Galileo spacecraft.
Numerical Methods for Initial Value Problems.
1980-07-01
of general multistep methods for ordinary differential equations a4 to implement an efficient algorithm for the solution of stiff equations . Still...integral equations II. Roundoff error for variants of Gaussian elimination III. Multistep methods for ordinary differential equations IV. Multi-grid...62 -! Paige III. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS ....... 63 1. Equivalent Forms of Multistep
Efficient multiple time-stepping algorithms of higher order
NASA Astrophysics Data System (ADS)
Demirel, Abdullah; Niegemann, Jens; Busch, Kurt; Hochbruck, Marlis
2015-03-01
Multiple time-stepping (MTS) algorithms allow to efficiently integrate large systems of ordinary differential equations, where a few stiff terms restrict the timestep of an otherwise non-stiff system. In this work, we discuss a flexible class of MTS techniques, based on multistep methods. Our approach contains several popular methods as special cases and it allows for the easy construction of novel and efficient higher-order MTS schemes. In addition, we demonstrate how to adapt the stability contour of the non-stiff time-integration to the physical system at hand. This allows significantly larger timesteps when compared to previously known multistep MTS approaches. As an example, we derive novel predictor-corrector (PCMTS) schemes specifically optimized for the time-integration of damped wave equations on locally refined meshes. In a set of numerical experiments, we demonstrate the performance of our scheme on discontinuous Galerkin time-domain (DGTD) simulations of Maxwell's equations.
Optimisation of assembly scheduling in VCIM systems using genetic algorithm
NASA Astrophysics Data System (ADS)
Dao, Son Duy; Abhary, Kazem; Marian, Romeo
2017-01-01
Assembly plays an important role in any production system as it constitutes a significant portion of the lead time and cost of a product. Virtual computer-integrated manufacturing (VCIM) system is a modern production system being conceptually developed to extend the application of traditional computer-integrated manufacturing (CIM) system to global level. Assembly scheduling in VCIM systems is quite different from one in traditional production systems because of the difference in the working principles of the two systems. In this article, the assembly scheduling problem in VCIM systems is modeled and then an integrated approach based on genetic algorithm (GA) is proposed to search for a global optimised solution to the problem. Because of dynamic nature of the scheduling problem, a novel GA with unique chromosome representation and modified genetic operations is developed herein. Robustness of the proposed approach is verified by a numerical example.
Exploring Neutrino Oscillation Parameter Space with a Monte Carlo Algorithm
NASA Astrophysics Data System (ADS)
Espejel, Hugo; Ernst, David; Cogswell, Bernadette; Latimer, David
2015-04-01
The χ2 (or likelihood) function for a global analysis of neutrino oscillation data is first calculated as a function of the neutrino mixing parameters. A computational challenge is to obtain the minima or the allowed regions for the mixing parameters. The conventional approach is to calculate the χ2 (or likelihood) function on a grid for a large number of points, and then marginalize over the likelihood function. As the number of parameters increases with the number of neutrinos, making the calculation numerically efficient becomes necessary. We implement a new Monte Carlo algorithm (D. Foreman-Mackey, D. W. Hogg, D. Lang and J. Goodman, Publications of the Astronomical Society of the Pacific, 125 306 (2013)) to determine its computational efficiency at finding the minima and allowed regions. We examine a realistic example to compare the historical and the new methods.
ANALYSIS OF A NUMERICAL SOLVER FOR RADIATIVE TRANSPORT EQUATION.
Gao, Hao; Zhao, Hongkai
2013-01-01
We analyze a numerical algorithm for solving radiative transport equation with vacuum or reflection boundary condition that was proposed in [4] with angular discretization by finite element method and spatial discretization by discontinuous Galerkin or finite difference method.
NASA Astrophysics Data System (ADS)
Liliana Gheorghian, Mariana
2014-05-01
beginning of the XXI century" with the participation of several schools in the country in 2009 and 2011. The papers presented were diverse and gave examples of various teaching experiences and scientific information. Topics by the teachers: The impact of tourism on the environment, Tornadoes, Natural science and environmental education in school, Air Pollution and health, Ecological education of children from primary school, The effects of electromagnetic radiation, Formation of an ecological mentality using chemistry, Why should we protect water, Environmental education, Education for the future, SOS Nature, Science in the twenty-first century, etc. Topics by students: Nature- the palace of thermal phenomena, Life depends on heat, Water Mysteries, Global Heating, The Mysterious universe, etc. In March 2013 our school hosted an interesting exchange of ideas on environmental issues between our students and those from Bulgaria, Poland and Turkey, during a symposium of the Comenius multilateral project "Conserving Nature". In order to present the results of protecting nature in their communities, two projects "Citizen" qualified in the Program Civitas in the autumn of 2013. "The Battle" continues both in nature and in classrooms, in order to preserve the environment.
Numerical tsunami modeling and the bottom relief
NASA Astrophysics Data System (ADS)
Kulikov, E. A.; Gusiakov, V. K.; Ivanova, A. A.; Baranov, B. V.
2016-11-01
The effect of the quality of bathymetric data on the accuracy of tsunami-wave field calculation is considered. A review of the history of the numerical tsunami modeling development is presented. Particular emphasis is made on the World Ocean bottom models. It is shown that the modern digital bathymetry maps, for example, GEBCO, do not adequately simulate the sea bottom in numerical models of wave propagation, leading to considerable errors in estimating the maximum tsunami run-ups on the coast.
Numerical quadratures for approximate computation of ERBS
NASA Astrophysics Data System (ADS)
Zanaty, Peter
2013-12-01
In the ground-laying paper [3] on expo-rational B-splines (ERBS), the default numerical method for approximate computation of the integral with C∞-smooth integrand in the definition of ERBS is Romberg integration. In the present work, a variety of alternative numerical quadrature methods for computation of ERBS and other integrals with smooth integrands are studied, and their performance is compared on several benchmark examples.
Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods
NASA Technical Reports Server (NTRS)
Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark
2002-01-01
Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.
Numerical study of Taylor bubbles with adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Pain, Chris; Matar, Omar; Hasan, Abbas; Azzopardi, Barry
2014-11-01
The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube. This type of bubble flow regime often occurs in gas-liquid slug flows in many industrial applications, including oil-and-gas production, chemical and nuclear reactors, and heat exchangers. The objective of this study is to investigate the fluid dynamics of Taylor bubbles rising in a vertical pipe filled with oils of extremely high viscosity (mimicking the ``heavy oils'' found in the oil-and-gas industry). A modelling and simulation framework is presented here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rise and reduce the computational effort without sacrificing accuracy. The numerical framework consists of a mixed control-volume and finite-element formulation, a ``volume of fluid''-type method for the interface capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Numerical examples of some benchmark tests and the dynamics of Taylor bubbles are presented to show the capability of this method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
Three-dimensional numerical simulations of three-phase flows
NASA Astrophysics Data System (ADS)
Pavlidis, Dimitrios; Xie, Zhizhua; Salinas, Pablo; Pain, Chris; Matar, Omar
2015-11-01
The objective of this study is to investigate the fluid dynamics of three-dimensional three-phase flow problems, such as droplet impact on a gas-liquid interface and bubble rising through a liquid-liquid interface. An adaptive unstructured mesh modelling framework is employed here to study three-phase flow problems, which can modify and adapt unstructured meshes to better represent the underlying physics of multiphase problems and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a `volume of fluid' type method for the interface capturing based on a compressive control volume advection method and second-order finite element methods, and a force-balanced algorithm for the surface tension implementation, minimising the spurious velocities often found in such flow simulations. The surface tension coefficient decomposition method has been employed to deal with surface tension pairing between different phases via a compositional approach. Numerical examples of some benchmark tests and the dynamics of three-phase flows are presented to demonstrate the ability of this method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
A numerical approach to finding general stationary vacuum black holes
NASA Astrophysics Data System (ADS)
Adam, Alexander; Kitchen, Sam; Wiseman, Toby
2012-08-01
The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon, this equation has previously been shown to be elliptic, and Ricci flow and Newton’s method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes which is general enough to include many interesting higher dimensional solutions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson’s boundary conditions. We demonstrate both Newton’s method and Ricci flow to find these Lorentzian solutions.
Algorithmic deformation of matrix factorisations
NASA Astrophysics Data System (ADS)
Carqueville, Nils; Dowdy, Laura; Recknagel, Andreas
2012-04-01
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these algorithms and apply them to several examples. Apart from explicit results in concrete cases, this leads to a novel way to generate new matrix factorisations via nilpotent substitutions, and to criteria whether boundary obstructions can be lifted by bulk deformations.
Numerical Aspects of Atomic Physics: Helium Basis Sets and Matrix Diagonalization
NASA Astrophysics Data System (ADS)
Jentschura, Ulrich; Noble, Jonathan
2014-03-01
We present a matrix diagonalization algorithm for complex symmetric matrices, which can be used in order to determine the resonance energies of auto-ionizing states of comparatively simple quantum many-body systems such as helium. The algorithm is based in multi-precision arithmetic and proceeds via a tridiagonalization of the complex symmetric (not necessarily Hermitian) input matrix using generalized Householder transformations. Example calculations involving so-called PT-symmetric quantum systems lead to reference values which pertain to the imaginary cubic perturbation (the imaginary cubic anharmonic oscillator). We then proceed to novel basis sets for the helium atom and present results for Bethe logarithms in hydrogen and helium, obtained using the enhanced numerical techniques. Some intricacies of ``canned'' algorithms such as those used in LAPACK will be discussed. Our algorithm, for complex symmetric matrices such as those describing cubic resonances after complex scaling, is faster than LAPACK's built-in routines, for specific classes of input matrices. It also offer flexibility in terms of the calculation of the so-called implicit shift, which is used in order to ``pivot'' the system toward the convergence to diagonal form. We conclude with a wider overview.
Universality in numerical computations with random data.
Deift, Percy A; Menon, Govind; Olver, Sheehan; Trogdon, Thomas
2014-10-21
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance) is a random variable, called the halting time. Two-component universality is observed for the fluctuations of the halting time--i.e., the histogram for the halting times, centered by the sample average and scaled by the sample variance, collapses to a universal curve, independent of the input data distribution, as the dimension increases. Thus, up to two components--the sample average and the sample variance--the statistics for the halting time are universally prescribed. The case studies include six standard numerical algorithms as well as a model of neural computation and decision-making. A link to relevant software is provided for readers who would like to do computations of their own.
Visualizing output for a data learning algorithm
NASA Astrophysics Data System (ADS)
Carson, Daniel; Graham, James; Ternovskiy, Igor
2016-05-01
This paper details the process we went through to visualize the output for our data learning algorithm. We have been developing a hierarchical self-structuring learning algorithm based around the general principles of the LaRue model. One example of a proposed application of this algorithm would be traffic analysis, chosen because it is conceptually easy to follow and there is a significant amount of already existing data and related research material with which to work with. While we choose the tracking of vehicles for our initial approach, it is by no means the only target of our algorithm. Flexibility is the end goal, however, we still need somewhere to start. To that end, this paper details our creation of the visualization GUI for our algorithm, the features we included and the initial results we obtained from our algorithm running a few of the traffic based scenarios we designed.
CADDIS Volume 3. Examples and Applications: Analytical Examples
Examples illustrating the use of statistical analysis to support different types of evidence, stream temperature, temperature inferred from macroinverterbate, macroinvertebrate responses, zinc concentrations, observed trait characteristics.
Numerical recipes for mold filling simulation
Kothe, D.; Juric, D.; Lam, K.; Lally, B.
1998-07-01
Has the ability to simulate the filling of a mold progressed to a point where an appropriate numerical recipe achieves the desired results? If results are defined to be topological robustness, computational efficiency, quantitative accuracy, and predictability, all within a computational domain that faithfully represents complex three-dimensional foundry molds, then the answer unfortunately remains no. Significant interfacial flow algorithm developments have occurred over the last decade, however, that could bring this answer closer to maybe. These developments have been both evolutionary and revolutionary, will continue to transpire for the near future. Might they become useful numerical recipes for mold filling simulations? Quite possibly. Recent progress in algorithms for interface kinematics and dynamics, linear solution methods, computer science issues such as parallelization and object-oriented programming, high resolution Navier-Stokes (NS) solution methods, and unstructured mesh techniques, must all be pursued as possible paths toward higher fidelity mold filling simulations. A detailed exposition of these algorithmic developments is beyond the scope of this paper, hence the authors choose to focus here exclusively on algorithms for interface kinematics. These interface tracking algorithms are designed to model the movement of interfaces relative to a reference frame such as a fixed mesh. Current interface tracking algorithm choices are numerous, so is any one best suited for mold filling simulation? Although a clear winner is not (yet) apparent, pros and cons are given in the following brief, critical review. Highlighted are those outstanding interface tracking algorithm issues the authors feel can hamper the reliable modeling of today`s foundry mold filling processes.
Recurrent neural networks training with stable bounding ellipsoid algorithm.
Yu, Wen; de Jesús Rubio, José
2009-06-01
Bounding ellipsoid (BE) algorithms offer an attractive alternative to traditional training algorithms for neural networks, for example, backpropagation and least squares methods. The benefits include high computational efficiency and fast convergence speed. In this paper, we propose an ellipsoid propagation algorithm to train the weights of recurrent neural networks for nonlinear systems identification. Both hidden layers and output layers can be updated. The stability of the BE algorithm is proven.
Performance Comparison Of Evolutionary Algorithms For Image Clustering
NASA Astrophysics Data System (ADS)
Civicioglu, P.; Atasever, U. H.; Ozkan, C.; Besdok, E.; Karkinli, A. E.; Kesikoglu, A.
2014-09-01
Evolutionary computation tools are able to process real valued numerical sets in order to extract suboptimal solution of designed problem. Data clustering algorithms have been intensively used for image segmentation in remote sensing applications. Despite of wide usage of evolutionary algorithms on data clustering, their clustering performances have been scarcely studied by using clustering validation indexes. In this paper, the recently proposed evolutionary algorithms (i.e., Artificial Bee Colony Algorithm (ABC), Gravitational Search Algorithm (GSA), Cuckoo Search Algorithm (CS), Adaptive Differential Evolution Algorithm (JADE), Differential Search Algorithm (DSA) and Backtracking Search Optimization Algorithm (BSA)) and some classical image clustering techniques (i.e., k-means, fcm, som networks) have been used to cluster images and their performances have been compared by using four clustering validation indexes. Experimental test results exposed that evolutionary algorithms give more reliable cluster-centers than classical clustering techniques, but their convergence time is quite long.
Some nonlinear space decomposition algorithms
Tai, Xue-Cheng; Espedal, M.
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Source mask optimization using real-coded genetic algorithms
NASA Astrophysics Data System (ADS)
Yang, Chaoxing; Wang, Xiangzhao; Li, Sikun; Erdmann, Andreas
2013-04-01
Source mask optimization (SMO) is considered to be one of the technologies to push conventional 193nm lithography to its ultimate limits. In comparison with other SMO methods that use an inverse problem formulation, SMO based on genetic algorithm (GA) requires very little knowledge of the process, and has the advantage of flexible problem formulation. Recent publications on SMO using a GA employ a binary-coded GA. In general, the performance of a GA depends not only on the merit or fitness function, but also on the parameters, operators and their algorithmic implementation. In this paper, we propose a SMO method using real-coded GA where the source and mask solutions are represented by floating point strings instead of bit strings. Besides from that, the selection, crossover, and mutation operators are replaced by corresponding floating-point versions. Both binary-coded and real-coded genetic algorithms were implemented in two versions of SMO and compared in numerical experiments, where the target patterns are staggered contact holes and a logic pattern with critical dimensions of 100 nm, respectively. The results demonstrate the performance improvement of the real-coded GA in comparison to the binary-coded version. Specifically, these improvements can be seen in a better convergence behavior. For example, the numerical experiments for the logic pattern showed that the average number of generations to converge to a proper fitness of 6.0 using the real-coded method is 61.8% (100 generations) less than that using binary-coded method.
Harmony search optimization algorithm for a novel transportation problem in a consolidation network
NASA Astrophysics Data System (ADS)
Davod Hosseini, Seyed; Akbarpour Shirazi, Mohsen; Taghi Fatemi Ghomi, Seyed Mohammad
2014-11-01
This article presents a new harmony search optimization algorithm to solve a novel integer programming model developed for a consolidation network. In this network, a set of vehicles is used to transport goods from suppliers to their corresponding customers via two transportation systems: direct shipment and milk run logistics. The objective of this problem is to minimize the total shipping cost in the network, so it tries to reduce the number of required vehicles using an efficient vehicle routing strategy in the solution approach. Solving several numerical examples confirms that the proposed solution approach based on the harmony search algorithm performs much better than CPLEX in reducing both the shipping cost in the network and computational time requirement, especially for realistic size problem instances.
NASA Technical Reports Server (NTRS)
Acikmese, Behcet A.; Carson, John M., III
2005-01-01
A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Carson, John M., III
2006-01-01
A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.
[A study for time-history waveform synthesis of algorithm in shock response spectrum (SRS)].
Liu, Hong-ying; Ma, Ai-jun
2002-12-01
Objective. To present an effective on-line SRS time-history waveform synthesis method for simulating pyrotechnic shock environment with electrodynamic shakers. Method. A procedure was developed for synthesizing a SRS time-history waveform according to a general principle. The effect of three main parameters to waveform's shape, amplitude of acceleration and duration were investigated. A modification method of SRS's amplitude and an optimal algorithm of time-history waveform were presented. Result. The algorithm was used to generate a time-history waveform that could satisfy SRS's accuracy requirement and electrodynamic shaker's acceleration limitation. Conclusion. The numerical example indicates that the developed method is effective. The synthesized time-history waveform can be used to simulate pyrotechnic shock environment using electrodynamic shakers.
Query by image example: The CANDID approach
Kelly, P.M.; Cannon, M.; Hush, D.R.
1995-02-01
CANDID (Comparison Algorithm for Navigating Digital Image Databases) was developed to enable content-based retrieval of digital imagery from large databases using a query-by-example methodology. A user provides an example image to the system, and images in the database that are similar to that example are retrieved. The development of CANDID was inspired by the N-gram approach to document fingerprinting, where a ``global signature`` is computed for every document in a database and these signatures are compared to one another to determine the similarity between any two documents. CANDID computes a global signature for every image in a database, where the signature is derived from various image features such as localized texture, shape, or color information. A distance between probability density functions of feature vectors is then used to compare signatures. In this paper, the authors present CANDID and highlight two results from their current research: subtracting a ``background`` signature from every signature in a database in an attempt to improve system performance when using inner-product similarity measures, and visualizing the contribution of individual pixels in the matching process. These ideas are applicable to any histogram-based comparison technique.
Numerical estimation of densities
NASA Astrophysics Data System (ADS)
Ascasibar, Y.; Binney, J.
2005-01-01
We present a novel technique, dubbed FIESTAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FIESTAS assigns a volume to each point by means of a binary tree. Density is then computed by integrating over an adaptive kernel. As a first test, we construct several Monte Carlo realizations of a Hernquist profile and recover the particle density in both real and phase space. At a given point, Poisson noise causes the unsmoothed estimates to fluctuate by a factor of ~2 regardless of the number of particles. This spread can be reduced to about 1dex (~26 per cent) by our smoothing procedure. The density range over which the estimates are unbiased widens as the particle number increases. Our tests show that real-space densities obtained with an SPH kernel are significantly more biased than those yielded by FIESTAS. In phase space, about 10 times more particles are required in order to achieve a similar accuracy. As a second application we have estimated phase-space densities in a dark matter halo from a cosmological simulation. We confirm the results of Arad, Dekel & Klypin that the highest values of f are all associated with substructure rather than the main halo, and that the volume function v(f) ~f-2.5 over about four orders of magnitude in f. We show that a modified version of the toy model proposed by Arad et al. explains this result and suggests that the departures of v(f) from power-law form are not mere numerical artefacts. We conclude that our algorithm accurately measures the phase-space density up to the limit where discreteness effects render the simulation itself unreliable. Computationally, FIESTAS is orders of magnitude faster than the method based on Delaunay tessellation that Arad et al. employed, making it practicable to recover smoothed density estimates for sets of 109 points in six dimensions.
Numerical integration of asymptotic solutions of ordinary differential equations
NASA Technical Reports Server (NTRS)
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Numerical treatment of shocks in unsteady potential flow computation
NASA Astrophysics Data System (ADS)
Schippers, H.
1985-04-01
For moving shocks in unsteady transonic potential flow, an implicit fully-conservative finite-difference algorithm is presented. It is based on time-linearization and mass-flux splitting. For the one-dimensional problem of a traveling shock-wave, this algorithm is compared with the method of Goorjian and Shankar. The algorithm was implemented in the computer program TULIPS for the computation of transonic unsteady flow about airfoils. Numerical results for a pitching ONERA M6 airfoil are presented.
Airplane numerical simulation for the rapid prototyping process
NASA Astrophysics Data System (ADS)
Roysdon, Paul F.
Airplane Numerical Simulation for the Rapid Prototyping Process is a comprehensive research investigation into the most up-to-date methods for airplane development and design. Uses of modern engineering software tools, like MatLab and Excel, are presented with examples of batch and optimization algorithms which combine the computing power of MatLab with robust aerodynamic tools like XFOIL and AVL. The resulting data is demonstrated in the development and use of a full non-linear six-degrees-of-freedom simulator. The applications for this numerical tool-box vary from un-manned aerial vehicles to first-order analysis of manned aircraft. A Blended-Wing-Body airplane is used for the analysis to demonstrate the flexibility of the code from classic wing-and-tail configurations to less common configurations like the blended-wing-body. This configuration has been shown to have superior aerodynamic performance -- in contrast to their classic wing-and-tube fuselage counterparts -- and have reduced sensitivity to aerodynamic flutter as well as potential for increased engine noise abatement. Of course without a classic tail elevator to damp the nose up pitching moment, and the vertical tail rudder to damp the yaw and possible rolling aerodynamics, the challenges in lateral roll and yaw stability, as well as pitching moment are not insignificant. This thesis work applies the tools necessary to perform the airplane development and optimization on a rapid basis, demonstrating the strength of this tool through examples and comparison of the results to similar airplane performance characteristics published in literature.
Online Pairwise Learning Algorithms.
Ying, Yiming; Zhou, Ding-Xuan
2016-04-01
Pairwise learning usually refers to a learning task that involves a loss function depending on pairs of examples, among which the most notable ones are bipartite ranking, metric learning, and AUC maximization. In this letter we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS) that we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works (Kar, Sriperumbudur, Jain, & Karnick, 2013 ; Wang, Khardon, Pechyony, & Jones, 2012 ), which require that the iterates are restricted to a bounded domain or the loss function is strongly convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem that guarantees the almost sure convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely used kernels in the setting of pairwise learning and illustrate the convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.
A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems
NASA Astrophysics Data System (ADS)
Carpio, Jaime; Prieto, Juan Luis; Vera, Marcos
2016-02-01
A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogen-air flame/vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.
Fontana, W.
1990-12-13
In this paper complex adaptive systems are defined by a self- referential loop in which objects encode functions that act back on these objects. A model for this loop is presented. It uses a simple recursive formal language, derived from the lambda-calculus, to provide a semantics that maps character strings into functions that manipulate symbols on strings. The interaction between two functions, or algorithms, is defined naturally within the language through function composition, and results in the production of a new function. An iterated map acting on sets of functions and a corresponding graph representation are defined. Their properties are useful to discuss the behavior of a fixed size ensemble of randomly interacting functions. This function gas'', or Turning gas'', is studied under various conditions, and evolves cooperative interaction patterns of considerable intricacy. These patterns adapt under the influence of perturbations consisting in the addition of new random functions to the system. Different organizations emerge depending on the availability of self-replicators.
High-resolution algorithms for the Navier-Stokes equations for generalized discretizations
NASA Astrophysics Data System (ADS)
Mitchell, Curtis Randall
Accurate finite volume solution algorithms for the two dimensional Navier Stokes equations and the three dimensional Euler equations for both structured and unstructured grid topologies are presented. Results for two dimensional quadrilateral and triangular elements and three dimensional tetrahedral elements will be provided. Fundamental to the solution algorithm is a technique for generating multidimensional polynomials which model the spatial variation of the flow variables. Cell averaged data is used to reconstruct pointwise distributions of the dependent variables. The reconstruction errors are evaluated on triangular meshes. The implementation of the algorithm is unique in that three reconstructions are performed for each cell face in the domain. Two of the reconstructions are used to evaluate the inviscid fluxes and correspond to the right and left interface states needed for the solution of a Riemann problem. The third reconstruction is used to evaluate the viscous fluxes. The gradient terms that appear in the viscous fluxes are formed by simply differentiating the polynomial. By selecting the appropriate cell control volumes, centered, upwind and upwind-biased stencils are possible. Numerical calculations in two dimensions include solutions to elliptic boundary value problems, Ringlebs' flow, an inviscid shock reflection, a flat plate boundary layer, and a shock induced separation over a flat plate. Three dimensional results include the ONERA M6 wing. All of the unstructured grids were generated using an advancing front mesh generation procedure. Modifications to the three dimensional grid generator were necessary to discretize the surface grids for bodies with high curvature. In addition, mesh refinement algorithms were implemented to improve the surface grid integrity. Examples include a Glasair fuselage, High Speed Civil Transport, and the ONERA M6 wing. The role of reconstruction as applied to adaptive remeshing is discussed and a new first order error
NASA Technical Reports Server (NTRS)
Merceret, Francis; Lane, John; Immer, Christopher; Case, Jonathan; Manobianco, John
2005-01-01
The contour error map (CEM) algorithm and the software that implements the algorithm are means of quantifying correlations between sets of time-varying data that are binarized and registered on spatial grids. The present version of the software is intended for use in evaluating numerical weather forecasts against observational sea-breeze data. In cases in which observational data come from off-grid stations, it is necessary to preprocess the observational data to transform them into gridded data. First, the wind direction is gridded and binarized so that D(i,j;n) is the input to CEM based on forecast data and d(i,j;n) is the input to CEM based on gridded observational data. Here, i and j are spatial indices representing 1.25-km intervals along the west-to-east and south-to-north directions, respectively; and n is a time index representing 5-minute intervals. A binary value of D or d = 0 corresponds to an offshore wind, whereas a value of D or d = 1 corresponds to an onshore wind. CEM includes two notable subalgorithms: One identifies and verifies sea-breeze boundaries; the other, which can be invoked optionally, performs an image-erosion function for the purpose of attempting to eliminate river-breeze contributions in the wind fields.
Five-dimensional Janis-Newman algorithm
NASA Astrophysics Data System (ADS)
Erbin, Harold; Heurtier, Lucien
2015-08-01
The Janis-Newman algorithm has been shown to be successful in finding new stationary solutions of four-dimensional gravity. Attempts for a generalization to higher dimensions have already been found for the restricted cases with only one angular momentum. In this paper we propose an extension of this algorithm to five-dimensions with two angular momenta—using the prescription of Giampieri—through two specific examples, that are the Myers-Perry and BMPV black holes. We also discuss possible enlargements of our prescriptions to other dimensions and maximal number of angular momenta, and show how dimensions higher than six appear to be much more challenging to treat within this framework. Nonetheless this general algorithm provides a unification of the formulation in d=3,4,5 of the Janis-Newman algorithm, from which several examples are exposed, including the BTZ black hole.
Extremal polynomials and methods of optimization of numerical algorithms
Lebedev, V I
2004-10-31
Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.
Towards High Resolution Numerical Algorithms for Wave Dominated Physical Phenomena
2009-01-30
couple these elements using Finite- Volume-like surface Riemann solvers. This hybrid, dual-layer design allows DGTD to combine advantages from both of...electromagnetic waves , J. Comput. Phys., 114 (1994), pp. 185-200. [62] F. COLLINO, High order absorbing boundary conditions for wave propagation...formulation with high order absorbing boundary conditions for time-dependent waves , Comput. Meth. Appl. Mech., 195 (2006), pp. 3666-3690. [69] M. GUDDATI
Novel Numerical Algorithms for Sensing, Discrimination, and Control
1990-03-09
throughput specifications. At the front end of the imaging data stream, individual pixel level processing for filtering, contrasting, contouring requires...100 MHz clock rates for 32-bit data arriving at 10-40 MHz frame rates. Imaging processing at the back end looks for patterns or "global" parameters and...observations suggest, however, that a CZT requires 2N log N operations whereas the FFT requires only N log N operations. Hence, the CZT is not
Internal labelling problem: an algorithmic procedure
NASA Astrophysics Data System (ADS)
Campoamor-Stursberg, Rutwig
2011-01-01
Combining the decomposition of Casimir operators induced by the embedding of a subalgebra into a semisimple Lie algebra with the properties of commutators of subgroup scalars, an analytical algorithm for the computation of missing label operators with the commutativity requirement is proposed. Two new criteria for subgroups scalars to commute are given. The algorithm is completed with a recursive method to construct orthonormal bases of states. As examples to illustrate the procedure, four labelling problems are explicitly studied.
NASA Astrophysics Data System (ADS)
Stühler, Sven; Fleissner, Florian; Eberhard, Peter
2016-11-01
We present an extended particle model for the discrete element method that on the one hand is tetrahedral in shape and on the other hand is capable to describe deformations. The deformations of the tetrahedral particles require a framework to interrelate the particle strains and resulting stresses. Hence, adaptations from the finite element method were used. This allows to link the two methods and to adequately describe material and simulation parameters separately in each scope. Due to the complexity arising of the non-spherical tetrahedral geometry, all possible contact combinations of vertices, edges, and surfaces must be considered by the used contact detection algorithm. The deformations of the particles make the contact evaluation even more challenging. Therefore, a robust contact detection algorithm based on an optimization approach that exploits temporal coherence is presented. This algorithm is suitable for general {R}^{{n}} simplices. An evaluation of the robustness of this algorithm is performed using a numerical example. In order to create complex geometries, bonds between these deformable particles are introduced. This coupling via the tetrahedra faces allows the simulation bonding of deformable bodies composed of several particles. Numerical examples are presented and validated with results that are obtained by the same simulation setup modeled with the finite element method. The intention of using these bonds is to be able to model fracture and material failure. Therefore, the bonds between the particles are not lasting and feature a release mechanism based on a predefined criterion.
NASA Astrophysics Data System (ADS)
Taitano, W. T.; Chacón, L.; Simakov, A. N.; Molvig, K.
2015-09-01
In this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional Rosenbluth-Fokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single- and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and to exhibit manifestly positive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.
Constructing Programs from Example Computations.
ERIC Educational Resources Information Center
Bierman, A. W.; Krishnaswamy, R.
This paper describes the construction and implementation of an autoprogramming system. An autoprogrammer is an interactive computer programming system which automatically constructs computer programs from example computations executed by the user. The example calculations are done in a scratch pad fashion at a computer display, and the system…
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
Algorithm for in-flight gyroscope calibration
NASA Technical Reports Server (NTRS)
Davenport, P. B.; Welter, G. L.
1988-01-01
An optimal algorithm for the in-flight calibration of spacecraft gyroscope systems is presented. Special consideration is given to the selection of the loss function weight matrix in situations in which the spacecraft attitude sensors provide significantly more accurate information in pitch and yaw than in roll, such as will be the case in the Hubble Space Telescope mission. The results of numerical tests that verify the accuracy of the algorithm are discussed.
Jamming cancellation algorithm for wideband imaging radar
NASA Astrophysics Data System (ADS)
Zheng, Yibin; Yu, Kai-Bor
1998-10-01
We describe a jamming cancellation algorithm for wide-band imaging radar. After reviewing high range resolution imaging principle, several key factors affecting jamming cancellation performances, such as the 'instantaneous narrow-band' assumption, bandwidth, de-chirped interference, are formulated and analyzed. Some numerical simulation results, using a hypothetical phased array radar and synthetic point targets, are presented. The results demonstrated the effectiveness of the proposed algorithm.
Numerical Boundary Condition Procedures
NASA Technical Reports Server (NTRS)
1981-01-01
Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.
Numerical simulation of steady supersonic flow. [spatial marching
NASA Technical Reports Server (NTRS)
Schiff, L. B.; Steger, J. L.
1981-01-01
A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.
A modified WTC algorithm for the Painlevé test of nonlinear variable-coefficient PDEs
NASA Astrophysics Data System (ADS)
Zhao, Yin-Long; Liu, Yin-Ping; Li, Zhi-Bin
2009-11-01
A modified WTC algorithm for the Painlevé test of nonlinear PDEs with variable coefficients is proposed. Compared to the Kruskal's simplification algorithm, the modified algorithm further simplifies the computation in the third step of the Painlevé test for variable-coefficient PDEs to some extent. Two examples illustrate the proposed modified algorithm.
Approximation concepts for numerical airfoil optimization
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.
1979-01-01
An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems.
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.
Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou
2015-01-01
Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models
Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou
2015-01-01
Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409
High order hybrid numerical simulations of two dimensional detonation waves
NASA Technical Reports Server (NTRS)
Cai, Wei
1993-01-01
In order to study multi-dimensional unstable detonation waves, a high order numerical scheme suitable for calculating the detailed transverse wave structures of multidimensional detonation waves was developed. The numerical algorithm uses a multi-domain approach so different numerical techniques can be applied for different components of detonation waves. The detonation waves are assumed to undergo an irreversible, unimolecular reaction A yields B. Several cases of unstable two dimensional detonation waves are simulated and detailed transverse wave interactions are documented. The numerical results show the importance of resolving the detonation front without excessive numerical viscosity in order to obtain the correct cellular patterns.
Algorithm Animation with Galant.
Stallmann, Matthias F
2017-01-01
Although surveys suggest positive student attitudes toward the use of algorithm animations, it is not clear that they improve learning outcomes. The Graph Algorithm Animation Tool, or Galant, challenges and motivates students to engage more deeply with algorithm concepts, without distracting them with programming language details or GUIs. Even though Galant is specifically designed for graph algorithms, it has also been used to animate other algorithms, most notably sorting algorithms.
NASA Astrophysics Data System (ADS)
Qu, Shan; Zhou, Hui; Liu, Renwu; Chen, Yangkang; Zu, Shaohuan; Yu, Sa; Yuan, Jiang; Yang, Yahui
2016-08-01
In this paper, an improved algorithm is proposed to separate blended seismic data. We formulate the deblending problem as a regularization problem in both common receiver domain and frequency domain. It is suitable for different kinds of coding methods such as random time delay discussed in this paper. Two basic approximation frames, which are iterative shrinkage-thresholding algorithm (ISTA) and fast iterative shrinkage-thresholding algorithm (FISTA), are compared. We also derive the Lipschitz constant used in approximation frames. In order to achieve a faster convergence and higher accuracy, we propose to use firm-thresholding function as the thresholding function in ISTA and FISTA. Two synthetic blended examples demonstrate that the performances of four kinds of algorithms (ISTA with soft- and firm-thresholding, FISTA with soft- and firm-thresholding) are all effective, and furthermore FISTA with a firm-thresholding operator exhibits the most robust behavior. Finally, we show one numerically blended field data example processed by FISTA with firm-thresholding function.
Asynchronous Event-Driven Particle Algorithms
Donev, A
2007-08-30
We present, in a unifying way, the main components of three asynchronous event-driven algorithms for simulating physical systems of interacting particles. The first example, hard-particle molecular dynamics (MD), is well-known. We also present a recently-developed diffusion kinetic Monte Carlo (DKMC) algorithm, as well as a novel stochastic molecular-dynamics algorithm that builds on the Direct Simulation Monte Carlo (DSMC). We explain how to effectively combine event-driven and classical time-driven handling, and discuss some promises and challenges for event-driven simulation of realistic physical systems.
Dual format algorithm implementation with gotcha data
NASA Astrophysics Data System (ADS)
Gorham, LeRoy A.; Rigling, Brian D.
2012-05-01
The Dual Format Algorithm (DFA) is an alternative to the Polar Format Algorithm (PFA) where the image is formed first to an arbitrary grid instead of a Cartesian grid. The arbitrary grid is specifically chosen to allow for more efficient application of defocus and distortion corrections that occur due to range curvature. We provide a description of the arbitrary image grid and show that the quadratic phase errors are isolated along a single dimension of the image. We describe an application of the DFA to circular SAR data and analyze the image focus. For an example SAR dataset, the DFA doubles the focused image size of the PFA algorithm with post imaging corrections.
Numerical approaches to simulation of multi-core fibers
NASA Astrophysics Data System (ADS)
Chekhovskoy, I. S.; Paasonen, V. I.; Shtyrina, O. V.; Fedoruk, M. P.
2017-04-01
We propose generalizations of two numerical algorithms to solve the system of linearly coupled nonlinear Schrödinger equations (NLSEs) describing the propagation of light pulses in multi-core optical fibers. An iterative compact dissipative second-order accurate in space and fourth-order accurate in time scheme is the first numerical method. This compact scheme has strong stability due to inclusion of the additional dissipative term. The second algorithm is a generalization of the split-step Fourier method based on Padé approximation of the matrix exponential. We compare a computational efficiency of both algorithms and show that the compact scheme is more efficient in terms of performance for solving a large system of coupled NLSEs. We also present the parallel implementation of the numerical algorithms for shared memory systems using OpenMP.