NASA Astrophysics Data System (ADS)
Miao, J. C.; Zhu, P.; Shi, G. L.; Chen, G. L.
2008-01-01
Numerical stability is an important issue for any integral procedure. Since sub-cycling algorithm has been presented by Belytschko et al. (Comput Methods Appl Mech Eng 17/18: 259-275, 1979), various kinds of these integral procedures were developed in later 20 years and their stability were widely studied. However, on how to apply the sub-cycling to flexible multi-body dynamics (FMD) is still a lack of investigation up to now. A particular sub-cycling algorithm for the FMD based on the central difference method was introduced in detail in part I (Miao et al. in Comp Mech doi: 10.1007/s00466-007-0183-9) of this paper. Adopting an integral approximation operator method, stability of the presented algorithm is transformed to a generalized eigenvalue problem in the paper and is discussed by solving the problem later. Numerical examples are performed to verify the availability and efficiency of the algorithm further.
Practical algorithmic probability: an image inpainting example
NASA Astrophysics Data System (ADS)
Potapov, Alexey; Scherbakov, Oleg; Zhdanov, Innokentii
2013-12-01
Possibility of practical application of algorithmic probability is analyzed on an example of image inpainting problem that precisely corresponds to the prediction problem. Such consideration is fruitful both for the theory of universal prediction and practical image inpaiting methods. Efficient application of algorithmic probability implies that its computation is essentially optimized for some specific data representation. In this paper, we considered one image representation, namely spectral representation, for which an image inpainting algorithm is proposed based on the spectrum entropy criterion. This algorithm showed promising results in spite of very simple representation. The same approach can be used for introducing ALP-based criterion for more powerful image representations.
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.
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 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.
Analyzing milestoning networks for molecular kinetics: Definitions, algorithms, and examples
NASA Astrophysics Data System (ADS)
Viswanath, Shruthi; Kreuzer, Steven M.; Cardenas, Alfredo E.; Elber, Ron
2013-11-01
Network representations are becoming increasingly popular for analyzing kinetic data from techniques like Milestoning, Markov State Models, and Transition Path Theory. Mapping continuous phase space trajectories into a relatively small number of discrete states helps in visualization of the data and in dissecting complex dynamics to concrete mechanisms. However, not only are molecular networks derived from molecular dynamics simulations growing in number, they are also getting increasingly complex, owing partly to the growth in computer power that allows us to generate longer and better converged trajectories. The increased complexity of the networks makes simple interpretation and qualitative insight of the molecular systems more difficult to achieve. In this paper, we focus on various network representations of kinetic data and algorithms to identify important edges and pathways in these networks. The kinetic data can be local and partial (such as the value of rate coefficients between states) or an exact solution to kinetic equations for the entire system (such as the stationary flux between vertices). In particular, we focus on the Milestoning method that provides fluxes as the main output. We proposed Global Maximum Weight Pathways as a useful tool for analyzing molecular mechanism in Milestoning networks. A closely related definition was made in the context of Transition Path Theory. We consider three algorithms to find Global Maximum Weight Pathways: Recursive Dijkstra's, Edge-Elimination, and Edge-List Bisection. The asymptotic efficiency of the algorithms is analyzed and numerical tests on finite networks show that Edge-List Bisection and Recursive Dijkstra's algorithms are most efficient for sparse and dense networks, respectively. Pathways are illustrated for two examples: helix unfolding and membrane permeation. Finally, we illustrate that networks based on local kinetic information can lead to incorrect interpretation of molecular mechanisms.
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.
Digital super-resolution microscopy using example-based algorithm
NASA Astrophysics Data System (ADS)
Ishikawa, Shinji; Hayasaki, Yoshio
2015-05-01
We propose a super-resolution microscopy with a confocal optical setup and an example-based algorithm. The example-based super-resolution algorithm was performed by an example database which is constructed by learning a lot of sets of a high-resolution patch and a low-resolution patch. The high-resolution patch is a part of the high-resolution image of an object model expressed in a computer, and the low-resolution patch is calculated from the high-resolution patch in consideration with a spatial property of an optical microscope. In the reconstruction process, a low-resolution image observed by the confocal optical setup with an image sensor is converted to the super-resolved high-resolution image selected by a pattern matching method from the example database. We demonstrate the adequate selection of the patch size and the weighting superposition method performs the super resolution with a low signal-to noise ratio.
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. PMID:26266271
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. PMID:26266271
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.
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.
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.
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.
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).
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.
Experimentally constructing finite difference algorithms in numerical relativity
NASA Astrophysics Data System (ADS)
Anderson, Matthew; Neilsen, David; Matzner, Richard
2002-04-01
Computational studies of gravitational waves require numerical algorithms with long-term stability (necessary for convergence). However, constructing stable finite difference algorithms (FDA) for the ADM formulation of the Einstein equations, especially in multiple dimensions, has proven difficult. Most FDA's are constructed using rules of thumb gained from experience with simple model equations. To search for FDA's with improved stability, we adopt a brute-force approach, where we systematically test thousands of numerical schemes. We sort the spatial derivatives of the Einstein equations into groups, and parameterize each group by finite difference type (centered or upwind) and order. Furthermore, terms proportional to the constraints are added to the evolution equations with additional parameters. A spherically symmetric, excised Schwarzschild black hole (one dimension) and linearized waves in multiple dimensions are used as model systems to evaluate the different numerical schemes.
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)
Determining the Numerical Stability of Quantum Chemistry Algorithms.
Knizia, Gerald; Li, Wenbin; Simon, Sven; Werner, Hans-Joachim
2011-08-01
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. PMID:26606614
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.
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.
A numerical algorithm for magnetohydrodynamics of ablated materials.
Lu, Tianshi; Du, Jian; Samulyak, Roman
2008-07-01
A numerical algorithm for the simulation of magnetohydrodynamics in partially ionized ablated material is described. For the hydro part, the hyperbolic conservation laws with electromagnetic terms is solved using techniques developed for free surface flows; for the electromagnetic part, the electrostatic approximation is applied and an elliptic equation for electric potential is solved. The algorithm has been implemented in the frame of front tracking, which explicitly tracks geometrically complex evolving interfaces. An elliptic solver based on the embedded boundary method were implemented for both two- and three-dimensional simulations. A surface model on the interface between the solid target and the ablated vapor has also been developed as well as a numerical model for the equation of state which accounts for atomic processes in the ablated material. The code has been applied to simulations of the pellet ablation in a magnetically confined plasma and the laser-ablated plasma plume expansion in magnetic fields. PMID:19051925
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.
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 review of…
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.
Improvements in algorithms for phenotype inference: the NAT2 example.
Selinski, Silvia; Blaszkewicz, Meinolf; Ickstadt, Katja; Hengstler, Jan G; Golka, Klaus
2014-02-01
Numerous studies have analyzed the impact of N-acetyltransferase 2 (NAT2) polymorphisms on drug efficacy, side effects as well as cancer risk. Here, we present the state of the art of deriving haplotypes from polymorphisms and discuss the available software. PHASE v2.1 is currently considered a gold standard for NAT2 haplotype assignment. In vitro studies have shown that some slow acetylation genotypes confer reduced protein stability. This has been observed particularly for G191A, T341C and G590A. Substantial ethnic variations of the acetylation status have been described. Probably, upcoming agriculture and the resulting change in diet caused a selection pressure for slow acetylation. In recent years much research has been done to reduce the complexity of NAT2 genotyping. Deriving the haplotype from seven SNPs is still considered a gold standard. However, meanwhile several studies have shown that a two-SNP combination, C282T and T341C, results in a similarly good distinction in Caucasians. However, attempts to further reduce complexity to only one 'tagging SNP' (rs1495741) may lead to wrong predictions where phenotypically slow acetylators were genotyped as intermediate or rapid. Numerous studies have shown that slow NAT2 haplotypes are associated with increased urinary bladder cancer risk and increased risk of anti-tuberculosis drug-induced hepatotoxicity. A drawback of the current practice of solely discriminating slow, intermediate and rapid genotypes for phenotype inference is limited resolution of differences between slow acetylators. Future developments to differentiate between slow and ultra-slow genotypes may further improve individualized drug dosing and epidemiological studies of cancer risk. PMID:24524665
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.
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.
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. PMID:26914586
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. PMID:19341374
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.
NASA Astrophysics Data System (ADS)
Acebrón, Juan A.; Rodríguez-Rozas, Ángel
2013-10-01
An efficient numerical method based on a probabilistic representation for the Vlasov-Poisson system of equations in the Fourier space has been derived. This has been done theoretically for arbitrary dimensional problems, and particularized to unidimensional problems for numerical purposes. Such a representation has been validated theoretically in the linear regime comparing the solution obtained with the classical results of the linear Landau damping. The numerical strategy followed requires generating suitable random trees combined with a Padé approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contributions to the solution coming from trees with arbitrary number of branches. These contributions, coming in general from multi-dimensional definite integrals, are efficiently computed by a quasi-Monte Carlo method. It is shown how the accuracy of the method can be effectively increased by considering more terms of the series. The new representation was used successfully to develop a Probabilistic Domain Decomposition method suited for massively parallel computers, which improves the scalability found in classical methods. Finally, a few numerical examples based on classical phenomena such as the non-linear Landau damping, and the two streaming instability are given, illustrating the remarkable performance of the algorithm, when compared the results with those obtained using a classical method.
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.
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 analysis of EPR spectra. 7. The simplex algorithm
NASA Astrophysics Data System (ADS)
Beckwith, Athelstan L. J.; Brumby, Steven
The Simplex algorithm is well suited to the least-squares analysis of highly complex EPR spectra. The application of the algorithm to the analysis of the spectra of benzo[ a]pyrenyl-6-oxy, chloro(methoxycarbonyl)methyl, and cyano(methoxy)methyl free radicals is described.
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 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
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
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.
On vortex loops and filaments: three examples of numerical predictions of flows containing vortices.
Krause, Egon
2003-01-01
Vortex motion plays a dominant role in many flow problems. This article aims at demonstrating some of the characteristic features of vortices with the aid of numerical solutions of the governing equations of fluid mechanics, the Navier-Stokes equations. Their discretized forms will first be reviewed briefly. Thereafter three problems of fluid flow involving vortex loops and filaments are discussed. In the first, the time-dependent motion and the mutual interaction of two colliding vortex rings are discussed, predicted in good agreement with experimental observations. The second example shows how vortex rings are generated, move, and interact with each other during the suction stroke in the cylinder of an automotive engine. The numerical results, validated with experimental data, suggest that vortex rings can be used to influence the spreading of the fuel droplets prior to ignition and reduce the fuel consumption. In the third example, it is shown that vortices can also occur in aerodynamic flows over delta wings at angle of attack as well as pipe flows: of particular interest for technical applications of these flows is the situation in which the vortex cores are destroyed, usually referred to as vortex breakdown or bursting. Although reliable breakdown criteria could not be established as yet, the numerical predictions obtained so far are found to agree well with the few experimental data available in the recent literature. PMID:12545239
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.
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.
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.
Stochastic algorithms for the analysis of numerical flame simulations
Bell, John B.; Day, Marcus S.; Grcar, Joseph F.; Lijewski, Michael J.
2004-04-26
Recent progress in simulation methodologies and high-performance parallel computers have made it is possible to perform detailed simulations of multidimensional reacting flow phenomena using comprehensive kinetics mechanisms. As simulations become larger and more complex, it becomes increasingly difficult to extract useful information from the numerical solution, particularly regarding the interactions of the chemical reaction and diffusion processes. In this paper we present a new diagnostic tool for analysis of numerical simulations of reacting flow. Our approach is based on recasting an Eulerian flow solution in a Lagrangian frame. Unlike a conventional Lagrangian view point that follows the evolution of a volume of the fluid, we instead follow specific chemical elements, e.g., carbon, nitrogen, etc., as they move through the system . From this perspective an ''atom'' is part of some molecule of a species that is transported through the domain by advection and diffusion. Reactions cause the atom to shift from one chemical host species to another and the subsequent transport of the atom is given by the movement of the new species. We represent these processes using a stochastic particle formulation that treats advection deterministically and models diffusion and chemistry as stochastic processes. In this paper, we discuss the numerical issues in detail and demonstrate that an ensemble of stochastic trajectories can accurately capture key features of the continuum solution. The capabilities of this diagnostic are then demonstrated by applications to study the modulation of carbon chemistry during a vortex-flame interaction, and the role of cyano chemistry in rm NO{sub x} production for a steady diffusion flame.
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.
Copps, Kevin D.; Carnes, Brian R.
2008-04-01
We examine algorithms for the finite element approximation of thermal contact models. We focus on the implementation of thermal contact algorithms in SIERRA Mechanics. Following the mathematical formulation of models for tied contact and resistance contact, we present three numerical algorithms: (1) the multi-point constraint (MPC) algorithm, (2) a resistance algorithm, and (3) a new generalized algorithm. We compare and contrast both the correctness and performance of the algorithms in three test problems. We tabulate the convergence rates of global norms of the temperature solution on sequentially refined meshes. We present the results of a parameter study of the effect of contact search tolerances. We outline best practices in using the software for predictive simulations, and suggest future improvements to the implementation.
NASA Astrophysics Data System (ADS)
Prather, M. J.; Zhu, X.
2003-12-01
Improved numerical methods for transport of trace species in the atmosphere and ocean continue to be developed. Typically, these algorithms are evaluated against existing methods using analytic or idealized test cases, but the NASA Global Modeling Initiative now provides a realistic framework for evaluating their accuracy in full chemistry-transport models (CTM). GMI's modular approach is combined with parallel simulations in the UCI CTM to quantify the differences between two relatively accurate tracer transport algorithms (Lin-Rood, Prather 2nd-order moments), including the impact of forcing a positive-definite, ripple-free tracer abundance. We use a range of simplified atmospheric chemical tracers (radon-lead, fossil-fuel CO2, industrial and biomass CO) with the meteorology from the Goddard Institute for Space Studies global climate model (4 deg by 5 deg with 23 layers) that includes three-hourly integrated winds, boundary-layer physics, entraining and non-entraining convection, large-scale and convective precipitation, updrafts and downdrafts. The relative accuracy of the different methods is considered in terms of forward and inverse calculations. We thank the entire GMI team, especially the researchers at LLNL and GSFC who have built and maintained the GMI modeling capability.
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
Comparison of Fully Numerical Predictor-Corrector and Apollo Skip Entry Guidance Algorithms
NASA Astrophysics Data System (ADS)
Brunner, Christopher W.; Lu, Ping
2012-09-01
The dramatic increase in computational power since the Apollo program has enabled the development of numerical predictor-corrector (NPC) entry guidance algorithms that allow on-board accurate determination of a vehicle's trajectory. These algorithms are sufficiently mature to be flown. They are highly adaptive, especially in the face of extreme dispersion and off-nominal situations compared with reference-trajectory following algorithms. The performance and reliability of entry guidance are critical to mission success. This paper compares the performance of a recently developed fully numerical predictor-corrector entry guidance (FNPEG) algorithm with that of the Apollo skip entry guidance. Through extensive dispersion testing, it is clearly demonstrated that the Apollo skip entry guidance algorithm would be inadequate in meeting the landing precision requirement for missions with medium (4000-7000 km) and long (>7000 km) downrange capability requirements under moderate dispersions chiefly due to poor modeling of atmospheric drag. In the presence of large dispersions, a significant number of failures occur even for short-range missions due to the deviation from planned reference trajectories. The FNPEG algorithm, on the other hand, is able to ensure high landing precision in all cases tested. All factors considered, a strong case is made for adopting fully numerical algorithms for future skip entry missions.
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
NASARC - NUMERICAL ARC SEGMENTATION ALGORITHM FOR A RADIO CONFERENCE
NASA Technical Reports Server (NTRS)
Whyte, W. A.
1994-01-01
NASARC was developed from the general planning principles and decisions of both sessions of the World Administrative Radio Conference on the Use of the Geostationary Satellite Orbit and on the Planning of Space Services Utilizing It (WARC-85, WARC-88). NASARC was written to help countries satisfy requirements for nation-wide Fixed Satellite services from at least one orbital position within a predetermined arc. The NASARC-generated predetermined arcs are each based on a common arc segment visible to a group of compatible service areas, and provide a means of generating a highly flexible allotment plan with a reduced need for coordination among administrations. The selection of particular groupings of service areas and their associated predetermined arcs is made according to a heuristic approach using several figures of merit designed to confront the most difficult allotment problems. NASARC attempts to select groupings and predetermined arc sizes so that the requirements of all administrations are met before the available orbital arc is exhausted. The predetermined arcs allow considerable freedom of choice in the positioning of space stations for all members of any grouping. The approach to allotment planning for which NASARC was designed consists of two phases. The first is the use of NASARC to identify predetermined arc segments common to groups of administrations. Those administrations within a group and sharing a common predetermined arc segment would be able to position their individual space stations at any one of a number of orbital positions within the predetermined arc. The second phase involves the use of a plan synthesis program (such as the ORBIT program resident at the International Frequency Registration Board in Geneva, Switzerland) to identify example scenarios of specific space station placements. NASARC software is modular, and consists of several programs to be run in sequence. The grouping module, NASARC1, identifies compatible groups of several
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
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.
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.
NASA Astrophysics Data System (ADS)
Mikesell, T. Dylan; Malcolm, Alison E.; Yang, Di; Haney, Matthew M.
2015-07-01
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 compare all three methods 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 good 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.
Wang, Peng; Zhu, Zhouquan; Huang, Shuai
2013-01-01
This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions. PMID:24385879
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.
Zhu, Zhouquan
2013-01-01
This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions. PMID:24385879
NASA Astrophysics Data System (ADS)
Simpson, Matthew J.; Landman, Kerry A.; Newgreen, Donald F.
2006-08-01
A numerical algorithm to simulate chemotactic and/or diffusive migration on a one-dimensional growing domain is developed. The domain growth can be spatially nonuniform and the growth-derived advection term must be discretised. The hyperbolic terms in the conservation equations associated with chemotactic migration and domain growth are accurately discretised using an explicit central scheme. Generality of the algorithm is maintained using an operator split technique to simulate diffusive migration implicitly. The resulting algorithm is applicable for any combination of diffusive and/or chemotactic migration on a growing domain with a general growth-induced velocity field. The accuracy of the algorithm is demonstrated by testing the results against some simple analytical solutions and in an inter-code comparison. The new algorithm demonstrates that the form of nonuniform growth plays a critical role in determining whether a population of migratory cells is able to overcome the domain growth and fully colonise the domain.
Burtsev, S.; Camassa, R.; Timofeyev, I.
1998-11-20
The authors implement two different algorithms for computing numerically the direct Zakharov-Shabat eigenvalue problem on the infinite line. The first algorithm replaces the potential in the eigenvalue problem by a piecewise-constant approximation, which allows one to solve analytically the corresponding ordinary differential equation. The resulting algorithm is of second order in the step size. The second algorithm uses the fourth-order Runge-Kutta method. They test and compare the performance of these two algorithms on three exactly solvable potentials. They find that even though the Runge-Kutta method is of higher order, this extra accuracy can be lost because of the additional dependence of its numerical error on the eigenvalue. this limits the usefulness of the Runge-Kutta algorithm to a region inside the unit circle around the origin in the complex plane of the eigenvalues. For the computation of the continuous spectrum density, this limitation is particularly severe, as revealed by the spectral decomposition of the L{sup 2}-norm of a solution to the nonlinear Schroedinger equation. They show that no such limitations exist for the piecewise-constant algorithm. In particular, this scheme converges uniformly for both continuous and discrete spectrum components.
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.
Nguyen, Tam H.; Song, Junho; Paulino, Glaucio H.
2008-02-15
Probabilistic fracture analyses are performed for investigating uncertain fracture response of Functionally Graded Material (FGM) structures. The First-Order-Reliability-Method (FORM) is implemented into an existing Finite Element code for FGM (FE-FGM), which was previously developed at the University of Illinois at Urbana-Champaign. The computational simulation will be used in order to estimate the probability of crack initiation with uncertainties in the material properties only. The two-step probability analysis method proposed in the companion paper is illustrated by a numerical example of a composite strip with an edge crack. First, the reliability index of a crack initiation event is estimated as we vary the mean and standard deviation of the slope and the location of the inflection point of the spatial profile of Young's modulus. Secondly, the reliability index is estimated as we vary the standard deviation and the correlation length of the random field that characterize the random spatial fluctuation of Young's modulus. Also investigated is the relative importance of the uncertainties in the toughness compared to those in Young's modulus.
A numerical algorithm suggested by problems of transport in periodic media - The matrix case.
NASA Technical Reports Server (NTRS)
Allen, R. C., Jr.; Burgmeier, J. W.; Mundorff, P.; Wing, G. M.
1972-01-01
Extension of Allen and Wing's (1970) previous work on problems of transport in periodic media to the matrix case. A method in the form of a complete set of equations is presented that may be used without any further analytical work by investigators interested in computing solutions to problems of the type the method is designed to handle. All the formulas have been checked out numerically, and their effectiveness is demonstrated by numerical examples.
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.
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).
NASA Technical Reports Server (NTRS)
Nacozy, P. E.
1984-01-01
The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.
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. 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.
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.
Numerical advection algorithms and their role in atmospheric transport and chemistry models
NASA Technical Reports Server (NTRS)
Rood, Richard B.
1987-01-01
During the last 35 years, well over 100 algorithms for modeling advection processes have been described and tested. This review summarizes the development and improvements that have taken place. The nature of the errors caused by numerical approximation to the advection equation are highlighted. Then the particular devices that have been proposed to remedy these errors are discussed. The extensive literature comparing transport algorithms is reviewed. Although there is no clear cut 'best' algorithm, several conclusions can be made. Spectral and pseudospectral techniques consistently provide the highest degree of accuracy, but expense and difficulties assuring positive mixing ratios are serious drawbacks. Schemes which consider fluid slabs bounded by grid points (volume schemes), rather than the simple specification of constituent values at the grid points, provide accurate positive definite results.
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
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 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.
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 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.
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.
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.
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, 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
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. PMID:27293424
NASA Astrophysics Data System (ADS)
Feng, Kunpeng; Zhou, Tong; Cui, Jiwen; Tan, Jiubin
2014-11-01
This paper presents a novel example-based super-resolution (SR) algorithm with improved k-means cluster. In this algorithm, genetic k-means (GKM) with hybrid particle swarm optimization (HPSO) is employed to improve the reconstruction of high-resolution (HR) images, and a pre-processing of classification in frequency is used to accelerate the procedure. Self-redundancy across different scales of a natural image is also utilized to build attached training set to expand example-based information. Meanwhile, a reconstruction algorithm based on hybrid supervise locally linear embedding (HSLLE) is proposed which uses training sets, high-resolution images and self-redundancy across different scales of a natural image. Experimental results show that patches are classified rapidly in training set processing session and the runtime of reconstruction is half of traditional algorithm at least in super-resolution session. And clustering and attached training set lead to a better recovery of low-resolution (LR) image.
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.
Localized vortices in a nonlinear shallow water model: examples and numerical experiments
NASA Astrophysics Data System (ADS)
Beisel, S. A.; Tolchennikov, A. A.
2016-06-01
Exact solutions of the system of nonlinear shallow water equations on paraboloid are constructed by the method of group analysis. These solutions describe fast wave motion of the fluid layer and slow evolution of symmetric localized vortices. Explicit formulae are obtained for asymptotic solution related to the linear shallow water approximation. Numerical methods are used by the modeling the trajectory of the vortex center in the case of asymmetric vortices.
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.
1986-01-01
Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.
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
NASA Astrophysics Data System (ADS)
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.
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)
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.
Shock focusing flow field simulated by a high-resolution numerical algorithm
NASA Astrophysics Data System (ADS)
Jung, Y. G.; Chang, K. S.
2012-11-01
Shock-focusing concave reflector is a very simple and effective tool to obtain a high-pressure pulse wave near the physical focal point. In the past, many optical images were obtained through experimental studies. However, measurement of field variables is not easy because the phenomenon is of short duration and the magnitude of shock waves is varied from pulse to pulse due to poor reproducibility. Using a wave propagation algorithm and the Cartesian embedded boundary method, we have successfully obtained numerical schlieren images that resemble the experimental results. By the numerical results, various field variables, such as pressure, density and vorticity, become available for the better understanding and design of shock focusing devices.
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.
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 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
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
NASA Astrophysics Data System (ADS)
Dong, Suchuan
2015-11-01
This talk focuses on simulating the motion of a mixture of N (N>=2) immiscible incompressible fluids with given densities, dynamic viscosities and pairwise surface tensions. We present an N-phase formulation within the phase field framework that is thermodynamically consistent, in the sense that the formulation satisfies the conservations of mass/momentum, the second law of thermodynamics and Galilean invariance. We also present an efficient algorithm for numerically simulating the N-phase system. The algorithm has overcome the issues caused by the variable coefficient matrices associated with the variable mixture density/viscosity and the couplings among the (N-1) phase field variables and the flow variables. We compare simulation results with the Langmuir-de Gennes theory to demonstrate that the presented method produces physically accurate results for multiple fluid phases. Numerical experiments will be presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts to demonstrate the capabilities of the method for studying the interactions among multiple types of fluid interfaces. Support from NSF and ONR is gratefully acknowledged.
Forsström, J
1992-01-01
The ID3 algorithm for inductive learning was tested using preclassified material for patients suspected to have a thyroid illness. Classification followed a rule-based expert system for the diagnosis of thyroid function. Thus, the knowledge to be learned was limited to the rules existing in the knowledge base of that expert system. The learning capability of the ID3 algorithm was tested with an unselected learning material (with some inherent missing data) and with a selected learning material (no missing data). The selected learning material was a subgroup which formed a part of the unselected learning material. When the number of learning cases was increased, the accuracy of the program improved. When the learning material was large enough, an increase in the learning material did not improve the results further. A better learning result was achieved with the selected learning material not including missing data as compared to unselected learning material. With this material we demonstrate a weakness in the ID3 algorithm: it can not find available information from good example cases if we add poor examples to the data. PMID:1551737
Numerical modelling of agricultural products on the example of bean and yellow lupine seeds
NASA Astrophysics Data System (ADS)
Anders, Andrzej; Kaliniewicz, Zdzisław; Markowski, Piotr
2015-10-01
Numerical models of bean seeds cv. Złota Saxa and yellow lupine seeds cv. Juno were generated with the use of a 3D scanner, the geometric parameters of seeds were determined based on the models developed, and compared with the results of digital image analysis and micrometer measurements. Measurements of seed length, width and thickness performed with the use of a micrometer, 3D scanner and digital image analysis produced similar results that did not differ significantly at α = 0.05. The micrometer delivered the simplest and fastest measurements. The mean surface area of bean seeds cv. Złota Saxa and yellow lupine seeds cv. Juno, calculated with the use of mathematical formulas based on the results of micrometer measurements and digital image analysis, differed significantly from the mean surface area determined with a 3D scanner. No significant differences in seed volume were observed when this parameter was measured with a 3D scanner and determined with the use of mathematical formulas based on the results of digital image analysis and micrometer measurements. The only differences were noted when the volume of yellow lupine seeds cv. Juno was measured in a 25 ml liquid pycnometer.
Anor, Tomer; Madsen, Joseph R; Dupont, Pierre
2011-05-01
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. PMID:22270831
Anor, Tomer; Madsen, Joseph R.; Dupont, Pierre
2011-01-01
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. PMID:22270831
Fast numerical algorithms for fitting multiresolution hybrid shape models to brain MRI.
Vemuri, B C; Guo, Y; Lai, S H; Leonard, C M
1997-09-01
In this paper, we present new and fast numerical algorithms for shape recovery from brain MRI using multiresolution hybrid shape models. In this modeling framework, shapes are represented by a core rigid shape characterized by a superquadric function and a superimposed displacement function which is characterized by a membrane spline discretized using the finite-element method. Fitting the model to brain MRI data is cast as an energy minimization problem which is solved numerically. We present three new computational methods for model fitting to data. These methods involve novel mathematical derivations that lead to efficient numerical solutions of the model fitting problem. The first method involves using the nonlinear conjugate gradient technique with a diagonal Hessian preconditioner. The second method involves the nonlinear conjugate gradient in the outer loop for solving global parameters of the model and a preconditioned conjugate gradient scheme for solving the local parameters of the model. The third method involves the nonlinear conjugate gradient in the outer loop for solving the global parameters and a combination of the Schur complement formula and the alternating direction-implicit method for solving the local parameters of the model. We demonstrate the efficiency of our model fitting methods via experiments on several MR brain scans. PMID:9873915
NASA Astrophysics Data System (ADS)
Platnick, S.; Wind, G.; Zhang, Z.; Ackerman, S. A.; Maddux, B. C.
2012-12-01
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 1.6, 2.1, and 3.7 μm spectral channels. Cloud retrieval statistics are highly sensitive to how a pixel identified as being "not-clear" 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 (defined by immediate adjacency to "clear" MOD/MYD35 pixels) 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 1D 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 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.
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
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!
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.
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.
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 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.
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.
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.
2010-01-01
Background Ambulance response time is a crucial factor in patient survival. The number of emergency cases (EMS cases) requiring an ambulance is increasing due to changes in population demographics. This is decreasing ambulance response times to the emergency scene. This paper predicts EMS cases for 5-year intervals from 2020, to 2050 by correlating current EMS cases with demographic factors at the level of the census area and predicted population changes. It then applies a modified grouping genetic algorithm to compare current and future optimal locations and numbers of ambulances. Sets of potential locations were evaluated in terms of the (current and predicted) EMS case distances to those locations. Results Future EMS demands were predicted to increase by 2030 using the model (R2 = 0.71). The optimal locations of ambulances based on future EMS cases were compared with current locations and with optimal locations modelled on current EMS case data. Optimising the location of ambulance stations locations reduced the average response times by 57 seconds. Current and predicted future EMS demand at modelled locations were calculated and compared. Conclusions The reallocation of ambulances to optimal locations improved response times and could contribute to higher survival rates from life-threatening medical events. Modelling EMS case 'demand' over census areas allows the data to be correlated to population characteristics and optimal 'supply' locations to be identified. Comparing current and future optimal scenarios allows more nuanced planning decisions to be made. This is a generic methodology that could be used to provide evidence in support of public health planning and decision making. PMID:20109172
Hard Data Analytics Problems Make for Better Data Analysis Algorithms: Bioinformatics as an Example
Widera, Paweł; Lazzarini, Nicola; Krasnogor, Natalio
2014-01-01
Abstract Data mining and knowledge discovery techniques have greatly progressed in the last decade. They are now able to handle larger and larger datasets, process heterogeneous information, integrate complex metadata, and extract and visualize new knowledge. Often these advances were driven by new challenges arising from real-world domains, with biology and biotechnology a prime source of diverse and hard (e.g., high volume, high throughput, high variety, and high noise) data analytics problems. The aim of this article is to show the broad spectrum of data mining tasks and challenges present in biological data, and how these challenges have driven us over the years to design new data mining and knowledge discovery procedures for biodata. This is illustrated with the help of two kinds of case studies. The first kind is focused on the field of protein structure prediction, where we have contributed in several areas: by designing, through regression, functions that can distinguish between good and bad models of a protein's predicted structure; by creating new measures to characterize aspects of a protein's structure associated with individual positions in a protein's sequence, measures containing information that might be useful for protein structure prediction; and by creating accurate estimators of these structural aspects. The second kind of case study is focused on omics data analytics, a class of biological data characterized for having extremely high dimensionalities. Our methods were able not only to generate very accurate classification models, but also to discover new biological knowledge that was later ratified by experimentalists. Finally, we describe several strategies to tightly integrate knowledge extraction and data mining in order to create a new class of biodata mining algorithms that can natively embrace the complexity of biological data, efficiently generate accurate information in the form of classification/regression models, and extract valuable
NASA Astrophysics Data System (ADS)
Holm, D. D.; Ivanov, R. I.
2010-12-01
The Lax pair formulation of the two-component Camassa-Holm equation (CH2) is generalized to produce an integrable multi-component family, CH(n, k), of equations with n components and 1 <= |k| <= n velocities. All of the members of the CH(n, k) family show fluid-dynamics properties with coherent solitons following particle characteristics. We determine their Lie-Poisson Hamiltonian structures and give numerical examples of their soliton solution behaviour. We concentrate on the CH(2, k) family with one or two velocities, including the CH(2, -1) equation in the Dym position of the CH2 hierarchy. A brief discussion of the CH(3, 1) system reveals the underlying graded Lie-algebraic structure of the Hamiltonian formulation for CH(n, k) when n >= 3. Fondly recalling our late friend Jerry Marsden.
Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study.
Mow, V C; Gibbs, M C; Lai, W M; Zhu, W B; Athanasiou, K A
1989-01-01
Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments. PMID:2613721
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.
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)
Korneev, Boris; Levchenko, Vadim
2016-02-01
Interaction between a shock wave and an inhomogeneity in fluid has complicated behavior, including vortex and turbulence generating, mixing, shock wave scattering and reflection. In the present paper we deal with the numerical simulation of the considered process. The Euler equations of unsteady inviscid compressible three-dimensional flow are used into the four-equation model of multicomponent flow. These equations are discretized using the RKDG numerical method. It is implemented with the help of the DiamondTorre algorithm, so the effective GPGPU solver is obtained having outstanding computing properties. With its use we carry out several sets of numerical experiments of shock-bubble interaction problem. The bubble deformation and mixture formation is observed.
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.
Developmental Algorithms Have Meaning!
ERIC Educational Resources Information Center
Green, John
1997-01-01
Adapts Stanic and McKillip's ideas for the use of developmental algorithms to propose that the present emphasis on symbolic manipulation should be tempered with an emphasis on the conceptual understanding of the mathematics underlying the algorithm. Uses examples from the areas of numeric computation, algebraic manipulation, and equation solving…
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.
2015-07-01
In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.
Numerical Study of Three-Dimensional Flows Using Unfactored Upwind-Relaxation Sweeping Algorithm
NASA Astrophysics Data System (ADS)
Zha, G.-C.; Bilgen, E.
1996-05-01
The linear stability analysis of the unfactored upwind relaxation-sweeping (URS) algorithm for 3D flow field calculations has been carried out and it is shown that the URS algorithm is unconditionally stable. The algorithm is independent of the global sweeping direction selection. However, choosing the direction with relatively low variable gradient as the global sweeping direction results in a higher degree of stability. Three-dimensional compressible Euler equations are solved by using the implicit URS algorithm to study internal flows of a non-axisymmetric nozzle with a circular-to-rectangular transition duct and complex shock wave structures for a 3D channel flow. The efficiency and robustness of the URS algorithm has been demonstrated.
BLUM,T.
1999-09-14
The RIKEN BNL Research Center hosted its 19th workshop April 27th through May 1, 1999. The topic was Numerical Algorithms at Non-Zero Chemical Potential. QCD at a non-zero chemical potential (non-zero density) poses a long-standing unsolved challenge for lattice gauge theory. Indeed, it is the primary unresolved issue in the fundamental formulation of lattice gauge theory. The chemical potential renders conventional lattice actions complex, practically excluding the usual Monte Carlo techniques which rely on a positive definite measure for the partition function. This ''sign'' problem appears in a wide range of physical systems, ranging from strongly coupled electronic systems to QCD. The lack of a viable numerical technique at non-zero density is particularly acute since new exotic ''color superconducting'' phases of quark matter have recently been predicted in model calculations. A first principles confirmation of the phase diagram is desirable since experimental verification is not expected soon. At the workshop several proposals for new algorithms were made: cluster algorithms, direct simulation of Grassman variables, and a bosonization of the fermion determinant. All generated considerable discussion and seem worthy of continued investigation. Several interesting results using conventional algorithms were also presented: condensates in four fermion models, SU(2) gauge theory in fundamental and adjoint representations, and lessons learned from strong; coupling, non-zero temperature and heavy quarks applied to non-zero density simulations.
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. PMID:23518722
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
Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm
NASA Technical Reports Server (NTRS)
Kato, Hiromasa; Tannehill, John C.; Mehta, Unmeel B.
2003-01-01
A new parabolized Navier-Stokes (PNS) algorithm has been developed to efficiently compute magnetohydrodynamic (MHD) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. The MHD effects are modeled by introducing source terms into the PNS equation which can then be solved in a very efficient manner. To account for upstream (elliptic) effects, the flowfields are computed using multiple streamwise sweeps with an iterated PNS algorithm. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates and supersonic viscous flows in a rectangular MHD accelerator. The present results are in excellent agreement with previous complete Navier-Stokes calculations.
Structure of the Gabor matrix and efficient numerical algorithms for discrete Gabor expansions
NASA Astrophysics Data System (ADS)
Qiu, Sigang; Feichtinger, Hans G.
1994-09-01
The standard way to obtain suitable coefficients for the (non-orthogonal) Gabor expansion of a general signal for a given Gabor atom g and a pair of lattice constants in the (discrete) time/frequency plane, requires to compute the dual Gabor window function g- first. In this paper, we present an explicit description of the sparsity, the block and banded structure of the Gabor frame matrix G. On this basis efficient algorithms are developed for computing g- by solving the linear equation g- * G equals g with the conjugate- gradients method. Using the dual Gabor wavelet, a fast Gabor reconstruction algorithm with very low computational complexity is proposed.
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)
Wilkie, George J.; Dorland, William
2016-05-01
The δf particle-in-cell algorithm has been a useful tool in studying the physics of plasmas, particularly turbulent magnetized plasmas in the context of gyrokinetics. The reduction in noise due to not having to resolve the full distribution function indicates an efficiency advantage over the standard ("full-f") particle-in-cell. Despite its successes, the algorithm behaves strangely in some circumstances. In this work, we document a fully resolved numerical instability that occurs in the simplest of multiple-species test cases: the electrostatic ΩH mode. There is also a poorly understood numerical instability that occurs when one is under-resolved in particle number, which may require a prohibitively large number of particles to stabilize. Both of these are independent of the time-stepping scheme, and we conclude that they exist if the time advancement were exact. The exact analytic form of the algorithm is presented, and several schemes for mitigating these instabilities are also presented.
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
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
Kisselev, V B; Roberti, L; Perona, G
1995-12-20
The recently developed finite-element method for solution of the radiative transfer equation has been extended to compute the full azimuthal dependence of the radiance in a vertically inhomogeneous plane-parallel medium. The physical processes that are included in the algorithm are multiple scattering and bottom boundary bidirectional reflectivity. The incident radiation is a parallel flux on the top boundary that is characteristic for illumination of the atmosphere by the Sun in the UV, visible, and near-infrared regions of the electromagnetic spectrum. The theoretical basis is presented together with a number of applications to realistic atmospheres. The method is shown to be accurate even with a low number of grid points for most of the considered situations. The FORTRAN code for this algorithm is developed and is available for applications. PMID:21068966
NASA Astrophysics Data System (ADS)
Kisselev, Viatcheslav B.; Roberti, Laura; Perona, Giovanni
1995-12-01
The recently developed finite-element method for solution of the radiative transfer equation has been extended to compute the full azimuthal dependence of the radiance in a vertically inhomogeneous plane-parallel medium. The physical processes that are included in the algorithm are multiple scattering and bottom boundary bidirectional reflectivity. The incident radiation is a parallel flux on the top boundary that is characteristic for illumination of the atmosphere by the Sun in the UV, visible, and near-infrared regions of the electromagnetic spectrum. The theoretical basis is presented together with a number of applications to realistic atmospheres. The method is shown to be accurate even with a low number of grid points for most of the considered situations. The fortran code for this algorithm is developed and is available for applications.
Parallel technology for numerical modeling of fluid dynamics problems by high-accuracy algorithms
NASA Astrophysics Data System (ADS)
Gorobets, A. V.
2015-04-01
A parallel computation technology for modeling fluid dynamics problems by finite-volume and finite-difference methods of high accuracy is presented. The development of an algorithm, the design of a software implementation, and the creation of parallel programs for computations on large-scale computing systems are considered. The presented parallel technology is based on a multilevel parallel model combining various types of parallelism: with shared and distributed memory and with multiple and single instruction streams to multiple data flows.
NASA Astrophysics Data System (ADS)
Ersoy, Ozlem; Dag, Idris
2015-12-01
The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.
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.
Spouge, John L; Mariño-Ramírez, Leonardo; Sheetlin, Sergey L
2014-01-01
Some biological sequences contain subsequences of unusual composition; e.g. some proteins contain DNA binding domains, transmembrane regions and charged regions, and some DNA sequences contain repeats. The linear-time Ruzzo-Tompa (RT) algorithm finds subsequences of unusual composition, using a sequence of scores as input and the corresponding 'maximal segments' as output. In principle, permitting gaps in the output subsequences could improve sensitivity. Here, the input of the RT algorithm is generalised to a finite, totally ordered, weighted graph, so the algorithm locates paths of maximal weight through increasing but not necessarily adjacent vertices. By permitting the penalised deletion of unfavourable letters, the generalisation therefore includes gaps. The program RepWords, which finds inexact simple repeats in DNA, exemplifies the general concepts by out-performing a similar extant, ad hoc tool. With minimal programming effort, the generalised Ruzzo-Tompa algorithm could improve the performance of many programs for finding biological subsequences of unusual composition. PMID:24989859
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...
NASA Astrophysics Data System (ADS)
Wang, Jiong; Steinmann, Paul
2016-05-01
This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample's response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.
NASA Astrophysics Data System (ADS)
Belov, V. V.; Tarasenkov, M. V.
2015-11-01
An algorithm for atmospheric correction of satellite images combining the consideration of the main factors influencing imaging and a number of techniques allowing the computational time to be decreased considerably is analyzed. On the example of a series of images of the South of the Tomsk Region recorded from 7/13/2013 to 7/17/2013 with the low atmospheric turbidity, a comparison of the results of atmospheric correction using the suggested algorithm with the results obtained using the NASA MOD09 algorithm is performed. The correction error is estimated under assumption of a linear change of the reflection coefficient from image to image. Our comparison demonstrates that the results of correction differ within the correction error.
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.
An Effective Hybrid Firefly Algorithm with Harmony Search for Global Numerical Optimization
Guo, Lihong; Wang, Gai-Ge; Wang, Heqi; Wang, Dinan
2013-01-01
A hybrid metaheuristic approach by hybridizing harmony search (HS) and firefly algorithm (FA), namely, HS/FA, is proposed to solve function optimization. In HS/FA, the exploration of HS and the exploitation of FA are fully exerted, so HS/FA has a faster convergence speed than HS and FA. Also, top fireflies scheme is introduced to reduce running time, and HS is utilized to mutate between fireflies when updating fireflies. The HS/FA method is verified by various benchmarks. From the experiments, the implementation of HS/FA is better than the standard FA and other eight optimization methods. PMID:24348137
NASA Astrophysics Data System (ADS)
Hu, P.; Shi, D. Y.; Ying, L.; Shen, G. Z.; Chang, Y.; Liu, W. Q.
2013-05-01
Thermal-mechanical-transformation coupled theoretical model for hot stamping and rheological behavior of high strength steel at elevated temperatures were obtained through non-isothermal and isothermal tensile tests respectively in this work. The static explicit finite element equations for hot stamping were proposed based on thermal-mechanical-transformation coupled constitutive laws and nonlinear, large deformation analysis. According to these equations, the hot stamping module of KMAS (King Mesh Analysis System) was developed for the numerical simulation of sheet metal forming at elevated temperatures. Afterwards, the hot stamping simulation of a typical B-pillar conducted by the KMAS software was compared to the experiment. The comparison consists of the following sides: temperature distribution, thickness distribution and martensite fraction. The good agreement between numerical simulation and the experiment confirms that the multi-field coupled constitutive laws and the KMAS software can predict hot stamping process accurately.
Stamnes, K; Tsay, S C; Wiscombe, W; Jayaweera, K
1988-06-15
We summarize an advanced, thoroughly documented, and quite general purpose discrete ordinate algorithm for time-independent transfer calculations in vertically inhomogeneous, nonisothermal, plane-parallel media. Atmospheric applications ranging from the UV to the radar region of the electromagnetic spectrum are possible. The physical processes included are thermal emission, scattering, absorption, and bidirectional reflection and emission at the lower boundary. The medium may be forced at the top boundary by parallel or diffuse radiation and by internal and boundary thermal sources as well. We provide a brief account of the theoretical basis as well as a discussion of the numerical implementation of the theory. The recent advances made by ourselves and our collaborators-advances in both formulation and numerical solution-are all incorporated in the algorithm. Prominent among these advances are the complete conquest of two illconditioning problems which afflicted all previous discrete ordinate implementations: (1) the computation of eigenvalues and eigenvectors and (2) the inversion of the matrix determining the constants of integration. Copies of the FORTRAN program on microcomputer diskettes are available for interested users. PMID:20531783
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.
NASA Astrophysics Data System (ADS)
Harries, Tim J.
2015-04-01
We present a set of new numerical methods that are relevant to calculating radiation pressure terms in hydrodynamics calculations, with a particular focus on massive star formation. The radiation force is determined from a Monte Carlo estimator and enables a complete treatment of the detailed microphysics, including polychromatic radiation and anisotropic scattering, in both the free-streaming and optically thick limits. Since the new method is computationally demanding we have developed two new methods that speed up the algorithm. The first is a photon packet splitting algorithm that enables efficient treatment of the Monte Carlo process in very optically thick regions. The second is a parallelization method that distributes the Monte Carlo workload over many instances of the hydrodynamic domain, resulting in excellent scaling of the radiation step. We also describe the implementation of a sink particle method that enables us to follow the accretion on to, and the growth of, the protostars. We detail the results of extensive testing and benchmarking of the new algorithms.
Mariño-Ramírez, Leonardo; Sheetlin, Sergey L.
2014-01-01
Background Some biological sequences contain subsequences of unusual composition, e.g., some proteins contain DNA binding domains, transmembrane regions, and charged regions; and some DNA sequences contain repeats. Requiring time linear in the length of an input sequence, the Ruzzo-Tompa (RT) Algorithm finds subsequences of unusual composition, using a sequence of scores as input and the corresponding “maximal segments” as output. (Loosely, maximal segments are the contiguous subsequences having greatest total score.) Just as gaps improved the sensitivity of BLAST, in principle gaps could help tune other tools, to improve sensitivity when searching for subsequences of unusual composition. Results Call a graph whose vertices are totally ordered a “totally ordered graph”. In a totally ordered graph, call a path whose vertices are in increasing order an “increasing path”. The input of the RT Algorithm can be generalized to a finite, totally ordered, weighted graph, so the algorithm then locates maximal segments, corresponding to increasing paths of maximal weight. The generalization permits penalized deletion of unfavorable letters from contiguous subsequences, so the generalized Ruzzo-Tompa algorithm can find subsequences with greatest total gapped scores. The search for inexact simple repeats in DNA exemplifies some of the concepts. For some limited types of repeats, RepWords, a repeat-finding tool based on the principled use of the Ruzzo-Tompa algorithm, performed better than a similar extant tool. Conclusions With minimal programming effort, the generalization of the Ruzzo-Tompa algorithm given in this article could improve the performance of many programs for finding biological subsequences of unusual composition. PMID:24989859
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 Astrophysics Data System (ADS)
Lakshminarayana, B.; Ho, Y.; Basson, A.
1993-07-01
The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake
NASA Technical Reports Server (NTRS)
Lakshminarayana, B.; Ho, Y.; Basson, A.
1993-01-01
The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake
NASA Astrophysics Data System (ADS)
Kuraz, Michal
2016-06-01
This paper presents pseudo-deterministic catchment runoff model based on the Richards equation model [1] - the governing equation for the subsurface flow. The subsurface flow in a catchment is described here by two-dimensional variably saturated flow (unsaturated and saturated). The governing equation is the Richards equation with a slight modification of the time derivative term as considered e.g. by Neuman [2]. The nonlinear nature of this problem appears in unsaturated zone only, however the delineation of the saturated zone boundary is a nonlinear computationally expensive issue. The simple one-dimensional Boussinesq equation was used here as a rough estimator of the saturated zone boundary. With this estimate the dd-adaptivity algorithm (see Kuraz et al. [4, 5, 6]) could always start with an optimal subdomain split, so it is now possible to avoid solutions of huge systems of linear equations in the initial iteration level of our Richards equation based runoff model.
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.
NASA Astrophysics Data System (ADS)
Bouallegue, Kais; Chaari, Abdessattar
In this study, one propose to study a numeric type strategy permitting the generation of any shape of path in view of the scheduling of the trajectories for a car-like mobile robot where the planned motions considered are continuous sequences in the space of the robot. These paths are programmed in order to have some types of closed or open trajectories. One is interested in the motion control of the robot from an initial position to a final position while optimizing the consumed energy in its alternated circular motion on both sides of the segment joining these two points. In this study, one presents a new method based on a numeric approach conceived from the kinematics equations of the robot. This new technique of numeric, adaptive and dynamic control of the robot is implemented on DSP21065L of the SHARC family. This algorithm assures the robot control of an initial position of departure to a final position of arrival without the existence of obstacles.
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.
A critical evaluation of numerical algorithms and flow physics in complex supersonic flows
NASA Astrophysics Data System (ADS)
Aradag, Selin
In this research, two different complex supersonic flows are selected to apply CFD to Navier-Stokes simulations. First test case is "Supersonic Flow over an Open Rectangular Cavity". Open cavity flow fields are remarkably complicated with internal and external regions that are coupled via self-sustained shear layer oscillations. Supersonic flow past a cavity has numerous applications in store carriage and release. Internal carriage of stores, which can be modeled using a cavity configuration, is used for supersonic aircraft in order to reduce radar cross section, aerodynamic drag and aerodynamic heating. Supersonic, turbulent, three-dimensional unsteady flow past an open rectangular cavity is simulated, to understand the physics and three-dimensional nature of the cavity flow oscillations. Influences of numerical parameters such as numerical flux scheme, computation time and flux limiter on the computed flow are determined. Two dimensional simulations are also performed for comparison purposes. The next test case is "The Computational Design of Boeing/AFOSR Mach 6 Wind Tunnel". Due to huge differences between geometrical scales, this problem is both challenging and computationally intensive. It is believed that most of the experimental data obtained from conventional ground testing facilities are not reliable due to high levels of noise associated with the acoustic fluctuations from the turbulent boundary layers on the wind tunnel walls. Therefore, it is very important to have quiet testing facilities for hypersonic flow research. The Boeing/AFOSR Mach 6 Wind tunnel in Purdue University has been designed as a quiet tunnel for which the noise level is an order of magnitude lower than that in conventional wind tunnels. However, quiet flow is achieved in the Purdue Mach 6 tunnel for only low Reynolds numbers. Early transition of the nozzle wall boundary layer has been identified as the cause of the test section noise. Separation bubbles on the bleed lip and associated
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 Astrophysics Data System (ADS)
Wan, H.; Rasch, P. J.; Zhang, K.; Kazil, J.; Leung, L. R.
2013-01-01
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 of nucleation rate in version two, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei (CCN) 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 Astrophysics Data System (ADS)
Wan, H.; Rasch, P. J.; Zhang, K.; Kazil, J.; Leung, L. R.
2013-06-01
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 a long time step is identified as the main reason for the large systematic biases in the old model. The remaining errors of nucleation rate in version two, related to the competition between condensation and nucleation, have a clear impact on the simulated concentration of cloud condensation nuclei (CCN) in the lower troposphere. These errors can be significantly reduced by employing solvers that handle production, condensation and nucleation at the same time. Lessons learned in this work underline the need for more caution when treating multi-timescale problems involving compensating and competing processes, a common occurrence in current climate models.
NASA Astrophysics Data System (ADS)
Abrams, Daniel S.
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 (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Fast algorithms for simulating many body Fermi systems are also provided in both first and second quantized descriptions. An efficient quantum algorithm for anti-symmetrization is given as well as a detailed discussion of a simulation of the Hubbard model. In addition, quantum algorithms that calculate numerical integrals and various characteristics of stochastic processes are described. Two techniques are given, both of which obtain an exponential speed increase in comparison to the fastest known classical deterministic algorithms and a quadratic speed increase in comparison to classical Monte Carlo (probabilistic) methods. I derive a simpler and slightly faster version of Grover's mean algorithm, show how to apply quantum counting to the problem, develop some variations of these algorithms, and show how both (apparently distinct) approaches can be understood from the same unified framework. Finally, the relationship between physics and computation is explored in some more depth, and it is shown that computational complexity theory depends very sensitively on physical laws. In particular, it is shown that nonlinear quantum mechanics allows for the polynomial time solution of NP-complete and #P oracle problems. Using the Weinberg model as a simple example, the explicit construction of the necessary gates is derived from the underlying physics. Nonlinear quantum algorithms are also presented using Polchinski type nonlinearities which do not allow for superluminal communication. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
NASA Astrophysics Data System (ADS)
Li, Cong; Lei, Jianshe
2014-10-01
In this paper, we focus on the influences of various parameters in the niching genetic algorithm inversion procedure on the results, such as various objective functions, the number of the models in each subpopulation, and the critical separation radius. The frequency-waveform integration (F-K) method is applied to synthesize three-component waveform data with noise in various epicentral distances and azimuths. Our results show that if we use a zero-th-lag cross-correlation function, then we will obtain the model with a faster convergence and a higher precision than other objective functions. The number of models in each subpopulation has a great influence on the rate of convergence and computation time, suggesting that it should be obtained through tests in practical problems. The critical separation radius should be determined carefully because it directly affects the multi-extreme values in the inversion. We also compare the inverted results from full-band waveform data and surface-wave frequency-band (0.02-0.1 Hz) data, and find that the latter is relatively poorer but still has a higher precision, suggesting that surface-wave frequency-band data can also be used to invert for the crustal structure.
NASA Astrophysics Data System (ADS)
Li, Cong; Lei, Jianshe
2014-09-01
In this paper, we focus on the influences of various parameters in the niching genetic algorithm inversion procedure on the results, such as various objective functions, the number of the models in each subpopulation, and the critical separation radius. The frequency-waveform integration (F-K) method is applied to synthesize three-component waveform data with noise in various epicentral distances and azimuths. Our results show that if we use a zero-th-lag cross-correlation function, then we will obtain the model with a faster convergence and a higher precision than other objective functions. The number of models in each subpopulation has a great influence on the rate of convergence and computation time, suggesting that it should be obtained through tests in practical problems. The critical separation radius should be determined carefully because it directly affects the multi-extreme values in the inversion. We also compare the inverted results from full-band waveform data and surface-wave frequency-band (0.02-0.1 Hz) data, and find that the latter is relatively poorer but still has a higher precision, suggesting that surface-wave frequency-band data can also be used to invert for the crustal structure.
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.
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.
NASA Astrophysics Data System (ADS)
Audet, Pascal
2016-03-01
The expanding fleet of broadband 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.
Angus, Simon D.; Piotrowska, Monika Joanna
2014-01-01
Multi-dose radiotherapy protocols (fraction dose and timing) currently used in the clinic are the product of human selection based on habit, received wisdom, physician experience and intra-day patient timetabling. However, due to combinatorial considerations, the potential treatment protocol space for a given total dose or treatment length is enormous, even for relatively coarse search; well beyond the capacity of traditional in-vitro methods. In constrast, high fidelity numerical simulation of tumor development is well suited to the challenge. Building on our previous single-dose numerical simulation model of EMT6/Ro spheroids, a multi-dose irradiation response module is added and calibrated to the effective dose arising from 18 independent multi-dose treatment programs available in the experimental literature. With the developed model a constrained, non-linear, search for better performing cadidate protocols is conducted within the vicinity of two benchmarks by genetic algorithm (GA) techniques. After evaluating less than 0.01% of the potential benchmark protocol space, candidate protocols were identified by the GA which conferred an average of 9.4% (max benefit 16.5%) and 7.1% (13.3%) improvement (reduction) on tumour cell count compared to the two benchmarks, respectively. Noticing that a convergent phenomenon of the top performing protocols was their temporal synchronicity, a further series of numerical experiments was conducted with periodic time-gap protocols (10 h to 23 h), leading to the discovery that the performance of the GA search candidates could be replicated by 17–18 h periodic candidates. Further dynamic irradiation-response cell-phase analysis revealed that such periodicity cohered with latent EMT6/Ro cell-phase temporal patterning. Taken together, this study provides powerful evidence towards the hypothesis that even simple inter-fraction timing variations for a given fractional dose program may present a facile, and highly cost
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
A quadratic weight selection algorithm. [for optimal flight control
NASA Technical Reports Server (NTRS)
Broussard, J. R.
1981-01-01
A new numerical algorithm is presented which determines a positive semi-definite state weighting matrix in the linear-quadratic optimal control design problem. The algorithm chooses the weighting matrix by placing closed-loop eigenvalues and eigenvectors near desired locations using optimal feedback gains. A simplified flight control design example is used to illustrate the algorithms capabilities.
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.
Stability of Bareiss algorithm
NASA Astrophysics Data System (ADS)
Bojanczyk, Adam W.; Brent, Richard P.; de Hoog, F. R.
1991-12-01
In this paper, we present a numerical stability analysis of Bareiss algorithm for solving a symmetric positive definite Toeplitz system of linear equations. We also compare Bareiss algorithm with Levinson algorithm and conclude that the former has superior numerical properties.
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 Technical Reports Server (NTRS)
Bui, Trong T.; Mankbadi, Reda R.
1995-01-01
Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.
Projector Method: theory and examples
Dahl, E.D.
1985-01-01
The Projector Method technique for numerically analyzing lattice gauge theories was developed to take advantage of certain simplifying features of gauge theory models. Starting from a very general notion of what the Projector Method is, the techniques are applied to several model problems. After these examples have traced the development of the actual algorithm from the general principles of the Projector Method, a direct comparison between the Projector and the Euclidean Monte Carlo is made, followed by a discussion of the application to Periodic Quantum Electrodynamics in two and three spatial dimensions. Some methods for improving the efficiency of the Projector in various circumstances are outlined. 10 refs., 7 figs. (LEW)
NASA Technical Reports Server (NTRS)
Yee, H. C.; Rai, Man Mohan (Technical Monitor)
1994-01-01
This lecture attempts to illustrate the basic ideas of how the recent advances in nonlinear dynamical systems theory (dynamics) can provide new insights into the understanding of numerical algorithms used in solving nonlinear differential equations (DEs). Examples will be given of the use of dynamics to explain unusual phenomena that occur in numerics. The inadequacy of the use of linearized analysis for the understanding of long time behavior of nonlinear problems will be illustrated, and the role of dynamics in studying the nonlinear stability, accuracy, convergence property and efficiency of using time- dependent approaches to obtaining steady-state numerical solutions in computational fluid dynamics (CFD) will briefly be explained.
Gurkiewicz, Meron; Korngreen, Alon
2007-01-01
The activity of trans-membrane proteins such as ion channels is the essence of neuronal transmission. The currently most accurate method for determining ion channel kinetic mechanisms is single-channel recording and analysis. Yet, the limitations and complexities in interpreting single-channel recordings discourage many physiologists from using them. Here we show that a genetic search algorithm in combination with a gradient descent algorithm can be used to fit whole-cell voltage-clamp data to kinetic models with a high degree of accuracy. Previously, ion channel stimulation traces were analyzed one at a time, the results of these analyses being combined to produce a picture of channel kinetics. Here the entire set of traces from all stimulation protocols are analysed simultaneously. The algorithm was initially tested on simulated current traces produced by several Hodgkin-Huxley–like and Markov chain models of voltage-gated potassium and sodium channels. Currents were also produced by simulating levels of noise expected from actual patch recordings. Finally, the algorithm was used for finding the kinetic parameters of several voltage-gated sodium and potassium channels models by matching its results to data recorded from layer 5 pyramidal neurons of the rat cortex in the nucleated outside-out patch configuration. The minimization scheme gives electrophysiologists a tool for reproducing and simulating voltage-gated ion channel kinetics at the cellular level. PMID:17784781
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. PMID:25202717
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.
Sheng, I. C.; Kuan, C. K.; Chen, Y. T.; Yang, J. Y.; Hsiung, G. Y.; Chen, J. R.
2010-06-23
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 Astrophysics Data System (ADS)
Saito, Kyosuke; Tanabe, Tadao; Oyama, Yutaka
2016-04-01
We have presented a numerical analysis to describe the behavior of a second harmonic generation (SHG) in THz regime by taking into account for both linear and nonlinear optical susceptibility. We employed a nonlinear finite-difference-time-domain (nonlinear FDTD) method to simulate SHG output characteristics in THz photonic crystal waveguide based on semi insulating gallium phosphide crystal. Unique phase matching conditions originated from photonic band dispersions with low group velocity are appeared, resulting in SHG output characteristics. This numerical study provides spectral information of SHG output in THz PC waveguide. THz PC waveguides is one of the active nonlinear optical devices in THz regime, and nonlinear FDTD method is a powerful tool to design photonic nonlinear THz devices.
NASA Technical Reports Server (NTRS)
Stamnes, Knut; Tsay, S.-CHEE; Jayaweera, Kolf; Wiscombe, Warren
1988-01-01
The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.
NASA Astrophysics Data System (ADS)
Stamnes, Knut; Tsay, S.-Chee; Jayaweera, Kolf; Wiscombe, Warren
1988-06-01
The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.
3D-radiation hydro simulations of disk-planet interactions. I. Numerical algorithm and test cases
NASA Astrophysics Data System (ADS)
Klahr, H.; Kley, W.
2006-01-01
We study the evolution of an embedded protoplanet in a circumstellar disk using the 3D-Radiation Hydro code TRAMP, and treat the thermodynamics of the gas properly in three dimensions. The primary interest of this work lies in the demonstration and testing of the numerical method. We show how far numerical parameters can influence the simulations of gap opening. We study a standard reference model under various numerical approximations. Then we compare the commonly used locally isothermal approximation to the radiation hydro simulation using an equation for the internal energy. Models with different treatments of the mass accretion process are compared. Often mass accumulates in the Roche lobe of the planet creating a hydrostatic atmosphere around the planet. The gravitational torques induced by the spiral pattern of the disk onto the planet are not strongly affected in the average magnitude, but the short time scale fluctuations are stronger in the radiation hydro models. An interesting result of this work lies in the analysis of the temperature structure around the planet. The most striking effect of treating the thermodynamics properly is the formation of a hot pressure-supported bubble around the planet with a pressure scale height of H/R ≈ 0.5 rather than a thin Keplerian circumplanetary accretion disk.
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)
Sun, Guodong; Mu, Mu
2016-01-01
An important source of uncertainty, which causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. Therefore, finding a subset among numerous physical parameters in numerical models in the atmospheric and oceanic sciences, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach in China. The results imply that nonlinear interactions among parameters play a key role in the identification of sensitive parameters in arid and semi-arid regions of China compared to those in northern, northeastern, and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.
NASA Astrophysics Data System (ADS)
Pearce, J. D.; Esler, J. G.
2010-10-01
A pseudo-spectral algorithm is presented for the solution of the rotating Green-Naghdi shallow water equations in two spatial dimensions. The equations are first written in vorticity-divergence form, in order to exploit the fact that time-derivatives then appear implicitly in the divergence equation only. A nonlinear equation must then be solved at each time-step in order to determine the divergence tendency. The nonlinear equation is solved by means of a simultaneous iteration in spectral space to determine each Fourier component. The key to the rapid convergence of the iteration is the use of a good initial guess for the divergence tendency, which is obtained from polynomial extrapolation of the solution obtained at previous time-levels. The algorithm is therefore best suited to be used with a standard multi-step time-stepping scheme (e.g. leap-frog). Two test cases are presented to validate the algorithm for initial value problems on a square periodic domain. The first test is to verify cnoidal wave speeds in one-dimension against analytical results. The second test is to ensure that the Miles-Salmon potential vorticity is advected as a parcel-wise conserved tracer throughout the nonlinear evolution of a perturbed jet subject to shear instability. The algorithm is demonstrated to perform well in each test. The resulting numerical model is expected to be of use in identifying paradigmatic behavior in mesoscale flows in the atmosphere and ocean in which both vortical, nonlinear and dispersive effects are important.
Numerical anomalies mimicking physical effects
NASA Astrophysics Data System (ADS)
Menikoff, R.
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)
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; Simons Collaboration on the Many-Electron Problem
2015-10-01
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. 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.
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.
A quasi-Monte Carlo Metropolis algorithm
Owen, Art B.; Tribble, Seth D.
2005-01-01
This work presents a version of the Metropolis–Hastings algorithm using quasi-Monte Carlo inputs. We prove that the method yields consistent estimates in some problems with finite state spaces and completely uniformly distributed inputs. In some numerical examples, the proposed method is much more accurate than ordinary Metropolis–Hastings sampling. PMID:15956207
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.; et al
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.
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)
Hu, Xuanyu; Jekeli, Christopher
2015-02-01
We present a comprehensive numerical analysis of spherical, spheroidal, and ellipsoidal harmonic series for gravitational field modeling near small moderately irregular bodies, such as the Martian moons. The comparison of model performances for these bodies is less intuitive and distinct than for a highly irregular object, such as Eros. The harmonic series models are each associated with a distinct surface, i.e., the Brillouin sphere, spheroid, or ellipsoid, which separates the regions of convergence and possible divergence for the parent infinite series. In their convergence regions, the models are subject only to omission errors representing the residual field variations not accounted for by the finite degree expansions. In the regions inside their respective Brillouin surfaces, the models are susceptible to amplification of omission errors and possible divergence effects, where the latter can be discerned if the error increases with an increase in the maximum degree of the model. We test the harmonic series models on the Martian moons, Phobos and Deimos, with moderate oblateness of 0.4. The possible divergence effects and amplified omission errors of the models are illustrated and quantified. The three models yield consistent results on a bounding sphere of Phobos in their common convergence region, with relative errors in potential of 0.01 and 0.001 % for expansions up to degree 10 and degree 20 respectively. On the surface of Phobos, the spherical and spheroidal models up to degree 10 both have maximum relative errors of 1 % in potential and 100 % in acceleration due ostensibly to divergence effect. Their performances deteriorate more severely on the more irregular Deimos. The ellipsoidal model exhibits much less distinct divergence behavior and proves more reliable in modeling both potential and acceleration, with respective maximum relative errors of 1 and 10 %, on both bodies. Our results show that for the Martian moons and other such moderately irregular
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.
NASA Astrophysics Data System (ADS)
Hässig, Marc; Duretz, Thibault; Rolland, Yann; Sosson, Marc
2016-05-01
The ophiolites of NE Anatolia and of the Lesser Caucasus (NALC) evidence an obduction over ∼200 km of oceanic lithosphere of Middle Jurassic age (c. 175-165 Ma) along an entire tectonic boundary (>1000 km) at around 90 Ma. The obduction process is characterized by four first order geological constraints: Ophiolites represent remnants of a single ophiolite nappe currently of only a few kilometres thick and 200 km long. The oceanic crust was old (∼80 Ma) at the time of its obduction. The presence of OIB-type magmatism emplaced up to 10 Ma prior to obduction preserved on top of the ophiolites is indicative of mantle upwelling processes (hotspot). The leading edge of the Taurides-Anatolides, represented by the South Armenian Block, did not experience pressures exceeding 0.8 GPa nor temperatures greater than ∼300 °C during underthrusting below the obducting oceanic lithosphere. An oceanic domain of a maximum 1000 km (from north to south) remained between Taurides-Anatolides and Pontides-Southern Eurasian Margin after the obduction. We employ two-dimensional thermo-mechanical numerical modelling in order to investigate obduction dynamics of a re-heated oceanic lithosphere. Our results suggest that thermal rejuvenation (i.e. reheating) of the oceanic domain, tectonic compression, and the structure of the passive margin are essential ingredients for enabling obduction. Afterwards, extension induced by far-field plate kinematics (subduction below Southern Eurasian Margin), facilitates the thinning of the ophiolite, the transport of the ophiolite on the continental domain, and the exhumation of continental basement through the ophiolite. The combined action of thermal rejuvenation and compression are ascribed to a major change in tectonic motions occurring at 110-90 Ma, which led to simultaneous obductions in the Oman (Arabia) and NALC regions.
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
Numerical Asymptotic Solutions Of Differential Equations
NASA Technical Reports Server (NTRS)
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
A Hybrid Parallel Preconditioning Algorithm For CFD
NASA Technical Reports Server (NTRS)
Barth,Timothy J.; Tang, Wei-Pai; Kwak, Dochan (Technical Monitor)
1995-01-01
A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.
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.
NASA Astrophysics Data System (ADS)
Imada, Masatoshi; Kashima, Tsuyoshi
2000-09-01
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.
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.
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.
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…
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.
Algorithmic Differentiation for Calculus-based Optimization
NASA Astrophysics Data System (ADS)
Walther, Andrea
2010-10-01
For numerous applications, the computation and provision of exact derivative information plays an important role for optimizing the considered system but quite often also for its simulation. This presentation introduces the technique of Algorithmic Differentiation (AD), a method to compute derivatives of arbitrary order within working precision. Quite often an additional structure exploitation is indispensable for a successful coupling of these derivatives with state-of-the-art optimization algorithms. The talk will discuss two important situations where the problem-inherent structure allows a calculus-based optimization. Examples from aerodynamics and nano optics illustrate these advanced optimization approaches.
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.
An efficient algorithm for solving the phase field crystal model
Cheng Mowei Warren, James A.
2008-06-01
We present and discuss the development of an unconditionally stable algorithm used to solve the evolution equations of the phase field crystal (PFC) model. This algorithm allows for an arbitrarily large algorithmic time step. As the basis for our analysis of the accuracy of this algorithm, we determine an effective time step in Fourier space. We then compare our calculations with a set of representative numerical results, and demonstrate that this algorithm is an effective approach for the study of the PFC models, yielding a time step effectively 180 times larger than the Euler algorithm for a representative set of material parameters. As the PFC model is just a simple example of a wide class of density functional theories, we expect this method will have wide applicability to modeling systems of considerable interest to the materials modeling communities.
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.
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.
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.
A new algorithm for L2 optimal model reduction
NASA Technical Reports Server (NTRS)
Spanos, J. T.; Milman, M. H.; Mingori, D. L.
1992-01-01
In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.
Lessor, K.S.
1988-08-26
The parallel algorithm of Ariyawansa, Sorensen, and Wets for approximating the values and subgradients of the recourse function in a stochastic program with complete recourse is implemented and timing results are reported for limited experimental trials. 14 refs., 6 figs., 8 tabs.
Numerical model for the Programmable Multirole Furnace (PMZF)
NASA Technical Reports Server (NTRS)
Kassemi, M.; Panzarella, C. H.; Destro-Sidik, K. E.; Krolikowski, C. R.; Licht, B. W.
1993-01-01
The present account of the Programmable Multizone Furnace numerical model uses various examples to illustrate the ways in which the model serves as an optimization, test, prediction, and visualization tool; a numerical PID-control algorithm obtains the desired sample temperature distributions and allows the model to solve an inverse heat transfer problem where the desired sample temperature profile is the input and the required heater power distribution is the output of numerical simulations. Parametric studies show how the total power consumption of the furnace is affected by such design variables as the conductivity.
Numerical Modeling of Ocean Acoustic Wavefields
NASA Astrophysics Data System (ADS)
Tappert, Frederick
1997-08-01
The U.S. Navy requires real-time ``acoustic performance prediction'' models in order to optimize sonar tactics in naval combat situations. The need for numerical models that solve the acoustic wave equation in realistic ocean environments is being met by a collaborative effort between university researchers, industrial contractors, and navy laboratory workers. This paper discusses one particularly successful numerical model, called the PE/SSF model, that was originally developed by the author. Here PE stands for Parabolic Equation, a good approximation to the elliptic Helmholtz equation; and SSF stands for the Split-Step Fourier algorithm, a highly efficient marching algorithm for solving parabolic type equations. These techniques are analyzed, and examples are displayed of ocean acoustic wavefields generated by the PE/SSF model.
A spectral canonical electrostatic algorithm
NASA Astrophysics Data System (ADS)
Webb, Stephen D.
2016-03-01
Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that the geometric structure of the underlying problem is preserved. Simulating a self-consistent system over many oscillations can introduce numerical artifacts such as grid heating. This unphysical heating stems from using non-symplectic methods on Hamiltonian systems. With this guidance, we derive an electrostatic algorithm using a discrete form of Hamilton’s principle. The resulting algorithm, a gridless spectral electrostatic macroparticle model, does not exhibit the unphysical heating typical of most particle-in-cell methods. We present results of this using a two-body problem as an example of the algorithm’s energy- and momentum-conserving properties.
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.
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.
Regularized shallow water equations for numerical simulation of flows with a moving shoreline
NASA Astrophysics Data System (ADS)
Bulatov, O. V.; Elizarova, T. G.
2016-04-01
A numerical algorithm for simulating free-surface flows based on regularized shallow water equations is adapted to flows involving moving dry-bed areas. Well-balanced versions of the algorithm are constructed. Test computations of flows with dry-bed areas in the cases of water runup onto a plane beach and a constant-slope beach are presented. An example of tsunami simulation is given.
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.
Algorithmically specialized parallel computers
Snyder, L.; Jamieson, L.H.; Gannon, D.B.; Siegel, H.J.
1985-01-01
This book is based on a workshop which dealt with array processors. Topics considered include algorithmic specialization using VLSI, innovative architectures, signal processing, speech recognition, image processing, specialized architectures for numerical computations, and general-purpose computers.
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.
Annealed Importance Sampling Reversible Jump MCMC algorithms
Karagiannis, Georgios; Andrieu, Christophe
2013-03-20
It will soon be 20 years since reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithms have been proposed. They have significantly extended the scope of Markov chain Monte Carlo simulation methods, offering the promise to be able to routinely tackle transdimensional sampling problems, as encountered in Bayesian model selection problems for example, in a principled and flexible fashion. Their practical efficient implementation, however, still remains a challenge. A particular difficulty encountered in practice is in the choice of the dimension matching variables (both their nature and their distribution) and the reversible transformations which allow one to define the one-to-one mappings underpinning the design of these algorithms. Indeed, even seemingly sensible choices can lead to algorithms with very poor performance. The focus of this paper is the development and performance evaluation of a method, annealed importance sampling RJ-MCMC (aisRJ), which addresses this problem by mitigating the sensitivity of RJ-MCMC algorithms to the aforementioned poor design. As we shall see the algorithm can be understood as being an “exact approximation” of an idealized MCMC algorithm that would sample from the model probabilities directly in a model selection set-up. Such an idealized algorithm may have good theoretical convergence properties, but typically cannot be implemented, and our algorithms can approximate the performance of such idealized algorithms to an arbitrary degree while not introducing any bias for any degree of approximation. Our approach combines the dimension matching ideas of RJ-MCMC with annealed importance sampling and its Markov chain Monte Carlo implementation. We illustrate the performance of the algorithm with numerical simulations which indicate that, although the approach may at first appear computationally involved, it is in fact competitive.
Reasoning about systolic algorithms
Purushothaman, S.; Subrahmanyam, P.A.
1988-12-01
The authors present a methodology for verifying correctness of systolic algorithms. The methodology is based on solving a set of Uniform Recurrence Equations obtained from a description of systolic algorithms as a set of recursive equations. They present an approach to mechanically verify correctness of systolic algorithms, using the Boyer-Moore theorem proven. A mechanical correctness proof of an example from the literature is also presented.
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.
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
Heuristic algorithms for constructing optimized structures of linear multihop lightwave networks
NASA Astrophysics Data System (ADS)
Banerjee, Subrata; Mukherjee, Biswanath; Sarkar, Dillip
1994-02-01
We propose to exploit the capabilities of emerging lightwave technology in order to construct photonic implementations of 'adaptive' and 'optimized' distributed queue dual bus (DQDB) structures. Two sets of heuristic optimization algorithms are formulated. The performance of these heuristics are compared, some of their properties are analyzed, while their other attractive properties are highlighted via numerical examples.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 ; 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.
Di Pierro, Michele; Elber, Ron; Leimkuhler, Benedict
2015-12-01
We present an algorithm termed COMPEL (COnstant Molecular Pressure with Ewald sum for Long range forces) to conduct simulations in the NPT ensemble. The algorithm combines novel features recently proposed in the literature to obtain a highly efficient and accurate numerical integrator. COMPEL exploits the concepts of molecular pressure, rapid stochastic relaxation to equilibrium, exact calculation of the contribution to the pressure of long-range nonbonded forces with Ewald summation, and the use of Trotter expansion to generate a robust, highly stable, symmetric, and accurate algorithm. Explicit implementation in the MOIL program and illustrative numerical examples are discussed. PMID:26616351
A Hybrid Shortest Path Algorithm for Navigation System
NASA Astrophysics Data System (ADS)
Cho, Hsun-Jung; Lan, Chien-Lun
2007-12-01
Combined with Geographic Information System (GIS) and Global Positioning System (GPS), the vehicle navigation system had become a quite popular product in daily life. A key component of the navigation system is the Shortest Path Algorithm. Navigation in real world must face a network consists of tens of thousands nodes and links, and even more. Under the limited computation capability of vehicle navigation equipment, it is difficult to satisfy the realtime response requirement that user expected. Hence, this study focused on shortest path algorithm that enhances the computation speed with less memory requirement. Several well-known algorithms such as Dijkstra, A* and hierarchical concepts were integrated to build hybrid algorithms that reduce searching space and improve searching speed. Numerical examples were conducted on Taiwan highway network that consists of more than four hundred thousands of links and nearly three hundred thousands of nodes. This real network was divided into two connected sub-networks (layers). The upper layer is constructed by freeways and expressways; the lower layer is constructed by local networks. Test origin-destination pairs were chosen randomly and divided into three distance categories; short, medium and long distances. The evaluation of outcome is judged by actual length and travel time. The numerical example reveals that the hybrid algorithm proposed by this research might be tens of thousands times faster than traditional Dijkstra algorithm; the memory requirement of the hybrid algorithm is also much smaller than the tradition algorithm. This outcome shows that this proposed algorithm would have an advantage over vehicle navigation system.
Fully efficient time-parallelized quantum optimal control algorithm
NASA Astrophysics Data System (ADS)
Riahi, M. K.; Salomon, J.; Glaser, S. J.; Sugny, D.
2016-04-01
We present a time-parallelization method that enables one to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver: the computational time is approximately divided by the number of available processors. The control of spin systems, molecular orientation, and Bose-Einstein condensates are used as illustrative examples to highlight the wide range of applications of this numerical scheme.
Newton algorithm for fitting transfer functions to frequency response measurements
NASA Technical Reports Server (NTRS)
Spanos, J. T.; Mingori, D. L.
1993-01-01
In this paper the problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type that converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second-order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions. Two numerical examples demonstrate the effectiveness of the algorithm.
NASA Technical Reports Server (NTRS)
Farhat, C.; Park, K. C.; Dubois-Pelerin, Y.
1991-01-01
An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.
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)