Numerical Algorithms for Acoustic Integrals - The Devil is in the Details

Science.gov (United States)

Brentner, Kenneth S.

1996-01-01

The accurate prediction of the aeroacoustic field generated by aerospace vehicles or nonaerospace machinery is necessary for designers to control and reduce source noise. Powerful computational aeroacoustic methods, based on various acoustic analogies (primarily the Lighthill acoustic analogy) and Kirchhoff methods, have been developed for prediction of noise from complicated sources, such as rotating blades. Both methods ultimately predict the noise through a numerical evaluation of an integral formulation. In this paper, we consider three generic acoustic formulations and several numerical algorithms that have been used to compute the solutions to these formulations. Algorithms for retarded-time formulations are the most efficient and robust, but they are difficult to implement for supersonic-source motion. Collapsing-sphere and emission-surface formulations are good alternatives when supersonic-source motion is present, but the numerical implementations of these formulations are more computationally demanding. New algorithms - which utilize solution adaptation to provide a specified error level - are needed.

THE NUMERICAL ALGORITHM FOR CALCULATING TEMPERATURE FIELDS OF THE PNEUMATIC TIRES DURING VULCANIZATION

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S. G. Tikhomirov

2015-01-01

Full Text Available In the article discussed the mathematical formulation and numerical algorithm for solving the problem of calculating the temperature field in the process vulcanizing of the product, whose the thermal characteristics are depended on the temperature. As a mathematical model considered the system of differential equations of heat conduction, taking into account the change in the coefficients of thermal conductivity and heat density in multilayer product of the temperature. The system of equations is solved for a given initial distribution of temperature and for a given (time-dependent temperatures on the border of the product to the press-mold and to the diaphragm. On the border of the contacts of adjacent layers are given the condition of continuity of temperature and heat flux. Change of the thermal conductivity from the time is approximated by linear functions. The activation energy of the vulcanization process is determined on the basis of experimental data obtained in the control test samples using a reometer. Considering the function representing the corresponding integrals of the thermal conductivity, the original system of differential equations is transformed to an equivalent system of differential equations convenient for constructing numerical algorithms for solving the problem. The resulting system of partial differential equations derived using the method of finite-difference approximation is replaced by a system of algebraic equations. Solution of the system of algebraic equations is carried out under the scheme explicit difference approximation. In the article calculated the temperature field for the tire at given initial and boundary conditions. Stability and accuracy of the numerical algorithm for solving the problem is demonstrated by the calculations performed with different sampling step along the time and space coordinates. Assessment of the degree of completion of the process is carried out by calculated equivalent time for

Theoretical and numerical study of an optimum design algorithm

International Nuclear Information System (INIS)

Destuynder, Philippe.

1976-08-01

This work can be separated into two main parts. First, the behavior of the solution of an elliptic variational equation is analyzed when the domain is submitted to a small perturbation. The case of inequations is also considered. Secondly the previous results are used for deriving an optimum design algorithm. This algorithm was suggested by the center-method proposed by Huard. Numerical results show the superiority of the method on other different optimization techniques [fr

Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows

Science.gov (United States)

Moitra, Stuti; Gatski, Thomas B.

1997-01-01

A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.

Validation of a numerical algorithm based on transformed equations

International Nuclear Information System (INIS)

Xu, H.; Barron, R.M.; Zhang, C.

2003-01-01

Generally, a typical equation governing a physical process, such as fluid flow or heat transfer, has three types of terms that involve partial derivatives, namely, the transient term, the convective terms and the diffusion terms. The major difficulty in obtaining numerical solutions of these partial differential equations is the discretization of the convective terms. The transient term is usually discretized using the first-order forward or backward differencing scheme. The diffusion terms are usually discretized using the central differencing scheme and no difficulty arises since these terms involve second-order spatial derivatives of the flow variables. The convective terms are non-linear and contain first-order spatial derivatives. The main difference between various numerical algorithms is the discretization of the convective terms. In the present study, an alternative approach to discretizing the governing equations is presented. In this algorithm, the governing equations are first transformed by introducing an exponential function to eliminate the convective terms in the equations. The proposed algorithm is applied to simulate some fluid flows with exact solutions to validate the proposed algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. The comparisons with the power-law scheme indicate that the proposed scheme exhibits better performance. (author)

Development of CAD implementing the algorithm of boundary elements’ numerical analytical method

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Yulia V. Korniyenko

2015-03-01

Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

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Tao Min

2014-01-01

Full Text Available This paper is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.

A hybrid artificial bee colony algorithm for numerical function optimization

Science.gov (United States)

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).

On a numerical algorithm for uncertain system | Abiola | Science ...

African Journals Online (AJOL)

A numerical method for computing stable control signals for system with bounded input disturbance is developed. The algorithm is an elaboration of the gradient technique and variable metric method for computing control variables in linear and non-linear optimization problems. This method is developed for an integral ...

Numerical methods design, analysis, and computer implementation of algorithms

CERN Document Server

Greenbaum, Anne

2012-01-01

Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book a...

Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations

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Benjamin M. Cowan

2013-04-01

Full Text Available We describe a modification to the finite-difference time-domain algorithm for electromagnetics on a Cartesian grid which eliminates numerical dispersion error in vacuum for waves propagating along a grid axis. We provide details of the algorithm, which generalizes previous work by allowing 3D operation with a wide choice of aspect ratio, and give conditions to eliminate dispersive errors along one or more of the coordinate axes. We discuss the algorithm in the context of laser-plasma acceleration simulation, showing significant reduction—up to a factor of 280, at a plasma density of 10^{23}  m^{-3}—of the dispersion error of a linear laser pulse in a plasma channel. We then compare the new algorithm with the standard electromagnetic update for laser-plasma accelerator stage simulations, demonstrating that by controlling numerical dispersion, the new algorithm allows more accurate simulation than is otherwise obtained. We also show that the algorithm can be used to overcome the critical but difficult challenge of consistent initialization of a relativistic particle beam and its fields in an accelerator simulation.

Fast numerical solution of KKR-CPA equations: Testing new algorithms

Energy Technology Data Exchange (ETDEWEB)

Bruno, E.; Florio, G.M.; Ginatempo, B.; Giuliano, E.S. (Universita di Messina (Italy))

1994-04-01

Some numerical methods for the solution of KKR-CPA equations are discussed and tested. New, efficient, computational algorithms are proposed, allowing a remarkable reduction of computing time and a good reliability in evaluating spectral quantities. 16 refs., 7 figs.

Numerical model updating technique for structures using firefly algorithm

Science.gov (United States)

Sai Kubair, K.; Mohan, S. C.

2018-03-01

Numerical model updating is a technique used for updating the existing experimental models for any structures related to civil, mechanical, automobiles, marine, aerospace engineering, etc. The basic concept behind this technique is updating the numerical models to closely match with experimental data obtained from real or prototype test structures. The present work involves the development of numerical model using MATLAB as a computational tool and with mathematical equations that define the experimental model. Firefly algorithm is used as an optimization tool in this study. In this updating process a response parameter of the structure has to be chosen, which helps to correlate the numerical model developed with the experimental results obtained. The variables for the updating can be either material or geometrical properties of the model or both. In this study, to verify the proposed technique, a cantilever beam is analyzed for its tip deflection and a space frame has been analyzed for its natural frequencies. Both the models are updated with their respective response values obtained from experimental results. The numerical results after updating show that there is a close relationship that can be brought between the experimental and the numerical models.

Numerical algorithm for rigid body position estimation using the quaternion approach

Science.gov (United States)

Zigic, Miodrag; Grahovac, Nenad

2017-11-01

This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.

Cone Algorithm of Spinning Vehicles under Dynamic Coning Environment

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Shuang-biao Zhang

2015-01-01

Full Text Available Due to the fact that attitude error of vehicles has an intense trend of divergence when vehicles undergo worsening coning environment, in this paper, the model of dynamic coning environment is derived firstly. Then, through investigation of the effect on Euler attitude algorithm for the equivalency of traditional attitude algorithm, it is found that attitude error is actually the roll angle error including drifting error and oscillating error, which is induced directly by dynamic coning environment and further affects the pitch angle and yaw angle through transferring. Based on definition of the cone frame and cone attitude, a cone algorithm is proposed by rotation relationship to calculate cone attitude, and the relationship between cone attitude and Euler attitude of spinning vehicle is established. Through numerical simulations with different conditions of dynamic coning environment, it is shown that the induced error of Euler attitude fluctuates by the variation of precession and nutation, especially by that of nutation, and the oscillating frequency of roll angle error is twice that of pitch angle error and yaw angle error. In addition, the rotation angle is more competent to describe the spinning process of vehicles under coning environment than Euler angle gamma, and the real pitch angle and yaw angle are calculated finally.

Researching on YH100 Numerical Control Servo Press Hydraulic Control System and Control Algorithm

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Kai LI

2014-09-01

Full Text Available In order to study the numerical control (NC servo press hydraulic control system and its control algorithm. The numerical control servo press performance and control principle of hydraulic control system are analyzed. According to the flow equation of the hydraulic control valve, hydraulic cylinder flow continuity equation and the force balance equation of the hydraulic cylinder with load press, the mathematical model of hydraulic control system is established. And the servo press hydraulic system transfer function is deduced. Introducing the suitable immune particle swarm control algorithm for servo press hydraulic system, and the control system block diagram is established. Immune algorithm is used to optimize new control parameters of the system and adopt the new optimization results to optimize the system simulation. The simulation result shows that the hydraulic system’s transition time controlled by the immune particle swarm algorithm is shorter than traditional ones, and the control performance is obviously improved. Finally it can be concluded that immune particle swarm PID control have these characteristics such as quickness, stability and accuracy. Applying this principle into application, the obtained YH100 numerical control servo press hydraulic control system meets the requirement.

Thickness determination in textile material design: dynamic modeling and numerical algorithms

International Nuclear Information System (INIS)

Xu, Dinghua; Ge, Meibao

2012-01-01

Textile material design is of paramount importance in the study of functional clothing design. It is therefore important to determine the dynamic heat and moisture transfer characteristics in the human body–clothing–environment system, which directly determine the heat–moisture comfort level of the human body. Based on a model of dynamic heat and moisture transfer with condensation in porous fabric at low temperature, this paper presents a new inverse problem of textile thickness determination (IPTTD). Adopting the idea of the least-squares method, we formulate the IPTTD into a function minimization problem. By means of the finite-difference method, quasi-solution method and direct search method for one-dimensional minimization problems, we construct iterative algorithms of the approximated solution for the IPTTD. Numerical simulation results validate the formulation of the IPTTD and demonstrate the effectiveness of the proposed numerical algorithms. (paper)

Modifying a numerical algorithm for solving the matrix equation X + AX T B = C

Science.gov (United States)

Vorontsov, Yu. O.

2013-06-01

Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.

Theory and applications of numerical analysis

CERN Document Server

Phillips, G M

1996-01-01

This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions

On the impact of communication complexity in the design of parallel numerical algorithms

Science.gov (United States)

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.

Seven-Spot Ladybird Optimization: A Novel and Efficient Metaheuristic Algorithm for Numerical Optimization

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Peng Wang

2013-01-01

Full Text Available 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.

Canonical algorithms for numerical integration of charged particle motion equations

Science.gov (United States)

Efimov, I. N.; Morozov, E. A.; Morozova, A. R.

2017-02-01

A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.

Analysis and Application of High Resolution Numerical Perturbation Algorithm for Convective-Diffusion Equation

International Nuclear Information System (INIS)

Gao Zhi; Shen Yi-Qing

2012-01-01

The high resolution numerical perturbation (NP) algorithm is analyzed and tested using various convective-diffusion equations. The NP algorithm is constructed by splitting the second order central difference schemes of both convective and diffusion terms of the convective-diffusion equation into upstream and downstream parts, then the perturbation reconstruction functions of the convective coefficient are determined using the power-series of grid interval and eliminating the truncated errors of the modified differential equation. The important nature, i.e. the upwind dominance nature, which is the basis to ensuring that the NP schemes are stable and essentially oscillation free, is firstly presented and verified. Various numerical cases show that the NP schemes are efficient, robust, and more accurate than the original second order central scheme

Numerical Laplace inversion in problems of elastodynamics: Comparison of four algorithms

Czech Academy of Sciences Publication Activity Database

Adámek, V.; Valeš, František; Červ, Jan

2017-01-01

Roč. 113, November (2017), s. 120-129 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GAP101/12/2315 Institutional support: RVO:61388998 Keywords : inverse Laplace transform * numerical algorithm * wave propagation * multi-precision computation * Maple code Subject RIV: BI - Acoustics OBOR OECD: Acoustics Impact factor: 3.000, year: 2016

Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

Science.gov (United States)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

A Numerical Algorithm and a Graphical Method to Size a Heat Exchanger

DEFF Research Database (Denmark)

Berning, Torsten

2011-01-01

This paper describes the development of a numerical algorithm and a graphical method that can be employed in order to determine the overall heat transfer coefficient inside heat exchangers. The method is based on an energy balance and utilizes the spreadsheet application software Microsoft Excel...

A Numerical Algorithm and a Graphical Method to Size a Heat Exchanger

DEFF Research Database (Denmark)

Berning, Torsten

2011-01-01

This paper describes the development of a numerical algorithm and a graphical method that can be employed in order to determine the overall heat transfer coefficient inside heat exchangers. The method is based on an energy balance and utilizes the spreadsheet application software Microsoft ExcelTM...

Numerical Algorithms for Personalized Search in Self-organizing Information Networks

CERN Document Server

Kamvar, Sep

2010-01-01

This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data. Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quad

Performance evaluation of 2D image registration algorithms with the numeric image registration and comparison platform

International Nuclear Information System (INIS)

Gerganov, G.; Kuvandjiev, V.; Dimitrova, I.; Mitev, K.; Kawrakow, I.

2012-01-01

The objective of this work is to present the capabilities of the NUMERICS web platform for evaluation of the performance of image registration algorithms. The NUMERICS platform is a web accessible tool which provides access to dedicated numerical algorithms for registration and comparison of medical images (http://numerics.phys.uni-sofia.bg). The platform allows comparison of noisy medical images by means of different types of image comparison algorithms, which are based on statistical tests for outliers. The platform also allows 2D image registration with different techniques like Elastic Thin-Plate Spline registration, registration based on rigid transformations, affine transformations, as well as non-rigid image registration based on Mobius transformations. In this work we demonstrate how the platform can be used as a tool for evaluation of the quality of the image registration process. We demonstrate performance evaluation of a deformable image registration technique based on Mobius transformations. The transformations are applied with appropriate cost functions like: Mutual information, Correlation coefficient, Sum of Squared Differences. The accent is on the results provided by the platform to the user and their interpretation in the context of the performance evaluation of 2D image registration. The NUMERICS image registration and image comparison platform provides detailed statistical information about submitted image registration jobs and can be used to perform quantitative evaluation of the performance of different image registration techniques. (authors)

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

Science.gov (United States)

Chierici, A.; Chirco, L.; Da Vià, R.; Manservisi, S.; Scardovelli, R.

2017-11-01

Nowadays the rapidly-increasing computational power allows scientists and engineers to perform numerical simulations of complex systems that can involve many scales and several different physical phenomena. In order to perform such simulations, two main strategies can be adopted: one may develop a new numerical code where all the physical phenomena of interest are modelled or one may couple existing validated codes. With the latter option, the creation of a huge and complex numerical code is avoided but efficient methods for data exchange are required since the performance of the simulation is highly influenced by its coupling techniques. In this work we propose a new algorithm that can be used for volume and/or boundary coupling purposes for both multiscale and multiphysics numerical simulations. The proposed algorithm is used for a multiscale simulation involving several CFD domains and monodimensional loops. We adopt the overlapping domain strategy, so the entire flow domain is simulated with the system code. We correct the system code solution by matching averaged inlet and outlet fields located at the boundaries of the CFD domains that overlap parts of the monodimensional loop. In particular we correct pressure losses and enthalpy values with source-sink terms that are imposed in the system code equations. The 1D-CFD coupling is a defective one since the CFD code requires point-wise values on the coupling interfaces and the system code provides only averaged quantities. In particular we impose, as inlet boundary conditions for the CFD domains, the mass flux and the mean enthalpy that are calculated by the system code. With this method the mass balance is preserved at every time step of the simulation. The coupling between consecutive CFD domains is not a defective one since with the proposed algorithm we can interpolate the field solutions on the boundary interfaces. We use the MED data structure as the base structure where all the field operations are

Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems.

Science.gov (United States)

Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

2015-11-11

Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.

Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs

Directory of Open Access Journals (Sweden)

Gene Frantz

2007-01-01

Full Text Available Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.

Numeric algorithms for parallel processors computer architectures with applications to the few-groups neutron diffusion equations

International Nuclear Information System (INIS)

Zee, S.K.

1987-01-01

A numeric algorithm and an associated computer code were developed for the rapid solution of the finite-difference method representation of the few-group neutron-diffusion equations on parallel computers. Applications of the numeric algorithm on both SIMD (vector pipeline) and MIMD/SIMD (multi-CUP/vector pipeline) architectures were explored. The algorithm was successfully implemented in the two-group, 3-D neutron diffusion computer code named DIFPAR3D (DIFfusion PARallel 3-Dimension). Numerical-solution techniques used in the code include the Chebyshev polynomial acceleration technique in conjunction with the power method of outer iteration. For inner iterations, a parallel form of red-black (cyclic) line SOR with automated determination of group dependent relaxation factors and iteration numbers required to achieve specified inner iteration error tolerance is incorporated. The code employs a macroscopic depletion model with trace capability for selected fission products' transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the DIFPAR3D code, for realistic simulation of power reactor cores. The physics models used were proven acceptable in separate benchmarking studies

Numerical algorithm for laser treatment of powder layer with variable thickness

Science.gov (United States)

Soboleva, Polina; Knyazeva, Anna

2017-12-01

Two-dimensional model of laser treatment of powder layer on the substrate is proposed in this paper. The model takes into account the shrinkage of powder layer due to the laser treatment. Three simplified variants of the model were studied. Firstly, the influence of optical properties of powder layer on the maximal temperature was researched. Secondly, two-dimensional model for given thickness of powder layer was studied where practically uniform temperature distribution across thin powder layer was demonstrated. Then, the numerical algorithm was developed to calculate the temperature field for the area of variable size. The impact of the optical properties of powder material on the character of the temperature distribution was researched numerically.

Comparative Study of Algorithms for the Numerical Simulation of Lattice QCD

International Nuclear Information System (INIS)

Luz, Fernando H. P.; Mendes, Tereza

2010-01-01

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.

Adaptive Numerical Algorithms in Space Weather Modeling

Science.gov (United States)

Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.;

A Nondominated Genetic Algorithm Procedure for Multiobjective Discrete Network Design under Demand Uncertainty

Directory of Open Access Journals (Sweden)

Bian Changzhi

2015-01-01

Full Text Available This paper addresses the multiobjective discrete network design problem under demand uncertainty. The OD travel demands are supposed to be random variables with the given probability distribution. The problem is formulated as a bilevel stochastic optimization model where the decision maker’s objective is to minimize the construction cost, the expectation, and the standard deviation of total travel time simultaneously and the user’s route choice is described using user equilibrium model on the improved network under all scenarios of uncertain demand. The proposed model generates globally near-optimal Pareto solutions for network configurations based on the Monte Carlo simulation and nondominated sorting genetic algorithms II. Numerical experiments implemented on Nguyen-Dupuis test network show trade-offs among construction cost, the expectation, and standard deviation of total travel time under uncertainty are obvious. Investment on transportation facilities is an efficient method to improve the network performance and reduce risk under demand uncertainty, but it has an obvious marginal decreasing effect.

Numerical analysis of bifurcations

International Nuclear Information System (INIS)

Guckenheimer, J.

1996-01-01

This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics

Numerical Simulation of the Heston Model under Stochastic Correlation

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Long Teng

2017-12-01

Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.

Modified SIMPLE algorithm for the numerical analysis of incompressible flows with free surface

International Nuclear Information System (INIS)

Mok, Jin Ho; Hong, Chun Pyo; Lee, Jin Ho

2005-01-01

While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipment or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented for the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm

Parallel Algorithm for Adaptive Numerical Integration

International Nuclear Information System (INIS)

Sujatmiko, M.; Basarudin, T.

1997-01-01

This paper presents an automation algorithm for integration using adaptive trapezoidal method. The interval is adaptively divided where the width of sub interval are different and fit to the behavior of its function. For a function f, an integration on interval [a,b] can be obtained, with maximum tolerance ε, using estimation (f, a, b, ε). The estimated solution is valid if the error is still in a reasonable range, fulfil certain criteria. If the error is big, however, the problem is solved by dividing it into to similar and independent sub problem on to separate [a, (a+b)/2] and [(a+b)/2, b] interval, i. e. ( f, a, (a+b)/2, ε/2) and (f, (a+b)/2, b, ε/2) estimations. The problems are solved in two different kinds of processor, root processor and worker processor. Root processor function ti divide a main problem into sub problems and distribute them to worker processor. The division mechanism may go further until all of the sub problem are resolved. The solution of each sub problem is then submitted to the root processor such that the solution for the main problem can be obtained. The algorithm is implemented on C-programming-base distributed computer networking system under parallel virtual machine platform

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

Science.gov (United States)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

A Direct Numerical Reconstruction Algorithm for the 3D Calderón Problem

DEFF Research Database (Denmark)

Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim

2011-01-01

In three dimensions Calderón's problem was addressed and solved in theory in the 1980s in a series of papers, but only recently the numerical implementation of the algorithm was initiated. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conducti...

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

Science.gov (United States)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Models and algorithms for midterm production planning under uncertainty: application of proximal decomposition methods

International Nuclear Information System (INIS)

Lenoir, A.

2008-01-01

We focus in this thesis, on the optimization process of large systems under uncertainty, and more specifically on solving the class of so-called deterministic equivalents with the help of splitting methods. The underlying application we have in mind is the electricity unit commitment problem under climate, market and energy consumption randomness, arising at EDF. We set the natural time-space-randomness couplings related to this application and we propose two new discretization schemes to tackle the randomness one, each of them based on non-parametric estimation of conditional expectations. This constitute an alternative to the usual scenario tree construction. We use the mathematical model consisting of the sum of two convex functions, a separable one and a coupling one. On the one hand, this simplified model offers a general framework to study decomposition-coordination algorithms by elapsing technicality due to a particular choice of subsystems. On the other hand, the convexity assumption allows to take advantage of monotone operators theory and to identify proximal methods as fixed point algorithms. We underlie the differential properties of the generalized reactions we are looking for a fixed point in order to derive bounds on the speed of convergence. Then we examine two families of decomposition-coordination algorithms resulting from operator splitting methods, namely Forward-Backward and Rachford methods. We suggest some practical method of acceleration of the Rachford class methods. To this end, we analyze the method from a theoretical point of view, furnishing as a byproduct explanations to some numerical observations. Then we propose as a response some improvements. Among them, an automatic updating strategy of scaling factors can correct a potential bad initial choice. The convergence proof is made easier thanks to stability results of some operator composition with respect to graphical convergence provided before. We also submit the idea of introducing

A numerical study of super-resolution through fast 3D wideband algorithm for scattering in highly-heterogeneous media

KAUST Repository

Létourneau, Pierre-David

2016-09-19

We present a wideband fast algorithm capable of accurately computing the full numerical solution of the problem of acoustic scattering of waves by multiple finite-sized bodies such as spherical scatterers in three dimensions. By full solution, we mean that no assumption (e.g. Rayleigh scattering, geometrical optics, weak scattering, Born single scattering, etc.) is necessary regarding the properties of the scatterers, their distribution or the background medium. The algorithm is also fast in the sense that it scales linearly with the number of unknowns. We use this algorithm to study the phenomenon of super-resolution in time-reversal refocusing in highly-scattering media recently observed experimentally (Lemoult et al., 2011), and provide numerical arguments towards the fact that such a phenomenon can be explained through a homogenization theory.

An efficient algorithm for bi-objective combined heat and power production planning under the emission trading scheme

International Nuclear Information System (INIS)

Rong, Aiying; Figueira, José Rui; Lahdelma, Risto

2014-01-01

Highlights: • Define fuel mix setting for the bi-objective CHP environmental/economic dispatch. • Develop an efficient algorithm for constructing the Pareto frontier for the problem. • Time complexity analysis is conducted for the proposed algorithm. • The algorithm is theoretically compared against a traditional algorithm. • The efficiency of the algorithm is justified by numerical results. - Abstract: The growing environmental awareness and the apparent conflicts between economic and environmental objectives turn energy planning problems naturally into multi-objective optimization problems. In the current study, mixed fuel combustion is considered as an option to achieve tradeoff between economic objective (associated with fuel cost) and emission objective (measured in CO 2 emission cost according to fuels and emission allowance price) because a fuel with higher emissions is usually cheaper than one with lower emissions. Combined heat and power (CHP) production is an important high-efficiency technology to promote under the emission trading scheme. In CHP production, the production planning of both commodities must be done in coordination. A long-term planning problem decomposes into thousands of hourly subproblems. In this paper, a bi-objective multi-period linear programming CHP planning model is presented first. Then, an efficient specialized merging algorithm for constructing the exact Pareto frontier (PF) of the problem is presented. The algorithm is theoretically and empirically compared against a modified dichotomic search algorithm. The efficiency and effectiveness of the algorithm is justified

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

Science.gov (United States)

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.

Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

Science.gov (United States)

Hennelly, Bryan M.; Sheridan, John T.

2005-05-01

By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

Parallel algorithms for numerical linear algebra

CERN Document Server

van der Vorst, H

1990-01-01

This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for p

Tests of a numerical algorithm for the linear instability study of flows on a sphere

Energy Technology Data Exchange (ETDEWEB)

Perez Garcia, Ismael; Skiba, Yuri N [Univerisidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico)

2001-04-01

A numerical algorithm for the normal mode instability of a steady nondivergent flow on a rotating sphere is developed. The algorithm accuracy is tested with zonal solutions of the nonlinear barotropic vorticity equation (Legendre polynomials, zonal Rossby-Harwitz waves and monopole modons). [Spanish] Ha sido desarrollado un algoritmo numerico para estudiar la inestabilidad lineal de un flujo estacionario no divergente en una esfera en rotacion. La precision del algoritmo se prueba con soluciones zonales de la ecuacion no lineal de vorticidad barotropica (polinomios de Legendre, ondas zonales Rossby-Harwitz y modones monopolares).

A hybrid bird mating optimizer algorithm with teaching-learning-based optimization for global numerical optimization

Directory of Open Access Journals (Sweden)

Qingyang Zhang

2015-02-01

Full Text Available Bird Mating Optimizer (BMO is a novel meta-heuristic optimization algorithm inspired by intelligent mating behavior of birds. However, it is still insufficient in convergence of speed and quality of solution. To overcome these drawbacks, this paper proposes a hybrid algorithm (TLBMO, which is established by combining the advantages of Teaching-learning-based optimization (TLBO and Bird Mating Optimizer (BMO. The performance of TLBMO is evaluated on 23 benchmark functions, and compared with seven state-of-the-art approaches, namely BMO, TLBO, Artificial Bee Bolony (ABC, Particle Swarm Optimization (PSO, Fast Evolution Programming (FEP, Differential Evolution (DE, Group Search Optimization (GSO. Experimental results indicate that the proposed method performs better than other existing algorithms for global numerical optimization.

A novel hybrid algorithm of GSA with Kepler algorithm for numerical optimization

Directory of Open Access Journals (Sweden)

Soroor Sarafrazi

2015-07-01

Full Text Available It is now well recognized that pure algorithms can be promisingly improved by hybridization with other techniques. One of the relatively new metaheuristic algorithms is Gravitational Search Algorithm (GSA which is based on the Newton laws. In this paper, to enhance the performance of GSA, a novel algorithm called “Kepler”, inspired by the astrophysics, is introduced. The Kepler algorithm is based on the principle of the first Kepler law. The hybridization of GSA and Kepler algorithm is an efficient approach to provide much stronger specialization in intensification and/or diversification. The performance of GSA–Kepler is evaluated by applying it to 14 benchmark functions with 20–1000 dimensions and the optimal approximation of linear system as a practical optimization problem. The results obtained reveal that the proposed hybrid algorithm is robust enough to optimize the benchmark functions and practical optimization problems.

NUMERICAL ALGORITHMS AT NON-ZERO CHEMICAL POTENTIAL. PROCEEDINGS OF RIKEN BNL RESEARCH CENTER WORKSHOP, VOLUME 19

International Nuclear Information System (INIS)

Blum, T.; Creutz, M.

1999-01-01

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

Hard decoding algorithm for optimizing thresholds under general Markovian noise

Science.gov (United States)

Chamberland, Christopher; Wallman, Joel; Beale, Stefanie; Laflamme, Raymond

2017-04-01

Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

Science.gov (United States)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Contact-impact algorithms on parallel computers

International Nuclear Information System (INIS)

Zhong Zhihua; Nilsson, Larsgunnar

1994-01-01

Contact-impact algorithms on parallel computers are discussed within the context of explicit finite element analysis. The algorithms concerned include a contact searching algorithm and an algorithm for contact force calculations. The contact searching algorithm is based on the territory concept of the general HITA algorithm. However, no distinction is made between different contact bodies, or between different contact surfaces. All contact segments from contact boundaries are taken as a single set. Hierarchy territories and contact territories are expanded. A three-dimensional bucket sort algorithm is used to sort contact nodes. The defence node algorithm is used in the calculation of contact forces. Both the contact searching algorithm and the defence node algorithm are implemented on the connection machine CM-200. The performance of the algorithms is examined under different circumstances, and numerical results are presented. ((orig.))

Accuracy verification methods theory and algorithms

CERN Document Server

Mali, Olli; Repin, Sergey

2014-01-01

The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating the theory and researchers developing applied algorithms that could be used in engineering and scientific computations for guaranteed and efficient error control.   The goals of the book are to (1) give a transparent explanation of the underlying mathematical theory in a style accessible not only to advanced numerical analysts but also to engineers and students; (2) present detailed step-by-step algorithms that follow from a theory; (3) discuss their advantages and drawbacks, areas of applicability, give recommendations and examples.

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

Science.gov (United States)

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.

RDEL: Restart Differential Evolution algorithm with Local Search Mutation for global numerical optimization

Directory of Open Access Journals (Sweden)

Ali Wagdy Mohamed

2014-11-01

Full Text Available In this paper, a novel version of Differential Evolution (DE algorithm based on a couple of local search mutation and a restart mechanism for solving global numerical optimization problems over continuous space is presented. The proposed algorithm is named as Restart Differential Evolution algorithm with Local Search Mutation (RDEL. In RDEL, inspired by Particle Swarm Optimization (PSO, a novel local mutation rule based on the position of the best and the worst individuals among the entire population of a particular generation is introduced. The novel local mutation scheme is joined with the basic mutation rule through a linear decreasing function. The proposed local mutation scheme is proven to enhance local search tendency of the basic DE and speed up the convergence. Furthermore, a restart mechanism based on random mutation scheme and a modified Breeder Genetic Algorithm (BGA mutation scheme is combined to avoid stagnation and/or premature convergence. Additionally, an exponent increased crossover probability rule and a uniform scaling factors of DE are introduced to promote the diversity of the population and to improve the search process, respectively. The performance of RDEL is investigated and compared with basic differential evolution, and state-of-the-art parameter adaptive differential evolution variants. It is discovered that the proposed modifications significantly improve the performance of DE in terms of quality of solution, efficiency and robustness.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

Science.gov (United States)

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

A Mass Conservative Numerical Solution for Two-Phase Flow in Porous Media With Application to Unsaturated Flow

DEFF Research Database (Denmark)

Celia, Michael A.; Binning, Philip John

1992-01-01

that the algorithm produces solutions that are essentially mass conservative and oscillation free, even in the presence of steep infiltrating fronts. When the algorithm is applied to the case of air and water flow in unsaturated soils, numerical results confirm the conditions under which Richards's equation is valid....... Numerical results also demonstrate the potential importance of air phase advection when considering contaminant transport in unsaturated soils. Comparison to several other numerical algorithms shows that the modified Picard approach offers robust, mass conservative solutions to the general equations...

Average-case analysis of numerical problems

CERN Document Server

2000-01-01

The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach. The analysis of average error and cost leads to new insight on numerical problems as well as to new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years and also contains new results. The problems under consideration include approximation/optimal recovery and numerical integration of univariate and multivariate functions as well as zero-finding and global optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided.

A Comparative Study of Differential Evolution, Particle Swarm Optimization, and Evolutionary Algorithms on Numerical Benchmark Problems

DEFF Research Database (Denmark)

Vesterstrøm, Jacob Svaneborg; Thomsen, Rene

2004-01-01

Several extensions to evolutionary algorithms (EAs) and particle swarm optimization (PSO) have been suggested during the last decades offering improved performance on selected benchmark problems. Recently, another search heuristic termed differential evolution (DE) has shown superior performance...... in several real-world applications. In this paper, we evaluate the performance of DE, PSO, and EAs regarding their general applicability as numerical optimization techniques. The comparison is performed on a suite of 34 widely used benchmark problems. The results from our study show that DE generally...... outperforms the other algorithms. However, on two noisy functions, both DE and PSO were outperformed by the EA....

A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric

DEFF Research Database (Denmark)

Zimmermann, Ralf

2017-01-01

We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm...... converges locally and exhibits a linear rate of convergence....

A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric

OpenAIRE

Zimmermann, Ralf

2016-01-01

We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear rate of convergence.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

Directory of Open Access Journals (Sweden)

Gonglin Yuan

Full Text Available Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1 βk ≥ 0 2 the search direction has the trust region property without the use of any line search method 3 the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Numerically pricing American options under the generalized mixed fractional Brownian motion model

Science.gov (United States)

Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying

2016-06-01

In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.

A numerical study of super-resolution through fast 3D wideband algorithm for scattering in highly-heterogeneous media

KAUST Repository

Lé tourneau, Pierre-David; Wu, Ying; Papanicolaou, George; Garnier, Josselin; Darve, Eric

2016-01-01

We present a wideband fast algorithm capable of accurately computing the full numerical solution of the problem of acoustic scattering of waves by multiple finite-sized bodies such as spherical scatterers in three dimensions. By full solution, we

Numerical thermal analysis and optimization of multi-chip LED module using response surface methodology and genetic algorithm

NARCIS (Netherlands)

Tang, Hong Yu; Ye, Huai Yu; Chen, Xian Ping; Qian, Cheng; Fan, Xue Jun; Zhang, G.Q.

2017-01-01

In this paper, the heat transfer performance of the multi-chip (MC) LED module is investigated numerically by using a general analytical solution. The configuration of the module is optimized with genetic algorithm (GA) combined with a response surface methodology. The space between chips, the

On the analytic and numeric optimisation of airplane trajectories under real atmospheric conditions

Science.gov (United States)

Gonzalo, J.; Domínguez, D.; López, D.

2014-12-01

From the beginning of aviation era, economic constraints have forced operators to continuously improve the planning of the flights. The revenue is proportional to the cost per flight and the airspace occupancy. Many methods, the first started in the middle of last century, have explore analytical, numerical and artificial intelligence resources to reach the optimal flight planning. In parallel, advances in meteorology and communications allow an almost real-time knowledge of the atmospheric conditions and a reliable, error-bounded forecast for the near future. Thus, apart from weather risks to be avoided, airplanes can dynamically adapt their trajectories to minimise their costs. International regulators are aware about these capabilities, so it is reasonable to envisage some changes to allow this dynamic planning negotiation to soon become operational. Moreover, current unmanned airplanes, very popular and often small, suffer the impact of winds and other weather conditions in form of dramatic changes in their performance. The present paper reviews analytic and numeric solutions for typical trajectory planning problems. Analytic methods are those trying to solve the problem using the Pontryagin principle, where influence parameters are added to state variables to form a split condition differential equation problem. The system can be solved numerically -indirect optimisation- or using parameterised functions -direct optimisation-. On the other hand, numerical methods are based on Bellman's dynamic programming (or Dijkstra algorithms), where the fact that two optimal trajectories can be concatenated to form a new optimal one if the joint point is demonstrated to belong to the final optimal solution. There is no a-priori conditions for the best method. Traditionally, analytic has been more employed for continuous problems whereas numeric for discrete ones. In the current problem, airplane behaviour is defined by continuous equations, while wind fields are given in a

Simultaneous and semi-alternating projection algorithms for solving split equality problems.

Science.gov (United States)

Dong, Qiao-Li; Jiang, Dan

2018-01-01

In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms.

Generalized random walk algorithm for the numerical modeling of complex diffusion processes

CERN Document Server

Vamos, C; Vereecken, H

2003-01-01

A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.

Generalized random walk algorithm for the numerical modeling of complex diffusion processes

International Nuclear Information System (INIS)

Vamos, Calin; Suciu, Nicolae; Vereecken, Harry

2003-01-01

A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested

Probabilistic numerics and uncertainty in computations.

Science.gov (United States)

Hennig, Philipp; Osborne, Michael A; Girolami, Mark

2015-07-08

We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

EM algorithm for one-shot device testing with competing risks under exponential distribution

International Nuclear Information System (INIS)

Balakrishnan, N.; So, H.Y.; Ling, M.H.

2015-01-01

This paper provides an extension of the work of Balakrishnan and Ling [1] by introducing a competing risks model into a one-shot device testing analysis under an accelerated life test setting. An Expectation Maximization (EM) algorithm is then developed for the estimation of the model parameters. An extensive Monte Carlo simulation study is carried out to assess the performance of the EM algorithm and then compare the obtained results with the initial estimates obtained by the Inequality Constrained Least Squares (ICLS) method of estimation. Finally, we apply the EM algorithm to a clinical data, ED01, to illustrate the method of inference developed here. - Highlights: • ALT data analysis for one-shot devices with competing risks is considered. • EM algorithm is developed for the determination of the MLEs. • The estimations of lifetime under normal operating conditions are presented. • The EM algorithm improves the convergence rate

Performance Comparison of Widely-Used Maximum Power Point Tracker Algorithms under Real Environmental Conditions

Directory of Open Access Journals (Sweden)

DURUSU, A.

2014-08-01

Full Text Available Maximum power point trackers (MPPTs play an essential role in extracting power from photovoltaic (PV panels as they make the solar panels to operate at the maximum power point (MPP whatever the changes of environmental conditions are. For this reason, they take an important place in the increase of PV system efficiency. MPPTs are driven by MPPT algorithms and a number of MPPT algorithms are proposed in the literature. The comparison of the MPPT algorithms in literature are made by a sun simulator based test system under laboratory conditions for short durations. However, in this study, the performances of four most commonly used MPPT algorithms are compared under real environmental conditions for longer periods. A dual identical experimental setup is designed to make a comparison between two the considered MPPT algorithms as synchronized. As a result of this study, the ranking among these algorithms are presented and the results show that Incremental Conductance (IC algorithm gives the best performance.

A Hybrid Maximum Power Point Tracking Approach for Photovoltaic Systems under Partial Shading Conditions Using a Modified Genetic Algorithm and the Firefly Algorithm

Directory of Open Access Journals (Sweden)

Yu-Pei Huang

2018-01-01

Full Text Available This paper proposes a modified maximum power point tracking (MPPT algorithm for photovoltaic systems under rapidly changing partial shading conditions (PSCs. The proposed algorithm integrates a genetic algorithm (GA and the firefly algorithm (FA and further improves its calculation process via a differential evolution (DE algorithm. The conventional GA is not advisable for MPPT because of its complicated calculations and low accuracy under PSCs. In this study, we simplified the GA calculations with the integration of the DE mutation process and FA attractive process. Results from both the simulation and evaluation verify that the proposed algorithm provides rapid response time and high accuracy due to the simplified processing. For instance, evaluation results demonstrate that when compared to the conventional GA, the execution time and tracking accuracy of the proposed algorithm can be, respectively, improved around 69.4% and 4.16%. In addition, in comparison to FA, the tracking speed and tracking accuracy of the proposed algorithm can be improved around 42.9% and 1.85%, respectively. Consequently, the major improvement of the proposed method when evaluated against the conventional GA and FA is tracking speed. Moreover, this research provides a framework to integrate multiple nature-inspired algorithms for MPPT. Furthermore, the proposed method is adaptable to different types of solar panels and different system formats with specifically designed equations, the advantages of which are rapid tracking speed with high accuracy under PSCs.

Multiobjective genetic algorithm approaches to project scheduling under risk

OpenAIRE

Kılıç, Murat; Kilic, Murat

2003-01-01

In this thesis, project scheduling under risk is chosen as the topic of research. Project scheduling under risk is defined as a biobjective decision problem and is formulated as a 0-1 integer mathematical programming model. In this biobjective formulation, one of the objectives is taken as the expected makespan minimization and the other is taken as the expected cost minimization. As the solution approach to this biobjective formulation genetic algorithm (GA) is chosen. After carefully invest...

Numerical modelling of closed-cell aluminium foam under dynamic loading

Science.gov (United States)

Hazell, Paul; Kader, M. A.; Islam, M. A.; Escobedo, J. P.; Saadatfar, M.

2015-06-01

Closed-cell aluminium foams are extensively used in aerospace and automobile industries. The understanding of their behaviour under impact loading conditions is extremely important since impact problems are directly related to design of these engineering structures. This research investigates the response of a closed-cell aluminium foam (CYMAT) subjected to dynamic loading using the finite element software ABAQUS/explicit. The aim of this research is to numerically investigate the material and structural properties of closed-cell aluminium foam under impact loading conditions with interest in shock propagation and its effects on cell wall deformation. A μ-CT based 3D foam geometry is developed to simulate the local cell collapse behaviours. A number of numerical techniques are applied for modelling the crush behaviour of aluminium foam to obtain the more accurate results. The simulation results are compared with experimental data. Comparison of the results shows a good correlation between the experimental results and numerical predictions.

Robust Floor Determination Algorithm for Indoor Wireless Localization Systems under Reference Node Failure

Directory of Open Access Journals (Sweden)

Kriangkrai Maneerat

2016-01-01

Full Text Available One of the challenging problems for indoor wireless multifloor positioning systems is the presence of reference node (RN failures, which cause the values of received signal strength (RSS to be missed during the online positioning phase of the location fingerprinting technique. This leads to performance degradation in terms of floor accuracy, which in turn affects other localization procedures. This paper presents a robust floor determination algorithm called Robust Mean of Sum-RSS (RMoS, which can accurately determine the floor on which mobile objects are located and can work under either the fault-free scenario or the RN-failure scenarios. The proposed fault tolerance floor algorithm is based on the mean of the summation of the strongest RSSs obtained from the IEEE 802.15.4 Wireless Sensor Networks (WSNs during the online phase. The performance of the proposed algorithm is compared with those of different floor determination algorithms in literature. The experimental results show that the proposed robust floor determination algorithm outperformed the other floor algorithms and can achieve the highest percentage of floor determination accuracy in all scenarios tested. Specifically, the proposed algorithm can achieve greater than 95% correct floor determination under the scenario in which 40% of RNs failed.

Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem

DEFF Research Database (Denmark)

Delbary, Fabrice; Knudsen, Kim

2014-01-01

to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...

Numerical modeling of materials under extreme conditions

CERN Document Server

Brown, Eric

2014-01-01

The book presents twelve state of the art contributions in the field of numerical modeling of materials subjected to large strain, high strain rates, large pressure and high stress triaxialities, organized into two sections. The first part is focused on high strain rate-high pressures such as those occurring in impact dynamics and shock compression related phenomena, dealing with material response identification, advanced modeling incorporating microstructure and damage, stress waves propagation in solids and structures response under impact. The latter part is focused on large strain-low strain rates applications such as those occurring in technological material processing, dealing with microstructure and texture evolution, material response at elevated temperatures, structural behavior under large strain and multi axial state of stress.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

Energy Technology Data Exchange (ETDEWEB)

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem

International Nuclear Information System (INIS)

Wei-Tao, Lu; Hua, Zhang; Shun-Jin, Wang

2008-01-01

Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge–Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP. (general)

New algorithm for Hartree-Fock variational equation

International Nuclear Information System (INIS)

Iwasawa, K.; Sakata, F.; Hashimoto, Y.; Terasaki, J.

1994-08-01

Aiming at microscopically understanding the shape-coexistence phenomena, a new algorithm for obtaining many self-consistent Hartree-Fock states is developed. In contrast with the conventional numerical method of solving the constrained Hartree-Fock equation which gives the most energetically favorable state under a given constrained condition, it can find many high-lying Hartree-Fock states as well as many continuous constraint Hartree-Fock solutions by dictating their configurations through some reference state. Numerical calculation is performed by using the Skyrme III. (author)

Algorithm for Extracting Digital Terrain Models under Forest Canopy from Airborne LiDAR Data

Directory of Open Access Journals (Sweden)

Almasi S. Maguya

2014-07-01

Full Text Available Extracting digital elevationmodels (DTMs from LiDAR data under forest canopy is a challenging task. This is because the forest canopy tends to block a portion of the LiDAR pulses from reaching the ground, hence introducing gaps in the data. This paper presents an algorithm for DTM extraction from LiDAR data under forest canopy. The algorithm copes with the challenge of low data density by generating a series of coarse DTMs by using the few ground points available and using trend surfaces to interpolate missing elevation values in the vicinity of the available points. This process generates a cloud of ground points from which the final DTM is generated. The algorithm has been compared to two other algorithms proposed in the literature in three different test sites with varying degrees of difficulty. Results show that the algorithm presented in this paper is more tolerant to low data density compared to the other two algorithms. The results further show that with decreasing point density, the differences between the three algorithms dramatically increased from about 0.5m to over 10m.

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

Science.gov (United States)

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Numerical Algorithm for Delta of Asian Option

Directory of Open Access Journals (Sweden)

Boxiang Zhang

2015-01-01

Full Text Available 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.

Film Cooling Optimization Using Numerical Computation of the Compressible Viscous Flow Equations and Simplex Algorithm

Directory of Open Access Journals (Sweden)

Ahmed M. Elsayed

2013-01-01

Full Text Available Film cooling is vital to gas turbine blades to protect them from high temperatures and hence high thermal stresses. In the current work, optimization of film cooling parameters on a flat plate is investigated numerically. The effect of film cooling parameters such as inlet velocity direction, lateral and forward diffusion angles, blowing ratio, and streamwise angle on the cooling effectiveness is studied, and optimum cooling parameters are selected. The numerical simulation of the coolant flow through flat plate hole system is carried out using the “CFDRC package” coupled with the optimization algorithm “simplex” to maximize overall film cooling effectiveness. Unstructured finite volume technique is used to solve the steady, three-dimensional and compressible Navier-Stokes equations. The results are compared with the published numerical and experimental data of a cylindrically round-simple hole, and the results show good agreement. In addition, the results indicate that the average overall film cooling effectiveness is enhanced by decreasing the streamwise angle for high blowing ratio and by increasing the lateral and forward diffusion angles. Optimum geometry of the cooling hole on a flat plate is determined. In addition, numerical simulations of film cooling on actual turbine blade are performed using the flat plate optimal hole geometry.

Numerical Simulation of the Propagation of Hydraulic and Natural Fracture Using Dijkstra’s Algorithm

Directory of Open Access Journals (Sweden)

Yanfang Wu

2016-07-01

Full Text Available Utilization of hydraulic-fracturing technology is dramatically increasing in exploitation of natural gas extraction. However the prediction of the configuration of propagated hydraulic fracture is extremely challenging. This paper presents a numerical method of obtaining the configuration of the propagated hydraulic fracture into discrete natural fracture network system. The method is developed on the basis of weighted fracture which is derived in combination of Dijkstra’s algorithm energy theory and vector method. Numerical results along with experimental data demonstrated that proposed method is capable of predicting the propagated hydraulic fracture configuration reasonably with high computation efficiency. Sensitivity analysis reveals a number of interesting observation results: the shortest path weight value decreases with increasing of fracture density and length, and increases with increasing of the angle between fractures to the maximum principal stress direction. Our method is helpful for evaluating the complexity of the discrete fracture network, to obtain the extension direction of the fracture.

Numerical Solution of Diffusion Models in Biomedical Imaging on Multicore Processors

Directory of Open Access Journals (Sweden)

Luisa D'Amore

2011-01-01

Full Text Available In this paper, we consider nonlinear partial differential equations (PDEs of diffusion/advection type underlying most problems in image analysis. As case study, we address the segmentation of medical structures. We perform a comparative study of numerical algorithms arising from using the semi-implicit and the fully implicit discretization schemes. Comparison criteria take into account both the accuracy and the efficiency of the algorithms. As measure of accuracy, we consider the Hausdorff distance and the residuals of numerical solvers, while as measure of efficiency we consider convergence history, execution time, speedup, and parallel efficiency. This analysis is carried out in a multicore-based parallel computing environment.

Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

Science.gov (United States)

Zhao, Ying; Shi, Luoyi

2017-01-01

This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong convergence of an algorithm can be verified in the infinite-dimensional Hilbert spaces. Moreover, several numerical results are given to show the effectiveness of our algorithm.

A quasi-Newton algorithm for large-scale nonlinear equations

Directory of Open Access Journals (Sweden)

Linghua Huang

2017-02-01

Full Text Available Abstract In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i a conjugate gradient (CG algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm’s initial point does not have any restrictions; (ii a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length α k $\\alpha_{k}$ . The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the 1 + q $1+q$ -order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

GENERAL: Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem

Science.gov (United States)

Lu, Wei-Tao; Zhang, Hua; Wang, Shun-Jin

2008-07-01

Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge-Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP.

Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

Science.gov (United States)

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)

Glowworm swarm optimization theory, algorithms, and applications

CERN Document Server

Kaipa, Krishnanand N

2017-01-01

This book provides a comprehensive account of the glowworm swarm optimization (GSO) algorithm, including details of the underlying ideas, theoretical foundations, algorithm development, various applications, and MATLAB programs for the basic GSO algorithm. It also discusses several research problems at different levels of sophistication that can be attempted by interested researchers. The generality of the GSO algorithm is evident in its application to diverse problems ranging from optimization to robotics. Examples include computation of multiple optima, annual crop planning, cooperative exploration, distributed search, multiple source localization, contaminant boundary mapping, wireless sensor networks, clustering, knapsack, numerical integration, solving fixed point equations, solving systems of nonlinear equations, and engineering design optimization. The book is a valuable resource for researchers as well as graduate and undergraduate students in the area of swarm intelligence and computational intellige...

The admissible portfolio selection problem with transaction costs and an improved PSO algorithm

Science.gov (United States)

Chen, Wei; Zhang, Wei-Guo

2010-05-01

In this paper, we discuss the portfolio selection problem with transaction costs under the assumption that there exist admissible errors on expected returns and risks of assets. We propose a new admissible efficient portfolio selection model and design an improved particle swarm optimization (PSO) algorithm because traditional optimization algorithms fail to work efficiently for our proposed problem. Finally, we offer a numerical example to illustrate the proposed effective approaches and compare the admissible portfolio efficient frontiers under different constraints.

A new free-surface stabilization algorithm for geodynamical modelling: Theory and numerical tests

Science.gov (United States)

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 (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 and stable for steep slopes, and also conclude that, for longer time steps, the optimal

Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm

Directory of Open Access Journals (Sweden)

Javier S. González-Salas

2016-01-01

Full Text Available A numerical study that uses detrended fluctuation analysis (DFA algorithm of time series obtained from linear and nonlinear dynamical systems is presented. The DFA algorithm behavior toward periodic and chaotic signals is investigated and the effect of the time scale under analysis is discussed. The displayed results prove that the DFA algorithm response is invariant (stable performance to initial condition and chaotic system parameters. An initial idea of DFA algorithm implementation for fine spectrum sensing (SS is proposed under two-stage spectrum sensor approach with test statistics based on the scaling exponent value. The outcomes demonstrate a promising new SS technique that can alleviate several imperfections such as noise power uncertainty and spatial correlation between the adjacent antenna array elements.

A cone-beam tomography system with a reduced size planar detector: A backprojection-filtration reconstruction algorithm as well as numerical and practical experiments

International Nuclear Information System (INIS)

Li Liang; Chen Zhiqiang; Zhang Li; Xing Yuxiang; Kang Kejun

2007-01-01

In a traditional cone-beam computed tomography (CT) system, the cost of product and computation is very high. In this paper, we develop a transversely truncated cone-beam X-ray CT system with a reduced-size detector positioned off-center, in which X-ray beams only cover half of the object. The existing filtered backprojection (FBP) or backprojection-filtration (BPF) algorithms are not directly applicable in this new system. Hence, we develop a BPF-type direct backprojection algorithm. Different from the traditional rebinning methods, our algorithm directly backprojects the pretreated projection data without rebinning. This makes the algorithm compact and computationally more efficient. Because of avoiding interpolation errors of rebinning process, higher spatial resolution is obtained. Finally, some numerical simulations and practical experiments are done to validate the proposed algorithm and compare with rebinning algorithm

Unsupervised learning algorithms

CERN Document Server

Aydin, Kemal

2016-01-01

This book summarizes the state-of-the-art in unsupervised learning. The contributors discuss how with the proliferation of massive amounts of unlabeled data, unsupervised learning algorithms, which can automatically discover interesting and useful patterns in such data, have gained popularity among researchers and practitioners. The authors outline how these algorithms have found numerous applications including pattern recognition, market basket analysis, web mining, social network analysis, information retrieval, recommender systems, market research, intrusion detection, and fraud detection. They present how the difficulty of developing theoretically sound approaches that are amenable to objective evaluation have resulted in the proposal of numerous unsupervised learning algorithms over the past half-century. The intended audience includes researchers and practitioners who are increasingly using unsupervised learning algorithms to analyze their data. Topics of interest include anomaly detection, clustering,...

Numerical simulation of supersonic over/under expanded jets using adaptive grid

International Nuclear Information System (INIS)

Talebi, S.; Shirani, E.

2001-05-01

Numerical simulation of supersonic under and over expanded jet was simulated. In order to achieve the solution efficiently and with high resolution, adaptive grid is used. The axisymmetric compressible, time dependent Navier-Stokes equations in body fitted curvilinear coordinate were solved numerically. The equations were discretized by using control volume, and the Van Leer flux splitting approach. The equations were solved implicitly. The obtained computer code was used to simulate four different cases of moderate and strong under and over expanded jet flows. The results show that with the adaptation of the grid, the various features of this complicated flow can be observed. It was shown that the adaptation method is very efficient and has the ability to make fine grids near the high gradient regions. (author)

Heuristic algorithms for feature selection under Bayesian models with block-diagonal covariance structure.

Science.gov (United States)

Foroughi Pour, Ali; Dalton, Lori A

2018-03-21

Many bioinformatics studies aim to identify markers, or features, that can be used to discriminate between distinct groups. In problems where strong individual markers are not available, or where interactions between gene products are of primary interest, it may be necessary to consider combinations of features as a marker family. To this end, recent work proposes a hierarchical Bayesian framework for feature selection that places a prior on the set of features we wish to select and on the label-conditioned feature distribution. While an analytical posterior under Gaussian models with block covariance structures is available, the optimal feature selection algorithm for this model remains intractable since it requires evaluating the posterior over the space of all possible covariance block structures and feature-block assignments. To address this computational barrier, in prior work we proposed a simple suboptimal algorithm, 2MNC-Robust, with robust performance across the space of block structures. Here, we present three new heuristic feature selection algorithms. The proposed algorithms outperform 2MNC-Robust and many other popular feature selection algorithms on synthetic data. In addition, enrichment analysis on real breast cancer, colon cancer, and Leukemia data indicates they also output many of the genes and pathways linked to the cancers under study. Bayesian feature selection is a promising framework for small-sample high-dimensional data, in particular biomarker discovery applications. When applied to cancer data these algorithms outputted many genes already shown to be involved in cancer as well as potentially new biomarkers. Furthermore, one of the proposed algorithms, SPM, outputs blocks of heavily correlated genes, particularly useful for studying gene interactions and gene networks.

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

International Nuclear Information System (INIS)

Aylott, Benjamin; Baker, John G; Camp, Jordan; Centrella, Joan; Boggs, William D; Buonanno, Alessandra; Boyle, Michael; Buchman, Luisa T; Chu, Tony; Brady, Patrick R; Brown, Duncan A; Bruegmann, Bernd; Cadonati, Laura; Campanelli, Manuela; Faber, Joshua; Chatterji, Shourov; Christensen, Nelson; Diener, Peter; Dorband, Nils; Etienne, Zachariah B

2009-01-01

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

Science.gov (United States)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Numerical simulation of thermomagnetic convection of cold water near its density maximum in a square enclosure under a magnetic quadrupole field

Energy Technology Data Exchange (ETDEWEB)

Shi, Er; Sun, Xiaoqin; He, Yecong; Jiang, Changwei, E-mail: cw_jiang@163.com [School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114 (China)

2017-06-15

Natural convection of cold water near its density maximum in a square enclosure is studied numerically under the influence of a magnetic quadrupole field without gravity. A generalized model which includes a non-Boussinesq parabolic density–temperature relationship is established. The governing equations in primitive variables are discretized using the finite-volume method and solved using the SIMPLE algorithm. The effects of magnetic force number, Rayleigh number and density inversion parameter on flow and heat transfer characteristics are analyzed. The results show that the primary flow pattern depends mainly on the density inversion parameter. Multi-cellular flow structures are observed for certain ranges of density inversion parameter independent of the value of Rayleigh number and magnetic force number. The heat transfer changes non-monotonically under combined actions of the quadrupole magnetic field and density inversion. (paper)

Word-length algorithm for language identification of under-resourced languages

Directory of Open Access Journals (Sweden)

Ali Selamat

2016-10-01

Full Text Available Language identification is widely used in machine learning, text mining, information retrieval, and speech processing. Available techniques for solving the problem of language identification do require large amount of training text that are not available for under-resourced languages which form the bulk of the World’s languages. The primary objective of this study is to propose a lexicon based algorithm which is able to perform language identification using minimal training data. Because language identification is often the first step in many natural language processing tasks, it is necessary to explore techniques that will perform language identification in the shortest possible time. Hence, the second objective of this research is to study the effect of the proposed algorithm on the run-time performance of language identification. Precision, recall, and F1 measures were used to determine the effectiveness of the proposed word length algorithm using datasets drawn from the Universal Declaration of Human Rights Act in 15 languages. The experimental results show good accuracy on language identification at the document level and at the sentence level based on the available dataset. The improved algorithm also showed significant improvement in run time performance compared with the spelling checker approach.

Wavefront-ray grid FDTD algorithm

OpenAIRE

ÇİYDEM, MEHMET

2016-01-01

A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Num...

Observation and Numerical Experiments for Drag Coefficient Under Typhoon Wind Forcing

Institute of Scientific and Technical Information of China (English)

CAO Huiqiu; ZHOU Liangming; LI Shuiqing; WANG Zhifeng

2017-01-01

This paper presents a study on drag coefficients under typhoon wind forcing based on observations and numerical experiments.The friction velocity and wind speed are measured at a marine observation platform in the South China Sea.Three typhoons:SOULIK (2013),TRAMI (2013) and FITOW (2013) are observed at a buoy station in the northeast sea area of Pingtan Island.A new parameterization is formulated for the wind drag coefficient as a function of wind speed.It is found that the drag coefficient (Ca) increases linearly with the slope of 0.083× 10-3 for wind speed less than 24 m s-1.To investigate the drag coefficient under higher wind conditions,three numerical experiments are implemented for these three typhoons using SWAN wave model.The wind input data are objective reanalysis datasets,which are assimilated with many sources and provided every six hours with the resolution of 0.125° ×0.125°.The numerical simulation results show a good agreement with wave observation data under typhoon wind forcing.The results indicate that the drag coefficient levels off with the linear slope of 0.012× 10-3 for higher wind speeds (less than 34 m s-1) and the new parameterization improvese the simulation accuracy compared with the Wu (1982) default used in SWAN.

The Performance Evaluation of an IEEE 802.11 Network Containing Misbehavior Nodes under Different Backoff Algorithms

Directory of Open Access Journals (Sweden)

Trong-Minh Hoang

2017-01-01

Full Text Available Security of any wireless network is always an important issue due to its serious impacts on network performance. Practically, the IEEE 802.11 medium access control can be violated by several native or smart attacks that result in downgrading network performance. In recent years, there are several studies using analytical model to analyze medium access control (MAC layer misbehavior issue to explore this problem but they have focused on binary exponential backoff only. Moreover, a practical condition such as the freezing backoff issue is not included in the previous models. Hence, this paper presents a novel analytical model of the IEEE 802.11 MAC to thoroughly understand impacts of misbehaving node on network throughput and delay parameters. Particularly, the model can express detailed backoff algorithms so that the evaluation of the network performance under some typical attacks through numerical simulation results would be easy.

Large eddy simulation of spray and combustion characteristics with realistic chemistry and high-order numerical scheme under diesel engine-like conditions

International Nuclear Information System (INIS)

Zhou, Lei; Luo, Kai Hong; Qin, Wenjin; Jia, Ming; Shuai, Shi Jin

2015-01-01

Highlights: • MUSCL differencing scheme in LES method is used to investigate liquid fuel spray and combustion process. • Using MUSCL can accurately capture the gas phase velocity distribution and liquid spray features. • Detailed chemistry mechanism with a parallel algorithm was used to calculate combustion process. • Increasing oxygen concentration can decrease ignition delay time and flame LOL. - Abstract: The accuracy of large eddy simulation (LES) for turbulent combustion depends on suitably implemented numerical schemes and chemical mechanisms. In the original KIVA3V code, finite difference schemes such as QSOU (Quasi-second-order upwind) and PDC (Partial Donor Cell Differencing) cannot achieve good results or even computational stability when using coarse grids due to large numerical diffusion. In this paper, the MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) differencing scheme is implemented into KIVA3V-LES code to calculate the convective term. In the meantime, Lu’s n-heptane reduced 58-species mechanisms (Lu, 2011) is used to calculate chemistry with a parallel algorithm. Finally, improved models for spray injection are also employed. With these improvements, the KIVA3V-LES code is renamed as KIVALES-CP (Chemistry with Parallel algorithm) in this study. The resulting code was used to study the gas–liquid two phase jet and combustion under various diesel engine-like conditions in a constant volume vessel. The results show that using the MUSCL scheme can accurately capture the spray shape and fuel vapor penetration using even a coarse grid, in comparison with the Sandia experimental data. Similarly good results are obtained for three single-component fuels, i-Octane (C8H18), n-Dodecanese (C12H26), and n-Hexadecane (C16H34) with very different physical properties. Meanwhile the improved methodology is able to accurately predict ignition delay and flame lift-off length (LOL) under different oxygen concentrations from 10% to 21

Tunable output-frequency filter algorithm for imaging through scattering media under LED illumination

Science.gov (United States)

Zhou, Meiling; Singh, Alok Kumar; Pedrini, Giancarlo; Osten, Wolfgang; Min, Junwei; Yao, Baoli

2018-03-01

We present a tunable output-frequency filter (TOF) algorithm to reconstruct the object from noisy experimental data under low-power partially coherent illumination, such as LED, when imaging through scattering media. In the iterative algorithm, we employ Gaussian functions with different filter windows at different stages of iteration process to reduce corruption from experimental noise to search for a global minimum in the reconstruction. In comparison with the conventional iterative phase retrieval algorithm, we demonstrate that the proposed TOF algorithm achieves consistent and reliable reconstruction in the presence of experimental noise. Moreover, the spatial resolution and distinctive features are retained in the reconstruction since the filter is applied only to the region outside the object. The feasibility of the proposed method is proved by experimental results.

Numerical Investigation of Acoustic Emission Events of Argillaceous Sandstones under Confining Pressure

Directory of Open Access Journals (Sweden)

Zhaohui Chong

2017-01-01

Full Text Available At the laboratory scale, locating acoustic emission (AE events is a comparatively mature method for evaluating cracks in rock materials, and the method plays an important role in numerical simulations. This study is aimed at developing a quantitative method for the measurement of acoustic emission (AE events in numerical simulations. Furthermore, this method was applied to estimate the crack initiation, propagation, and coalescence in rock materials. The discrete element method-acoustic emission model (DEM-AE model was developed using an independent subprogram. This model was designed to calculate the scalar seismic tensor of particles in the process of movement and further to determine the magnitude of AE events. An algorithm for identifying the same spatiotemporal AE event is being presented. To validate the model, a systematic physical experiment and numerical simulation for argillaceous sandstones were performed to present a quantitative comparison of the results with confining pressure. The results showed good agreement in terms of magnitude and spatiotemporal evolution between the simulation and the physical experiment. Finally, the magnitude of AE events was analyzed, and the relationship between AE events and microcracks was discussed. This model can provide the research basis for preventing seismic hazards caused by underground coal mining.

Numerical Asymptotic Solutions Of Differential Equations

Science.gov (United States)

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 numerical model for simulating electroosmotic micro- and nanochannel flows under non-Boltzmann equilibrium

Energy Technology Data Exchange (ETDEWEB)

Kim, Kyoungjin; Kwak, Ho Sang [School of Mechanical Engineering, Kumoh National Institute of Technology, 1 Yangho, Gumi, Gyeongbuk 730-701 (Korea, Republic of); Song, Tae-Ho, E-mail: kimkj@kumoh.ac.kr, E-mail: hskwak@kumoh.ac.kr, E-mail: thsong@kaist.ac.kr [Department of Mechanical, Aerospace and Systems Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong, Yuseong, Daejeon 305-701 (Korea, Republic of)

2011-08-15

This paper describes a numerical model for simulating electroosmotic flows (EOFs) under non-Boltzmann equilibrium in a micro- and nanochannel. The transport of ionic species is represented by employing the Nernst-Planck equation. Modeling issues related to numerical difficulties are discussed, which include the handling of boundary conditions based on surface charge density, the associated treatment of electric potential and the evasion of nonlinearity due to the electric body force. The EOF in the entrance region of a straight channel is examined. The numerical results show that the present model is useful for the prediction of the EOFs requiring a fine resolution of the electric double layer under either the Boltzmann equilibrium or non-equilibrium. Based on the numerical results, the correlation between the surface charge density and the zeta potential is investigated.

Algorithmic mathematics

CERN Document Server

Hougardy, Stefan

2016-01-01

Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

Science.gov (United States)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Distributed parameter estimation in unreliable sensor networks via broadcast gossip algorithms.

Science.gov (United States)

Wang, Huiwei; Liao, Xiaofeng; Wang, Zidong; Huang, Tingwen; Chen, Guo

2016-01-01

In this paper, we present an asynchronous algorithm to estimate the unknown parameter under an unreliable network which allows new sensors to join and old sensors to leave, and can tolerate link failures. Each sensor has access to partially informative measurements when it is awakened. In addition, the proposed algorithm can avoid the interference among messages and effectively reduce the accumulated measurement and quantization errors. Based on the theory of stochastic approximation, we prove that our proposed algorithm almost surely converges to the unknown parameter. Finally, we present a numerical example to assess the performance and the communication cost of the algorithm. Copyright © 2015 Elsevier Ltd. All rights reserved.

Theory and algorithms for solving large-scale numerical problems. Application to the management of electricity production

International Nuclear Information System (INIS)

Chiche, A.

2012-01-01

This manuscript deals with large-scale optimization problems, and more specifically with solving the electricity unit commitment problem arising at EDF. First, we focused on the augmented Lagrangian algorithm. The behavior of that algorithm on an infeasible convex quadratic optimization problem is analyzed. It is shown that the algorithm finds a point that satisfies the shifted constraints with the smallest possible shift in the sense of the Euclidean norm and that it minimizes the objective on the corresponding shifted constrained set. The convergence to such a point is realized at a global linear rate, which depends explicitly on the augmentation parameter. This suggests us a rule for determining the augmentation parameter to control the speed of convergence of the shifted constraint norm to zero. This rule has the advantage of generating bounded augmentation parameters even when the problem is infeasible. As a by-product, the algorithm computes the smallest translation in the Euclidean norm that makes the constraints feasible. Furthermore, this work provides solution methods for stochastic optimization industrial problems decomposed on a scenario tree, based on the progressive hedging algorithm introduced by [Rockafellar et Wets, 1991]. We also focus on the convergence of that algorithm. On the one hand, we offer a counter-example showing that the algorithm could diverge if its augmentation parameter is iteratively updated. On the other hand, we show how to recover the multipliers associated with the non-dualized constraints defined on the scenario tree from those associated with the corresponding constraints of the scenario subproblems. Their convergence is also analyzed for convex problems. The practical interest of theses solutions techniques is corroborated by numerical experiments performed on the electric production management problem. We apply the progressive hedging algorithm to a realistic industrial problem. More precisely, we solve the French medium

Numerical computation of solar neutrino flux attenuated by the MSW mechanism

Science.gov (United States)

Kim, Jai Sam; Chae, Yoon Sang; Kim, Jung Dae

1999-07-01

We compute the survival probability of an electron neutrino in its flight through the solar core experiencing the Mikheyev-Smirnov-Wolfenstein effect with all three neutrino species considered. We adopted a hybrid method that uses an accurate approximation formula in the non-resonance region and numerical integration in the non-adiabatic resonance region. The key of our algorithm is to use the importance sampling method for sampling the neutrino creation energy and position and to find the optimum radii to start and stop numerical integration. We further developed a parallel algorithm for a message passing parallel computer. By using an idea of job token, we have developed a dynamical load balancing mechanism which is effective under any irregular load distributions

A fuzzy controller design for nuclear research reactors using the particle swarm optimization algorithm

International Nuclear Information System (INIS)

Coban, Ramazan

2011-01-01

Research highlights: → A closed-loop fuzzy logic controller based on the particle swarm optimization algorithm was proposed for controlling the power level of nuclear research reactors. → The proposed control system was tested for various initial and desired power levels, and it could control the reactor successfully for most situations. → The proposed controller is robust against the disturbances. - Abstract: In this paper, a closed-loop fuzzy logic controller based on the particle swarm optimization algorithm is proposed for controlling the power level of nuclear research reactors. The principle of the fuzzy logic controller is based on the rules constructed from numerical experiments made by means of a computer code for the core dynamics calculation and from human operator's experience and knowledge. In addition to these intuitive and experimental design efforts, consequent parts of the fuzzy rules are optimally (or near optimally) determined using the particle swarm optimization algorithm. The contribution of the proposed algorithm to a reactor control system is investigated in details. The performance of the controller is also tested with numerical simulations in numerous operating conditions from various initial power levels to desired power levels, as well as under disturbance. It is shown that the proposed control system performs satisfactorily under almost all operating conditions, even in the case of very small initial power levels.

A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions.

Science.gov (United States)

He, Chenlong; Feng, Zuren; Ren, Zhigang

2018-01-01

In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.

A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions.

Directory of Open Access Journals (Sweden)

Chenlong He

Full Text Available In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.

Numerical Algorithms for Deterministic Impulse Control Models with Applications

NARCIS (Netherlands)

Grass, D.; Chahim, M.

2012-01-01

Abstract: In this paper we describe three different algorithms, from which two (as far as we know) are new in the literature. We take both the size of the jump as the jump times as decision variables. The first (new) algorithm considers an Impulse Control problem as a (multipoint) Boundary Value

Algorithmically specialized parallel computers

CERN Document Server

Snyder, Lawrence; Gannon, Dennis B

1985-01-01

Algorithmically Specialized Parallel Computers focuses on the concept and characteristics of an algorithmically specialized computer.This book discusses the algorithmically specialized computers, algorithmic specialization using VLSI, and innovative architectures. The architectures and algorithms for digital signal, speech, and image processing and specialized architectures for numerical computations are also elaborated. Other topics include the model for analyzing generalized inter-processor, pipelined architecture for search tree maintenance, and specialized computer organization for raster

Numerical Analysis of Ginzburg-Landau Models for Superconductivity.

Science.gov (United States)

Coskun, Erhan

Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.

Numerical algorithms in secondary creep

International Nuclear Information System (INIS)

Feijoo, R.A.; Taroco, E.

1980-01-01

The problem of stationary creep is presented as well as its variational formulation, when weak constraints are established, capable of assuring one single solution. A second, so-called elasto-creep problem, is further analysed, together with its variational formulation. It is shown that its stationary solution coincides with that of the stationary creep and the advantages of this formulation with respect to the former one is emphasized. Some numerical applications showing the efficiency of the method propesed are finally presented [pt

A subzone reconstruction algorithm for efficient staggered compatible remapping

Energy Technology Data Exchange (ETDEWEB)

Starinshak, D.P., E-mail: starinshak1@llnl.gov; Owen, J.M., E-mail: mikeowen@llnl.gov

2015-09-01

Staggered-grid Lagrangian hydrodynamics algorithms frequently make use of subzonal discretization of state variables for the purposes of improved numerical accuracy, generality to unstructured meshes, and exact conservation of mass, momentum, and energy. For Arbitrary Lagrangian–Eulerian (ALE) methods using a geometric overlay, it is difficult to remap subzonal variables in an accurate and efficient manner due to the number of subzone–subzone intersections that must be computed. This becomes prohibitive in the case of 3D, unstructured, polyhedral meshes. A new procedure is outlined in this paper to avoid direct subzonal remapping. The new algorithm reconstructs the spatial profile of a subzonal variable using remapped zonal and nodal representations of the data. The reconstruction procedure is cast as an under-constrained optimization problem. Enforcing conservation at each zone and node on the remapped mesh provides the set of equality constraints; the objective function corresponds to a quadratic variation per subzone between the values to be reconstructed and a set of target reference values. Numerical results for various pure-remapping and hydrodynamics tests are provided. Ideas for extending the algorithm to staggered-grid radiation-hydrodynamics are discussed as well as ideas for generalizing the algorithm to include inequality constraints.

Linear programming algorithms and applications

CERN Document Server

Vajda, S

1981-01-01

This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage­ ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...

Numerical simulation of deformation and fracture of space protective shell structures from concrete and fiber concrete under pulse loading

International Nuclear Information System (INIS)

Radchenko, P A; Batuev, S P; Radchenko, A V; Plevkov, V S

2015-01-01

This paper presents results of numerical simulation of interaction between aircraft Boeing 747-400 and protective shell of nuclear power plant. The shell is presented as complex multilayered cellular structure comprising layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was held three-dimensionally using the author's algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. The dynamics of stress-strain state and fracture of structure were studied. Destruction is described using two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of shell cellular structure—cells start to destruct in unloading wave, originating after output of compression wave to the free surfaces of cells. (paper)

Parallel Algorithm Solves Coupled Differential Equations

Science.gov (United States)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

Science.gov (United States)

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.

A modified three-term PRP conjugate gradient algorithm for optimization models.

Science.gov (United States)

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

Directory of Open Access Journals (Sweden)

Mio Horai

2016-01-01

Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

Improved numerical algorithm and experimental validation of a system thermal-hydraulic/CFD coupling method for multi-scale transient simulations of pool-type reactors

International Nuclear Information System (INIS)

Toti, A.; Vierendeels, J.; Belloni, F.

2017-01-01

Highlights: • A system thermal-hydraulic/CFD coupling methodology is proposed for high-fidelity transient flow analyses. • The method is based on domain decomposition and implicit numerical scheme. • A novel interface Quasi-Newton algorithm is implemented to improve stability and convergence rate. • Preliminary validation analyses on the TALL-3D experiment. - Abstract: The paper describes the development and validation of a coupling methodology between the best-estimate system thermal-hydraulic code RELAP5-3D and the CFD code FLUENT, conceived for high fidelity plant-scale safety analyses of pool-type reactors. The computational tool is developed to assess the impact of three-dimensional phenomena occurring in accidental transients such as loss of flow (LOF) in the research reactor MYRRHA, currently in the design phase at the Belgian Nuclear Research Centre, SCK• CEN. A partitioned, implicit domain decomposition coupling algorithm is implemented, in which the coupled domains exchange thermal-hydraulics variables at coupling boundary interfaces. Numerical stability and interface convergence rates are improved by a novel interface Quasi-Newton algorithm, which is compared in this paper with previously tested numerical schemes. The developed computational method has been assessed for validation purposes against the experiment performed at the test facility TALL-3D, operated by the Royal Institute of Technology (KTH) in Sweden. This paper details the results of the simulation of a loss of forced convection test, showing the capability of the developed methodology to predict transients influenced by local three-dimensional phenomena.

Parallel algorithms for nuclear reactor analysis via domain decomposition method

International Nuclear Information System (INIS)

Kim, Yong Hee

1995-02-01

In this thesis, the neutron diffusion equation in reactor physics is discretized by the finite difference method and is solved on a parallel computer network which is composed of T-800 transputers. T-800 transputer is a message-passing type MIMD (multiple instruction streams and multiple data streams) architecture. A parallel variant of Schwarz alternating procedure for overlapping subdomains is developed with domain decomposition. The thesis provides convergence analysis and improvement of the convergence of the algorithm. The convergence of the parallel Schwarz algorithms with DN(or ND), DD, NN, and mixed pseudo-boundary conditions(a weighted combination of Dirichlet and Neumann conditions) is analyzed for both continuous and discrete models in two-subdomain case and various underlying features are explored. The analysis shows that the convergence rate of the algorithm highly depends on the pseudo-boundary conditions and the theoretically best one is the mixed boundary conditions(MM conditions). Also it is shown that there may exist a significant discrepancy between continuous model analysis and discrete model analysis. In order to accelerate the convergence of the parallel Schwarz algorithm, relaxation in pseudo-boundary conditions is introduced and the convergence analysis of the algorithm for two-subdomain case is carried out. The analysis shows that under-relaxation of the pseudo-boundary conditions accelerates the convergence of the parallel Schwarz algorithm if the convergence rate without relaxation is negative, and any relaxation(under or over) decelerates convergence if the convergence rate without relaxation is positive. Numerical implementation of the parallel Schwarz algorithm on an MIMD system requires multi-level iterations: two levels for fixed source problems, three levels for eigenvalue problems. Performance of the algorithm turns out to be very sensitive to the iteration strategy. In general, multi-level iterations provide good performance when

Efficient algorithms for flow simulation related to nuclear reactor safety

International Nuclear Information System (INIS)

Gornak, Tatiana

2013-01-01

Safety analysis is of ultimate importance for operating Nuclear Power Plants (NPP). The overall modeling and simulation of physical and chemical processes occuring in the course of an accident is an interdisciplinary problem and has origins in fluid dynamics, numerical analysis, reactor technology and computer programming. The aim of the study is therefore to create the foundations of a multi-dimensional non-isothermal fluid model for a NPP containment and software tool based on it. The numerical simulations allow to analyze and predict the behavior of NPP systems under different working and accident conditions, and to develop proper action plans for minimizing the risks of accidents, and/or minimizing the consequences of possible accidents. A very large number of scenarios have to be simulated, and at the same time acceptable accuracy for the critical parameters, such as radioactive pollution, temperature, etc., have to be achieved. The existing software tools are either too slow, or not accurate enough. This thesis deals with developing customized algorithm and software tools for simulation of isothermal and non-isothermal flows in a containment pool of NPP. Requirements to such a software are formulated, and proper algorithms are presented. The goal of the work is to achieve a balance between accuracy and speed of calculation, and to develop customized algorithm for this special case. Different discretization and solution approaches are studied and those which correspond best to the formulated goal are selected, adjusted, and when possible, analysed. Fast directional splitting algorithm for Navier-Stokes equations in complicated geometries, in presence of solid and porous obstacles, is in the core of the algorithm. Developing suitable pre-processor and customized domain decomposition algorithms are essential part of the overall algorithm amd software. Results from numerical simulations in test geometries and in real geometries are presented and discussed.

Algorithms

Indian Academy of Sciences (India)

ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...

A Finite Difference, Semi-implicit, Equation-of-State Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples

KAUST Repository

Saavedra, Sebastian

2012-07-01

The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance (VB), two-phase, equation-of-state, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and composition-dependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PR-EOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phase-splitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programming development.

A Hybrid Genetic-Simulated Annealing Algorithm for the Location-Inventory-Routing Problem Considering Returns under E-Supply Chain Environment

Science.gov (United States)

Guo, Hao; Fu, Jing

2013-01-01

Facility location, inventory control, and vehicle routes scheduling are critical and highly related problems in the design of logistics system for e-business. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Many of returned merchandise have no quality defects, which can reenter sales channels just after a simple repackaging process. Focusing on the existing problem in e-commerce logistics system, we formulate a location-inventory-routing problem model with no quality defects returns. To solve this NP-hard problem, an effective hybrid genetic simulated annealing algorithm (HGSAA) is proposed. Results of numerical examples show that HGSAA outperforms GA on computing time, optimal solution, and computing stability. The proposed model is very useful to help managers make the right decisions under e-supply chain environment. PMID:24489489

A hybrid genetic-simulated annealing algorithm for the location-inventory-routing problem considering returns under e-supply chain environment.

Science.gov (United States)

Li, Yanhui; Guo, Hao; Wang, Lin; Fu, Jing

2013-01-01

Facility location, inventory control, and vehicle routes scheduling are critical and highly related problems in the design of logistics system for e-business. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Many of returned merchandise have no quality defects, which can reenter sales channels just after a simple repackaging process. Focusing on the existing problem in e-commerce logistics system, we formulate a location-inventory-routing problem model with no quality defects returns. To solve this NP-hard problem, an effective hybrid genetic simulated annealing algorithm (HGSAA) is proposed. Results of numerical examples show that HGSAA outperforms GA on computing time, optimal solution, and computing stability. The proposed model is very useful to help managers make the right decisions under e-supply chain environment.

A Hybrid Genetic-Simulated Annealing Algorithm for the Location-Inventory-Routing Problem Considering Returns under E-Supply Chain Environment

Directory of Open Access Journals (Sweden)

Yanhui Li

2013-01-01

Full Text Available Facility location, inventory control, and vehicle routes scheduling are critical and highly related problems in the design of logistics system for e-business. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Many of returned merchandise have no quality defects, which can reenter sales channels just after a simple repackaging process. Focusing on the existing problem in e-commerce logistics system, we formulate a location-inventory-routing problem model with no quality defects returns. To solve this NP-hard problem, an effective hybrid genetic simulated annealing algorithm (HGSAA is proposed. Results of numerical examples show that HGSAA outperforms GA on computing time, optimal solution, and computing stability. The proposed model is very useful to help managers make the right decisions under e-supply chain environment.

Numerical simulation of void growth under dynamic loading

International Nuclear Information System (INIS)

Iqbal, A.

1996-01-01

Following a brief general review of developments in material behavior under high strain rates, a cylindrical cell surrounding a spherical void in OFHC copper is numerically simulated by Zerri-Armstrong model. This simulation results show that the plastic deformation tends to be concentrated in the vicinity of voids either in the axial or transverse direction depending upon the stress state. This event is associated with the accelerated void through accompanying coalescence causing ductile fracture. A3-node triangular mesh generation code used as input for finite element code is developed by a 'Central Generation' technique. (author)

Present status on numerical algorithms and benchmark tests for point kinetics and quasi-static approximate kinetics

International Nuclear Information System (INIS)

Ise, Takeharu

1976-12-01

Review studies have been made on algorithms of numerical analysis and benchmark tests on point kinetics and quasistatic approximate kinetics computer codes to perform efficiently benchmark tests on space-dependent neutron kinetics codes. Point kinetics methods have now been improved since they can be directly applied to the factorization procedures. Methods based on Pade rational function give numerically stable solutions and methods on matrix-splitting are interested in the fact that they are applicable to the direct integration methods. An improved quasistatic (IQ) approximation is the best and the most practical method; it is numerically shown that the IQ method has a high stability and precision and the computation time which is about one tenth of that of the direct method. IQ method is applicable to thermal reactors as well as fast reactors and especially fitted for fast reactors to which many time steps are necessary. Two-dimensional diffusion kinetics codes are most practicable though there exist also three-dimensional diffusion kinetics code as well as two-dimensional transport kinetics code. On developing a space-dependent kinetics code, in any case, it is desirable to improve the method so as to have a high computing speed for solving static diffusion and transport equations. (auth.)

Cell light scattering characteristic numerical simulation research based on FDTD algorithm

Science.gov (United States)

Lin, Xiaogang; Wan, Nan; Zhu, Hao; Weng, Lingdong

2017-01-01

In this study, finite-difference time-domain (FDTD) algorithm has been used to work out the cell light scattering problem. Before beginning to do the simulation contrast, finding out the changes or the differences between normal cells and abnormal cells which may be cancerous or maldevelopment is necessary. The preparation of simulation are building up the simple cell model of cell which consists of organelles, nucleus and cytoplasm and setting up the suitable precision of mesh. Meanwhile, setting up the total field scattering field source as the excitation source and far field projection analysis group is also important. Every step need to be explained by the principles of mathematic such as the numerical dispersion, perfect matched layer boundary condition and near-far field extrapolation. The consequences of simulation indicated that the position of nucleus changed will increase the back scattering intensity and the significant difference on the peak value of scattering intensity may result from the changes of the size of cytoplasm. The study may help us find out the regulations based on the simulation consequences and the regulations can be meaningful for early diagnosis of cancers.

Opposite Degree Algorithm and Its Applications

Directory of Open Access Journals (Sweden)

Xiao-Guang Yue

2015-12-01

Full Text Available The opposite (Opposite Degree, referred to as OD algorithm is an intelligent algorithm proposed by Yue Xiaoguang et al. Opposite degree algorithm is mainly based on the concept of opposite degree, combined with the idea of design of neural network and genetic algorithm and clustering analysis algorithm. The OD algorithm is divided into two sub algorithms, namely: opposite degree - numerical computation (OD-NC algorithm and opposite degree - Classification computation (OD-CC algorithm.

Fast quantum search algorithm for databases of arbitrary size and its implementation in a cavity QED system

International Nuclear Information System (INIS)

Li, H.Y.; Wu, C.W.; Liu, W.T.; Chen, P.X.; Li, C.Z.

2011-01-01

We propose a method for implementing the Grover search algorithm directly in a database containing any number of items based on multi-level systems. Compared with the searching procedure in the database with qubits encoding, our modified algorithm needs fewer iteration steps to find the marked item and uses the carriers of the information more economically. Furthermore, we illustrate how to realize our idea in cavity QED using Zeeman's level structure of atoms. And the numerical simulation under the influence of the cavity and atom decays shows that the scheme could be achieved efficiently within current state-of-the-art technology. -- Highlights: ► A modified Grover algorithm is proposed for searching in an arbitrary dimensional Hilbert space. ► Our modified algorithm requires fewer iteration steps to find the marked item. ► The proposed method uses the carriers of the information more economically. ► A scheme for a six-item Grover search in cavity QED is proposed. ► Numerical simulation under decays shows that the scheme can be achieved with enough fidelity.

Blind signal processing algorithms under DC biased Gaussian noise

Science.gov (United States)

Kim, Namyong; Byun, Hyung-Gi; Lim, Jeong-Ok

2013-05-01

Distortions caused by the DC-biased laser input can be modeled as DC biased Gaussian noise and removing DC bias is important in the demodulation process of the electrical signal in most optical communications. In this paper, a new performance criterion and a related algorithm for unsupervised equalization are proposed for communication systems in the environment of channel distortions and DC biased Gaussian noise. The proposed criterion utilizes the Euclidean distance between the Dirac-delta function located at zero on the error axis and a probability density function of biased constant modulus errors, where constant modulus error is defined by the difference between the system out and a constant modulus calculated from the transmitted symbol points. From the results obtained from the simulation under channel models with fading and DC bias noise abruptly added to background Gaussian noise, the proposed algorithm converges rapidly even after the interruption of DC bias proving that the proposed criterion can be effectively applied to optical communication systems corrupted by channel distortions and DC bias noise.

BALL - biochemical algorithms library 1.3

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Stöckel Daniel

2010-10-01

Full Text Available Abstract Background The Biochemical Algorithms Library (BALL is a comprehensive rapid application development framework for structural bioinformatics. It provides an extensive C++ class library of data structures and algorithms for molecular modeling and structural bioinformatics. Using BALL as a programming toolbox does not only allow to greatly reduce application development times but also helps in ensuring stability and correctness by avoiding the error-prone reimplementation of complex algorithms and replacing them with calls into the library that has been well-tested by a large number of developers. In the ten years since its original publication, BALL has seen a substantial increase in functionality and numerous other improvements. Results Here, we discuss BALL's current functionality and highlight the key additions and improvements: support for additional file formats, molecular edit-functionality, new molecular mechanics force fields, novel energy minimization techniques, docking algorithms, and support for cheminformatics. Conclusions BALL is available for all major operating systems, including Linux, Windows, and MacOS X. It is available free of charge under the Lesser GNU Public License (LPGL. Parts of the code are distributed under the GNU Public License (GPL. BALL is available as source code and binary packages from the project web site at http://www.ball-project.org. Recently, it has been accepted into the debian project; integration into further distributions is currently pursued.

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

A new efficient algorithm for computing the imprecise reliability of monotone systems

International Nuclear Information System (INIS)

Utkin, Lev V.

2004-01-01

Reliability analysis of complex systems by partial information about reliability of components and by different conditions of independence of components may be carried out by means of the imprecise probability theory which provides a unified framework (natural extension, lower and upper previsions) for computing the system reliability. However, the application of imprecise probabilities to reliability analysis meets with a complexity of optimization problems which have to be solved for obtaining the system reliability measures. Therefore, an efficient simplified algorithm to solve and decompose the optimization problems is proposed in the paper. This algorithm allows us to practically implement reliability analysis of monotone systems under partial and heterogeneous information about reliability of components and under conditions of the component independence or the lack of information about independence. A numerical example illustrates the algorithm

New algorithms for motion error detection of numerical control machine tool by laser tracking measurement on the basis of GPS principle

Science.gov (United States)

Wang, Jindong; Chen, Peng; Deng, Yufen; Guo, Junjie

2018-01-01

As a three-dimensional measuring instrument, the laser tracker is widely used in industrial measurement. To avoid the influence of angle measurement error on the overall measurement accuracy, the multi-station and time-sharing measurement with a laser tracker is introduced on the basis of the global positioning system (GPS) principle in this paper. For the proposed method, how to accurately determine the coordinates of each measuring point by using a large amount of measured data is a critical issue. Taking detecting motion error of a numerical control machine tool, for example, the corresponding measurement algorithms are investigated thoroughly. By establishing the mathematical model of detecting motion error of a machine tool with this method, the analytical algorithm concerning on base station calibration and measuring point determination is deduced without selecting the initial iterative value in calculation. However, when the motion area of the machine tool is in a 2D plane, the coefficient matrix of base station calibration is singular, which generates a distortion result. In order to overcome the limitation of the original algorithm, an improved analytical algorithm is also derived. Meanwhile, the calibration accuracy of the base station with the improved algorithm is compared with that with the original analytical algorithm and some iterative algorithms, such as the Gauss-Newton algorithm and Levenberg-Marquardt algorithm. The experiment further verifies the feasibility and effectiveness of the improved algorithm. In addition, the different motion areas of the machine tool have certain influence on the calibration accuracy of the base station, and the corresponding influence of measurement error on the calibration result of the base station depending on the condition number of coefficient matrix are analyzed.

Interactive Numerical and Symbolic Analysis: A New Paradigm for Teaching Electronics

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Jean-Claude Thomassian

2008-09-01

Full Text Available Analog Insydes, Mathematica’s symbolic circuit analysis toolbox, uses modern algorithms of expression simplification depending on comparisons with a numerical reference solution of the circuit under investigation. Some insight is offered on how the complexity of an expression barrier is overcome followed by two classical examples, a BJT emitter follower and a MOSFET common-gate amplifier stage to illustrate the proposed method at work. A concluding section discusses that time spent teaching introductory electronics by computer-aided circuit analysis, interactive numerical and symbolic, is a worthwhile investment.

The BR eigenvalue algorithm

Energy Technology Data Exchange (ETDEWEB)

Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics

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.

Numerical analysis for the conjugate heat transfer of skin under various temperature conditions of contrast therapy

Energy Technology Data Exchange (ETDEWEB)

Park, Da Ae; Oh, Han Nah; Choi, Hyoung Gwon [Dept. of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of); Jeon, Byoung Jin; Kim, Eun Jeoung; Lee, Seung Deok [Yonsei University, Seoul (Korea, Republic of)

2015-11-15

In this paper, the contrast therapy of skin was numerically investigated by solving the conjugate heat transfer problem. A finite volume method based on the SIMPLE algorithm was adopted to solve the axisymmetric incompressible Navier-Stokes equations, coupled with an energy equation. These equations are strongly coupled with the Pennes bio-heat equation in order to consider the effect of blood perfusion rate. We investigated the thermal response of skin at some selected depths for various input temperature profiles of a stimulator for contrast therapy. From the numerical simulations, the regions with cold/hot threshold temperatures were found for five input temperature profiles. It was shown that the temperature varies mildly for different input profiles as the depth increases, owing to the Pennes effect. The input temperatures for effective hot/cold stimulation of dermis layer were found to be 47 degrees C and 7 degrees C, respectively. The present numerical results will be used for finding an optimal temperature profile of a stimulator for contrast therapy.

The instanton method and its numerical implementation in fluid mechanics

Science.gov (United States)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-08-01

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.

The instanton method and its numerical implementation in fluid mechanics

International Nuclear Information System (INIS)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-01-01

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin–Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler–Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier–Stokes equations. (topical review)

Numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation

International Nuclear Information System (INIS)

Braumann, Andreas; Kraft, Markus; Wagner, Wolfgang

2010-01-01

This paper is concerned with computational aspects of a multidimensional population balance model of a wet granulation process. Wet granulation is a manufacturing method to form composite particles, granules, from small particles and binders. A detailed numerical study of a stochastic particle algorithm for the solution of a five-dimensional population balance model for wet granulation is presented. Each particle consists of two types of solids (containing pores) and of external and internal liquid (located in the pores). Several transformations of particles are considered, including coalescence, compaction and breakage. A convergence study is performed with respect to the parameter that determines the number of numerical particles. Averaged properties of the system are computed. In addition, the ensemble is subdivided into practically relevant size classes and analysed with respect to the amount of mass and the particle porosity in each class. These results illustrate the importance of the multidimensional approach. Finally, the kinetic equation corresponding to the stochastic model is discussed.

Lorentz covariant canonical symplectic algorithms for dynamics of charged particles

Science.gov (United States)

Wang, Yulei; Liu, Jian; Qin, Hong

2016-12-01

In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSAs) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of a discrete symplectic structure and the Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which are difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when the Lorentz factor varies.

Numerical methods and parallel algorithms for fast transient strongly coupled fluid-structure dynamics

International Nuclear Information System (INIS)

Faucher, V.

2014-01-01

This HDR is dedicated to the research in the framework of fast transient dynamics for industrial fluid-structure systems carried in the Laboratory of Dynamic Studies from CEA, implementing new numerical methods for the modelling of complex systems and the parallel solution of large coupled problems on supercomputers. One key issue for the proposed approaches is the limitation to its minimum of the number of non-physical parameters, to cope with constraints arising from the area of usage of the concepts: safety for both nuclear applications (CEA, EDF) and aeronautics (ONERA), protection of the citizen (EC/JRC) in particular. Kinematic constraints strongly coupling structures (namely through unilateral contact) or fluid and structures (with both conformant or non-conformant meshes depending on the geometrical situation) are handled through exact methods including Lagrange Multipliers, with consequences on the solution strategy to be dealt with. This latter aspect makes EPX, the simulation code where the methods are integrated, a singular tool in the community of fast transient dynamics software. The document mainly relies on a description of the modelling needs for industrial fast transient scenarios, for nuclear applications in particular, and the proposed solutions built in the framework of the collaboration between CEA, EDF (via the LaMSID laboratory) and the LaMCoS laboratory from INSA Lyon. The main considered examples are the tearing of the fluid-filled tank after impact, the Code Disruptive Accident for a Generation IV reactor or the ruin of reinforced concrete structures under impact. Innovative models and parallel algorithms are thus proposed, allowing to carry out with robustness and performance the corresponding simulations on supercomputers made of interconnected multi-core nodes, with a strict preservation of the quality of the physical solution. This was particularly the main point of the ANR RePDyn project (2010-2013), with CEA as the pilot. (author

Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Algorithm for Large-Scale Box-Constrained Optimization

Directory of Open Access Journals (Sweden)

Qiuyu Wang

2014-01-01

descent method at first finite number of steps and then by conjugate gradient method subsequently. Under some appropriate conditions, we show that the algorithm converges globally. Numerical experiments and comparisons by using some box-constrained problems from CUTEr library are reported. Numerical comparisons illustrate that the proposed method is promising and competitive with the well-known method—L-BFGS-B.

Numerical studies of fermionic field theories at large-N

International Nuclear Information System (INIS)

Dickens, T.A.

1987-01-01

A description of an algorithm, which may be used to study large-N theories with or without fermions, is presented. As an initial test of the method, the spectrum of continuum QCD in 1 + 1 dimensions is determined and compared to previously obtained results. Exact solutions of 1 + 1 dimensional lattice versions of the free fermion theory, the Gross-Neveu model, and QCD are obtained. Comparison of these exact results with results from the numerical algorithm is used to test the algorithms, and more importantly, to determine the errors incurred from the approximations used in the numerical technique. Numerical studies of the above three lattice theories in higher dimensions are also presented. The results are again compared to exact solutions for free fermions and the Gross-Neveu model; perturbation theory is used to derive expansions with which the numerical results for QCD may be compared. The numerical algorithm may also be used to study the euclidean formulation of lattice gauge theories. Results for 1 + 1 dimensional euclidean lattice QCD are compared to the exact solution of this model

Numerical methods using Matlab

CERN Document Server

Lindfield, George

2012-01-01

Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use

Improved algorithm for solving nonlinear parabolized stability equations

International Nuclear Information System (INIS)

Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

2016-01-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

Selective epidemic vaccination under the performant routing algorithms

Science.gov (United States)

Bamaarouf, O.; Alweimine, A. Ould Baba; Rachadi, A.; EZ-Zahraouy, H.

2018-04-01

Despite the extensive research on traffic dynamics and epidemic spreading, the effect of the routing algorithms strategies on the traffic-driven epidemic spreading has not received an adequate attention. It is well known that more performant routing algorithm strategies are used to overcome the congestion problem. However, our main result shows unexpectedly that these algorithms favor the virus spreading more than the case where the shortest path based algorithm is used. In this work, we studied the virus spreading in a complex network using the efficient path and the global dynamic routing algorithms as compared to shortest path strategy. Some previous studies have tried to modify the routing rules to limit the virus spreading, but at the expense of reducing the traffic transport efficiency. This work proposed a solution to overcome this drawback by using a selective vaccination procedure instead of a random vaccination used often in the literature. We found that the selective vaccination succeeded in eradicating the virus better than a pure random intervention for the performant routing algorithm strategies.

Numerical Optimization Algorithms and Software for Systems Biology

Energy Technology Data Exchange (ETDEWEB)

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.

A New Modified Firefly Algorithm

Directory of Open Access Journals (Sweden)

Medha Gupta

2016-07-01

Full Text Available Nature inspired meta-heuristic algorithms studies the emergent collective intelligence of groups of simple agents. Firefly Algorithm is one of the new such swarm-based metaheuristic algorithm inspired by the flashing behavior of fireflies. The algorithm was first proposed in 2008 and since then has been successfully used for solving various optimization problems. In this work, we intend to propose a new modified version of Firefly algorithm (MoFA and later its performance is compared with the standard firefly algorithm along with various other meta-heuristic algorithms. Numerical studies and results demonstrate that the proposed algorithm is superior to existing algorithms.

Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

Science.gov (United States)

Chen, Wei

2015-07-01

In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

Solvent-assisted multistage nonequilibrium electron transfer in rigid supramolecular systems: Diabatic free energy surfaces and algorithms for numerical simulations

Science.gov (United States)

Feskov, Serguei V.; Ivanov, Anatoly I.

2018-03-01

An approach to the construction of diabatic free energy surfaces (FESs) for ultrafast electron transfer (ET) in a supramolecule with an arbitrary number of electron localization centers (redox sites) is developed, supposing that the reorganization energies for the charge transfers and shifts between all these centers are known. Dimensionality of the coordinate space required for the description of multistage ET in this supramolecular system is shown to be equal to N - 1, where N is the number of the molecular centers involved in the reaction. The proposed algorithm of FES construction employs metric properties of the coordinate space, namely, relation between the solvent reorganization energy and the distance between the two FES minima. In this space, the ET reaction coordinate zn n' associated with electron transfer between the nth and n'th centers is calculated through the projection to the direction, connecting the FES minima. The energy-gap reaction coordinates zn n' corresponding to different ET processes are not in general orthogonal so that ET between two molecular centers can create nonequilibrium distribution, not only along its own reaction coordinate but along other reaction coordinates too. This results in the influence of the preceding ET steps on the kinetics of the ensuing ET. It is important for the ensuing reaction to be ultrafast to proceed in parallel with relaxation along the ET reaction coordinates. Efficient algorithms for numerical simulation of multistage ET within the stochastic point-transition model are developed. The algorithms are based on the Brownian simulation technique with the recrossing-event detection procedure. The main advantages of the numerical method are (i) its computational complexity is linear with respect to the number of electronic states involved and (ii) calculations can be naturally parallelized up to the level of individual trajectories. The efficiency of the proposed approach is demonstrated for a model

Consumers' Kansei Needs Clustering Method for Product Emotional Design Based on Numerical Design Structure Matrix and Genetic Algorithms.

Science.gov (United States)

Yang, Yan-Pu; Chen, Deng-Kai; Gu, Rong; Gu, Yu-Feng; Yu, Sui-Huai

2016-01-01

Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design.

Efficiency Analysis of the Parallel Implementation of the SIMPLE Algorithm on Multiprocessor Computers

Science.gov (United States)

Lashkin, S. V.; Kozelkov, A. S.; Yalozo, A. V.; Gerasimov, V. Yu.; Zelensky, D. K.

2017-12-01

This paper describes the details of the parallel implementation of the SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. The iteration schemes for the serial and parallel versions of the SIMPLE algorithm are implemented. In the description of the parallel implementation, special attention is paid to computational data exchange among processors under the condition of the grid model decomposition using fictitious cells. We discuss the specific features for the storage of distributed matrices and implementation of vector-matrix operations in parallel mode. It is shown that the proposed way of matrix storage reduces the number of interprocessor exchanges. A series of numerical experiments illustrates the effect of the multigrid SLAE solver tuning on the general efficiency of the algorithm; the tuning involves the types of the cycles used (V, W, and F), the number of iterations of a smoothing operator, and the number of cells for coarsening. Two ways (direct and indirect) of efficiency evaluation for parallelization of the numerical algorithm are demonstrated. The paper presents the results of solving some internal and external flow problems with the evaluation of parallelization efficiency by two algorithms. It is shown that the proposed parallel implementation enables efficient computations for the problems on a thousand processors. Based on the results obtained, some general recommendations are made for the optimal tuning of the multigrid solver, as well as for selecting the optimal number of cells per processor.

Algorithm for study on the stressed-strained state of thermonuclear device vacuum chambers under dynamic loads

International Nuclear Information System (INIS)

Zhuravleva, A.M.; Litvinov, V.B.

1982-01-01

The problem of dynamic analysis of stressed-strained state of vacuum chambers is vital for large thermonuclear devices during the stall of the plasma-filament apd other tpansitional operation regimes when loading for a chamber are nonstationary. To plot a mathematical model the design of the vacuum chamber is discreted on the basis of the method of final elements. To approximate vacuum shell, a plate triangular element with 3 joint points and 5 parameters in the joint is used. It is obtained due to the unity of the bemded element and the element for the flat problem. To investigate nonstationary oscillations of vacuum chambers discreted on the basis of the method of final elements, it is suggested to use the numeric conversion of the Japlace transformation. On the basis of the algorithm suggested a program of numerical function conversion is developed. Test calculations have shown a good stability of the algorithm when selecting the values of transformation parameter in the range of lower intrinsic system frequencies. The advantage of the above method is in the fact that the time-structure shift function is found instantly in the form of the series for the whole time interval and does not require temporary steps, which bring about large expenses of counting time and error accumulation

Engineering local optimality in quantum Monte Carlo algorithms

Science.gov (United States)

Pollet, Lode; Van Houcke, Kris; Rombouts, Stefan M. A.

2007-08-01

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and can have a winding number larger than zero. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin- S models.

Development of a stereolithography (STL input and computer numerical control (CNC output algorithm for an entry-level 3-D printer

Directory of Open Access Journals (Sweden)

Brown, Andrew

2014-08-01

Full Text Available This paper presents a prototype Stereolithography (STL file format slicing and tool-path generation algorithm, which serves as a data front-end for a Rapid Prototyping (RP entry- level three-dimensional (3-D printer. Used mainly in Additive Manufacturing (AM, 3-D printers are devices that apply plastic, ceramic, and metal, layer by layer, in all three dimensions on a flat surface (X, Y, and Z axis. 3-D printers, unfortunately, cannot print an object without a special algorithm that is required to create the Computer Numerical Control (CNC instructions for printing. An STL algorithm therefore forms a critical component for Layered Manufacturing (LM, also referred to as RP. The purpose of this study was to develop an algorithm that is capable of processing and slicing an STL file or multiple files, resulting in a tool-path, and finally compiling a CNC file for an entry-level 3- D printer. The prototype algorithm was implemented for an entry-level 3-D printer that utilises the Fused Deposition Modelling (FDM process or Solid Freeform Fabrication (SFF process; an AM technology. Following an experimental method, the full data flow path for the prototype algorithm was developed, starting with STL data files, and then processing the STL data file into a G-code file format by slicing the model and creating a tool-path. This layering method is used by most 3-D printers to turn a 2-D object into a 3-D object. The STL algorithm developed in this study presents innovative opportunities for LM, since it allows engineers and architects to transform their ideas easily into a solid model in a fast, simple, and cheap way. This is accomplished by allowing STL models to be sliced rapidly, effectively, and without error, and finally to be processed and prepared into a G-code print file.

The quantum walk search algorithm: Factors affecting efficiency

OpenAIRE

Lovett, Neil B.; Everitt, Matthew; Heath, Robert M.; Kendon, Viv

2011-01-01

We numerically study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA \\textbf{67} 052307] and the factors which affect its efficiency in finding an individual state from an unsorted set. Previous work has focused purely on the effects of the dimensionality of the dataset to be searched. Here, we consider the effects of interpolating between dimensions, connectivity of the dataset, and the possibility of disorder in the underlying substrate: all these factors affect the effic...

Scientific applications and numerical algorithms on the midas multiprocessor system

International Nuclear Information System (INIS)

Logan, D.; Maples, C.

1986-01-01

The MIDAS multiprocessor system is a multi-level, hierarchial structure designed at the Advanced Computer Architecture Laboratory of the University of California's Lawrence Berkeley Laboratory. A two-stage, 11-processor system has been operational for over a year and is currently undergoing expansion. It has been employed to investigate the performance of different methods of decomposing various problems and algorithms into a multiprocessor environment. The results of such tests on a variety of applications such as scientific data analysis, Monte Carlo calculations, and image processing, are discussed. Often such decompositions involve investigating the parallel structure of fundamental algorithms. Several basic algorithms dealing with random number generation, matrix diagonalization, fast Fourier transforms, and finite element methods in solving partial differential equations are also discussed. The performance and projected extensibilities of these decompositions on the MIDAS system are reported

Numerical simulation methods to richtmyer-meshkov instabilities

International Nuclear Information System (INIS)

Zhou Ning; Yu Yan; Tang Weijun

2003-01-01

Front tracking algorithms have generally assumed that the computational medium is divided into piece-wise smooth subdomains bounded by interfaces and that strong wave interactions are solved via Riemann solutions. However, in multi-dimensional cases, the Riemann solution of multiple shock wave interactions are far more complicated and still subject to analytical study. For this reason, it is very desirable to be able to track contact discontinuities only. A new numerical algorithm to couple a tracked contact surface and an untracked strong shock wave are described. The new tracking algorithm reduces the complication of computation, and maintains the sharp resolution of the contact surface. The numerical results are good. (authors)

Bearing Fault Diagnosis under Variable Speed Using Convolutional Neural Networks and the Stochastic Diagonal Levenberg-Marquardt Algorithm

Directory of Open Access Journals (Sweden)

Viet Tra

2017-12-01

Full Text Available This paper presents a novel method for diagnosing incipient bearing defects under variable operating speeds using convolutional neural networks (CNNs trained via the stochastic diagonal Levenberg-Marquardt (S-DLM algorithm. The CNNs utilize the spectral energy maps (SEMs of the acoustic emission (AE signals as inputs and automatically learn the optimal features, which yield the best discriminative models for diagnosing incipient bearing defects under variable operating speeds. The SEMs are two-dimensional maps that show the distribution of energy across different bands of the AE spectrum. It is hypothesized that the variation of a bearing’s speed would not alter the overall shape of the AE spectrum rather, it may only scale and translate it. Thus, at different speeds, the same defect would yield SEMs that are scaled and shifted versions of each other. This hypothesis is confirmed by the experimental results, where CNNs trained using the S-DLM algorithm yield significantly better diagnostic performance under variable operating speeds compared to existing methods. In this work, the performance of different training algorithms is also evaluated to select the best training algorithm for the CNNs. The proposed method is used to diagnose both single and compound defects at six different operating speeds.

Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

International Nuclear Information System (INIS)

Wei, J.; Yang, S.

2013-01-01

In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

Numerical linear algebra a concise introduction with Matlab and Julia

CERN Document Server

Bornemann, Folkmar

2018-01-01

This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.

Archimedean copula estimation of distribution algorithm based on artificial bee colony algorithm

Institute of Scientific and Technical Information of China (English)

Haidong Xu; Mingyan Jiang; Kun Xu

2015-01-01

The artificial bee colony (ABC) algorithm is a com-petitive stochastic population-based optimization algorithm. How-ever, the ABC algorithm does not use the social information and lacks the knowledge of the problem structure, which leads to in-sufficiency in both convergent speed and searching precision. Archimedean copula estimation of distribution algorithm (ACEDA) is a relatively simple, time-economic and multivariate correlated EDA. This paper proposes a novel hybrid algorithm based on the ABC algorithm and ACEDA cal ed Archimedean copula estima-tion of distribution based on the artificial bee colony (ACABC) algorithm. The hybrid algorithm utilizes ACEDA to estimate the distribution model and then uses the information to help artificial bees to search more efficiently in the search space. Six bench-mark functions are introduced to assess the performance of the ACABC algorithm on numerical function optimization. Experimen-tal results show that the ACABC algorithm converges much faster with greater precision compared with the ABC algorithm, ACEDA and the global best (gbest)-guided ABC (GABC) algorithm in most of the experiments.

A Multiuser Detector Based on Artificial Bee Colony Algorithm for DS-UWB Systems

Directory of Open Access Journals (Sweden)

Zhendong Yin

2013-01-01

Full Text Available Artificial Bee Colony (ABC algorithm is an optimization algorithm based on the intelligent behavior of honey bee swarm. The ABC algorithm was developed to solve optimizing numerical problems and revealed premising results in processing time and solution quality. In ABC, a colony of artificial bees search for rich artificial food sources; the optimizing numerical problems are converted to the problem of finding the best parameter which minimizes an objective function. Then, the artificial bees randomly discover a population of initial solutions and then iteratively improve them by employing the behavior: moving towards better solutions by means of a neighbor search mechanism while abandoning poor solutions. In this paper, an efficient multiuser detector based on a suboptimal code mapping multiuser detector and artificial bee colony algorithm (SCM-ABC-MUD is proposed and implemented in direct-sequence ultra-wideband (DS-UWB systems under the additive white Gaussian noise (AWGN channel. The simulation results demonstrate that the BER and the near-far effect resistance performances of this proposed algorithm are quite close to those of the optimum multiuser detector (OMD while its computational complexity is much lower than that of OMD. Furthermore, the BER performance of SCM-ABC-MUD is not sensitive to the number of active users and can obtain a large system capacity.

Improved algorithm for solving nonlinear parabolized stability equations

Science.gov (United States)

Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

2016-08-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

Damage Detection in Railway Truss Bridges Employing Data Sensitivity under Bayesian Framework: A Numerical Investigation

Directory of Open Access Journals (Sweden)

Kanta Prajapat

2017-01-01

Full Text Available In general, for a structure it is quite difficult to get information about all of its modes through its dynamic response under ambient or external excitation. Therefore, it is vital to exhaustively use the available information in the acquired modal data to detect any damage in the structures. Further, in a Bayesian algorithm, it can be quite beneficial if a damage localization algorithm is first used to localize damage in the structure. In this way, the number of unknown parameters in the Bayesian algorithm can be reduced significantly and thus, the efficiency of Bayesian algorithm can be enhanced. This study exploits a mode shape and its derivative based approach to localize damage in truss type structures. For damage quantification purpose, a parameter sensitivity based prediction error variance approach in Bayesian model updating is employed, which allows extracting maximum information available in the modal data. This work employs the sensitivity based Bayesian algorithm to determine the posterior confidence in truss type railway bridges. Results of the study show that the proposed approach can efficiently detect and quantify damage in railway truss bridges.

Research on Geometric Positioning Algorithm of License Plate in Multidimensional Parameter Space

Directory of Open Access Journals (Sweden)

Yinhua Huan

2014-05-01

Full Text Available Considering features of vehicle license plate location method which commonly used, in order to search a consistent location for reference images with license plates feature in multidimensional parameter space, a new algorithm of geometric location is proposed. Geometric location algorithm main include model training and real time search. Which not only adapt the gray-scale linearity and the gray non-linear changes, but also support changes of scale and angle. Compared with the mainstream locating software, numerical results shows under the same test conditions that the position deviation of geometric positioning algorithm is less than 0.5 pixel. Without taking into account the multidimensional parameter space, Geometric positioning algorithm position deviation is less than 1.0 pixel and angle deviation is less than 1.0 degree taking into account the multidimensional parameter space. This algorithm is robust, simple, practical and is better than the traditional method.

Scalable algorithms for contact problems

CERN Document Server

Dostál, Zdeněk; Sadowská, Marie; Vondrák, Vít

2016-01-01

This book presents a comprehensive and self-contained treatment of the authors’ newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. It covers BEM discretization, jumping coefficients, floating bodies, mortar non-penetration conditions, etc. The exposition is divided into four parts, the first of which reviews appropriate facets of linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete, including continuous formulation, discretization, decomposition, optimality results, and numerical experimen...

Experimental and Numerical Investigation of Local Scour Around Submarine Piggyback Pipeline Under Steady Current

Science.gov (United States)

Zhao, Enjin; Shi, Bing; Qu, Ke; Dong, Wenbin; Zhang, Jing

2018-04-01

As a new type of submarine pipeline, the piggyback pipeline has been gradually adopted in engineering practice to enhance the performance and safety of submarine pipelines. However, limited simulation work and few experimental studies have been published on the scour around the piggyback pipeline under steady current. This study numerically and experimentally investigates the local scour of the piggyback pipe under steady current. The influence of prominent factors such as pipe diameter, inflow Reynolds number, and gap between the main and small pipes, on the maximum scour depth have been examined and discussed in detail. Furthermore, one formula to predict the maximum scour depth under the piggyback pipeline has been derived based on the theoretical analysis of scour equilibrium. The feasibility of the proposed formula has been effectively calibrated by both experimental data and numerical results. The findings drawn from this study are instructive in the future design and application of the piggyback pipeline.

Using Coevolution Genetic Algorithm with Pareto Principles to Solve Project Scheduling Problem under Duration and Cost Constraints

Directory of Open Access Journals (Sweden)

Alexandr Victorovich Budylskiy

2014-06-01

Full Text Available This article considers the multicriteria optimization approach using the modified genetic algorithm to solve the project-scheduling problem under duration and cost constraints. The work contains the list of choices for solving this problem. The multicriteria optimization approach is justified here. The study describes the Pareto principles, which are used in the modified genetic algorithm. We identify the mathematical model of the project-scheduling problem. We introduced the modified genetic algorithm, the ranking strategies, the elitism approaches. The article includes the example.

Numerical Analysis on Failure Modes and Mechanisms of Mine Pillars under Shear Loading

Directory of Open Access Journals (Sweden)

Tianhui Ma

2016-01-01

Full Text Available Severe damage occurs frequently in mine pillars subjected to shear stresses. The empirical design charts or formulas for mine pillars are not applicable to orebodies under shear. In this paper, the failure process of pillars under shear stresses was investigated by numerical simulations using the rock failure process analysis (RFPA 2D software. The numerical simulation results indicate that the strength of mine pillars and the corresponding failure mode vary with different width-to-height ratios and dip angles. With increasing dip angle, stress concentration first occurs at the intersection between the pillar and the roof, leading to formation of microcracks. Damage gradually develops from the surface to the core of the pillar. The damage process is tracked with acoustic emission monitoring. The study in this paper can provide an effective means for understanding the failure mechanism, planning, and design of mine pillars.

Numerical Simulation of single-stage axial fan operation under dusty flow conditions

Science.gov (United States)

Minkov, L. L.; Pikushchak, E. V.

2017-11-01

Assessment of the aerodynamic efficiency of the single-stage axial flow fan under dusty flow conditions based on a numerical simulation using the computational package Ansys-Fluent is proposed. The influence of dust volume fraction on the dependences of the air volume flow rate and the pressure drop on the rotational speed of rotor is demonstrated. Matching functions for formulas describing a pressure drop and volume flow rate in dependence on the rotor speed and dust content are obtained by numerical simulation for the single-stage axial fan. It is shown that the aerodynamic efficiency of the single-stage axial flow fan decreases exponentially with increasing volume content of dust in the air.

Numerical analysis

CERN Document Server

Scott, L Ridgway

2011-01-01

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that ex...

Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Karlsen, K.H.; Risebro, N.H.; Towers, J.D.

2001-10-01

We consider a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a nonlinear hyperbolic partial differential equation with a flux function that depends discontinuously on height. The purpose of this contribution is to present and demonstrate two numerical methods for simulating continuous sedimentation: a front tracking method and a finite finite difference method. The basic building blocks in the front tracking method are the solutions of a finite number of certain Riemann problems and a procedure for tracking local collisions of shocks. The solutions of the Riemann problems are recalled herein and the front tracking algorithm is described. As an alternative to the front tracking method, a simple scalar finite difference algorithm is proposed. This method is based on discretizing the spatially varying flux parameters on a mesh that is staggered with respect to that of the conserved variable, resulting in a straightforward generalization of the well-known Engquist-Osher upwind finite difference method. The result is an easily implemented upwind shock capturing method. Numerical examples demonstrate that the front tracking and finite difference methods can be used as efficient and accurate simulation tools for continuous sedimentation. The numerical results for the finite difference method indicate that discontinuities in the local solids concentration are resolved sharply and agree with those produced by the front tracking method. The latter is free of numerical dissipation, which leads to sharply resolved concentration discontinuities, but is more complicated to implement than the former. Available mathematical results for the proposed numerical methods are also briefly reviewed. (author)

A Robust Parallel Algorithm for Combinatorial Compressed Sensing

Science.gov (United States)

Mendoza-Smith, Rodrigo; Tanner, Jared W.; Wechsung, Florian

2018-04-01

In previous work two of the authors have shown that a vector $x \\in \\mathbb{R}^n$ with at most $k Parallel-$\\ell_0$ decoding algorithm, where $\\mathrm{nnz}(A)$ denotes the number of nonzero entries in $A \\in \\mathbb{R}^{m \\times n}$. In this paper we present the Robust-$\\ell_0$ decoding algorithm, which robustifies Parallel-$\\ell_0$ when the sketch $Ax$ is corrupted by additive noise. This robustness is achieved by approximating the asymptotic posterior distribution of values in the sketch given its corrupted measurements. We provide analytic expressions that approximate these posteriors under the assumptions that the nonzero entries in the signal and the noise are drawn from continuous distributions. Numerical experiments presented show that Robust-$\\ell_0$ is superior to existing greedy and combinatorial compressed sensing algorithms in the presence of small to moderate signal-to-noise ratios in the setting of Gaussian signals and Gaussian additive noise.

A Hybrid Parallel Preconditioning Algorithm For CFD

Science.gov (United States)

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.

Effect of object functions on tomographic reconstruction a numerical study

International Nuclear Information System (INIS)

Babu Rao, C.; Baldev Raj; Ravichandran, V.S.; Munshi, P.

1996-01-01

Convolution back projection is the most widely used algorithm of computed tomography (CT). Theoretical studies show that under ideal conditions, the error in the reconstruction can be correlated with the second fourier space derivative of filter function and with the Laplacian of the object function. This paper looks into the second aspect of the error function. In this paper a systematic numerical study is presented on the effect to object functions on global and local errors. (author)

Numerical tools to predict the environmental loads for offshore structures under extreme weather conditions

Science.gov (United States)

Wu, Yanling

2018-05-01

In this paper, the extreme waves were generated using the open source computational fluid dynamic (CFD) tools — OpenFOAM and Waves2FOAM — using linear and nonlinear NewWave input. They were used to conduct the numerical simulation of the wave impact process. Numerical tools based on first-order (with and without stretching) and second-order NewWave are investigated. The simulation to predict force loading for the offshore platform under the extreme weather condition is implemented and compared.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

Science.gov (United States)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

Optimization model of conventional missile maneuvering route based on improved Floyd algorithm

Science.gov (United States)

Wu, Runping; Liu, Weidong

2018-04-01

Missile combat plays a crucial role in the victory of war under high-tech conditions. According to the characteristics of maneuver tasks of conventional missile units in combat operations, the factors influencing road maneuvering are analyzed. Based on road distance, road conflicts, launching device speed, position requirements, launch device deployment, Concealment and so on. The shortest time optimization model was built to discuss the situation of road conflict and the strategy of conflict resolution. The results suggest that in the process of solving road conflict, the effect of node waiting is better than detour to another way. In this study, we analyzed the deficiency of the traditional Floyd algorithm which may limit the optimal way of solving road conflict, and put forward the improved Floyd algorithm, meanwhile, we designed the algorithm flow which would be better than traditional Floyd algorithm. Finally, throgh a numerical example, the model and the algorithm were proved to be reliable and effective.

Eco-physiological Baltic picoplankton analysis and its implementation in Synechoccocus species life cycle numerical algorithm

Science.gov (United States)

Cieszyńska, Agata; Śliwińska-Wilczewska, Sylwia

2017-04-01

mixtures of conditions were applied in the laboratory experiments. Results from these experiments were the foundation to create picocyanobacteria life cycle algorithm - pico-bioalgorithm. The form of algorithm bases on the Ecological Regional Ocean Model formulas for functional phytoplankton groups. According to this, in pico-bioalgorithm the dependence on temperature and salinity of water body and the occurrence of nutrients are provided along with the coefficients determining mortality of picoplankton cells and coefficients of respiration and growth rates. In order to prescribe the limiting properties, modified Michaelis-Menten formula with squared arguments as a limiting function was used. Picoplanktonic organisms are very specific and can live in environments, which may be initially defined as impossible for such organisms to survive. The issue of picoplanktonic species inhabiting the Baltic Sea needs to be explored in details. Present study and proposed algorithm comprise an important step in this scientific exploration. This work has been funded by the National Centre of Science project (contract number: 2012/07/N/ST10/03485) entitled: "Improved understanding of phytoplankton blooms in the Baltic Sea based on numerical models and existing data sets". The Author (AC) received funding from National Centre of Sciences in doctoral scholarship program (contract number: 2016/20/T/ST10/00214);

DiamondTorre Algorithm for High-Performance Wave Modeling

Directory of Open Access Journals (Sweden)

Vadim Levchenko

2016-08-01

Full Text Available Effective algorithms of physical media numerical modeling problems’ solution are discussed. The computation rate of such problems is limited by memory bandwidth if implemented with traditional algorithms. The numerical solution of the wave equation is considered. A finite difference scheme with a cross stencil and a high order of approximation is used. The DiamondTorre algorithm is constructed, with regard to the specifics of the GPGPU’s (general purpose graphical processing unit memory hierarchy and parallelism. The advantages of these algorithms are a high level of data localization, as well as the property of asynchrony, which allows one to effectively utilize all levels of GPGPU parallelism. The computational intensity of the algorithm is greater than the one for the best traditional algorithms with stepwise synchronization. As a consequence, it becomes possible to overcome the above-mentioned limitation. The algorithm is implemented with CUDA. For the scheme with the second order of approximation, the calculation performance of 50 billion cells per second is achieved. This exceeds the result of the best traditional algorithm by a factor of five.

An efficient macro-cell placement algorithm

NARCIS (Netherlands)

Aarts, E.H.L.; Bont, de F.M.J.; Korst, J.H.M.; Rongen, J.M.J.

1991-01-01

A new approximation algorithm is presented for the efficient handling of large macro-cell placement problems. The algorithm combines simulated annealing with new features based on a hierarchical approach and a divide-and-conquer technique. Numerical results show that these features can lead to a

Governance by algorithms

Directory of Open Access Journals (Sweden)

Francesca Musiani

2013-08-01

Full Text Available Algorithms are increasingly often cited as one of the fundamental shaping devices of our daily, immersed-in-information existence. Their importance is acknowledged, their performance scrutinised in numerous contexts. Yet, a lot of what constitutes 'algorithms' beyond their broad definition as “encoded procedures for transforming input data into a desired output, based on specified calculations” (Gillespie, 2013 is often taken for granted. This article seeks to contribute to the discussion about 'what algorithms do' and in which ways they are artefacts of governance, providing two examples drawing from the internet and ICT realm: search engine queries and e-commerce websites’ recommendations to customers. The question of the relationship between algorithms and rules is likely to occupy an increasingly central role in the study and the practice of internet governance, in terms of both institutions’ regulation of algorithms, and algorithms’ regulation of our society.

Numerical analysis of reactor internals under hydrodynamic loads

Energy Technology Data Exchange (ETDEWEB)

Kim, Da Hye; Chang, Yoon Suk [Kyung Hee Univ., Yongin (Korea, Republic of); Jhung, Myung Jo [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)

2013-10-15

In the present study, six kinds of major equipment of a typical reactor internals were identified by incorporating recent research trend. Based on this, detailed numerical models were developed and used for establishment of optimum analysis methodology subjected to hydrodynamic loads. As a result, stress values of the major equipment were calculated through the acoustic-structure analysis under periodic hydrodynamic load and the turbulence-structure analysis under random hydrodynamic load. The numerical analysis scheme can be used for development of preventive action plan and management procedures of the reactor internals. Reactor internals installed in a pressure vessel have been exposed to harsh environment such as high neutron irradiation and temperature with complex fluid flow. As the increase of operational years of NPPs(Nuclear Power Plants), possibility of functional loss of the reactor internals is increased due to degradation caused by radiation embrittlement, thermal aging, fatigue, corrosion and FIV(Flow-Induced Vibration) etc. In practice, defects were detected at core support structure as well as upper and lower parts of structural assembly in European and United States NPPs. Recently, in a GALL(Generic Aging Lessons Learned) report, US NRC(Nuclear Regulatory Commission) identified reactor internals as a high priority component and addressed relevant management programs. In Korea, similar activities have been conducted for long-term operation beyond design lifetime but most of them were limited to qualitative evaluation based on examination and maintenance programs. Therefore, not only to reduce repair and replacement efforts but also to secure the stability of NPPs, necessity for development of quantitative evaluation technique as well as establishment of preventive action plan and management procedures is on the rise. The FIV represents the structural vibration phenomenon induced by liquid flow and generally occurs at contact surfaces. In the present

High-order accurate numerical algorithm for three-dimensional transport prediction

Energy Technology Data Exchange (ETDEWEB)

Pepper, D W [Savannah River Lab., Aiken, SC; Baker, A J

1980-01-01

The numerical solution of the three-dimensional pollutant transport equation is obtained with the method of fractional steps; advection is solved by the method of moments and diffusion by cubic splines. Topography and variable mesh spacing are accounted for with coordinate transformations. First estimate wind fields are obtained by interpolation to grid points surrounding specific data locations. Numerical results agree with results obtained from analytical Gaussian plume relations for ideal conditions. The numerical model is used to simulate the transport of tritium released from the Savannah River Plant on 2 May 1974. Predicted ground level air concentration 56 km from the release point is within 38% of the experimentally measured value.

Numerical simulation of hydrodynamic performance of ship under oblique conditions

Directory of Open Access Journals (Sweden)

CHEN Zhiming

2018-02-01

Full Text Available [Objectives] This paper is intended to study the viscous flow field around a ship under oblique conditions and provide a research basis for ship maneuverability. [Methods] Using commercial software STRA-CCM+, the SST k-ω turbulence model is selected to predict the hydrodynamic performance of the KVLCC2 model at different drift angles, and predict the hull flow field. The pressure distribution of the ship model at different drift angles is observed and the vortex shedding of the ship's hull and constraint streamlines on the hull's surface are also observed. [Results] The results show that numerical simulation can satisfy the demands of engineering application in the prediction of the lateral force, yaw moment and hull surface pressure distribution of a ship. [Conclusions] The research results of this paper can provide valuable references for the study of the flow separation phenomenon under oblique conditions.

A numeric comparison of variable selection algorithms for supervised learning

International Nuclear Information System (INIS)

Palombo, G.; Narsky, I.

2009-01-01

Datasets in modern High Energy Physics (HEP) experiments are often described by dozens or even hundreds of input variables. Reducing a full variable set to a subset that most completely represents information about data is therefore an important task in analysis of HEP data. We compare various variable selection algorithms for supervised learning using several datasets such as, for instance, imaging gamma-ray Cherenkov telescope (MAGIC) data found at the UCI repository. We use classifiers and variable selection methods implemented in the statistical package StatPatternRecognition (SPR), a free open-source C++ package developed in the HEP community ( (http://sourceforge.net/projects/statpatrec/)). For each dataset, we select a powerful classifier and estimate its learning accuracy on variable subsets obtained by various selection algorithms. When possible, we also estimate the CPU time needed for the variable subset selection. The results of this analysis are compared with those published previously for these datasets using other statistical packages such as R and Weka. We show that the most accurate, yet slowest, method is a wrapper algorithm known as generalized sequential forward selection ('Add N Remove R') implemented in SPR.

Fluid Dynamics Theory, Computation, and Numerical Simulation

CERN Document Server

Pozrikidis, Constantine

2009-01-01

Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice. There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. Matlab codes are presented and discussed for ...

Numerical linear algebra with applications using Matlab

CERN Document Server

Ford, William

2014-01-01

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for

A bibliography on parallel and vector numerical algorithms

Science.gov (United States)

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.

Numerical and experimental characterization of ceramic pebble beds under cycling mechanical loading

Energy Technology Data Exchange (ETDEWEB)

Pupeschi, S., E-mail: pupeschi.simone@hotmail.it [Institute for Applied Materials, Karlsruhe Institute of Technology (KIT) (Germany); Knitter, R.; Kamlah, M. [Institute for Applied Materials, Karlsruhe Institute of Technology (KIT) (Germany); Gan, Y. [School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006 (Australia)

2016-11-15

Highlights: • The effect of cyclic loading on the mechanical response of pebble beds was assessed. • Numerical simulations were performed with KIT-DEM code. • The numerical simulations were compared with the experimental outcomes. • A good qualitative agreement between experimental and simulation results was found. • The pebble size distribution affects the mechanical response of the assemblies. - Abstract: All solid breeder concepts considered to be tested in ITER (International Thermonuclear Experimental Reactor), make use of lithium-based ceramics in the form of pebble-packed beds as tritium breeder. A thorough understanding of the thermal and mechanical properties of the ceramic pebble beds under fusion relevant conditions is essential for the design of the breeder blanket modules of future fusion reactors. In this study, the effect of cyclic loading on the mechanical behaviour of pebble bed assemblies was investigated using a Discrete Element Method (DEM) code. The numerical simulations were compared with the experimental outcomes. The results of numerical simulations show that the pebble size distribution affects noticeably the stress-strain behaviour of the assemblies. A good qualitative agreement between experimental and simulation results was found in terms of difference between residual strains of consecutive cycles. An increase of the oedometric modulus with the compressive load was observed for all investigated compositions in both experimental and DEM simulations. The numerical results show an increase of the oedometric modulus (E) with progressive compaction of the assemblies due to the cycling loading, while no significant influence of the pebbles size distribution was observed.

Numerical methods in software and analysis

CERN Document Server

Rice, John R

1992-01-01

Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm

A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints

International Nuclear Information System (INIS)

Jian Jinbao; Li Jianling; Mo Xingde

2006-01-01

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998),5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported

A novel algorithm of artificial immune system for high-dimensional function numerical optimization

Institute of Scientific and Technical Information of China (English)

DU Haifeng; GONG Maoguo; JIAO Licheng; LIU Ruochen

2005-01-01

Based on the clonal selection theory and immune memory theory, a novel artificial immune system algorithm, immune memory clonal programming algorithm (IMCPA), is put forward. Using the theorem of Markov chain, it is proved that IMCPA is convergent. Compared with some other evolutionary programming algorithms (like Breeder genetic algorithm), IMCPA is shown to be an evolutionary strategy capable of solving complex machine learning tasks, like high-dimensional function optimization, which maintains the diversity of the population and avoids prematurity to some extent, and has a higher convergence speed.

A new three-dimensional manufacturing service composition method under various structures using improved Flower Pollination Algorithm

Science.gov (United States)

Zhang, Wenyu; Yang, Yushu; Zhang, Shuai; Yu, Dejian; Chen, Yong

2018-05-01

With the growing complexity of customer requirements and the increasing scale of manufacturing services, how to select and combine the single services to meet the complex demand of the customer has become a growing concern. This paper presents a new manufacturing service composition method to solve the multi-objective optimization problem based on quality of service (QoS). The proposed model not only presents different methods for calculating the transportation time and transportation cost under various structures but also solves the three-dimensional composition optimization problem, including service aggregation, service selection, and service scheduling simultaneously. Further, an improved Flower Pollination Algorithm (IFPA) is proposed to solve the three-dimensional composition optimization problem using a matrix-based representation scheme. The mutation operator and crossover operator of the Differential Evolution (DE) algorithm are also used to extend the basic Flower Pollination Algorithm (FPA) to improve its performance. Compared to Genetic Algorithm, DE, and basic FPA, the experimental results confirm that the proposed method demonstrates superior performance than other meta heuristic algorithms and can obtain better manufacturing service composition solutions.

Highly uniform parallel microfabrication using a large numerical aperture system

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zi-Yu; Su, Ya-Hui, E-mail: ustcsyh@ahu.edu.cn, E-mail: dongwu@ustc.edu.cn [School of Electrical Engineering and Automation, Anhui University, Hefei 230601 (China); Zhang, Chen-Chu; Hu, Yan-Lei; Wang, Chao-Wei; Li, Jia-Wen; Chu, Jia-Ru; Wu, Dong, E-mail: ustcsyh@ahu.edu.cn, E-mail: dongwu@ustc.edu.cn [CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China)

2016-07-11

In this letter, we report an improved algorithm to produce accurate phase patterns for generating highly uniform diffraction-limited multifocal arrays in a large numerical aperture objective system. It is shown that based on the original diffraction integral, the uniformity of the diffraction-limited focal arrays can be improved from ∼75% to >97%, owing to the critical consideration of the aperture function and apodization effect associated with a large numerical aperture objective. The experimental results, e.g., 3 × 3 arrays of square and triangle, seven microlens arrays with high uniformity, further verify the advantage of the improved algorithm. This algorithm enables the laser parallel processing technology to realize uniform microstructures and functional devices in the microfabrication system with a large numerical aperture objective.

A Numerical Model for Trickle Bed Reactors

Science.gov (United States)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

Science.gov (United States)

Puckett, Elbridge Gerry; Turcotte, Donald L.; He, Ying; Lokavarapu, Harsha; Robey, Jonathan M.; Kellogg, Louise H.

2018-03-01

Geochemical observations of mantle-derived rocks favor a nearly homogeneous upper mantle, the source of mid-ocean ridge basalts (MORB), and heterogeneous lower mantle regions. Plumes that generate ocean island basalts are thought to sample the lower mantle regions and exhibit more heterogeneity than MORB. These regions have been associated with lower mantle structures known as large low shear velocity provinces (LLSVPS) below Africa and the South Pacific. The isolation of these regions is attributed to compositional differences and density stratification that, consequently, have been the subject of computational and laboratory modeling designed to determine the parameter regime in which layering is stable and understanding how layering evolves. Mathematical models of persistent compositional interfaces in the Earth's mantle may be inherently unstable, at least in some regions of the parameter space relevant to the mantle. Computing approximations to solutions of such problems presents severe challenges, even to state-of-the-art numerical methods. Some numerical algorithms for modeling the interface between distinct compositions smear the interface at the boundary between compositions, such as methods that add numerical diffusion or 'artificial viscosity' in order to stabilize the algorithm. We present two new algorithms for maintaining high-resolution and sharp computational boundaries in computations of these types of problems: a discontinuous Galerkin method with a bound preserving limiter and a Volume-of-Fluid interface tracking algorithm. We compare these new methods with two approaches widely used for modeling the advection of two distinct thermally driven compositional fields in mantle convection computations: a high-order accurate finite element advection algorithm with entropy viscosity and a particle method that carries a scalar quantity representing the location of each compositional field. All four algorithms are implemented in the open source finite

Spurious Numerical Solutions Of Differential Equations

Science.gov (United States)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Numerical methods: Analytical benchmarking in transport theory

International Nuclear Information System (INIS)

Ganapol, B.D.

1988-01-01

Numerical methods applied to reactor technology have reached a high degree of maturity. Certainly one- and two-dimensional neutron transport calculations have become routine, with several programs available on personal computer and the most widely used programs adapted to workstation and minicomputer computational environments. With the introduction of massive parallelism and as experience with multitasking increases, even more improvement in the development of transport algorithms can be expected. Benchmarking an algorithm is usually not a very pleasant experience for the code developer. Proper algorithmic verification by benchmarking involves the following considerations: (1) conservation of particles, (2) confirmation of intuitive physical behavior, and (3) reproduction of analytical benchmark results. By using today's computational advantages, new basic numerical methods have been developed that allow a wider class of benchmark problems to be considered

Two parameter-tuned metaheuristic algorithms for the multi-level lot sizing and scheduling problem

Directory of Open Access Journals (Sweden)

S.M.T. Fatemi Ghomi

2012-10-01

Full Text Available This paper addresses the problem of lot sizing and scheduling problem for n-products and m-machines in flow shop environment where setups among machines are sequence-dependent and can be carried over. Many products must be produced under capacity constraints and allowing backorders. Since lot sizing and scheduling problems are well-known strongly NP-hard, much attention has been given to heuristics and metaheuristics methods. This paper presents two metaheuristics algorithms namely, Genetic Algorithm (GA and Imperialist Competitive Algorithm (ICA. Moreover, Taguchi robust design methodology is employed to calibrate the parameters of the algorithms for different size problems. In addition, the parameter-tuned algorithms are compared against a presented lower bound on randomly generated problems. At the end, comprehensive numerical examples are presented to demonstrate the effectiveness of the proposed algorithms. The results showed that the performance of both GA and ICA are very promising and ICA outperforms GA statistically.

Numerical simulation of flow and heat transfer of continous cast steel slab under traveling magnetic field

Directory of Open Access Journals (Sweden)

Gong Haijun

2013-03-01

Full Text Available A unified numerical model for simulating solidification transport phenomena (STP of steel slab in electromagnetic continuous casting (EMCC process was developed. In order to solve the multi-physics fields coupled problem conveniently, the complicated bidirectional coupled process between EM and STP was simplified as a unidirectional one, and a FEM/FVM-combined numerical simulation technique was adopted. The traveling magnetic fields (TMFs applied to the EMCC process were calculated using the ANSYS11.0 software, and then the EM-data output by ANSYS were converted to FVM-format using a data-format conversion program developed previously. Thereafter, the governing equations were solved using a pressure-based Direct-SIMPLE algorithm. The simulation results of the STP in CC-process show that, due to the influences of Lorentz force and Joule heat, the two strong circulating flows and the temperature field can be obviously damped and changed once TMF with one pair of poles (1-POPs or 2-POPs is applied, which would accordingly improve the quality of casting. It was found in the present research that the integrated actions of 2-POPs TMF are superior to 1-POPs. All the computations indicate that the present numerical model of EM-STP as well as the FEM/FVM-combined technique is successful.

Numerical algorithms for uniform Airy-type asymptotic expansions

NARCIS (Netherlands)

N.M. Temme (Nico)

1997-01-01

textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing

Numerical simulation of wave-current interaction under strong wind conditions

Science.gov (United States)

Larrañaga, Marco; Osuna, Pedro; Ocampo-Torres, Francisco Javier

2017-04-01

Although ocean surface waves are known to play an important role in the momentum and other scalar transfer between the atmosphere and the ocean, most operational numerical models do not explicitly include the terms of wave-current interaction. In this work, a numerical analysis about the relative importance of the processes associated with the wave-current interaction under strong off-shore wind conditions in Gulf of Tehuantepec (the southern Mexican Pacific) was carried out. The numerical system includes the spectral wave model WAM and the 3D hydrodynamic model POLCOMS, with the vertical turbulent mixing parametrized by the kappa-epsilon closure model. The coupling methodology is based on the vortex-force formalism. The hydrodynamic model was forced at the open boundaries using the HYCOM database and the wave model was forced at the open boundaries by remote waves from the southern Pacific. The atmospheric forcing for both models was provided by a local implementation of the WRF model, forced at the open boundaries using the CFSR database. The preliminary analysis of the model results indicates an effect of currents on the propagation of the swell throughout the study area. The Stokes-Coriolis term have an impact on the transient Ekman transport by modifying the Ekman spiral, while the Stokes drift has an effect on the momentum advection and the production of TKE, where the later induces a deepening of the mixing layer. This study is carried out in the framework of the project CONACYT CB-2015-01 255377 and RugDiSMar Project (CONACYT 155793).

Real-Time Attitude Control Algorithm for Fast Tumbling Objects under Torque Constraint

Science.gov (United States)

Tsuda, Yuichi; Nakasuka, Shinichi

This paper describes a new control algorithm for achieving any arbitrary attitude and angular velocity states of a rigid body, even fast and complicated tumbling rotations, under some practical constraints. This technique is expected to be applied for the attitude motion synchronization to capture a non-cooperative, tumbling object in such missions as removal of debris from orbit, servicing broken-down satellites for repairing or inspection, rescue of manned vehicles, etc. For this objective, we have introduced a novel control algorithm called Free Motion Path Method (FMPM) in the previous paper, which was formulated as an open-loop controller. The next step of this consecutive work is to derive a closed-loop FMPM controller, and as the preliminary step toward the objective, this paper attempts to derive a conservative state variables representation of a rigid body dynamics. 6-Dimensional conservative state variables are introduced in place of general angular velocity-attitude angle representation, and how to convert between both representations are shown in this paper.

Numerical ductile tearing simulation of circumferential cracked pipe tests under dynamic loading conditions

Energy Technology Data Exchange (ETDEWEB)

Nam, Hyun Suk; Kim, Ji Soo; Ryu, Ho Wan; Kim, Yun Jae [Dept. of Mechanical Engineering, Korea University, Seoul (Korea, Republic of); Kim, Jin Weon [Dept. of Nuclear Engineering, Chosun University, Gwangju (Korea, Republic of)

2016-10-15

This paper presents a numerical method to simulate ductile tearing in cracked components under high strain rates using finite element damage analysis. The strain rate dependence on tensile properties and multiaxial fracture strain is characterized by the model developed by Johnson and Cook. The damage model is then defined based on the ductility exhaustion concept using the strain rate dependent multiaxial fracture strain concept. The proposed model is applied to simulate previously published three cracked pipe bending test results under two different test speed conditions. Simulated results show overall good agreement with experimental results.

Hartree-Fock-Bogoliubov model: a theoretical and numerical perspective

International Nuclear Information System (INIS)

Paul, S.

2012-01-01

This work is devoted to the theoretical and numerical study of Hartree-Fock-Bogoliubov (HFB) theory for attractive quantum systems, which is one of the main methods in nuclear physics. We first present the model and its main properties, and then explain how to get numerical solutions. We prove some convergence results, in particular for the simple fixed point algorithm (sometimes called Roothaan). We show that it converges, or oscillates between two states, none of them being a solution. This generalizes to the HFB case previous results of Cances and Le Bris for the simpler Hartree-Fock model in the repulsive case. Following these authors, we also propose a relaxed constraint algorithm for which convergence is guaranteed. In the last part of the thesis, we illustrate the behavior of these algorithms by some numerical experiments. We first consider a system where the particles only interact through the Newton potential. Our numerical results show that the pairing matrix never vanishes, a fact that has not yet been proved rigorously. We then study a very simplified model for protons and neutrons in a nucleus. (author)

A CLASS OF NONMONOTONE TRUST REGION ALGORITHMS FOR LINEARLY CONSTRAINED OPTIMIZATION%线性约束优化的一类非单调信赖域算法

Institute of Scientific and Technical Information of China (English)

葛恒武; 陈中文

2002-01-01

We present a class of nonmonotone trust region algorithms for linearly constrained optimization in this paper.The algorithm may adjust automatically the scope of the monotonicity by the degree that the quadratic model is "trusted".Under the suitable conditions,it is proved that any limit point of the infinite sequence generated by the algorithm is the Kuhn-Tucker point of the primal problem.Finally,some numerical results show that the new algorithm is very effective.

Fluid dynamics theory, computation, and numerical simulation

CERN Document Server

Pozrikidis, C

2001-01-01

Fluid Dynamics Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes Two distinguishing features of the discourse are solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty Matlab codes are presented and discussed for a broad...

A Combinatorial Benders’ Cuts Algorithm for the Local Container Drayage Problem

Directory of Open Access Journals (Sweden)

Zhaojie Xue

2015-01-01

Full Text Available This paper examines the local container drayage problem under a special operation mode in which tractors and trailers can be separated; that is, tractors can be assigned to a new task at another location while trailers with containers are waiting for packing or unpacking. Meanwhile, the strategy of sharing empty containers between different customers is also considered to improve the efficiency and lower the operation cost. The problem is formulated as a vehicle routing and scheduling problem with temporal constraints. We adopt combinatorial benders’ cuts algorithm to solve this problem. Numerical experiments are performed on a group of randomly generated instances to test the performance of the proposed algorithm.

Cloud Particles Differential Evolution Algorithm: A Novel Optimization Method for Global Numerical Optimization

Directory of Open Access Journals (Sweden)

Wei Li

2015-01-01

Full Text Available We propose a new optimization algorithm inspired by the formation and change of the cloud in nature, referred to as Cloud Particles Differential Evolution (CPDE algorithm. The cloud is assumed to have three states in the proposed algorithm. Gaseous state represents the global exploration. Liquid state represents the intermediate process from the global exploration to the local exploitation. Solid state represents the local exploitation. The best solution found so far acts as a nucleus. In gaseous state, the nucleus leads the population to explore by condensation operation. In liquid state, cloud particles carry out macrolocal exploitation by liquefaction operation. A new mutation strategy called cloud differential mutation is introduced in order to solve a problem that the misleading effect of a nucleus may cause the premature convergence. In solid state, cloud particles carry out microlocal exploitation by solidification operation. The effectiveness of the algorithm is validated upon different benchmark problems. The results have been compared with eight well-known optimization algorithms. The statistical analysis on performance evaluation of the different algorithms on 10 benchmark functions and CEC2013 problems indicates that CPDE attains good performance.

Numerical simulation of time-dependent deformations under hygral and thermal transient conditions

International Nuclear Information System (INIS)

Roelfstra, P.E.

1987-01-01

Some basic concepts of numerical simulation of the formation of the microstructure of HCP are outlined. The aim is to replace arbitrary terms like aging by more realistic terms like bond density in the xerogel and bonds between hydrating particles of HCP. Actual state parameters such as temperature, humidity and degree of hydration can be determined under transient hygral and thermal conditions by solving numerically a series of appropriate coupled differential equations with given boundary conditions. Shrinkage of a composite structure without crack formation, based on calculated moisture distributions, has been determined with numerical concrete codes. The influence of crack formation, tensile strain-hardening and softening on the total deformation of a quasi-homogeneous drying material has been studied by means of model based on FEM. The difference between shrinkage without crack formation and shrinkage with crack formation can be quantified. Drying shrinkage and creep of concrete cannot be separated. The total deformation depends on the superimposed stress fields. Transient hygral deformation can be realistically predicted if the concept of point properties is applied rigorously. Transient thermal deformation has to be dealt with in the same way. (orig./HP)

The theory of hybrid stochastic algorithms

International Nuclear Information System (INIS)

Duane, S.; Kogut, J.B.

1986-01-01

The theory of hybrid stochastic algorithms is developed. A generalized Fokker-Planck equation is derived and is used to prove that the correct equilibrium distribution is generated by the algorithm. Systematic errors following from the discrete time-step used in the numerical implementation of the scheme are computed. Hybrid algorithms which simulate lattice gauge theory with dynamical fermions are presented. They are optimized in computer simulations and their systematic errors and efficiencies are studied. (orig.)

Numerical computations with GPUs

CERN Document Server

Kindratenko, Volodymyr

2014-01-01

This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to

Benchmarking the Algorithms to Detect Seasonal Signals Under Different Noise Conditions

Science.gov (United States)

Klos, A.; Bogusz, J.; Bos, M. S.

2017-12-01

Global Positioning System (GPS) position time series contain seasonal signals. Among the others, annual and semi-annual are the most powerful. Widely, these oscillations are modelled as curves with constant amplitudes, using the Weighted Least-Squares (WLS) algorithm. However, in reality, the seasonal signatures vary over time, as their geophysical causes are not constant. Different algorithms have been already used to cover this time-variability, as Wavelet Decomposition (WD), Singular Spectrum Analysis (SSA), Chebyshev Polynomial (CP) or Kalman Filter (KF). In this research, we employed 376 globally distributed GPS stations which time series contributed to the newest International Terrestrial Reference Frame (ITRF2014). We show that for c.a. 20% of stations the amplitudes of seasonal signal varies over time of more than 1.0 mm. Then, we compare the WD, SSA, CP and KF algorithms for a set of synthetic time series to quantify them under different noise conditions. We show that when variations of seasonal signals are ignored, the power-law character is biased towards flicker noise. The most reliable estimates of the variations were found to be given by SSA and KF. These methods also perform the best for other noise levels while WD, and to a lesser extend also CP, have trouble in separating the seasonal signal from the noise which leads to an underestimation in the spectral index of power-law noise of around 0.1. For real ITRF2014 GPS data we discovered, that SSA and KF are capable to model 49-84% and 77-90% of the variance of the true varying seasonal signals, respectively.

High-order hydrodynamic algorithms for exascale computing

Energy Technology Data Exchange (ETDEWEB)

Morgan, Nathaniel Ray [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-02-05

Hydrodynamic algorithms are at the core of many laboratory missions ranging from simulating ICF implosions to climate modeling. The hydrodynamic algorithms commonly employed at the laboratory and in industry (1) typically lack requisite accuracy for complex multi- material vortical flows and (2) are not well suited for exascale computing due to poor data locality and poor FLOP/memory ratios. Exascale computing requires advances in both computer science and numerical algorithms. We propose to research the second requirement and create a new high-order hydrodynamic algorithm that has superior accuracy, excellent data locality, and excellent FLOP/memory ratios. This proposal will impact a broad range of research areas including numerical theory, discrete mathematics, vorticity evolution, gas dynamics, interface instability evolution, turbulent flows, fluid dynamics and shock driven flows. If successful, the proposed research has the potential to radically transform simulation capabilities and help position the laboratory for computing at the exascale.

An artificial bee colony algorithm for uncertain portfolio selection.

Science.gov (United States)

Chen, Wei

2014-01-01

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

Adaptive scheduling with postexamining user selection under nonidentical fading

KAUST Repository

Gaaloul, Fakhreddine

2012-11-01

This paper investigates an adaptive scheduling algorithm for multiuser environments with statistically independent but nonidentically distributed (i.n.d.) channel conditions. The algorithm aims to reduce feedback load by sequentially and arbitrarily examining the user channels. It also provides improved performance by realizing postexamining best user selection. The first part of the paper presents new formulations for the statistics of the signal-to-noise ratio (SNR) of the scheduled user under i.n.d. channel conditions. The second part capitalizes on the findings in the first part and presents various performance and processing complexity measures for adaptive discrete-time transmission. The results are then extended to investigate the effect of outdated channel estimates on the statistics of the scheduled user SNR, as well as some performance measures. Numerical results are provided to clarify the usefulness of the scheduling algorithm under perfect or outdated channel estimates. © 1967-2012 IEEE.

A New Numerical Scheme for Cosmic-Ray Transport

Science.gov (United States)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

Numerical simulation of flow in centrifugal pump under cavitation and sediment condition

International Nuclear Information System (INIS)

Lu, J L; Guo, P C; Zheng, X B; Zhao, Q; Luo, X Q

2012-01-01

The sediment concentration is very high in many rivers in the world, especially in China. The pumps that designed for the clear water are usually seriously abraded. The probability of pump cavitation is greatly enhanced due to the existence of sand. Under the joint action and mutual promotion of sand erosion and cavitation, serious abrasion could occurred, and the hydraulic performance of the pump may be greatly descended, meanwhile the safety and stability of the whole pump are greatly threatened. Therefore, it is significant to investigate the cavitation characteristic of pump under sediment flow condition. In this paper, the flow in a single stage centrifugal pump under cleat water and sediment flow conditions was numerically simulated. The cavitation performance under clear water was firstly analyzed. Then, The pressure, velocity and solid particle distribution in centrifugal pump under different particle diameter and different particle concentration was investigated by using the two-fluid model; The area and extent of erosion was illustrated by using the particle track model. Finally, the influence of mixed sand on centrifugal pump performance was investigated.

e-DMDAV: A new privacy preserving algorithm for wearable enterprise information systems

Science.gov (United States)

Zhang, Zhenjiang; Wang, Xiaoni; Uden, Lorna; Zhang, Peng; Zhao, Yingsi

2018-04-01

Wearable devices have been widely used in many fields to improve the quality of people's lives. More and more data on individuals and businesses are collected by statistical organizations though those devices. Almost all of this data holds confidential information. Statistical Disclosure Control (SDC) seeks to protect statistical data in such a way that it can be released without giving away confidential information that can be linked to specific individuals or entities. The MDAV (Maximum Distance to Average Vector) algorithm is an efficient micro-aggregation algorithm belonging to SDC. However, the MDAV algorithm cannot survive homogeneity and background knowledge attacks because it was designed for static numerical data. This paper proposes a systematic dynamic-updating anonymity algorithm based on MDAV called the e-DMDAV algorithm. This algorithm introduces a new parameter and a table to ensure that the k records in one cluster with the range of the distinct values in each cluster is no less than e for numerical and non-numerical datasets. This new algorithm has been evaluated and compared with the MDAV algorithm. The simulation results show that the new algorithm outperforms MDAV in terms of minimizing distortion and disclosure risk with a similar computational cost.

Numerical Analysis of Multiscale Computations

CERN Document Server

Engquist, Björn; Tsai, Yen-Hsi R

2012-01-01

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

New Parallel Algorithms for Landscape Evolution Model

Science.gov (United States)

Jin, Y.; Zhang, H.; Shi, Y.

2017-12-01

Most landscape evolution models (LEM) developed in the last two decades solve the diffusion equation to simulate the transportation of surface sediments. This numerical approach is difficult to parallelize due to the computation of drainage area for each node, which needs huge amount of communication if run in parallel. In order to overcome this difficulty, we developed two parallel algorithms for LEM with a stream net. One algorithm handles the partition of grid with traditional methods and applies an efficient global reduction algorithm to do the computation of drainage areas and transport rates for the stream net; the other algorithm is based on a new partition algorithm, which partitions the nodes in catchments between processes first, and then partitions the cells according to the partition of nodes. Both methods focus on decreasing communication between processes and take the advantage of massive computing techniques, and numerical experiments show that they are both adequate to handle large scale problems with millions of cells. We implemented the two algorithms in our program based on the widely used finite element library deal.II, so that it can be easily coupled with ASPECT.

Modular Regularization Algorithms

DEFF Research Database (Denmark)

Jacobsen, Michael

2004-01-01

The class of linear ill-posed problems is introduced along with a range of standard numerical tools and basic concepts from linear algebra, statistics and optimization. Known algorithms for solving linear inverse ill-posed problems are analyzed to determine how they can be decomposed into indepen...

The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method

Directory of Open Access Journals (Sweden)

Liang Shen

2017-01-01

Full Text Available There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user’s risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the K-shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.

Particle algorithms for population dynamics in flows

International Nuclear Information System (INIS)

Perlekar, Prasad; Toschi, Federico; Benzi, Roberto; Pigolotti, Simone

2011-01-01

We present and discuss particle based algorithms to numerically study the dynamics of population subjected to an advecting flow condition. We discuss few possible variants of the algorithms and compare them in a model compressible flow. A comparison against appropriate versions of the continuum stochastic Fisher equation (sFKPP) is also presented and discussed. The algorithms can be used to study populations genetics in fluid environments.

Sensitivity Analysis of a CPAM Inverse Algorithm for Composite Laminates Characterization

Directory of Open Access Journals (Sweden)

Farshid Masoumi

2017-01-01

Full Text Available Using experimental data and numerical simulations, a new combined technique is presented for characterization of thin and thick orthotropic composite laminates. Four or five elastic constants, as well as ply orientation angles, are considered as the unknown parameters. The material characterization is first examined for isotropic plates under different boundary conditions to evaluate the method’s accuracy. The proposed algorithm, so-called CPAM (Combined Programs of ABAQUS and MATLAB, utilizes an optimization procedure and makes simultaneous use of vibration test data together with their corresponding numerical solutions. The numerical solutions are based on a commercial finite element package for efficiently identifying the material properties. An inverse method based on particle swarm optimization algorithm is further provided using MATLAB software. The error function to be minimized is the sum of squared differences between experimental and simulated data of eigenfrequencies. To evaluate the robustness of the model’s results in the presence of uncertainty and unwanted noises, a sensitivity analysis that employs Gaussian disorder model is directly applied to the measured frequencies. The results with high accuracy confirm the validity and capability of the present method in simultaneous determination of mechanical constants and fiber orientation angles of composite laminates as compared to prior methods.

Conditionally-uniform Feasible Grid Search Algorithm

DEFF Research Database (Denmark)

Dziubinski, Matt P.

We present and evaluate a numerical optimization method (together with an algorithm for choosing the starting values) pertinent to the constrained optimization problem arising in the estimation of the GARCH models with inequality constraints, in particular the Simplied Component GARCH Model...... (SCGARCH), together with algorithms for the objective function and analytical gradient computation for SCGARCH....

Unified algorithm for partial differential equations and examples of numerical computation

International Nuclear Information System (INIS)

Watanabe, Tsuguhiro

1999-01-01

A new unified algorithm is proposed to solve partial differential equations which describe nonlinear boundary value problems, eigenvalue problems and time developing boundary value problems. The algorithm is composed of implicit difference scheme and multiple shooting scheme and is named as HIDM (Higher order Implicit Difference Method). A new prototype computer programs for 2-dimensional partial differential equations is constructed and tested successfully to several problems. Extension of the computer programs to 3 or more higher order dimension problems will be easy due to the direct product type difference scheme. (author)

KAM Tori Construction Algorithms

Science.gov (United States)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

Towards High Resolution Numerical Algorithms for Wave Dominated Physical Phenomena

Science.gov (United States)

2009-01-30

Modelling and Numerical Analysis, 40(5):815-841, 2006. [31] Michael Dumbser, Martin Kaser, and Eleuterio F. Toro. An arbitrary high-order Discontinuous...proximation of PML, SIAM J. Numer. Anal., 41 (2003), pp. 287-305. [60] E. BECACHE, S. FAUQUEUX, AND P. JOLY , Stability of perfectly matched layers, group...time-domain performance analysis, IEEE Trans, on Magnetics, 38 (2002), pp. 657- 660. [64] J. DIAZ AND P. JOLY , An analysis of higher-order boundary

Bilinear Inverse Problems: Theory, Algorithms, and Applications

Science.gov (United States)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical

A multi-pattern hash-binary hybrid algorithm for URL matching in the HTTP protocol.

Directory of Open Access Journals (Sweden)

Ping Zeng

Full Text Available In this paper, based on our previous multi-pattern uniform resource locator (URL binary-matching algorithm called HEM, we propose an improved multi-pattern matching algorithm called MH that is based on hash tables and binary tables. The MH algorithm can be applied to the fields of network security, data analysis, load balancing, cloud robotic communications, and so on-all of which require string matching from a fixed starting position. Our approach effectively solves the performance problems of the classical multi-pattern matching algorithms. This paper explores ways to improve string matching performance under the HTTP protocol by using a hash method combined with a binary method that transforms the symbol-space matching problem into a digital-space numerical-size comparison and hashing problem. The MH approach has a fast matching speed, requires little memory, performs better than both the classical algorithms and HEM for matching fields in an HTTP stream, and it has great promise for use in real-world applications.

Numerical solution of plasma fluid equations using locally refined grids

International Nuclear Information System (INIS)

Colella, P.

1997-01-01

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results

Modern algorithms for large sparse eigenvalue problems

International Nuclear Information System (INIS)

Meyer, A.

1987-01-01

The volume is written for mathematicians interested in (numerical) linear algebra and in the solution of large sparse eigenvalue problems, as well as for specialists in engineering, who use the considered algorithms in the investigation of eigenoscillations of structures, in reactor physics, etc. Some variants of the algorithms based on the idea of a gradient-type direction of movement are presented and their convergence properties are discussed. From this, a general strategy for the direct use of preconditionings for the eigenvalue problem is derived. In this new approach the necessity of the solution of large linear systems is entirely avoided. Hence, these methods represent a new alternative to some other modern eigenvalue algorithms, as they show a slightly slower convergence on the one hand but essentially lower numerical and data processing problems on the other hand. A brief description and comparison of some well-known methods (i.e. simultaneous iteration, Lanczos algorithm) completes this volume. (author)

A Simple But Effective Canonical Dual Theory Unified Algorithm for Global Optimization

OpenAIRE

Zhang, Jiapu

2011-01-01

Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems sometimes is very difficult. This paper presents a very simple but very effective canonical duality theory (CDT) unified global optimization algorithm. This algorithm has convergence is proved in this paper. More important, for this CDT-unified algorithm, numerous...

Efficient Out of Core Sorting Algorithms for the Parallel Disks Model.

Science.gov (United States)

Kundeti, Vamsi; Rajasekaran, Sanguthevar

2011-11-01

In this paper we present efficient algorithms for sorting on the Parallel Disks Model (PDM). Numerous asymptotically optimal algorithms have been proposed in the literature. However many of these merge based algorithms have large underlying constants in the time bounds, because they suffer from the lack of read parallelism on PDM. The irregular consumption of the runs during the merge affects the read parallelism and contributes to the increased sorting time. In this paper we first introduce a novel idea called the dirty sequence accumulation that improves the read parallelism. Secondly, we show analytically that this idea can reduce the number of parallel I/O's required to sort the input close to the lower bound of [Formula: see text]. We experimentally verify our dirty sequence idea with the standard R-Way merge and show that our idea can reduce the number of parallel I/Os to sort on PDM significantly.

Newton algorithm for Hamiltonian characterization in quantum control

International Nuclear Information System (INIS)

Ndong, M; Sugny, D; Salomon, J

2014-01-01

We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank–Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of the basin of convergence and the non-uniqueness of the solution. (paper)

Adiabatic quantum algorithm for search engine ranking.

Science.gov (United States)

Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A

2012-06-08

We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.

A New Language Design for Prototyping Numerical Computation

Directory of Open Access Journals (Sweden)

Thomas Derby

1996-01-01

Full Text Available To naturally and conveniently express numerical algorithms, considerable expressive power is needed in the languages in which they are implemented. The language Matlab is widely used by numerical analysts for this reason. Expressiveness or ease-of-use can also result in a loss of efficiency, as is the case with Matlab. In particular, because numerical analysts are highly interested in the performance of their algorithms, prototypes are still often implemented in languages such as Fortran. In this article we describe a language design that is intended to both provide expressiveness for numerical computation, and at the same time provide performance guarantees. In our language, EQ, we attempt to include both syntactic and semantic features that correspond closely to the programmer's model of the problem, including unordered equations, large-granularity state transitions, and matrix notation. The resulting language does not fit into standard language categories such as functional or imperative but has features of both paradigms. We also introduce the notion of language dependability, which is the idea that a language should guarantee that certain program transformations are performed by all implementations. We first describe the interesting features of EQ, and then present three examples of algorithms written using it. We also provide encouraging performance results from an initial implementation of our language.

NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.

Energy Technology Data Exchange (ETDEWEB)

LUCCIO, A.; D' IMPERIO, N.; MALITSKY, N.

2005-09-12

Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.

GPS-Free Localization Algorithm for Wireless Sensor Networks

Directory of Open Access Journals (Sweden)

Lei Wang

2010-06-01

Full Text Available Localization is one of the most fundamental problems in wireless sensor networks, since the locations of the sensor nodes are critical to both network operations and most application level tasks. A GPS-free localization scheme for wireless sensor networks is presented in this paper. First, we develop a standardized clustering-based approach for the local coordinate system formation wherein a multiplication factor is introduced to regulate the number of master and slave nodes and the degree of connectivity among master nodes. Second, using homogeneous coordinates, we derive a transformation matrix between two Cartesian coordinate systems to efficiently merge them into a global coordinate system and effectively overcome the flip ambiguity problem. The algorithm operates asynchronously without a centralized controller; and does not require that the location of the sensors be known a priori. A set of parameter-setting guidelines for the proposed algorithm is derived based on a probability model and the energy requirements are also investigated. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results. We also compare the performance of the proposed algorithm under a variety multiplication factor, node density and node communication radius scenario. Experiments show that our algorithm outperforms existing mechanisms in terms of accuracy and convergence time.

Neutronic rebalance algorithms for SIMMER

International Nuclear Information System (INIS)

Soran, P.D.

1976-05-01

Four algorithms to solve the two-dimensional neutronic rebalance equations in SIMMER are investigated. Results of the study are presented and indicate that a matrix decomposition technique with a variable convergence criterion is the best solution algorithm in terms of accuracy and calculational speed. Rebalance numerical stability problems are examined. The results of the study can be applied to other neutron transport codes which use discrete ordinates techniques

Algorithms For Integrating Nonlinear Differential Equations

Science.gov (United States)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

An Efficient Algorithm for Unconstrained Optimization

Directory of Open Access Journals (Sweden)

Sergio Gerardo de-los-Cobos-Silva

2015-01-01

Full Text Available This paper presents an original and efficient PSO algorithm, which is divided into three phases: (1 stabilization, (2 breadth-first search, and (3 depth-first search. The proposed algorithm, called PSO-3P, was tested with 47 benchmark continuous unconstrained optimization problems, on a total of 82 instances. The numerical results show that the proposed algorithm is able to reach the global optimum. This work mainly focuses on unconstrained optimization problems from 2 to 1,000 variables.

Numerical Method based on SIMPLE Algorithm for a Two-Phase Flow with Non-condensable Gas

International Nuclear Information System (INIS)

Kim, Jong Tae

2009-08-01

In this study, a numerical method based on SIMPLE algorithm for a two-phase flow with non-condensable gas has been developed in order to simulate thermal hydraulics in a containment of a nuclear power plant. As governing equations, it adopts a two-fluid three-field model for the two-phase flows. The three fields include gas, drops, and continuous liquid. The gas field can contains vapor and non-condensable gases such as air and hydrogen. In order to resolve mixing phenomena of gas species, gas transport equations for each species base on the gas mass fractions are solved with gas phase governing equations such as mass, momentum and energy equations. Methods to evaluate the properties of the gas species were implemented in the code. They are constant or polynomial function based a user input and a property library from Chemkin and JANAF table for gas specific heat. Properties for the gas mixture which are dependent on mole fractions of the gas species were evaluated by a mix rule

An Algorithm for the Convolution of Legendre Series

KAUST Repository

Hale, Nicholas; Townsend, Alex

2014-01-01

An O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N 2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the improved efficiency over the existing algorithm. © 2014 Society for Industrial and Applied Mathematics.

New MPPT algorithm for PV applications based on hybrid dynamical approach

KAUST Repository

Elmetennani, Shahrazed

2016-10-24

This paper proposes a new Maximum Power Point Tracking (MPPT) algorithm for photovoltaic applications using the multicellular converter as a stage of power adaptation. The proposed MPPT technique has been designed using a hybrid dynamical approach to model the photovoltaic generator. The hybrid dynamical theory has been applied taking advantage of the particular topology of the multicellular converter. Then, a hybrid automata has been established to optimize the power production. The maximization of the produced solar energy is achieved by switching between the different operative modes of the hybrid automata, which is conditioned by some invariance and transition conditions. These conditions have been validated by simulation tests under different conditions of temperature and irradiance. Moreover, the performance of the proposed algorithm has been then evaluated by comparison with standard MPPT techniques numerically and by experimental tests under varying external working conditions. The results have shown the interesting features that the hybrid MPPT technique presents in terms of performance and simplicity for real time implementation.

New MPPT algorithm for PV applications based on hybrid dynamical approach

KAUST Repository

Elmetennani, Shahrazed; Laleg-Kirati, Taous-Meriem; Djemai, M.; Tadjine, M.

2016-01-01

This paper proposes a new Maximum Power Point Tracking (MPPT) algorithm for photovoltaic applications using the multicellular converter as a stage of power adaptation. The proposed MPPT technique has been designed using a hybrid dynamical approach to model the photovoltaic generator. The hybrid dynamical theory has been applied taking advantage of the particular topology of the multicellular converter. Then, a hybrid automata has been established to optimize the power production. The maximization of the produced solar energy is achieved by switching between the different operative modes of the hybrid automata, which is conditioned by some invariance and transition conditions. These conditions have been validated by simulation tests under different conditions of temperature and irradiance. Moreover, the performance of the proposed algorithm has been then evaluated by comparison with standard MPPT techniques numerically and by experimental tests under varying external working conditions. The results have shown the interesting features that the hybrid MPPT technique presents in terms of performance and simplicity for real time implementation.

Numerical simulation of diurnally varying thermal environment in a street canyon under haze-fog conditions

Science.gov (United States)

Tan, Zijing; Dong, Jingliang; Xiao, Yimin; Tu, Jiyuan

2015-10-01

The impact of haze-fog on surface temperature, flow pattern, pollutant dispersion and pedestrian thermal comfort are investigated using computational fluid dynamics (CFD) approach based on a three-dimensional street canyon model under different haze-fog conditions. In this study, light extinction coefficient (Kex) is adopted to represent haze-fog pollution level. Numerical simulations are performed for different Kex values at four representative time events (1000 LST, 1300 LST, 1600 LST and 2000 LST). The numerical results suggest that the surface temperature is strongly affected by the haze-fog condition. Surface heating induced by the solar radiation is enhanced by haze-fog, as higher surface temperature is observed under thicker haze-fog condition. Moreover, the temperature difference between sunlit and shadow surfaces is reduced, while that for the two shadow surfaces is slightly increased. Therefore, the surface temperature among street canyon facets becomes more evenly distributed under heavy haze-fog conditions. In addition, flow patterns are considerably altered by different haze-fog conditions, especially for the afternoon (1600 LST) case, in which thermal-driven flow has opposite direction as that of the wind-driven flow direction. Consequently, pollutants such as vehicular emissions will accumulate at pedestrian level, and pedestrian thermal comfort may lower under thicker haze-fog condition.

A Unified Differential Evolution Algorithm for Global Optimization

Energy Technology Data Exchange (ETDEWEB)

Qiang, Ji; Mitchell, Chad

2014-06-24

Abstract?In this paper, we propose a new unified differential evolution (uDE) algorithm for single objective global optimization. Instead of selecting among multiple mutation strategies as in the conventional differential evolution algorithm, this algorithm employs a single equation as the mutation strategy. It has the virtue of mathematical simplicity and also provides users the flexbility for broader exploration of different mutation strategies. Numerical tests using twelve basic unimodal and multimodal functions show promising performance of the proposed algorithm in comparison to convential differential evolution algorithms.

Evaluation of Underwater Image Enhancement Algorithms under Different Environmental Conditions

Directory of Open Access Journals (Sweden)

Marino Mangeruga

2018-01-01

Full Text Available Underwater images usually suffer from poor visibility, lack of contrast and colour casting, mainly due to light absorption and scattering. In literature, there are many algorithms aimed to enhance the quality of underwater images through different approaches. Our purpose was to identify an algorithm that performs well in different environmental conditions. We have selected some algorithms from the state of the art and we have employed them to enhance a dataset of images produced in various underwater sites, representing different environmental and illumination conditions. These enhanced images have been evaluated through some quantitative metrics. By analysing the results of these metrics, we tried to understand which of the selected algorithms performed better than the others. Another purpose of our research was to establish if a quantitative metric was enough to judge the behaviour of an underwater image enhancement algorithm. We aim to demonstrate that, even if the metrics can provide an indicative estimation of image quality, they could lead to inconsistent or erroneous evaluations.

Fermion cluster algorithms

International Nuclear Information System (INIS)

Chandrasekharan, Shailesh

2000-01-01

Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion world lines. This solution leads to the possibility of designing fermion cluster algorithms in certain cases. Using the example of free non-relativistic fermions we discuss the ideas underlying the algorithm

A Hybrid Algorithm for Optimizing Multi- Modal Functions

Institute of Scientific and Technical Information of China (English)

Li Qinghua; Yang Shida; Ruan Youlin

2006-01-01

A new genetic algorithm is presented based on the musical performance. The novelty of this algorithm is that a new genetic algorithm, mimicking the musical process of searching for a perfect state of harmony, which increases the robustness of it greatly and gives a new meaning of it in the meantime, has been developed. Combining the advantages of the new genetic algorithm, simplex algorithm and tabu search, a hybrid algorithm is proposed. In order to verify the effectiveness of the hybrid algorithm, it is applied to solving some typical numerical function optimization problems which are poorly solved by traditional genetic algorithms. The experimental results show that the hybrid algorithm is fast and reliable.

On the efficiency of chaos optimization algorithms for global optimization

International Nuclear Information System (INIS)

Yang Dixiong; Li Gang; Cheng Gengdong

2007-01-01

Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions

Design of PID Controller Simulator based on Genetic Algorithm

Directory of Open Access Journals (Sweden)

Fahri VATANSEVER

2013-08-01

Full Text Available PID (Proportional Integral and Derivative controllers take an important place in the field of system controlling. Various methods such as Ziegler-Nichols, Cohen-Coon, Chien Hrones Reswick (CHR and Wang-Juang-Chan are available for the design of such controllers benefiting from the system time and frequency domain data. These controllers are in compliance with system properties under certain criteria suitable to the system. Genetic algorithms have become widely used in control system applications in parallel to the advances in the field of computer and artificial intelligence. In this study, PID controller designs have been carried out by means of classical methods and genetic algorithms and comparative results have been analyzed. For this purpose, a graphical user interface program which can be used for educational purpose has been developed. For the definite (entered transfer functions, the suitable P, PI and PID controller coefficients have calculated by both classical methods and genetic algorithms and many parameters and responses of the systems have been compared and presented numerically and graphically

Algorithms for Brownian first-passage-time estimation

Science.gov (United States)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Biased Monte Carlo algorithms on unitary groups

International Nuclear Information System (INIS)

Creutz, M.; Gausterer, H.; Sanielevici, S.

1989-01-01

We introduce a general updating scheme for the simulation of physical systems defined on unitary groups, which eliminates the systematic errors due to inexact exponentiation of algebra elements. The essence is to work directly with group elements for the stochastic noise. Particular cases of the scheme include the algorithm of Metropolis et al., overrelaxation algorithms, and globally corrected Langevin and hybrid algorithms. The latter are studied numerically for the case of SU(3) theory

A discontinuous Galerkin method for numerical pricing of European options under Heston stochastic volatility

Science.gov (United States)

Hozman, J.; Tichý, T.

2016-12-01

The paper is based on the results from our recent research on multidimensional option pricing problems. We focus on European option valuation when the price movement of the underlying asset is driven by a stochastic volatility following a square root process proposed by Heston. The stochastic approach incorporates a new additional spatial variable into this model and makes it very robust, i.e. it provides a framework to price a variety of options that is closer to reality. The main topic is to present the numerical scheme arising from the concept of discontinuous Galerkin methods and applicable to the Heston option pricing model. The numerical results are presented on artificial benchmarks as well as on reference market data.

Algorithms for worst-case tolerance optimization

DEFF Research Database (Denmark)

Schjær-Jacobsen, Hans; Madsen, Kaj

1979-01-01

New algorithms are presented for the solution of optimum tolerance assignment problems. The problems considered are defined mathematically as a worst-case problem (WCP), a fixed tolerance problem (FTP), and a variable tolerance problem (VTP). The basic optimization problem without tolerances...... is denoted the zero tolerance problem (ZTP). For solution of the WCP we suggest application of interval arithmetic and also alternative methods. For solution of the FTP an algorithm is suggested which is conceptually similar to algorithms previously developed by the authors for the ZTP. Finally, the VTP...... is solved by a double-iterative algorithm in which the inner iteration is performed by the FTP- algorithm. The application of the algorithm is demonstrated by means of relatively simple numerical examples. Basic properties, such as convergence properties, are displayed based on the examples....

Numerical solution of kinetics equation for point defects accumulation in metals under irradiation

International Nuclear Information System (INIS)

Aldzhambekova, G.T.; Iskakov, B.M.

1999-01-01

In the report the mathematical model, describing processes of generation and accumulation of defects in solids under irradiation is considered. The equations of this model take into account the velocity of Frenkel pairs generation, the mutual recombination of vacancies and the interstitials, as well as velocity of defects absorption by discharge channeling of vacancies and interstitials. By Runge-Kutta method the numerical solution of the model was carried out

Fast algorithms for transport models. Final report, June 1, 1993--May 31, 1994

International Nuclear Information System (INIS)

Manteuffel, T.

1994-12-01

The focus of this project is the study of multigrid and multilevel algorithms for the numerical solution of Boltzmann models of the transport of neutral and charged particles. In previous work a fast multigrid algorithm was developed for the numerical solution of the Boltzmann model of neutral particle transport in slab geometry assuming isotropic scattering. The new algorithm is extremely fast in the thick diffusion limit; the multigrid v-cycle convergence factor approaches zero as the mean-free-path between collisions approaches zero, independent of the mesh. Also, a fast multilevel method was developed for the numerical solution of the Boltzmann model of charged particle transport in the thick Fokker-Plank limit for slab geometry. Parallel implementations were developed for both algorithms

A matter of timing: identifying significant multi-dose radiotherapy improvements by numerical simulation and genetic algorithm search.

Directory of Open Access Journals (Sweden)

Simon D Angus

Full Text Available 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

A matter of timing: identifying significant multi-dose radiotherapy improvements by numerical simulation and genetic algorithm search.

Science.gov (United States)

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-effecitive means

Inertial algorithms for the stationary Navier-Stokes equations

NARCIS (Netherlands)

Hou, Yanren; Mattheij, R.M.M.

2003-01-01

Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed

A state space algorithm for the spectral factorization

NARCIS (Netherlands)

Kraffer, F.; Kraffer, F.; Kwakernaak, H.

1997-01-01

This paper presents an algorithm for the spectral factorization of a para-Hermitian polynomial matrix. The algorithm is based on polynomial matrix to state space and vice versa conversions, and avoids elementary polynomial operations in computations; It relies on well-proven methods of numerical

Eigenvalue Decomposition-Based Modified Newton Algorithm

Directory of Open Access Journals (Sweden)

Wen-jun Wang

2013-01-01

Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.

Numerical simulation of the shot peening process under previous loading conditions

International Nuclear Information System (INIS)

Romero-Ángeles, B; Urriolagoitia-Sosa, G; Torres-San Miguel, C R; Molina-Ballinas, A; Benítez-García, H A; Vargas-Bustos, J A; Urriolagoitia-Calderón, G

2015-01-01

This research presents a numerical simulation of the shot peening process and determines the residual stress field induced into a component with a previous loading history. The importance of this analysis is based on the fact that mechanical elements under shot peening are also subjected to manufacturing processes, which convert raw material into finished product. However, material is not provided in a virgin state, it has a previous loading history caused by the manner it is fabricated. This condition could alter some beneficial aspects of the residual stress induced by shot peening and could accelerate the crack nucleation and propagation progression. Studies were performed in beams subjected to strain hardening in tension (5ε y ) before shot peening was applied. Latter results were then compared in a numerical assessment of an induced residual stress field by shot peening carried out in a component (beam) without any previous loading history. In this paper, it is clearly shown the detrimental or beneficial effect that previous loading history can bring to the mechanical component and how it can be controlled to improve the mechanical behavior of the material

Dynamic Brazilian Test of Rock Under Intermediate Strain Rate: Pendulum Hammer-Driven SHPB Test and Numerical Simulation

Science.gov (United States)

Zhu, W. C.; Niu, L. L.; Li, S. H.; Xu, Z. H.

2015-09-01

The tensile strength of rock subjected to dynamic loading constitutes many engineering applications such as rock drilling and blasting. The dynamic Brazilian test of rock specimens was conducted with the split Hopkinson pressure bar (SHPB) driven by pendulum hammer, in order to determine the indirect tensile strength of rock under an intermediate strain rate ranging from 5.2 to 12.9 s-1, which is achieved when the incident bar is impacted by pendulum hammer with different velocities. The incident wave excited by pendulum hammer is triangular in shape, featuring a long rising time, and it is considered to be helpful for achieving a constant strain rate in the rock specimen. The dynamic indirect tensile strength of rock increases with strain rate. Then, the numerical simulator RFPA-Dynamics, a well-recognized software for simulating the rock failure under dynamic loading, is validated by reproducing the Brazilian test of rock when the incident stress wave retrieved at the incident bar is input as the boundary condition, and then it is employed to study the Brazilian test of rock under the higher strain rate. Based on the numerical simulation, the strain-rate dependency of tensile strength and failure pattern of the Brazilian disc specimen under the intermediate strain rate are numerically simulated, and the associated failure mechanism is clarified. It is deemed that the material heterogeneity should be a reason for the strain-rate dependency of rock.

A modeling and numerical algorithm for thermoporomechanics in multiple porosity media for naturally fractured reservoirs

Science.gov (United States)

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

Partially linearized algorithms in gyrokinetic particle simulation

Energy Technology Data Exchange (ETDEWEB)

Dimits, A.M.; Lee, W.W.

1990-10-01

In this paper, particle simulation algorithms with time-varying weights for the gyrokinetic Vlasov-Poisson system have been developed. The primary purpose is to use them for the removal of the selected nonlinearities in the simulation of gradient-driven microturbulence so that the relative importance of the various nonlinear effects can be assessed. It is hoped that the use of these procedures will result in a better understanding of the transport mechanisms and scaling in tokamaks. Another application of these algorithms is for the improvement of the numerical properties of the simulation plasma. For instance, implementations of such algorithms (1) enable us to suppress the intrinsic numerical noise in the simulation, and (2) also make it possible to regulate the weights of the fast-moving particles and, in turn, to eliminate the associated high frequency oscillations. Examples of their application to drift-type instabilities in slab geometry are given. We note that the work reported here represents the first successful use of the weighted algorithms in particle codes for the nonlinear simulation of plasmas.

Partially linearized algorithms in gyrokinetic particle simulation

International Nuclear Information System (INIS)

Dimits, A.M.; Lee, W.W.

1990-10-01

In this paper, particle simulation algorithms with time-varying weights for the gyrokinetic Vlasov-Poisson system have been developed. The primary purpose is to use them for the removal of the selected nonlinearities in the simulation of gradient-driven microturbulence so that the relative importance of the various nonlinear effects can be assessed. It is hoped that the use of these procedures will result in a better understanding of the transport mechanisms and scaling in tokamaks. Another application of these algorithms is for the improvement of the numerical properties of the simulation plasma. For instance, implementations of such algorithms (1) enable us to suppress the intrinsic numerical noise in the simulation, and (2) also make it possible to regulate the weights of the fast-moving particles and, in turn, to eliminate the associated high frequency oscillations. Examples of their application to drift-type instabilities in slab geometry are given. We note that the work reported here represents the first successful use of the weighted algorithms in particle codes for the nonlinear simulation of plasmas

Genetic Algorithms in Wind Turbine Airfoil Design

Energy Technology Data Exchange (ETDEWEB)

Grasso, F. [ECN Wind Energy, Petten (Netherlands); Bizzarrini, N.; Coiro, D.P. [Department of Aerospace Engineering, University of Napoli ' Federico II' , Napoli (Italy)

2011-03-15

One key element in the aerodynamic design of wind turbines is the use of specially tailored airfoils to increase the ratio of energy capture to the loading and thereby to reduce cost of energy. This work is focused on the design of a wind turbine airfoil by using numerical optimization. Firstly, the optimization approach is presented; a genetic algorithm is used, coupled with RFOIL solver and a composite Bezier geometrical parameterization. A particularly sensitive point is the choice and implementation of constraints; in order to formalize in the most complete and effective way the design requirements, the effects of activating specific constraints are discussed. A numerical example regarding the design of a high efficiency airfoil for the outer part of a blade by using genetic algorithms is illustrated and the results are compared with existing wind turbine airfoils. Finally a new hybrid design strategy is illustrated and discussed, in which the genetic algorithms are used at the beginning of the design process to explore a wide domain. Then, the gradient based algorithms are used in order to improve the first stage optimum.

Closed-Form Algorithm for 3-D Near-Field OFDM Signal Localization under Uniform Circular Array.

Science.gov (United States)

Su, Xiaolong; Liu, Zhen; Chen, Xin; Wei, Xizhang

2018-01-14

Due to its widespread application in communications, radar, etc., the orthogonal frequency division multiplexing (OFDM) signal has become increasingly urgent in the field of localization. Under uniform circular array (UCA) and near-field conditions, this paper presents a closed-form algorithm based on phase difference for estimating the three-dimensional (3-D) location (azimuth angle, elevation angle, and range) of the OFDM signal. In the algorithm, considering that it is difficult to distinguish the frequency of the OFDM signal's subcarriers and the phase-based method is always affected by errors of the frequency estimation, this paper employs sparse representation (SR) to obtain the super-resolution frequencies and the corresponding phases of subcarriers. Further, as the phase differences of the adjacent sensors including azimuth angle, elevation angle and range parameters can be expressed as indefinite equations, the near-field OFDM signal's 3-D location is obtained by employing the least square method, where the phase differences are based on the average of the estimated subcarriers. Finally, the performance of the proposed algorithm is demonstrated by several simulations.

Heuristics for the Economic Production Quantity Problem under Restrictions on Production and Maintenance Time

Directory of Open Access Journals (Sweden)

Qi Xu

2016-01-01

Full Text Available This paper proposes an economic production quantity problem with the maximal production run time and minimal preventive maintenance time over a finite planning horizon. The objective is to find the efficient production and maintenance policy to minimize the total cost composed of production, maintenance, shortages, and holding costs under the restriction on the production run time and the preventive maintenance time. The production and maintenance decisions include the production and maintenance frequencies and the production run and the maintenance time. The variability and the boundedness of the production run and maintenance time make the problem difficult to solve. Two heuristic algorithms are developed using different techniques based on the optimal properties of the relaxed problem. The performance comparison between the two algorithms is illustrated by numerical examples. The numerical results show that, for the most part, there exists a heuristic algorithm which is more effective than the other.

Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

International Nuclear Information System (INIS)

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-01-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. (paper)

Numerical evaluation of a robust self-triggered MPC algorithm

NARCIS (Netherlands)

Brunner, F.D.; Heemels, W.P.M.H.; Allgöwer, F.

2016-01-01

We present numerical examples demonstrating the efficacy of a recently proposed self-triggered model predictive control scheme for disturbed linear discrete-time systems with hard constraints on the input and state. In order to reduce the amount of communication between the controller and the

Algorithms for Reinforcement Learning

CERN Document Server

Szepesvari, Csaba

2010-01-01

Reinforcement learning is a learning paradigm concerned with learning to control a system so as to maximize a numerical performance measure that expresses a long-term objective. What distinguishes reinforcement learning from supervised learning is that only partial feedback is given to the learner about the learner's predictions. Further, the predictions may have long term effects through influencing the future state of the controlled system. Thus, time plays a special role. The goal in reinforcement learning is to develop efficient learning algorithms, as well as to understand the algorithms'

Formulation and numerical implementation of micro-scale boundary conditions for particle aggregates

NARCIS (Netherlands)

Liu, J.; Bosco, E.; Suiker, A.S.J.

2017-01-01

Novel numerical algorithms are presented for the implementation of micro-scale boundary conditions of particle aggregates modelled with the discrete element method. The algorithms are based on a servo-control methodology, using a feedback principle comparable to that of algorithms commonly applied

Quantum approximate optimization algorithm for MaxCut: A fermionic view

Science.gov (United States)

Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.

2018-02-01

Farhi et al. recently proposed a class of quantum algorithms, the quantum approximate optimization algorithm (QAOA), for approximately solving combinatorial optimization problems (E. Farhi et al., arXiv:1411.4028; arXiv:1412.6062; arXiv:1602.07674). A level-p QAOA circuit consists of p steps; in each step a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2 p times for which these two Hamiltonians are applied are the parameters of the algorithm, which are to be optimized classically for the best performance. As p increases, parameter optimization becomes inefficient due to the curse of dimensionality. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here we analytically and numerically study parameter setting for the QAOA applied to MaxCut. For the level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MaxCut, the "ring of disagrees," or the one-dimensional antiferromagnetic ring, we provide an analysis for an arbitrarily high level. Using a fermionic representation, the evolution of the system under the QAOA translates into quantum control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of the QAOA for any p . It also greatly simplifies the numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional submanifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm

Energy Technology Data Exchange (ETDEWEB)

Sheng, Zheng, E-mail: 19994035@sina.com [College of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101 (China); Wang, Jun; Zhou, Bihua [National Defense Key Laboratory on Lightning Protection and Electromagnetic Camouflage, PLA University of Science and Technology, Nanjing 210007 (China); Zhou, Shudao [College of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101 (China); Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044 (China)

2014-03-15

This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.

Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm

International Nuclear Information System (INIS)

Sheng, Zheng; Wang, Jun; Zhou, Bihua; Zhou, Shudao

2014-01-01

This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm

Numerical evaluation of cracked pipes under dynamic loading

International Nuclear Information System (INIS)

Petit, M.; Jamet, P.

1989-01-01

In order to apply the leak-before-break concept to piping systems, the behavior of cracked pipes under dynamic, and especially seismic, loadings must be studied. A simple finite element model of a cracked pipe has been developed and implemented in the general purpose computer code CASTEM 2000. The model is a generalization of the approach proposed by Paris and Tada (1). Considered loads are bending moment and axial force (representing thermal expansion and internal pressure.) The elastic characteristics of the model are determined using the Zahoor formulae for the geometry-dependent factors. Owing to the material behabior plasticity must be taken into account. To represent the crack growth, the material is defined by two characteristic values: J 1c which is the level of energy corresponding to crack initiation and the tearing modulus, T, which governs the length of propagation of the crack. For dynamic loads, unilateral conditions are imposed to represent crack closure. The model has been used for the design of dynamic tests to be conducted on shaking tables. Test principle is briefly described and numerical results are presented. Finally evaluation of margin, due to plasticity, in comparison with the standard design procedure is made

Parameterized Algorithms for Survivable Network Design with Uniform Demands

DEFF Research Database (Denmark)

Bang-Jensen, Jørgen; Klinkby Knudsen, Kristine Vitting; Saurabh, Saket

2018-01-01

problem in combinatorial optimization that captures numerous well-studied problems in graph theory and graph algorithms. Consequently, there is a long line of research into exact-polynomial time algorithms as well as approximation algorithms for various restrictions of this problem. An important...... that SNDP is W[1]-hard for both arc and vertex connectivity versions on digraphs. The core of our algorithms is composed of new combinatorial results on connectivity in digraphs and undirected graphs....

Study and simulation of a parallel numerical processing machine

International Nuclear Information System (INIS)

Bel Hadj, Slaheddine

1981-12-01

This study has been carried out in the perspective of the implementation on a minicomputer of the NEPTUNIX package (software for the resolution of very large algebra-differential equation systems). Aiming at increasing the system performance, a previous research work has shown the necessity of reducing the execution time of certain numerical computation tasks, which are of frequent use. It has also demonstrated the feasibility of handling these tasks with efficient algorithms of parallel type. The present work deals with the study and simulation of a parallel architecture processor adapted to the fast execution of these algorithms. A minicomputer fitted with a connection to such a parallel processor, has a greatly extended computing power. Then the architecture of a parallel numerical processor, based on the use of VLSI microprocessors and co-processors, is described. Its design aims at the best cost / performance ratio. The last part deals with the simulation processor with the 'CHAMBOR' program. Results show an increasing factor of 30 in speed, in comparison with the execution on a MITRA 15 minicomputer. Moreover the conflicts importance, mainly at the level of access to a shared resource is evaluated. Although this implementation has been designed having in mind a dedicated application, other uses could be envisaged, particularly for the simulation of nuclear reactors: operator guiding system, the behavioural study under accidental circumstances, etc. (author) [fr

Numerical approach to the inverse convection-diffusion problem

International Nuclear Information System (INIS)

Yang, X-H; She, D-X; Li, J-Q

2008-01-01

In this paper, the inverse problem on source term identification in convection-diffusion equation is transformed into an optimization problem. To reduce the computational cost and improve computational accuracy for the optimization problem, a new algorithm, chaos real-coded hybrid-accelerating evolution algorithm (CRHAEA), is proposed, in which an initial population is generated by chaos mapping, and new chaos mutation and simplex evolution operation are used. With the shrinking of searching range, CRHAEA gradually directs to an optimal result with the excellent individuals obtained by real-coded evolution algorithm. Its convergence is analyzed. Its efficiency is demonstrated by 15 test functions. Numerical simulation shows that CRHAEA has some advantages over the real-coded accelerated evolution algorithm, the chaos algorithm and the pure random search algorithm

Numerical semigroups in a problem about economic incentives for consumers

OpenAIRE

Robles-Pérez, Aureliano M.; Rosales, José Carlos

2016-01-01

Motivated by a promotion to increase the number of musical downloads, we introduce the concept of $C$-incentive and show an algorithm that compute the smallest $C$-incentive containing a subset $X \\subseteq {\\mathbb N}$. On the other hand, in order to study $C$-incentives, we see that we can focus on numerical $C$-incentives. Then, we establish that the set formed by all numerical $C$-incentives is a Frobenius pseudo-variety and we show an algorithmic process to recurrently build such a pseud...

Agent-based Algorithm for Spatial Distribution of Objects

KAUST Repository

Collier, Nathan

2012-06-02

In this paper we present an agent-based algorithm for the spatial distribution of objects. The algorithm is a generalization of the bubble mesh algorithm, initially created for the point insertion stage of the meshing process of the finite element method. The bubble mesh algorithm treats objects in space as bubbles, which repel and attract each other. The dynamics of each bubble are approximated by solving a series of ordinary differential equations. We present numerical results for a meshing application as well as a graph visualization application.

Numerical approach of the quantum circuit theory

Energy Technology Data Exchange (ETDEWEB)

Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.

2017-03-15

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

Numerical approach of the quantum circuit theory

International Nuclear Information System (INIS)

Silva, J.J.B.; Duarte-Filho, G.C.; Almeida, F.A.G.

2017-01-01

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

Numerical approach of the quantum circuit theory

Science.gov (United States)

Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.

2017-03-01

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

Evaluation of sea-surface photosynthetically available radiation algorithms under various sky conditions and solar elevations.

Science.gov (United States)

Somayajula, Srikanth Ayyala; Devred, Emmanuel; Bélanger, Simon; Antoine, David; Vellucci, V; Babin, Marcel

2018-04-20

In this study, we report on the performance of satellite-based photosynthetically available radiation (PAR) algorithms used in published oceanic primary production models. The performance of these algorithms was evaluated using buoy observations under clear and cloudy skies, and for the particular case of low sun angles typically encountered at high latitudes or at moderate latitudes in winter. The PAR models consisted of (i) the standard one from the NASA-Ocean Biology Processing Group (OBPG), (ii) the Gregg and Carder (GC) semi-analytical clear-sky model, and (iii) look-up-tables based on the Santa Barbara DISORT atmospheric radiative transfer (SBDART) model. Various combinations of atmospheric inputs, empirical cloud corrections, and semi-analytical irradiance models yielded a total of 13 (11 + 2 developed in this study) different PAR products, which were compared with in situ measurements collected at high frequency (15 min) at a buoy site in the Mediterranean Sea (the "BOUée pour l'acquiSition d'une Série Optique à Long termE," or, "BOUSSOLE" site). An objective ranking method applied to the algorithm results indicated that seven PAR products out of 13 were well in agreement with the in situ measurements. Specifically, the OBPG method showed the best overall performance with a root mean square difference (RMSD) (bias) of 19.7% (6.6%) and 10% (6.3%) followed by the look-up-table method with a RMSD (bias) of 25.5% (6.8%) and 9.6% (2.6%) at daily and monthly scales, respectively. Among the four methods based on clear-sky PAR empirically corrected for cloud cover, the Dobson and Smith method consistently underestimated daily PAR while the Budyko formulation overestimated daily PAR. Empirically cloud-corrected methods using cloud fraction (CF) performed better under quasi-clear skies (CF0.7), however, all methods showed larger RMSD differences (biases) ranging between 32% and 80.6% (-54.5%-8.7%). Finally, three methods tested for low sun elevations revealed

An ant colony optimization algorithm for phylogenetic estimation under the minimum evolution principle

Directory of Open Access Journals (Sweden)

Milinkovitch Michel C

2007-11-01

Full Text Available Abstract Background Distance matrix methods constitute a major family of phylogenetic estimation methods, and the minimum evolution (ME principle (aiming at recovering the phylogeny with shortest length is one of the most commonly used optimality criteria for estimating phylogenetic trees. The major difficulty for its application is that the number of possible phylogenies grows exponentially with the number of taxa analyzed and the minimum evolution principle is known to belong to the NP MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8xdX7Kaeeiuaafaaa@3888@-hard class of problems. Results In this paper, we introduce an Ant Colony Optimization (ACO algorithm to estimate phylogenies under the minimum evolution principle. ACO is an optimization technique inspired from the foraging behavior of real ant colonies. This behavior is exploited in artificial ant colonies for the search of approximate solutions to discrete optimization problems. Conclusion We show that the ACO algorithm is potentially competitive in comparison with state-of-the-art algorithms for the minimum evolution principle. This is the first application of an ACO algorithm to the phylogenetic estimation problem.

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding.

Science.gov (United States)

Wang, Xiaogang; Chen, Wen; Chen, Xudong

2014-09-22

We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

Toward human-centered algorithm design

Directory of Open Access Journals (Sweden)

Eric PS Baumer

2017-07-01

Full Text Available As algorithms pervade numerous facets of daily life, they are incorporated into systems for increasingly diverse purposes. These systems’ results are often interpreted differently by the designers who created them than by the lay persons who interact with them. This paper offers a proposal for human-centered algorithm design, which incorporates human and social interpretations into the design process for algorithmically based systems. It articulates three specific strategies for doing so: theoretical, participatory, and speculative. Drawing on the author’s work designing and deploying multiple related systems, the paper provides a detailed example of using a theoretical approach. It also discusses findings pertinent to participatory and speculative design approaches. The paper addresses both strengths and challenges for each strategy in helping to center the process of designing algorithmically based systems around humans.

A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation

Directory of Open Access Journals (Sweden)

S. Battal Gazi Karakoç

2016-02-01

Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.  

Modification of the algorithm for steam turbine control under loading drop

International Nuclear Information System (INIS)

Nikitin, Yu.V.; Mirnyj, V.A.; Gritsenko, V.N.; Nesterov, L.V.

1989-01-01

Problem related to powerful steam turbine control in case of emergency loading drop is considered. Two laws of control creating conditions for qualitative operation of control system under conditions considered are compared. The system of turbine control comprises the turbine major actuating mechanisms (electrohydraulic transducer, high-pressure servomotor, cut-off slide valve) actuating mechanisms of pulse discharge channel (low-pressure servomotor cut-off slide valve, low-pressure servomotor) and regulator. The frequency of the turbine rotor rotation is the parameter to be controlled in the mode of loading drop. The algorithms considered are based on linear variant of the optimal control theory. One of them is realized in electrohydraulic system of the K-750-65/3000 turbine control at the Ignalinsk NPP

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

Science.gov (United States)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Numerical Simulation of Liquid Sloshing Problem under Resonant Excitation

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Fu-kun Gui

2014-04-01

Full Text Available Numerical simulations were conducted to investigate the fluid resonance in partially filled rectangular tank based on the OpenFOAM package of viscous fluid model. The numerical model was validated by the available theoretical, numerical, and experimental data. The study was mainly focused on the large amplitude sloshing motion and the corresponding impact force around the resonant condition. It was found that, for the 2D situation, the double pressure peaks happened near to the side walls around the still water level. And they were corresponding to the local free surface rising up and set-down, respectively. The impulsive loads on the tank corner with extreme magnitudes were observed as the free surface impacted the ceiling. The 3D numerical results showed that the free surface amplitudes along the side walls varied diversely, depending on the direction and frequency of the external excitation. The characteristics of the pressure around the still water level and tank ceiling were also presented. According to the computational results, it was found that the 2D numerical model can predict the impact loads near the still water level as accurately as 3D model. However, the impulsive pressure near the tank ceiling corner was remarkably underestimated.

Hardware Acceleration of Adaptive Neural Algorithms.

Energy Technology Data Exchange (ETDEWEB)

James, Conrad D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-11-01

As tradit ional numerical computing has faced challenges, researchers have turned towards alternative computing approaches to reduce power - per - computation metrics and improve algorithm performance. Here, we describe an approach towards non - conventional computing that strengthens the connection between machine learning and neuroscience concepts. The Hardware Acceleration of Adaptive Neural Algorithms (HAANA) project ha s develop ed neural machine learning algorithms and hardware for applications in image processing and cybersecurity. While machine learning methods are effective at extracting relevant features from many types of data, the effectiveness of these algorithms degrades when subjected to real - world conditions. Our team has generated novel neural - inspired approa ches to improve the resiliency and adaptability of machine learning algorithms. In addition, we have also designed and fabricated hardware architectures and microelectronic devices specifically tuned towards the training and inference operations of neural - inspired algorithms. Finally, our multi - scale simulation framework allows us to assess the impact of microelectronic device properties on algorithm performance.

Mathematical modelling and numerical resolution of multi-phase compressible fluid flows problems

International Nuclear Information System (INIS)

Lagoutiere, Frederic

2000-01-01

This work deals with Eulerian compressible multi-species fluid dynamics, the species being either mixed or separated (with interfaces). The document is composed of three parts. The first parts devoted to the numerical resolution of model problems: advection equation, Burgers equation, and Euler equations, in dimensions one and two. The goal is to find a precise method, especially for discontinuous initial conditions, and we develop non dissipative algorithms. They are based on a downwind finite-volume discretization under some stability constraints. The second part treats of the mathematical modelling of fluids mixtures. We construct and analyse a set of multi-temperature and multi-pressure models that are entropy, symmetrizable, hyperbolic, not ever conservative. In the third part, we apply the ideas developed in the first part (downwind discretization) to the numerical resolution of the partial differential problems we have constructed for fluids mixtures in the second part. We present some numerical results in dimensions one and two. (author) [fr

Development status of the experimental and numerical load analysis of package units CASTOR registered under drop test conditions

International Nuclear Information System (INIS)

Voelzer, Walter; Schaefer, Marc; Rumanus, Erkan; Liedtke, Ralph; Brehmer, Frank

2012-01-01

The mechanical integrity of package units CASTOR registered for a 9-m drop test under accident conditions has to be demonstrated according the requirements of IAEA among others. For reduction of the loads the containers have to be equipped with shock absorbers on the bottom and top sides. The determination of loads under drop test conditions can be performed with experimental or numerical methods. Due to the complexity of the load state and the verification of results both methods are usually used for integrity demonstration. The numerical codes have to model the short-term dynamic behavior of the whole container for different drop orientations and temperatures, local stress states have to be quantifiable for assessment. One of the problems is the modeling of the material behavior of wood that is used in the shock absorbers. The so far used energetic calculation approach will be replaced by a dynamic approach, the numerical models will have to be verified by experimental drop tests.

Numerical Treatment of Two-phase Flow in Porous Media Including Specific Interfacial Area

KAUST Repository

El-Amin, Mohamed

2015-06-01

In this work, we present a numerical treatment for the model of two-phase flow in porous media including specific interfacial area. For numerical discretization we use the cell-centered finite difference (CCFD) method based on the shifting-matrices method which can reduce the time-consuming operations. A new iterative implicit algorithm has been developed to solve the problem under consideration. All advection and advection-like terms that appear in saturation equation and interfacial area equation are treated using upwind schemes. Selected simulation results such as pc–Sw–awn surface, capillary pressure, saturation and specific interfacial area with various values of model parameters have been introduced. The simulation results show a good agreement with those in the literature using either pore network modeling or Darcy scale modeling.

Numerical analysis using Sage

CERN Document Server

Anastassiou, George A

2015-01-01

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application.  Answers may be verified using Sage.  The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®.  Sage is  open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a p...

Greedy algorithms for high-dimensional non-symmetric linear problems***

Directory of Open Access Journals (Sweden)

Cancès E.

2013-12-01

Full Text Available In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor product functions, each term of which is iteratively computed via a greedy algorithm ? . There exists a good theoretical framework for these methods in the case of (linear and nonlinear symmetric elliptic problems. However, the convergence results are not valid any more as soon as the problems under consideration are not symmetric. We present here a review of the main algorithms proposed in the literature to circumvent this difficulty, together with some new approaches. The theoretical convergence results and the practical implementation of these algorithms are discussed. Their behaviors are illustrated through some numerical examples. Dans cet article, nous présentons une famille de méthodes numériques pour résoudre des problèmes linéaires non symétriques en grande dimension. Le principe de ces approches est de représenter une fonction dépendant d’un grand nombre de variables sous la forme d’une somme de fonctions produit tensoriel, dont chaque terme est calculé itérativement via un algorithme glouton ? . Ces méthodes possèdent de bonnes propriétés théoriques dans le cas de problèmes elliptiques symétriques (linéaires ou non linéaires, mais celles-ci ne sont plus valables dès lors que les problèmes considérés ne sont plus symétriques. Nous présentons une revue des principaux algorithmes proposés dans la littérature pour contourner cette difficulté ainsi que de nouvelles approches que nous proposons. Les résultats de convergence théoriques et la mise en oeuvre pratique de ces algorithmes sont détaillés et leur comportement est illustré au travers d’exemples numériques.

Analytical and numerical analysis of frictional damage in quasi brittle materials

Science.gov (United States)

Zhu, Q. Z.; Zhao, L. Y.; Shao, J. F.

2016-07-01

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori-Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress-strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

Science.gov (United States)

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well

Object-Oriented Implementation of Adaptive Mesh Refinement Algorithms

Directory of Open Access Journals (Sweden)

William Y. Crutchfield

1993-01-01

Full Text Available We describe C++ classes that simplify development of adaptive mesh refinement (AMR algorithms. The classes divide into two groups, generic classes that are broadly useful in adaptive algorithms, and application-specific classes that are the basis for our AMR algorithm. We employ two languages, with C++ responsible for the high-level data structures, and Fortran responsible for low-level numerics. The C++ implementation is as fast as the original Fortran implementation. Use of inheritance has allowed us to extend the original AMR algorithm to other problems with greatly reduced development time.

Principal component analysis networks and algorithms

CERN Document Server

Kong, Xiangyu; Duan, Zhansheng

2017-01-01

This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.

Matlab programming for numerical analysis

CERN Document Server

Lopez, Cesar

2014-01-01

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become

Algorithmic Principles of Mathematical Programming

NARCIS (Netherlands)

Faigle, Ulrich; Kern, Walter; Still, Georg

2002-01-01

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear

FRAMEWORK FOR COMPARING SEGMENTATION ALGORITHMS

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G. Sithole

2015-05-01

Full Text Available The notion of a ‘Best’ segmentation does not exist. A segmentation algorithm is chosen based on the features it yields, the properties of the segments (point sets it generates, and the complexity of its algorithm. The segmentation is then assessed based on a variety of metrics such as homogeneity, heterogeneity, fragmentation, etc. Even after an algorithm is chosen its performance is still uncertain because the landscape/scenarios represented in a point cloud have a strong influence on the eventual segmentation. Thus selecting an appropriate segmentation algorithm is a process of trial and error. Automating the selection of segmentation algorithms and their parameters first requires methods to evaluate segmentations. Three common approaches for evaluating segmentation algorithms are ‘goodness methods’, ‘discrepancy methods’ and ‘benchmarks’. Benchmarks are considered the most comprehensive method of evaluation. This paper shortcomings in current benchmark methods are identified and a framework is proposed that permits both a visual and numerical evaluation of segmentations for different algorithms, algorithm parameters and evaluation metrics. The concept of the framework is demonstrated on a real point cloud. Current results are promising and suggest that it can be used to predict the performance of segmentation algorithms.

Structure-preserving algorithms for oscillatory differential equations II

CERN Document Server

Wu, Xinyuan; Shi, Wei

2015-01-01

This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods.  The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and sc...

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

Science.gov (United States)

Bui, Trong T.

1999-01-01

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Some nonlinear space decomposition algorithms

Energy Technology Data Exchange (ETDEWEB)

Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)

1996-12-31

Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.

Analysis of Electromagnetic Propagation from MHz to THz with a Memory-Optimised CPML-FDTD Algorithm

Directory of Open Access Journals (Sweden)

A. Rodríguez-Sánchez

2018-01-01

Full Text Available FDTD method opened a fertile research area on the numerical analysis of electromagnetic phenomena under a wide range of media and propagation conditions, providing an extensive analysis of electromagnetic behaviour like propagation, reflection, refraction, and multitrajectory phenomena. In this paper, we present an optimised FDTD-CPML algorithm, focused in saving memory while increasing the performance of the algorithm. We particularly implement FDTD-CPML method at high frequency bands, used in several telecommunications applications as well as in nanoelectromagnetism. We show an analysis of the performance of the algorithm in single and double precision, as well as a stability of the algorithm analysis, from where we conclude that the implemented CPML ABC constitutes a robust choice in terms of precision and accuracy for the high frequencies herein considered. It is important to recall that the CPML ABC parameters provided in this paper are fixed for the tested range of frequencies, that is, from MHz to THz.

Time-advance algorithms based on Hamilton's principle

International Nuclear Information System (INIS)

Lewis, H.R.; Kostelec, P.J.

1993-01-01

Time-advance algorithms based on Hamilton's variational principle are being developed for application to problems in plasma physics and other areas. Hamilton's principle was applied previously to derive a system of ordinary differential equations in time whose solution provides an approximation to the evolution of a plasma described by the Vlasov-Maxwell equations. However, the variational principle was not used to obtain an algorithm for solving the ordinary differential equations numerically. The present research addresses the numerical solution of systems of ordinary differential equations via Hamilton's principle. The basic idea is first to choose a class of functions for approximating the solution of the ordinary differential equations over a specific time interval. Then the parameters in the approximating function are determined by applying Hamilton's principle exactly within the class of approximating functions. For example, if an approximate solution is desired between time t and time t + Δ t, the class of approximating functions could be polynomials in time up to some degree. The issue of how to choose time-advance algorithms is very important for achieving efficient, physically meaningful computer simulations. The objective is to reliably simulate those characteristics of an evolving system that are scientifically most relevant. Preliminary numerical results are presented, including comparisons with other computational methods

Structure-preserving geometric algorithms for plasma physics and beam physics

Science.gov (United States)

Qin, Hong

2017-10-01

Standard algorithms in the plasma physics and beam physics do not possess the long-term accuracy and fidelity required in the study of multi-scale dynamics, because they do not preserve the geometric structures of the physical systems, such as the local energy-momentum conservation, symplectic structure and gauge symmetry. As a result, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty, since 2008 structure-preserving geometric algorithms have been developed. This new generation of algorithms utilizes advanced techniques, such as interpolating differential forms, canonical and non-canonical symplectic integrators, and finite element exterior calculus to guarantee gauge symmetry and charge conservation, and the conservation of energy-momentum and symplectic structure. It is our vision that future numerical capabilities in plasma physics and beam physics will be based on the structure-preserving geometric algorithms.

Combinatorial optimization theory and algorithms

CERN Document Server

Korte, Bernhard

2018-01-01

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial opti...

Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning

Science.gov (United States)

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

Pole placement algorithm for control of civil structures subjected to earthquake excitation

Directory of Open Access Journals (Sweden)

Nikos Pnevmatikos

2017-04-01

Full Text Available In this paper the control algorithm for controlled civil structures subjected to earthquake excitation is thoroughly investigated. The objective of this work is the control of structures by means of the pole placement algorithm, in order to improve their response against earthquake actions. Successful application of the algorithm requires judicious placement of the closed-loop eigenvalues from the part of the designer. The pole placement algorithm was widely applied to control mechanical systems. In this paper, a modification in the mathematical background of the algorithm in order to be suitable for civil fixed structures is primarily presented. The proposed approach is demonstrated by numerical simulations for the control of both single and multi-degree of freedom systems subjected to seismic actions. Numerical results have shown that the control algorithm is efficient in reducing the response of building structures, with small amount of required control forces.

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

Institute of Scientific and Technical Information of China (English)

WANG; Shunjin; ZHANG; Hua

2006-01-01

The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

Inversion algorithms for the spherical Radon and cosine transform

International Nuclear Information System (INIS)

Louis, A K; Riplinger, M; Spiess, M; Spodarev, E

2011-01-01

We consider two integral transforms which are frequently used in integral geometry and related fields, namely the spherical Radon and cosine transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulae or algorithms for atomic measures have been derived, which are not so important for applications. We focus on two- and three-dimensional cases, where we also show that our method leads to a regularization. Numerical results are presented and show the validity of the resulting algorithms. First, we use synthetic data for the inversion of the Radon transform. Then we apply the algorithm for the inversion of the cosine transform to reconstruct the directional distribution of line processes from finitely many intersections of their lines with test lines (2D) or planes (3D), respectively. Finally we apply our method to analyse a series of microscopic two- and three-dimensional images of a fibre system

Numerical simulations of the O(3) and CP1 models using the Langevin equations and the Metropolis algorithm

International Nuclear Information System (INIS)

Abdalla, E.; Carneiro, C.E.I.

1988-12-01

The O(3) model, the pure CP 1 model and the CP 1 model minimally coupled to fermions are numerically simulated. The equivalence between the O(3) and the bound state of the pure CP 1 model is investigated. It is shown that: the relations g O(3 ) = 2 g CP 1 and E O(3 )= 2E CP 1 + 2, for the coupling constants and energies hold beyond the classical level; the mass gap as a function of the coupling is the same for both models. The mass gap for the CP 1 minimally coupled to fermions is also calculated. The calculations are performed using different techniques. The proposal by Namiki and colaborators to enforce constraints on Langevin equations and Parisi's technique to calculate correlation functions via Langevin equations is tested. The results are compared with those obtained using the multi-hit Metropolis algorithm. (author) [pt

Numerical methods for Bayesian inference in the face of aging

International Nuclear Information System (INIS)

Clarotti, C.A.; Villain, B.; Procaccia, H.

1996-01-01

In recent years, much attention has been paid to Bayesian methods for Risk Assessment. Until now, these methods have been studied from a theoretical point of view. Researchers have been mainly interested in: studying the effectiveness of Bayesian methods in handling rare events; debating about the problem of priors and other philosophical issues. An aspect central to the Bayesian approach is numerical computation because any safety/reliability problem, in a Bayesian frame, ends with a problem of numerical integration. This aspect has been neglected until now because most Risk studies assumed the Exponential model as the basic probabilistic model. The existence of conjugate priors makes numerical integration unnecessary in this case. If aging is to be taken into account, no conjugate family is available and the use of numerical integration becomes compulsory. EDF (National Board of Electricity, of France) and ENEA (National Committee for Energy, New Technologies and Environment, of Italy) jointly carried out a research program aimed at developing quadrature methods suitable for Bayesian Interference with underlying Weibull or gamma distributions. The paper will illustrate the main results achieved during the above research program and will discuss, via some sample cases, the performances of the numerical algorithms which on the appearance of stress corrosion cracking in the tubes of Steam Generators of PWR French power plants. (authors)

Role of Brittle Behaviour of Soft Calcarenites Under Low Confinement: Laboratory Observations and Numerical Investigation

Science.gov (United States)

Lollino, Piernicola; Andriani, Gioacchino Francesco

2017-07-01

The strength decay that occurs in the post-peak stage, under low confinement stress, represents a key factor of the stress-strain behaviour of rocks. However, for soft rocks this issue is generally underestimated or even neglected in the solution of boundary value problems, as for example those concerning the stability of underground cavities or rocky cliffs. In these cases, the constitutive models frequently used in limit equilibrium analyses or more sophisticated numerical calculations are, respectively, rigid-plastic or elastic-perfectly plastic. In particular, most of commercial continuum-based numerical codes propose a variety of constitutive models, including elasticity, elasto-plasticity, strain-softening and elasto-viscoplasticity, which are not exhaustive in simulating the progressive failure mechanisms affecting brittle rock materials, these being characterized by material detachment and crack opening and propagation. As a consequence, a numerical coupling with mechanical joint propagation is needed to cope with fracture mechanics. Therefore, continuum-based applications that treat the simulation of the failure processes of intact rock masses at low stress levels may need the adoption of numerical techniques capable of implementing fracture mechanics and rock brittleness concepts, as it is shown in this paper. This work is aimed at highlighting, for some applications of rock mechanics, the essential role of post-peak brittleness of soft rocks by means of the application of a hybrid finite-discrete element method. This method allows for a proper simulation of the brittle rock behaviour and the related mechanism of fracture propagation. In particular, the paper presents two ideal problems, represented by a shallow underground cave and a vertical cliff, for which the evolution of the stability conditions is investigated by comparing the solutions obtained implementing different brittle material responses with those resulting from the assumption of perfectly

Time Reversal Reconstruction Algorithm Based on PSO Optimized SVM Interpolation for Photoacoustic Imaging

Directory of Open Access Journals (Sweden)

Mingjian Sun

2015-01-01

Full Text Available Photoacoustic imaging is an innovative imaging technique to image biomedical tissues. The time reversal reconstruction algorithm in which a numerical model of the acoustic forward problem is run backwards in time is widely used. In the paper, a time reversal reconstruction algorithm based on particle swarm optimization (PSO optimized support vector machine (SVM interpolation method is proposed for photoacoustics imaging. Numerical results show that the reconstructed images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation based time reversal algorithm, which can provide higher imaging quality by using significantly fewer measurement positions or scanning times.

Numerical Simulation of Interactions between Corrosion Pits on Stainless Steel under Loading Conditions

International Nuclear Information System (INIS)

Wang, Haitao; Han, En-Hou

2017-01-01

The interactions between corrosion pits on stainless steel under loading conditions are studied by using a cellular automata model coupled with finite element method at a mesoscopic scale. The cellular automata model focuses on a metal/film/electrolyte system, including anodic dissolution, passivation, diffusion of hydrogen ions and salt film hydrolysis. The Chopard block algorithm is used to improve the diffusion simulation efficiency. The finite element method is used to calculate the stress concentration on the pit surface during pit growth, and the effect of local stress and strain on anodic current is obtained by using the Gutman model, which is used as the boundary conditions of the cellular automata model. The transient current characteristics of the interactions between corrosion pits under different simulation factors including the breakdown of the passive film at the pit mouth and the diffusion of hydrogen ions are analyzed. The analysis of the pit stability product shows that the simulation results are close to the experimental conclusions.

Numerical Simulation of Interactions between Corrosion Pits on Stainless Steel under Loading Conditions

Energy Technology Data Exchange (ETDEWEB)

Wang, Haitao; Han, En-Hou [Chinese Academy of Sciences, Shenyang (China)

2017-04-15

The interactions between corrosion pits on stainless steel under loading conditions are studied by using a cellular automata model coupled with finite element method at a mesoscopic scale. The cellular automata model focuses on a metal/film/electrolyte system, including anodic dissolution, passivation, diffusion of hydrogen ions and salt film hydrolysis. The Chopard block algorithm is used to improve the diffusion simulation efficiency. The finite element method is used to calculate the stress concentration on the pit surface during pit growth, and the effect of local stress and strain on anodic current is obtained by using the Gutman model, which is used as the boundary conditions of the cellular automata model. The transient current characteristics of the interactions between corrosion pits under different simulation factors including the breakdown of the passive film at the pit mouth and the diffusion of hydrogen ions are analyzed. The analysis of the pit stability product shows that the simulation results are close to the experimental conclusions.

An Initial Examination for Verifying Separation Algorithms by Simulation

Science.gov (United States)

White, Allan L.; Neogi, Natasha; Herencia-Zapana, Heber

2012-01-01

An open question in algorithms for aircraft is what can be validated by simulation where the simulation shows that the probability of undesirable events is below some given 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 proposes a goal based on the number of flights per year in several regions. The paper examines the probabilistic interpretation of this goal and computes the number of trials needed to establish it at an equivalent confidence level. Since any simulation is likely to consider the algorithms for only one type of event and there are several types of events, the paper examines under what conditions this separate consideration is valid. This paper is an initial effort, and as such, it considers separation maneuvers, which are elementary but include numerous aspects of aircraft behavior. The scenario includes decisions under uncertainty since the position of each aircraft is only known to the other by broadcasting where GPS believes each aircraft to be (ADS-B). Each aircraft operates under feedback control with perturbations. It is shown that a scenario three or 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.

Improved numerical methods for quantum field theory (Outstanding junior investigator award)

International Nuclear Information System (INIS)

Sokal, A.D.

1992-01-01

We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo, Swendsen-Wang and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory

Improved numerical methods for quantum field theory (Outstanding junior investigator award)

International Nuclear Information System (INIS)

Sokal, A.D.

1993-01-01

We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo (MGMC), Swendsen-Wang (SW) and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory

Efficient numerical methods for fluid- and electrodynamics on massively parallel systems

Energy Technology Data Exchange (ETDEWEB)

Zudrop, Jens

2016-07-01

In the last decade, computer technology has evolved rapidly. Modern high performance computing systems offer a tremendous amount of computing power in the range of a few peta floating point operations per second. In contrast, numerical software development is much slower and most existing simulation codes cannot exploit the full computing power of these systems. Partially, this is due to the numerical methods themselves and partially it is related to bottlenecks within the parallelization concept and its data structures. The goal of the thesis is the development of numerical algorithms and corresponding data structures to remedy both kinds of parallelization bottlenecks. The approach is based on a co-design of the numerical schemes (including numerical analysis) and their realizations in algorithms and software. Various kinds of applications, from multicomponent flows (Lattice Boltzmann Method) to electrodynamics (Discontinuous Galerkin Method) to embedded geometries (Octree), are considered and efficiency of the developed approaches is demonstrated for large scale simulations.

An optimal iterative algorithm to solve Cauchy problem for Laplace equation

KAUST Repository

Majeed, Muhammad Usman; Laleg-Kirati, Taous-Meriem

2015-01-01

iterative algorithm is developed that minimizes the mean square error in states. Finite difference discretization schemes are used to discretize first order system. After numerical discretization algorithm equations are derived taking inspiration from Kalman

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

Science.gov (United States)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Improved 3-D turbomachinery CFD algorithm

Science.gov (United States)

Janus, J. Mark; Whitfield, David L.

1988-01-01

The building blocks of a computer algorithm developed for the time-accurate flow analysis of rotating machines are described. The flow model is a finite volume method utilizing a high resolution approximate Riemann solver for interface flux definitions. This block LU implicit numerical scheme possesses apparent unconditional stability. Multi-block composite gridding is used to orderly partition the field into a specified arrangement. Block interfaces, including dynamic interfaces, are treated such as to mimic interior block communication. Special attention is given to the reduction of in-core memory requirements by placing the burden on secondary storage media. Broad applicability is implied, although the results presented are restricted to that of an even blade count configuration. Several other configurations are presently under investigation, the results of which will appear in subsequent publications.

Research on data auto-analysis algorithms in the explosive detection system

International Nuclear Information System (INIS)

Wang Haidong; Li Yuanjing; Yang Yigang; Li Tiezhu; Chen Boxian; Cheng Jianping

2006-01-01

This paper mainly describe some auto-analysis algorithms in explosive detection system with TNA method. These include the auto-calibration algorithm when disturbed by other factors, MCA auto-calibration algorithm with calibrated spectrum, the auto-fitting and integral of hydrogen and nitrogen elements data. With these numerical algorithms, the authors can automatically and precisely analysis the gamma-spectra and ultimately achieve the explosive auto-detection. (authors)

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Science.gov (United States)

Soize, C.

2017-11-01

This paper deals with the optimal design of a titanium mesoscale implant in a cortical bone for which the apparent elasticity tensor is modeled by a non-Gaussian random field at mesoscale, which has been experimentally identified. The external applied forces are also random. The design parameters are geometrical dimensions related to the geometry of the implant. The stochastic elastostatic boundary value problem is discretized by the finite element method. The objective function and the constraints are related to normal, shear, and von Mises stresses inside the cortical bone. The constrained nonconvex optimization problem in presence of uncertainties is solved by using a probabilistic learning algorithm that allows for considerably reducing the numerical cost with respect to the classical approaches.

Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.

Science.gov (United States)

Zabet, K; Rossiter, J A; Haber, R; Abdullah, M

2017-11-01

This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant. Copyright © 2017 ISA. All rights reserved.

Numerical simulations on a high-temperature particle moving in coolant

International Nuclear Information System (INIS)

Li Xiaoyan; Shang Zhi; Xu Jijun

2006-01-01

This study considers the coupling effect between film boiling heat transfer and evaporation drag around a hot-particle in cold liquid. Taking momentum and energy equations of the vapor film into account, a transient single particle model under FCI conditions has been established. The numerical simulations on a high-temperature particle moving in coolant have been performed using Gear algorithm. Adaptive dynamic boundary method is adopted during simulating to matching the dynamic boundary that is caused by vapor film changing. Based on the method presented above, the transient process of high-temperature particles moving in coolant can be simulated. The experimental results prove the validity of the HPMC model. (authors)

Optimal pricing and replenishment policies for instantaneous deteriorating items with backlogging and trade credit under inflation

Science.gov (United States)

Sundara Rajan, R.; Uthayakumar, R.

2017-12-01

In this paper we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation and trade credit. Demand rate is a linear function of selling price and decreases negative exponentially with time over a finite planning horizon. Shortages are allowed and partially backlogged. Under these conditions, we model the retailer's inventory system as a profit maximization problem to determine the optimal selling price, optimal order quantity and optimal replenishment time. An easy-to-use algorithm is developed to determine the optimal replenishment policies for the retailer. We also provide optimal present value of profit when shortages are completely backlogged as a special case. Numerical examples are presented to illustrate the algorithm provided to obtain optimal profit. And we also obtain managerial implications from numerical examples to substantiate our model. The results show that there is an improvement in total profit from complete backlogging rather than the items being partially backlogged.

Error and symmetry analysis of Misner's algorithm for spherical harmonic decomposition on a cubic grid

International Nuclear Information System (INIS)

Fiske, David R

2006-01-01

Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must perform some sort of interpolation in order to compute them when data are stored on a cubic lattice. Misner (2004 Class. Quantum Grav. 21 S243) presented a novel algorithm for computing the spherical harmonic components of data represented on a cubic grid, which has been found in real applications to be both efficient and robust to the presence of mesh refinement boundaries. At the same time, however, practical applications of the algorithm require knowledge of how the truncation errors of the algorithm depend on the various parameters in the algorithm. Based on analytic arguments and experience using the algorithm in real numerical simulations, I explore these dependences and provide a rule of thumb for choosing the parameters based on the truncation errors of the underlying data. I also demonstrate that symmetries in the spherical harmonics themselves allow for an even more efficient implementation of the algorithm than was suggested by Misner in his original paper

Decoherence in optimized quantum random-walk search algorithm

International Nuclear Information System (INIS)

Zhang Yu-Chao; Bao Wan-Su; Wang Xiang; Fu Xiang-Qun

2015-01-01

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative. (paper)

Final Technical Report [Scalable methods for electronic excitations and optical responses of nanostructures: mathematics to algorithms to observables

Energy Technology Data Exchange (ETDEWEB)

Saad, Yousef

2014-03-19

The master project under which this work is funded had as its main objective to develop computational methods for modeling electronic excited-state and optical properties of various nanostructures. The specific goals of the computer science group were primarily to develop effective numerical algorithms in Density Functional Theory (DFT) and Time Dependent Density Functional Theory (TDDFT). There were essentially four distinct stated objectives. The first objective was to study and develop effective numerical algorithms for solving large eigenvalue problems such as those that arise in Density Functional Theory (DFT) methods. The second objective was to explore so-called linear scaling methods or Methods that avoid diagonalization. The third was to develop effective approaches for Time-Dependent DFT (TDDFT). Our fourth and final objective was to examine effective solution strategies for other problems in electronic excitations, such as the GW/Bethe-Salpeter method, and quantum transport problems.

Computer program for regional assessment of lung perfusion defect. Part II - verification of the algorithm

International Nuclear Information System (INIS)

Stefaniak, B.

2002-01-01

As described earlier, a dedicated computer program was developed for quantitative evaluation of regional lung perfusion defects, visualized by pulmonary scintigraphy. The correctness of the basic assumptions accepted to construct the algorithms and of the all program functions needed to be checked, before application of the program into the clinical routine. The aim of this study was to verified the program using various software instruments and physical models. Evaluation of the proposed method was performed using software procedures, physical lung phantom, and selected lung image.The reproducibility of lung regions, defined by the program was found excellent. No significant distortion of registered data was observed after ROI transformation into the circle and retransformation into the original shape. The obtained results comprised parametric presentation of activity defects as well as a set of numerical indices which defined extent and intensity of decreased counts density. Among these indices PD2 and DM* were proved the most suitable for the above purposes. The obtained results indicate that the algorithms used for the program construction were correct and suitable for the aim of the study. The above algorithms enable function under study to be presented graphically with true imaging of activity distribution, as well as numerical indices, defining extent and intensity of activity defects to calculated. (author)

Seismic active control by a heuristic-based algorithm

International Nuclear Information System (INIS)

Tang, Yu.

1996-01-01

A heuristic-based algorithm for seismic active control is generalized to permit consideration of the effects of control-structure interaction and actuator dynamics. Control force is computed at onetime step ahead before being applied to the structure. Therefore, the proposed control algorithm is free from the problem of time delay. A numerical example is presented to show the effectiveness of the proposed control algorithm. Also, two indices are introduced in the paper to assess the effectiveness and efficiency of control laws

Numerical study on lithium titanate battery thermal response under adiabatic condition

International Nuclear Information System (INIS)

Sun, Qiujuan; Wang, Qingsong; Zhao, Xuejuan; Sun, Jinhua; Lin, Zijing

2015-01-01

Highlights: • The thermal behavior of lithium titanate battery during cycling was investigated. • The temperature rate in charging was less than that of discharging in the cycling. • The temperature difference was less than 0.02 °C at 0.5 C in adiabatic condition. • The temperature distribution and thermal runaway of the battery were predicted. - Abstract: To analyze the thermal behavior of 945 mA h lithium titanate battery during charging and discharging processes, the experimental and numerical studies are performed in this work. The cathode and anode of the 945 mA h lithium titanate soft package battery are the lithium nickel–cobalt–manganese-oxide and lithium titanate, respectively. In the experiment, an Accelerating Rate Calorimeter combined with battery cycler is employed to investigate the electrochemical–thermal behavior during charge–discharge cycling under the adiabatic condition. In numerical simulation, one electrochemical-thermal model is adopted to predict the thermal response and validated with the experimental results. From both experimental and simulated results, the profile of potential and current, the heat generation, the temperature, the temperature changing rate and the temperature distribution in the cell are obtained and thermal runaway is predicted. The analysis of the electrochemical and thermal behavior is beneficial for the commercial application of lithium titanate battery in the fields of electric vehicles and hybrid electric vehicles

Kernel Optimum Nearly-analytical Discretization (KOND) algorithm

International Nuclear Information System (INIS)

Kondoh, Yoshiomi; Hosaka, Yasuo; Ishii, Kenji

1992-10-01

Two applications of the Kernel Optimum Nearly-analytical Discretization (KOND) algorithm to the parabolic- and the hyperbolic type equations a presented in detail to lead to novel numerical schemes with very high numerical accuracy. It is demonstrated numerically that the two dimensional KOND-P scheme for the parabolic type yields quite less numerical error by over 2-3 orders and reduces the CPU time to about 1/5 for a common numerical accuracy, compared with the conventional explicit scheme of reference. It is also demonstrated numerically that the KOND-H scheme for the hyperbolic type yields fairly less diffusive error and has fairly high stability for both of the linear- and the nonlinear wave propagations compared with other conventional schemes. (author)

Investigation of eddy currents in the components of the dynamic ergodic divertor of TEXTOR using analytical and numerical approaches

International Nuclear Information System (INIS)

Giesen, B.; Neubauer, O.; Bondarchuk, E.; Doinikov, N.; Kitaev, B.; Obidenko, T.; Panin, A.

2003-01-01

Analytical and numerical approaches for the calculation of eddy currents in mechanical structures of the TEXTOR tokamak in view of operating the dynamic ergodic divertor (DED) coil system fed with the alternating current up to 15 kA at frequencies up to 10 kHz are described. The design of the in-vessel components located close to the DED coils requires detailed investigation of eddy current effects to avoid unacceptable heating and forces. Different approaches depending on skin-layer depths compared with the body dimensions are analyzed. The applied algorithms are based on analytical and simplified numerical methods. Precision and application range of these algorithms have been checked by a numerical code. The simplified technique is rather effective for first step engineering estimation and gives a good understanding for the problem. In a certain parameter range, it results in even precise values and can be used for design optimization of the structures without huge efforts in numerical modeling. After modification of the component's shape prototypes have been manufactured and successfully tested in a full-scale model under the real DED field. The design recommendations resulting from the eddy current studies contributed significantly to the optimized lay out of the DED in-vessel components

Summary of research in applied mathematics, numerical analysis, and computer sciences

Science.gov (United States)

1986-01-01

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

Numerical solution of integral equations, describing mass spectrum of vector mesons

International Nuclear Information System (INIS)

Zhidkov, E.P.; Nikonov, E.G.; Sidorov, A.V.; Skachkov, N.B.; Khoromskij, B.N.

1988-01-01

The description of the numerical algorithm for solving quasipotential integral equation in impulse space is presented. The results of numerical computations of the vector meson mass spectrum and the leptonic decay width are given in comparison with the experimental data

High-accuracy numerical integration of charged particle motion – with application to ponderomotive force

International Nuclear Information System (INIS)

Furukawa, Masaru; Ohkawa, Yushiro; Matsuyama, Akinobu

2016-01-01

A high-accuracy numerical integration algorithm for a charged particle motion is developed. The algorithm is based on the Hamiltonian mechanics and the operator decomposition. The algorithm is made to be time-reversal symmetric, and its order of accuracy can be increased to any order by using a recurrence formula. One of the advantages is that it is an explicit method. An effective way to decompose the time evolution operator is examined; the Poisson tensor is decomposed and non-canonical variables are adopted. The algorithm is extended to a time dependent fields' case by introducing the extended phase space. Numerical tests showing the performance of the algorithm are presented. One is the pure cyclotron motion for a long time period, and the other is a charged particle motion in a rapidly oscillating field. (author)

Numerical simulation of bubble behavior in subcooled flow boiling under velocity and temperature gradient

International Nuclear Information System (INIS)

Bahreini, Mohammad; Ramiar, Abas; Ranjbar, Ali Akbar

2015-01-01

Highlights: • Condensing bubble is numerically investigated using VOF model in OpenFOAM package. • Bubble mass reduces as it goes through condensation and achieves higher velocities. • At a certain time the slope of changing bubble diameter with time, varies suddenly. • Larger bubbles experience more lateral migration to higher velocity regions. • Bubbles migrate back to a lower velocity region for higher liquid subcooling rates. - Abstract: In this paper, numerical simulation of the bubble condensation in the subcooled boiling flow is performed. The interface between two-phase is tracked via the volume of fluid (VOF) method with continuous surface force (CSF) model, implemented in the open source OpenFOAM CFD package. In order to simulate the condensing bubble with the OpenFOAM code, the original energy equation and mass transfer model for phase change have been modified and a new solver is developed. The Newtonian flow is solved using the finite volume scheme based on the pressure implicit with splitting of operators (PISO) algorithm. Comparison of the simulation results with previous experimental data revealed that the model predicted well the behavior of the actual condensing bubble. The bubble lifetime is almost proportional to bubble initial size and is prolonged by increasing the system pressure. In addition, the initial bubble size, subcooling of liquid and velocity gradient play an important role in the bubble deformation behavior. Velocity gradient makes the bubble move to the higher velocity region and the subcooling rate makes it to move back to the lower velocity region.

Numerical simulation of bubble behavior in subcooled flow boiling under velocity and temperature gradient

Energy Technology Data Exchange (ETDEWEB)

Bahreini, Mohammad, E-mail: m.bahreini1990@gmail.com; Ramiar, Abas, E-mail: aramiar@nit.ac.ir; Ranjbar, Ali Akbar, E-mail: ranjbar@nit.ac.ir

2015-11-15

Highlights: • Condensing bubble is numerically investigated using VOF model in OpenFOAM package. • Bubble mass reduces as it goes through condensation and achieves higher velocities. • At a certain time the slope of changing bubble diameter with time, varies suddenly. • Larger bubbles experience more lateral migration to higher velocity regions. • Bubbles migrate back to a lower velocity region for higher liquid subcooling rates. - Abstract: In this paper, numerical simulation of the bubble condensation in the subcooled boiling flow is performed. The interface between two-phase is tracked via the volume of fluid (VOF) method with continuous surface force (CSF) model, implemented in the open source OpenFOAM CFD package. In order to simulate the condensing bubble with the OpenFOAM code, the original energy equation and mass transfer model for phase change have been modified and a new solver is developed. The Newtonian flow is solved using the finite volume scheme based on the pressure implicit with splitting of operators (PISO) algorithm. Comparison of the simulation results with previous experimental data revealed that the model predicted well the behavior of the actual condensing bubble. The bubble lifetime is almost proportional to bubble initial size and is prolonged by increasing the system pressure. In addition, the initial bubble size, subcooling of liquid and velocity gradient play an important role in the bubble deformation behavior. Velocity gradient makes the bubble move to the higher velocity region and the subcooling rate makes it to move back to the lower velocity region.

Privacy preserving randomized gossip algorithms

KAUST Repository

Hanzely, Filip; Konečný , Jakub; Loizou, Nicolas; Richtarik, Peter; Grishchenko, Dmitry

2017-01-01

In this work we present three different randomized gossip algorithms for solving the average consensus problem while at the same time protecting the information about the initial private values stored at the nodes. We give iteration complexity bounds for all methods, and perform extensive numerical experiments.

Privacy preserving randomized gossip algorithms

KAUST Repository

Hanzely, Filip

2017-06-23

In this work we present three different randomized gossip algorithms for solving the average consensus problem while at the same time protecting the information about the initial private values stored at the nodes. We give iteration complexity bounds for all methods, and perform extensive numerical experiments.

Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

Science.gov (United States)

Li, Xiao; Scaglione, Anna

2013-11-01

The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

A delta-rule model of numerical and non-numerical order processing.

Science.gov (United States)

Verguts, Tom; Van Opstal, Filip

2014-06-01

Numerical and non-numerical order processing share empirical characteristics (distance effect and semantic congruity), but there are also important differences (in size effect and end effect). At the same time, models and theories of numerical and non-numerical order processing developed largely separately. Currently, we combine insights from 2 earlier models to integrate them in a common framework. We argue that the same learning principle underlies numerical and non-numerical orders, but that environmental features determine the empirical differences. Implications for current theories on order processing are pointed out. PsycINFO Database Record (c) 2014 APA, all rights reserved.

A Two-Stage Algorithm for the Closed-Loop Location-Inventory Problem Model Considering Returns in E-Commerce

Directory of Open Access Journals (Sweden)

Yanhui Li

2014-01-01

Full Text Available Facility location and inventory control are critical and highly related problems in the design of logistics system for e-commerce. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Focusing on the existing problem in e-commerce logistics system, we formulate a closed-loop location-inventory problem model considering returned merchandise to minimize the total cost which is produced in both forward and reverse logistics networks. To solve this nonlinear mixed programming model, an effective two-stage heuristic algorithm named LRCAC is designed by combining Lagrangian relaxation with ant colony algorithm (AC. Results of numerical examples show that LRCAC outperforms ant colony algorithm (AC on optimal solution and computing stability. The proposed model is able to help managers make the right decisions under e-commerce environment.

Excel spreadsheet in teaching numerical methods

Science.gov (United States)

Djamila, Harimi

2017-09-01

One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.

Parallel computing: numerics, applications, and trends

National Research Council Canada - National Science Library

Trobec, Roman; Vajteršic, Marián; Zinterhof, Peter

2009-01-01

... and/or distributed systems. The contributions to this book are focused on topics most concerned in the trends of today's parallel computing. These range from parallel algorithmics, programming, tools, network computing to future parallel computing. Particular attention is paid to parallel numerics: linear algebra, differential equations, numerica...

Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

Directory of Open Access Journals (Sweden)

Y. Saiki

2007-09-01

Full Text Available An infinite number of unstable periodic orbits (UPOs are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

Verification of the coupled space-angle adaptivity algorithm for the finite element-spherical harmonics method via the method of manufactured solutions

International Nuclear Information System (INIS)

Park, H.; De Oliveira, C. R. E.

2007-01-01

This paper describes the verification of the recently developed space-angle self-adaptive algorithm for the finite element-spherical harmonics method via the Method of Manufactured Solutions. This method provides a simple, yet robust way for verifying the theoretical properties of the adaptive algorithm and interfaces very well with the underlying second-order, even-parity transport formulation. Simple analytic solutions in both spatial and angular variables are manufactured to assess the theoretical performance of the a posteriori error estimates. The numerical results confirm reliability of the developed space-angle error indicators. (authors)

An algorithm for simulating fracture of cohesive–frictional materials

International Nuclear Information System (INIS)

Nukala, Phani K V V; Barai, Pallab; Sampath, Rahul

2010-01-01

Fracture of disordered frictional granular materials is dominated by interfacial failure response that is characterized by de-cohesion followed by frictional sliding response. To capture such an interfacial failure response, we introduce a cohesive–friction random fuse model (CFRFM), wherein the cohesive response of the interface is represented by a linear stress–strain response until a failure threshold, which is then followed by a constant response at a threshold lower than the initial failure threshold to represent the interfacial frictional sliding mechanism. This paper presents an efficient algorithm for simulating fracture of such disordered frictional granular materials using the CFRFM. We note that, when applied to perfectly plastic disordered materials, our algorithm is both theoretically and numerically equivalent to the traditional tangent algorithm (Roux and Hansen 1992 J. Physique II 2 1007) used for such simulations. However, the algorithm is general and is capable of modeling discontinuous interfacial response. Our numerical simulations using the algorithm indicate that the local and global roughness exponents (ζ loc and ζ, respectively) of the fracture surface are equal to each other, and the two-dimensional crack roughness exponent is estimated to be ζ loc = ζ = 0.69 ± 0.03

Modified Covariance Matrix Adaptation – Evolution Strategy algorithm for constrained optimization under uncertainty, application to rocket design

Directory of Open Access Journals (Sweden)

Chocat Rudy

2015-01-01

Full Text Available The design of complex systems often induces a constrained optimization problem under uncertainty. An adaptation of CMA-ES(λ, μ optimization algorithm is proposed in order to efficiently handle the constraints in the presence of noise. The update mechanisms of the parametrized distribution used to generate the candidate solutions are modified. The constraint handling method allows to reduce the semi-principal axes of the probable research ellipsoid in the directions violating the constraints. The proposed approach is compared to existing approaches on three analytic optimization problems to highlight the efficiency and the robustness of the algorithm. The proposed method is used to design a two stage solid propulsion launch vehicle.

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

International Nuclear Information System (INIS)

Talamo, Alberto

2013-01-01

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

Energy Technology Data Exchange (ETDEWEB)

Talamo, Alberto, E-mail: alby@anl.gov [Nuclear Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439 (United States)

2013-05-01

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

KAUST Repository

Zenil, Hector

2018-02-24

We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumeration all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity---both theoretical and numerical---with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.

Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

KAUST Repository

Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

2018-01-01

We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumeration all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity---both theoretical and numerical---with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.

Taylor bubbles at high viscosity ratios: experiments and numerical simulations

Science.gov (United States)

Hewakandamby, Buddhika; Hasan, Abbas; Azzopardi, Barry; Xie, Zhihua; Pain, Chris; Matar, Omar

2015-11-01

The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube, often occurring in gas-liquid slug flows in many industrial applications, particularly oil and gas production. The objective of this study is to investigate the fluid dynamics of three-dimensional Taylor bubble rising in highly viscous silicone oil in a vertical pipe. An adaptive unstructured mesh modelling framework is adopted here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rising and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a `volume of fluid'-type method for the interface-capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Experimental results for the Taylor bubble shape and rise velocity are presented, together with numerical results for the dynamics of the bubbles. A comparison of the simulation predictions with experimental data available in the literature is also presented to demonstrate the capabilities of our numerical method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.

Jointly-check iterative decoding algorithm for quantum sparse graph codes

International Nuclear Information System (INIS)

Jun-Hu, Shao; Bao-Ming, Bai; Wei, Lin; Lin, Zhou

2010-01-01

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation (BP) algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement. (general)

Reliability of lifeline networks under seismic hazard

International Nuclear Information System (INIS)

Selcuk, A. Sevtap; Yuecemen, M. Semih

1999-01-01

Lifelines, such as pipelines, transportation, communication and power transmission systems, are networks which extend spatially over large geographical regions. The quantification of the reliability (survival probability) of a lifeline under seismic threat requires attention, as the proper functioning of these systems during or after a destructive earthquake is vital. In this study, a lifeline is idealized as an equivalent network with the capacity of its elements being random and spatially correlated and a comprehensive probabilistic model for the assessment of the reliability of lifelines under earthquake loads is developed. The seismic hazard that the network is exposed to is described by a probability distribution derived by using the past earthquake occurrence data. The seismic hazard analysis is based on the 'classical' seismic hazard analysis model with some modifications. An efficient algorithm developed by Yoo and Deo (Yoo YB, Deo N. A comparison of algorithms for terminal pair reliability. IEEE Transactions on Reliability 1988; 37: 210-215) is utilized for the evaluation of the network reliability. This algorithm eliminates the CPU time and memory capacity problems for large networks. A comprehensive computer program, called LIFEPACK is coded in Fortran language in order to carry out the numerical computations. Two detailed case studies are presented to show the implementation of the proposed model

Performance-based seismic design of steel frames utilizing colliding bodies algorithm.

Science.gov (United States)

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.

Dynamic Inertia Weight Binary Bat Algorithm with Neighborhood Search

Directory of Open Access Journals (Sweden)

Xingwang Huang

2017-01-01

Full Text Available Binary bat algorithm (BBA is a binary version of the bat algorithm (BA. It has been proven that BBA is competitive compared to other binary heuristic algorithms. Since the update processes of velocity in the algorithm are consistent with BA, in some cases, this algorithm also faces the premature convergence problem. This paper proposes an improved binary bat algorithm (IBBA to solve this problem. To evaluate the performance of IBBA, standard benchmark functions and zero-one knapsack problems have been employed. The numeric results obtained by benchmark functions experiment prove that the proposed approach greatly outperforms the original BBA and binary particle swarm optimization (BPSO. Compared with several other heuristic algorithms on zero-one knapsack problems, it also verifies that the proposed algorithm is more able to avoid local minima.

Energy footprint of advanced dense numerical linear algebra using tile algorithms on multicore architectures

KAUST Repository

Dongarra, Jack

2012-11-01

We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.

Energy footprint of advanced dense numerical linear algebra using tile algorithms on multicore architectures

KAUST Repository

Dongarra, Jack; Ltaief, Hatem; Luszczek, Piotr R.; Weaver, Vincent M.

2012-01-01

We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.

Numerical Studies of Homogenization under a Fast Cellular Flow

KAUST Repository

Iyer, Gautam

2012-09-13

We consider a two dimensional particle diffusing in the presence of a fast cellular flow confined to a finite domain. If the flow amplitude A is held fixed and the number of cells L 2 →∞, then the problem homogenizes; this has been well studied. Also well studied is the limit when L is fixed and A→∞. In this case the solution averages along stream lines. The double limit as both the flow amplitude A→∞and the number of cells L 2 →∞was recently studied [G. Iyer et al., preprint, arXiv:1108.0074]; one observes a sharp transition between the homogenization and averaging regimes occurring at A = L 2. This paper numerically studies a few theoretically unresolved aspects of this problem when both A and L are large that were left open in [G. Iyer et al., preprint, arXiv:1108.0074] using the numerical method devised in [G. A. Pavliotis, A. M. Stewart, and K. C. Zygalakis, J. Comput. Phys., 228 (2009), pp. 1030-1055]. Our treatment of the numerical method uses recent developments in the theory of modified equations for numerical integrators of stochastic differential equations [K. C. Zygalakis, SIAM J. Sci. Comput., 33 (2001), pp. 102-130]. © 2012 Society for Industrial and Applied Mathematics.

Numerical Studies of Homogenization under a Fast Cellular Flow

KAUST Repository

Iyer, Gautam; Zygalakis, Konstantinos C.

2012-01-01

We consider a two dimensional particle diffusing in the presence of a fast cellular flow confined to a finite domain. If the flow amplitude A is held fixed and the number of cells L 2 →∞, then the problem homogenizes; this has been well studied. Also well studied is the limit when L is fixed and A→∞. In this case the solution averages along stream lines. The double limit as both the flow amplitude A→∞and the number of cells L 2 →∞was recently studied [G. Iyer et al., preprint, arXiv:1108.0074]; one observes a sharp transition between the homogenization and averaging regimes occurring at A = L 2. This paper numerically studies a few theoretically unresolved aspects of this problem when both A and L are large that were left open in [G. Iyer et al., preprint, arXiv:1108.0074] using the numerical method devised in [G. A. Pavliotis, A. M. Stewart, and K. C. Zygalakis, J. Comput. Phys., 228 (2009), pp. 1030-1055]. Our treatment of the numerical method uses recent developments in the theory of modified equations for numerical integrators of stochastic differential equations [K. C. Zygalakis, SIAM J. Sci. Comput., 33 (2001), pp. 102-130]. © 2012 Society for Industrial and Applied Mathematics.

Atlas : A library for numerical weather prediction and climate modelling

Science.gov (United States)

Deconinck, Willem; Bauer, Peter; Diamantakis, Michail; Hamrud, Mats; Kühnlein, Christian; Maciel, Pedro; Mengaldo, Gianmarco; Quintino, Tiago; Raoult, Baudouin; Smolarkiewicz, Piotr K.; Wedi, Nils P.

2017-11-01

The algorithms underlying numerical weather prediction (NWP) and climate models that have been developed in the past few decades face an increasing challenge caused by the paradigm shift imposed by hardware vendors towards more energy-efficient devices. In order to provide a sustainable path to exascale High Performance Computing (HPC), applications become increasingly restricted by energy consumption. As a result, the emerging diverse and complex hardware solutions have a large impact on the programming models traditionally used in NWP software, triggering a rethink of design choices for future massively parallel software frameworks. In this paper, we present Atlas, a new software library that is currently being developed at the European Centre for Medium-Range Weather Forecasts (ECMWF), with the scope of handling data structures required for NWP applications in a flexible and massively parallel way. Atlas provides a versatile framework for the future development of efficient NWP and climate applications on emerging HPC architectures. The applications range from full Earth system models, to specific tools required for post-processing weather forecast products. The Atlas library thus constitutes a step towards affordable exascale high-performance simulations by providing the necessary abstractions that facilitate the application in heterogeneous HPC environments by promoting the co-design of NWP algorithms with the underlying hardware.

The Finite Element Numerical Modelling of 3D Magnetotelluric

Directory of Open Access Journals (Sweden)

Ligang Cao

2014-01-01

Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.

Achieving numerical accuracy and high performance using recursive tile LU factorization with partial pivoting

KAUST Repository

Dongarra, Jack

2013-09-18

The LU factorization is an important numerical algorithm for solving systems of linear equations in science and engineering and is a characteristic of many dense linear algebra computations. For example, it has become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected by the TOP500 website. Multicore processors continue to present challenges to the development of fast and robust numerical software due to the increasing levels of hardware parallelism and widening gap between core and memory speeds. In this context, the difficulty in developing new algorithms for the scientific community resides in the combination of two goals: achieving high performance while maintaining the accuracy of the numerical algorithm. This paper proposes a new approach for computing the LU factorization in parallel on multicore architectures, which not only improves the overall performance but also sustains the numerical quality of the standard LU factorization algorithm with partial pivoting. While the update of the trailing submatrix is computationally intensive and highly parallel, the inherently problematic portion of the LU factorization is the panel factorization due to its memory-bound characteristic as well as the atomicity of selecting the appropriate pivots. Our approach uses a parallel fine-grained recursive formulation of the panel factorization step and implements the update of the trailing submatrix with the tile algorithm. Based on conflict-free partitioning of the data and lockless synchronization mechanisms, our implementation lets the overall computation flow naturally without contention. The dynamic runtime system called QUARK is then able to schedule tasks with heterogeneous granularities and to transparently introduce algorithmic lookahead. The performance results of our implementation are competitive compared to the currently available software packages and libraries. For example

Achieving numerical accuracy and high performance using recursive tile LU factorization with partial pivoting

KAUST Repository

Dongarra, Jack; Faverge, Mathieu; Ltaief, Hatem; Luszczek, Piotr R.

2013-01-01

The LU factorization is an important numerical algorithm for solving systems of linear equations in science and engineering and is a characteristic of many dense linear algebra computations. For example, it has become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected by the TOP500 website. Multicore processors continue to present challenges to the development of fast and robust numerical software due to the increasing levels of hardware parallelism and widening gap between core and memory speeds. In this context, the difficulty in developing new algorithms for the scientific community resides in the combination of two goals: achieving high performance while maintaining the accuracy of the numerical algorithm. This paper proposes a new approach for computing the LU factorization in parallel on multicore architectures, which not only improves the overall performance but also sustains the numerical quality of the standard LU factorization algorithm with partial pivoting. While the update of the trailing submatrix is computationally intensive and highly parallel, the inherently problematic portion of the LU factorization is the panel factorization due to its memory-bound characteristic as well as the atomicity of selecting the appropriate pivots. Our approach uses a parallel fine-grained recursive formulation of the panel factorization step and implements the update of the trailing submatrix with the tile algorithm. Based on conflict-free partitioning of the data and lockless synchronization mechanisms, our implementation lets the overall computation flow naturally without contention. The dynamic runtime system called QUARK is then able to schedule tasks with heterogeneous granularities and to transparently introduce algorithmic lookahead. The performance results of our implementation are competitive compared to the currently available software packages and libraries. For example

Numerical investigation of the inverse blackbody radiation problem

International Nuclear Information System (INIS)

Xin Tan, Guo-zhen Yang, Ben-yuan Gu

1994-01-01

A numerical algorithm for the inverse blackbody radiation problem, which is the determination of the temperature distribution of a thermal radiator (TDTR) from its total radiated power spectrum (TRPS), is presented, based on the general theory of amplitude-phase retrieval. With application of this new algorithm, the ill-posed nature of the Fredholm equation of the first kind can be largely overcome and a convergent solution to high accuracy can be obtained. By incorporation of the hybrid input-output algorithm into our algorithm, the convergent process can be substantially expedited and the stagnation problem of the solution can be averted. From model calculations it is found that the new algorithm can also provide a robust reconstruction of the TDTR from the noise-corrupted data of the TRPS. Therefore the new algorithm may offer a useful approach to solving the ill-posed inverse problem. 18 refs., 9 figs

On the numerical verification of industrial codes

International Nuclear Information System (INIS)

Montan, Sethy Akpemado

2013-01-01

Numerical verification of industrial codes, such as those developed at EDF R and D, is required to estimate the precision and the quality of computed results, even more for code running in HPC environments where millions of instructions are performed each second. These programs usually use external libraries (MPI, BLACS, BLAS, LAPACK). In this context, it is required to have a tool as non intrusive as possible to avoid rewriting the original code. In this regard, the CADNA library, which implements the Discrete Stochastic Arithmetic, appears to be one of a promising approach for industrial applications. In the first part of this work, we are interested in an efficient implementation of the BLAS routine DGEMM (General Matrix Multiply) implementing Discrete Stochastic Arithmetic. The implementation of a basic algorithm for matrix product using stochastic types leads to an overhead greater than 1000 for a matrix of 1024 * 1024 compared to the standard version and commercial versions of xGEMM. Here, we detail different solutions to reduce this overhead and the results we have obtained. A new routine Dgemm- CADNA have been designed. This routine has allowed to reduce the overhead from 1100 to 35 compare to optimized BLAS implementations (GotoBLAS). Then, we focus on the numerical verification of Telemac-2D computed results. Performing a numerical validation with the CADNA library shows that more than 30% of the numerical instabilities occurring during an execution come from the dot product function. A more accurate implementation of the dot product with compensated algorithms is presented in this work. We show that implementing these kinds of algorithms, in order to improve the accuracy of computed results does not alter the code performance. (author)

Validation of a numerical FSI simulation of an aortic BMHV by in vitro PIV experiments.

Science.gov (United States)

Annerel, S; Claessens, T; Degroote, J; Segers, P; Vierendeels, J

2014-08-01

In this paper, a validation of a recently developed fluid-structure interaction (FSI) coupling algorithm to simulate numerically the dynamics of an aortic bileaflet mechanical heart valve (BMHV) is performed. This validation is done by comparing the numerical simulation results with in vitro experiments. For the in vitro experiments, the leaflet kinematics and flow fields are obtained via the particle image velocimetry (PIV) technique. Subsequently, the same case is numerically simulated by the coupling algorithm and the resulting leaflet kinematics and flow fields are obtained. Finally, the results are compared, revealing great similarity in leaflet motion and flow fields between the numerical simulation and the experimental test. Therefore, it is concluded that the developed algorithm is able to capture very accurately all the major leaflet kinematics and dynamics and can be used to study and optimize the design of BMHVs. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

Numerical Analysis of Vibrations of Structures under Moving Inertial Load

CERN Document Server

Bajer, Czeslaw I

2012-01-01

Moving inertial loads are applied to structures in civil engineering, robotics, and mechanical engineering. Some fundamental books exist, as well as thousands of research papers. Well known is the book by L. Frýba, Vibrations of Solids and Structures Under Moving Loads, which describes almost all problems concerning non-inertial loads. This book presents broad description of numerical tools successfully applied to structural dynamic analysis. Physically we deal with non-conservative systems. The discrete approach formulated with the use of the classical finite element method results in elemental matrices, which can be directly added to global structure matrices. A more general approach is carried out with the space-time finite element method. In such a case, a trajectory of the moving concentrated parameter in space and time can be simply defined. We consider structures described by pure hyperbolic differential equations such as strings and structures described by hyperbolic-parabolic differential equations ...

Numerical Flexural Strength Analysis of Thermally Stressed Delaminated Composite Structure under Sinusoidal Loading

Science.gov (United States)

Hirwani, C. K.; Biswash, S.; Mehar, K.; Panda, S. K.

2018-03-01

In this article, we investigate the thermomechanical deflection characteristics of the debonded composite plate structure using an isoparametric type of higher-order finite element model. The current formulation is derived using higher-order kinematic theory and the displacement variables described as constant along the thickness direction whereas varying nonlinearly for the in-plane directions. The present mid-plane kinematic model mainly obsoletes the use of shear correction factor as in the other lower-order theories. The separation between the adjacent layers is modeled via the sub-laminate technique and the intermittent continuity conditions imposed to avoid the mathematical ill conditions. The governing equation of equilibrium of the damaged plate structure under the combined state of loading are obtained using the variational principle and solved numerically to compute the deflection values. Further, the convergence test has been performed by refining the numbers of elements and validated through comparing the present results with available published values. The usefulness of the proposed formulation has been discussed by solving the different kind of numerical examples including the size, location and position of delamination.

Response-only modal identification using random decrement algorithm with time-varying threshold level

International Nuclear Information System (INIS)

Lin, Chang Sheng; Tseng, Tse Chuan

2014-01-01

Modal Identification from response data only is studied for structural systems under nonstationary ambient vibration. The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm with time-varying threshold level. In the conventional random decrement algorithm, the threshold level for evaluating random dec signatures is defined as the standard deviation value of response data of the reference channel. The distortion of random dec signatures may be, however, induced by the error involved in noise from the original response data in practice. To improve the accuracy of identification, a modification of the sampling procedure in random decrement algorithm is proposed for modal-parameter identification from the nonstationary ambient response data. The time-varying threshold level is presented for the acquisition of available sample time history to perform averaging analysis, and defined as the temporal root-mean-square function of structural response, which can appropriately describe a wide variety of nonstationary behaviors in reality, such as the time-varying amplitude (variance) of a nonstationary process in a seismic record. Numerical simulations confirm the validity and robustness of the proposed modal-identification method from nonstationary ambient response data under noisy conditions.

Impact-friction vibrations of tubular systems. Numerical simulation and experimental validation

International Nuclear Information System (INIS)

Jacquart, G.

1993-05-01

This note presents a summary on the numerical developments made to simulate impact-friction vibrations of tubular systems, detailing the algorithms used and the expression of impact and friction forces. A synthesis of the experimental results obtained on MASSIF workbench is also presented, as well as their comparison with numerical computations in order to validate the numerical approach. (author). 5 refs

A genetic-algorithm-aided stochastic optimization model for regional air quality management under uncertainty.

Science.gov (United States)

Qin, Xiaosheng; Huang, Guohe; Liu, Lei

2010-01-01

A genetic-algorithm-aided stochastic optimization (GASO) model was developed in this study for supporting regional air quality management under uncertainty. The model incorporated genetic algorithm (GA) and Monte Carlo simulation techniques into a general stochastic chance-constrained programming (CCP) framework and allowed uncertainties in simulation and optimization model parameters to be considered explicitly in the design of least-cost strategies. GA was used to seek the optimal solution of the management model by progressively evaluating the performances of individual solutions. Monte Carlo simulation was used to check the feasibility of each solution. A management problem in terms of regional air pollution control was studied to demonstrate the applicability of the proposed method. Results of the case study indicated the proposed model could effectively communicate uncertainties into the optimization process and generate solutions that contained a spectrum of potential air pollutant treatment options with risk and cost information. Decision alternatives could be obtained by analyzing tradeoffs between the overall pollutant treatment cost and the system-failure risk due to inherent uncertainties.

Implementation and analysis of an adaptive multilevel Monte Carlo algorithm

KAUST Repository

Hoel, Hakon; Von Schwerin, Erik; Szepessy, Anders; Tempone, Raul

2014-01-01

We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of solutions to Itô stochastic dierential equations (SDE). The work [11] proposed and analyzed an MLMC method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a single level Euler-Maruyama Monte Carlo method from O(TOL-3) to O(TOL-2 log(TOL-1)2) for a mean square error of O(TOL2). Later, the work [17] presented an MLMC method using a hierarchy of adaptively re ned, non-uniform time discretizations, and, as such, it may be considered a generalization of the uniform time discretizationMLMC method. This work improves the adaptiveMLMC algorithms presented in [17] and it also provides mathematical analysis of the improved algorithms. In particular, we show that under some assumptions our adaptive MLMC algorithms are asymptotically accurate and essentially have the correct complexity but with improved control of the complexity constant factor in the asymptotic analysis. Numerical tests include one case with singular drift and one with stopped diusion, where the complexity of a uniform single level method is O(TOL-4). For both these cases the results con rm the theory, exhibiting savings in the computational cost for achieving the accuracy O(TOL) from O(TOL-3) for the adaptive single level algorithm to essentially O(TOL-2 log(TOL-1)2) for the adaptive MLMC algorithm. © 2014 by Walter de Gruyter Berlin/Boston 2014.

Numerical Methods for Partial Differential Equations

CERN Document Server

Guo, Ben-yu

1987-01-01

These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

Inverse Problems in Geodynamics Using Machine Learning Algorithms

Science.gov (United States)

Shahnas, M. H.; Yuen, D. A.; Pysklywec, R. N.

2018-01-01

During the past few decades numerical studies have been widely employed to explore the style of circulation and mixing in the mantle of Earth and other planets. However, in geodynamical studies there are many properties from mineral physics, geochemistry, and petrology in these numerical models. Machine learning, as a computational statistic-related technique and a subfield of artificial intelligence, has rapidly emerged recently in many fields of sciences and engineering. We focus here on the application of supervised machine learning (SML) algorithms in predictions of mantle flow processes. Specifically, we emphasize on estimating mantle properties by employing machine learning techniques in solving an inverse problem. Using snapshots of numerical convection models as training samples, we enable machine learning models to determine the magnitude of the spin transition-induced density anomalies that can cause flow stagnation at midmantle depths. Employing support vector machine algorithms, we show that SML techniques can successfully predict the magnitude of mantle density anomalies and can also be used in characterizing mantle flow patterns. The technique can be extended to more complex geodynamic problems in mantle dynamics by employing deep learning algorithms for putting constraints on properties such as viscosity, elastic parameters, and the nature of thermal and chemical anomalies.

Space-time spectral collocation algorithm for solving time-fractional Tricomi-type equations

Directory of Open Access Journals (Sweden)

Abdelkawy M.A.

2016-01-01

Full Text Available We introduce a new numerical algorithm for solving one-dimensional time-fractional Tricomi-type equations (T-FTTEs. We used the shifted Jacobi polynomials as basis functions and the derivatives of fractional is evaluated by the Caputo definition. The shifted Jacobi Gauss-Lobatt algorithm is used for the spatial discretization, while the shifted Jacobi Gauss-Radau algorithmis applied for temporal approximation. Substituting these approximations in the problem leads to a system of algebraic equations that greatly simplifies the problem. The proposed algorithm is successfully extended to solve the two-dimensional T-FTTEs. Extensive numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Practical algorithms for simulation and reconstruction of digital in-line holograms.

Science.gov (United States)

Latychevskaia, Tatiana; Fink, Hans-Werner

2015-03-20

Here we present practical methods for simulation and reconstruction of in-line digital holograms recorded with plane and spherical waves. The algorithms described here are applicable to holographic imaging of an object exhibiting absorption as well as phase-shifting properties. Optimal parameters, related to distances, sampling rate, and other factors for successful simulation and reconstruction of holograms are evaluated and criteria for the achievable resolution are worked out. Moreover, we show that the numerical procedures for the reconstruction of holograms recorded with plane and spherical waves are identical under certain conditions. Experimental examples of holograms and their reconstructions are also discussed.

Investigation of film boiling thermal hydraulics under FCI conditions. Results of a numerical study

Energy Technology Data Exchange (ETDEWEB)

Dinh, T.N.; Dinh, A.T.; Nourgaliev, R.R.; Sehgal, B.R. [Div. of Nuclear Power Safety Royal Inst. of Tech. (RIT), Brinellvaegen 60, 10044 Stockholm (Sweden)

1998-01-01

Film boiling on the surface of a high-temperature melt jet or of a melt particle is one of key phenomena governing the physics of fuel-coolant interactions (FCIs) which may occur during the course of a severe accident in a light water reactor (LWR). A number of experimental and analytical studies have been performed, in the past, to address film boiling heat transfer and the accompanying hydrodynamic aspects. Most of the experiments have, however, been performed for temperature and heat flux conditions, which are significantly lower than the prototypic conditions. For ex-vessel FCIs, high liquid subcooling can significantly affect the FCI thermal hydraulics. Presently, there are large uncertainties in predicting natural-convection film boiling of subcooled liquids on high-temperature surfaces. In this paper, research conducted at the Division of Nuclear Power Safety, Royal Institute of Technology (RIT/NPS), Stockholm, concerning film-boiling thermal hydraulics under FCI condition is presented. Notably, the focus is placed on the effects of (1) water subcooling, (2) high-temperature steam properties, (3) the radiation heat transfer and (4) mixing zone boiling dynamics, on the vapor film characteristics. Numerical investigations are performed using a novel CFD modeling concept named as the local-homogeneous-slip model (LHSM). Results of the analytical and numerical studies are discussed with respect to boiling dynamics under FCI conditions. (author)

A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

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Er Gao

2012-01-01

Full Text Available We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.

Determination of point of maximum likelihood in failure domain using genetic algorithms

International Nuclear Information System (INIS)

Obadage, A.S.; Harnpornchai, N.

2006-01-01

The point of maximum likelihood in a failure domain yields the highest value of the probability density function in the failure domain. The maximum-likelihood point thus represents the worst combination of random variables that contribute in the failure event. In this work Genetic Algorithms (GAs) with an adaptive penalty scheme have been proposed as a tool for the determination of the maximum likelihood point. The utilization of only numerical values in the GAs operation makes the algorithms applicable to cases of non-linear and implicit single and multiple limit state function(s). The algorithmic simplicity readily extends its application to higher dimensional problems. When combined with Monte Carlo Simulation, the proposed methodology will reduce the computational complexity and at the same time will enhance the possibility in rare-event analysis under limited computational resources. Since, there is no approximation done in the procedure, the solution obtained is considered accurate. Consequently, GAs can be used as a tool for increasing the computational efficiency in the element and system reliability analyses

A Low-Stress Algorithm for Fractions

Science.gov (United States)

Ruais, Ronald W.

1978-01-01

An algorithm is given for the addition and subtraction of fractions based on dividing the sum of diagonal numerator and denominator products by the product of the denominators. As an explanation of the teaching method, activities used in teaching are demonstrated. (MN)

Multi-objective optimization in the presence of practical constraints using non-dominated sorting hybrid cuckoo search algorithm

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M. Balasubbareddy

2015-12-01

Full Text Available A novel optimization algorithm is proposed to solve single and multi-objective optimization problems with generation fuel cost, emission, and total power losses as objectives. The proposed method is a hybridization of the conventional cuckoo search algorithm and arithmetic crossover operations. Thus, the non-linear, non-convex objective function can be solved under practical constraints. The effectiveness of the proposed algorithm is analyzed for various cases to illustrate the effect of practical constraints on the objectives' optimization. Two and three objective multi-objective optimization problems are formulated and solved using the proposed non-dominated sorting-based hybrid cuckoo search algorithm. The effectiveness of the proposed method in confining the Pareto front solutions in the solution region is analyzed. The results for single and multi-objective optimization problems are physically interpreted on standard test functions as well as the IEEE-30 bus test system with supporting numerical and graphical results and also validated against existing methods.

Numerical Limit Analysis of Precast Concrete Structures

DEFF Research Database (Denmark)

Herfelt, Morten Andersen; Poulsen, Peter Noe; Hoang, Linh Cao

2016-01-01

; the framework is based on the theory of rigid-plasticity, and the resulting mathematical optimisation problem can be solved efficiently using modern algorithms. This paper gives a brief introduction to convex optimisation and numerical limit analysis. The mathematical formulation of lower bound load...

Numerical methods on flow instabilities in steam generator

International Nuclear Information System (INIS)

Yoshikawa, Ryuji; Hamada, Hirotsugu; Ohshima, Hiroyuki; Yanagisawa, Hideki

2008-06-01

The phenomenon of two-phase flow instability is important for the design and operation of many industrial systems and equipment, such as steam generators. The designer's job is to predict the threshold of flow instability in order to design around it or compensate for it. So it is essential to understand the physical phenomena governing such instability and to develop computational tools to model the dynamics of boiling systems. In Japan Atomic Energy Agency, investigations on heat transfer characteristics of steam generator are being performed for the development of Sodium-cooled Fast Breeder Reactor. As one part of the research work, the evaluations of two-phase flow instability in the steam generator are being carried out experimentally and numerically. In this report, the numerical methods were studied for two-phase flow instability analysis in steam generator. For numerical simulation purpose, the special algorithm to calculate inlet flow rate iteratively with inlet pressure and outlet pressure as boundary conditions for the density-wave instability analysis was established. There was no need to solve property derivatives and large matrices, so the spurious numerical instabilities caused by discontinuous property derivatives at boiling boundaries were avoided. Large time-step was possible. The flow instability in single heat transfer tube was successfully simulated with homogeneous equilibrium model by using the present algorithm. Then the drift-flux model including the effects of subcooled boiling and two phase slip was adopted to improve the accuracy. The computer code was developed after selecting the correlations of drift velocity and distribution parameter. The capability of drift flux model together with the present algorithm for simulating density-wave instability in single tube was confirmed. (author)

Local multiplicative Schwarz algorithms for convection-diffusion equations

Science.gov (United States)

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.

An Adaptive Unified Differential Evolution Algorithm for Global Optimization

Energy Technology Data Exchange (ETDEWEB)

Qiang, Ji; Mitchell, Chad

2014-11-03

In this paper, we propose a new adaptive unified differential evolution algorithm for single-objective global optimization. Instead of the multiple mutation strate- gies proposed in conventional differential evolution algorithms, this algorithm employs a single equation unifying multiple strategies into one expression. It has the virtue of mathematical simplicity and also provides users the flexibility for broader exploration of the space of mutation operators. By making all control parameters in the proposed algorithm self-adaptively evolve during the process of optimization, it frees the application users from the burden of choosing appro- priate control parameters and also improves the performance of the algorithm. In numerical tests using thirteen basic unimodal and multimodal functions, the proposed adaptive unified algorithm shows promising performance in compari- son to several conventional differential evolution algorithms.

Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion

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Qiuyu Wang

2016-06-01

Full Text Available In this paper, we  propose a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point. This algorithm preserves the computational simplicity of classical proximal gradient algorithm where a singular value decomposition in proximal operator is involved. Global convergence is followed directly in the literature. Numerical results are reported to show the efficiency of the algorithm.

Explaining algorithms using metaphors

CERN Document Server

Forišek, Michal

2013-01-01

There is a significant difference between designing a new algorithm, proving its correctness, and teaching it to an audience. When teaching algorithms, the teacher's main goal should be to convey the underlying ideas and to help the students form correct mental models related to the algorithm. This process can often be facilitated by using suitable metaphors. This work provides a set of novel metaphors identified and developed as suitable tools for teaching many of the 'classic textbook' algorithms taught in undergraduate courses worldwide. Each chapter provides exercises and didactic notes fo

Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE

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Chunlong Sun

2017-01-01

Full Text Available The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem.

Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm

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Zaer Abo-Hammour

2014-01-01

Full Text Available A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch’s and Bratu’s problems. The underlying idea of the method is to convert the two differential problems into discrete versions by replacing each of the second derivatives by an appropriate difference quotient approximation. The new method has the following characteristics. First, it should not resort to more advanced mathematical tools; that is, the algorithm should be simple to understand and implement and should be thus easily accepted in the mathematical and physical application fields. Second, the algorithm is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical and physical problems. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. The algorithm is tested on different versions of Troesch’s and Bratu’s problems. Experimental results show that the proposed algorithm is effective, straightforward, and simple.