Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

KAUST Repository

Gottlieb, Sigal

2015-04-10

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

Linear Parameter Varying Versus Linear Time Invariant Reduced Order Controller Design of Turboprop Aircraft Dynamics

Directory of Open Access Journals (Sweden)

Widowati

2012-07-01

Full Text Available The applicability of parameter varying reduced order controllers to aircraft model is proposed. The generalization of the balanced singular perturbation method of linear time invariant (LTI system is used to reduce the order of linear parameter varying (LPV system. Based on the reduced order model the low-order LPV controller is designed by using synthesis technique. The performance of the reduced order controller is examined by applying it to lateral-directional control of aircraft model having 20th order. Furthermore, the time responses of the closed loop system with reduced order LPV controllers and reduced order LTI controller is compared. From the simulation results, the 8th order LPV controller can maintain stability and to provide the same level of closed-loop systems performance as the full-order LPV controller. It is different with the reduced-order LTI controller that cannot maintain stability and performance for all allowable parameter trajectories.

A Fault Detection Filtering for Networked Control Systems Based on Balanced Reduced-Order

Directory of Open Access Journals (Sweden)

Da-Meng Dai

2015-01-01

Full Text Available Due to the probability of the packet dropout in the networked control systems, a balanced reduced-order fault detection filter is proposed. In this paper, we first analyze the packet dropout effects in the networked control systems. Then, in order to obtain a robust fault detector for the packet dropout, we use the balanced structure to construct a reduced-order model for residual dynamics. Simulation results are provided to testify the proposed method.

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

Science.gov (United States)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with

Approaches for Reduced Order Modeling of Electrically Actuated von Karman Microplates

KAUST Repository

Saghir, Shahid

2016-07-25

This article presents and compares different approaches to develop reduced order models for the nonlinear von Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches are made for this case. Keywords: electrically actuated microplates, static analysis, dynamics of microplates, diaphragm vibration, large amplitude vibrations, nonlinear dynamics

Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

Science.gov (United States)

Yao, Weigang; Liou, Meng-Sing

2012-01-01

The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis

Improved Multilevel Fast Multipole Method for Higher-Order discretizations

DEFF Research Database (Denmark)

Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

2014-01-01

The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...

Reduced-Order Computational Model for Low-Frequency Dynamics of Automobiles

Directory of Open Access Journals (Sweden)

A. Arnoux

2013-01-01

Full Text Available A reduced-order model is constructed to predict, for the low-frequency range, the dynamical responses in the stiff parts of an automobile constituted of stiff and flexible parts. The vehicle has then many elastic modes in this range due to the presence of many flexible parts and equipment. A nonusual reduced-order model is introduced. The family of the elastic modes is not used and is replaced by an adapted vector basis of the admissible space of global displacements. Such a construction requires a decomposition of the domain of the structure in subdomains in order to control the spatial wave length of the global displacements. The fast marching method is used to carry out the subdomain decomposition. A probabilistic model of uncertainties is introduced. The parameters controlling the level of uncertainties are estimated solving a statistical inverse problem. The methodology is validated with a large computational model of an automobile.

Data-assisted reduced-order modeling of extreme events in complex dynamical systems.

Science.gov (United States)

Wan, Zhong Yi; Vlachas, Pantelis; Koumoutsakos, Petros; Sapsis, Themistoklis

2018-01-01

The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN) architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM) regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more significant in

Data-assisted reduced-order modeling of extreme events in complex dynamical systems.

Directory of Open Access Journals (Sweden)

Zhong Yi Wan

Full Text Available The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics, depends on the formulation and analysis of relevant, complex dynamical systems. Such dynamical systems are characterized by high intrinsic dimensionality with extreme events having the form of rare transitions that are several standard deviations away from the mean. Such systems are not amenable to classical order-reduction methods through projection of the governing equations due to the large intrinsic dimensionality of the underlying attractor as well as the complexity of the transient events. Alternatively, data-driven techniques aim to quantify the dynamics of specific, critical modes by utilizing data-streams and by expanding the dimensionality of the reduced-order model using delayed coordinates. In turn, these methods have major limitations in regions of the phase space with sparse data, which is the case for extreme events. In this work, we develop a novel hybrid framework that complements an imperfect reduced order model, with data-streams that are integrated though a recurrent neural network (RNN architecture. The reduced order model has the form of projected equations into a low-dimensional subspace that still contains important dynamical information about the system and it is expanded by a long short-term memory (LSTM regularization. The LSTM-RNN is trained by analyzing the mismatch between the imperfect model and the data-streams, projected to the reduced-order space. The data-driven model assists the imperfect model in regions where data is available, while for locations where data is sparse the imperfect model still provides a baseline for the prediction of the system state. We assess the developed framework on two challenging prototype systems exhibiting extreme events. We show that the blended approach has improved performance compared with methods that use either data streams or the imperfect model alone. Notably the improvement is more

Reliability-based design optimization via high order response surface method

International Nuclear Information System (INIS)

Li, Hong Shuang

2013-01-01

To reduce the computational effort of reliability-based design optimization (RBDO), the response surface method (RSM) has been widely used to evaluate reliability constraints. We propose an efficient methodology for solving RBDO problems based on an improved high order response surface method (HORSM) that takes advantage of an efficient sampling method, Hermite polynomials and uncertainty contribution concept to construct a high order response surface function with cross terms for reliability analysis. The sampling method generates supporting points from Gauss-Hermite quadrature points, which can be used to approximate response surface function without cross terms, to identify the highest order of each random variable and to determine the significant variables connected with point estimate method. The cross terms between two significant random variables are added to the response surface function to improve the approximation accuracy. Integrating the nested strategy, the improved HORSM is explored in solving RBDO problems. Additionally, a sampling based reliability sensitivity analysis method is employed to reduce the computational effort further when design variables are distributional parameters of input random variables. The proposed methodology is applied on two test problems to validate its accuracy and efficiency. The proposed methodology is more efficient than first order reliability method based RBDO and Monte Carlo simulation based RBDO, and enables the use of RBDO as a practical design tool.

A reduced order model of a quadruped walking system

International Nuclear Information System (INIS)

Sano, Akihito; Furusho, Junji; Naganuma, Nobuyuki

1990-01-01

Trot walking has recently been studied by several groups because of its stability and realizability. In the trot, diagonally opposed legs form pairs. While one pair of legs provides support, the other pair of legs swings forward in preparation for the next step. In this paper, we propose a reduced order model for the trot walking. The reduced order model is derived by using two dominant modes of the closed loop system in which the local feedback at each joint is implemented. It is shown by numerical examples that the obtained reduced order model can well approximate the original higher order model. (author)

AN OVERVIEW OF REDUCED ORDER MODELING TECHNIQUES FOR SAFETY APPLICATIONS

Energy Technology Data Exchange (ETDEWEB)

Mandelli, D.; Alfonsi, A.; Talbot, P.; Wang, C.; Maljovec, D.; Smith, C.; Rabiti, C.; Cogliati, J.

2016-10-01

The RISMC project is developing new advanced simulation-based tools to perform Computational Risk Analysis (CRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermal-hydraulic behavior of the reactors primary and secondary systems, but also external event temporal evolution and component/system ageing. Thus, this is not only a multi-physics problem being addressed, but also a multi-scale problem (both spatial, µm-mm-m, and temporal, seconds-hours-years). As part of the RISMC CRA approach, a large amount of computationally-expensive simulation runs may be required. An important aspect is that even though computational power is growing, the overall computational cost of a RISMC analysis using brute-force methods may be not viable for certain cases. A solution that is being evaluated to assist the computational issue is the use of reduced order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RISMC analysis computational cost by decreasing the number of simulation runs; for this analysis improvement we used surrogate models instead of the actual simulation codes. This article focuses on the use of reduced order modeling techniques that can be applied to RISMC analyses in order to generate, analyze, and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (microseconds instead of hours/days).

The Use Of Alternative Methods In Reducing Menopausal ...

African Journals Online (AJOL)

Background: Millions of women experience menopause every year, therefore the aim of this study is to determine the rates of application of alternative methods applied by women in order to reduce their complaints caused by menopause and alternative application methods. Materials and Methods: This study was carried ...

Hybrid reduced order modeling for assembly calculations

Energy Technology Data Exchange (ETDEWEB)

Bang, Youngsuk, E-mail: ysbang00@fnctech.com [FNC Technology, Co. Ltd., Yongin-si (Korea, Republic of); Abdel-Khalik, Hany S., E-mail: abdelkhalik@purdue.edu [Purdue University, West Lafayette, IN (United States); Jessee, Matthew A., E-mail: jesseema@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Mertyurek, Ugur, E-mail: mertyurek@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States)

2015-12-15

Highlights: • Reducing computational cost in engineering calculations. • Reduced order modeling algorithm for multi-physics problem like assembly calculation. • Non-intrusive algorithm with random sampling. • Pattern recognition in the components with high sensitive and large variation. - Abstract: While the accuracy of assembly calculations has considerably improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This manuscript extends those works to coupled code systems as currently employed in assembly calculations. Numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system.

Hybrid reduced order modeling for assembly calculations

International Nuclear Information System (INIS)

Bang, Youngsuk; Abdel-Khalik, Hany S.; Jessee, Matthew A.; Mertyurek, Ugur

2015-01-01

Highlights: • Reducing computational cost in engineering calculations. • Reduced order modeling algorithm for multi-physics problem like assembly calculation. • Non-intrusive algorithm with random sampling. • Pattern recognition in the components with high sensitive and large variation. - Abstract: While the accuracy of assembly calculations has considerably improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This manuscript extends those works to coupled code systems as currently employed in assembly calculations. Numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system.

Investigation and application of reduced-order methods for flows study in heat exchanger tube bundles

International Nuclear Information System (INIS)

Pomarede, M.

2012-01-01

The objective of this thesis is to study the ability of model reduction for investigations of flow-induced vibrations in heat exchangers tube bundle systems.These mechanisms are a cause of major concern because heat exchangers are key elements of nuclear power plants and on-board stoke-holds.In a first part, we give a recall on heat exchangers functioning and on vibratory problems to which they are prone. Then, complete calculations leaded with the CFD numerical code Code-Saturne are carried out, first for the flow around a single circular cylinder (fixed then elastically mounted) and then for the case of a tube bundle system submitted to cross-flow. Reduced-order method POD is applied to the flow resolution with fixed structures. The obtained results show the efficiency of this technique for such configurations, using stabilization methods for the dynamical system resolution in the tube-bundle case. Multiphase-POD, which is a method enabling the adaptation of POD to fluid-structure interactions, is applied. Large displacements of a single cylinder elastically mounted under cross-flow, corresponding to the lock-in phenomenon,are well reproduced with this reduction technique. In the same way, large displacements of a confined moving tube in a bundle are shown to be faithfully reconstructed.Finally, the use of model reduction is extended to parametric studies. First, we propose to use the method which consists in projecting Navier-Stokes equations for several values of the Reynolds number on to a unique POD basis. The results obtained confirm the fact that POD predictability is limited to a range of parameter values. Then, a basis interpolation method, constructed using Grassmann manifolds and allowing the construction of a POD basis from other pre-calculated basis, is applied to basic cases. (author)

Fast prediction and evaluation of eccentric inspirals using reduced-order models

Science.gov (United States)

Barta, Dániel; Vasúth, Mátyás

2018-06-01

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in gravitational-wave searches and parameter estimation without degrading the signal detectability, we propose a novel reduced-order-model (ROM) approach with applications to adiabatic 3PN-accurate inspiral waveforms of nonspinning sources that evolve on either highly or slightly eccentric orbits. We provide a singular-value decomposition-based reduced-basis method in the frequency domain to generate reduced-order approximations of any gravitational waves with acceptable accuracy and precision within the parameter range of the model. We construct efficient reduced bases comprised of a relatively small number of the most relevant waveforms over three-dimensional parameter-space covered by the template bank (total mass 2.15 M⊙≤M ≤215 M⊙ , mass ratio 0.01 ≤q ≤1 , and initial orbital eccentricity 0 ≤e0≤0.95 ). The ROM is designed to predict signals in the frequency band from 10 Hz to 2 kHz for aLIGO and aVirgo design sensitivity. Beside moderating the data reduction, finer sampling of fiducial templates improves the accuracy of surrogates. Considerable increase in the speedup from several hundreds to thousands can be achieved by evaluating surrogates for low-mass systems especially when combined with high-eccentricity.

Kohn–Sham exchange-correlation potentials from second-order reduced density matrices

Energy Technology Data Exchange (ETDEWEB)

Cuevas-Saavedra, Rogelio; Staroverov, Viktor N., E-mail: vstarove@uwo.ca [Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7 (Canada); Ayers, Paul W. [Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1 (Canada)

2015-12-28

We describe a practical algorithm for constructing the Kohn–Sham exchange-correlation potential corresponding to a given second-order reduced density matrix. Unlike conventional Kohn–Sham inversion methods in which such potentials are extracted from ground-state electron densities, the proposed technique delivers unambiguous results in finite basis sets. The approach can also be used to separate approximately the exchange and correlation potentials for a many-electron system for which the reduced density matrix is known. The algorithm is implemented for configuration-interaction wave functions and its performance is illustrated with numerical examples.

Reduced order modeling in topology optimization of vibroacoustic problems

DEFF Research Database (Denmark)

Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas

2017-01-01

complex 3D parts. The optimization process can therefore become highly time consuming due to the need to solve a large system of equations at each iteration. Projection-based parametric Model Order Reduction (pMOR) methods have successfully been applied for reducing the computational cost of material......There is an interest in introducing topology optimization techniques in the design process of structural-acoustic systems. In topology optimization, the design space must be finely meshed in order to obtain an accurate design, which results in large numbers of degrees of freedom when designing...... or size optimization in large vibroacoustic models; however, new challenges are encountered when dealing with topology optimization. Since a design parameter per element is considered, the total number of design variables becomes very large; this poses a challenge to most existing pMOR techniques, which...

Vibration of carbon nanotubes with defects: order reduction methods

Science.gov (United States)

Hudson, Robert B.; Sinha, Alok

2018-03-01

Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone-Wales defects, though the methods described can be extended to other defects.

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

Science.gov (United States)

Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

2018-04-01

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

Vascular stents: Coupling full 3-D with reduced-order structural models

International Nuclear Information System (INIS)

Avdeev, I; Shams, M

2010-01-01

Self-expanding nitinol stents are used to treat peripheral arterial disease. The peripheral arteries are subjected to a combination of mechanical forces such as compression, torsion, bending, and contraction. Most commercially available peripheral self-expanding stents are composed of a series of sub-millimeter V-shaped struts, which are laser-cut from a nitinol tube and surface-treated for better fatigue performance. The numerical stent models must accurately predict location and distribution of local stresses and strains caused by large arterial deformations. Full 3-D finite element non-linear analysis of an entire stent is computationally expensive to the point of being prohibitive, especially for longer stents. Reduced-order models based on beam or shell elements are fairly accurate in capturing global deformations, but are not very helpful in predicting stent failure. We propose a mixed approach that combines the full 3-D model and reduced-order models. Several global-local, full 3-D/reduced-order finite element models of a peripheral self-expanding stent were validated and compared with experimental data. The kinematic constraint method used to couple various elements together was found to be very efficient and easily applicable to commercial FEA codes. The proposed mixed models can be used to accurately predict stent failure based on realistic (patient-specific), non-linear kinematic behavior of peripheral arteries.

Disturbance estimation of nuclear power plant by using reduced-order model

International Nuclear Information System (INIS)

Tashima, Shin-ichi; Wakabayashi, Jiro

1983-01-01

An estimation method is proposed of multiplex disturbances which occur in a nuclear power plant. The method is composed of two parts: (i) the identification of a simplified model of multi-input and multi-output to describe the related system response, and (ii) the design of a Kalman filter to estimate the multiplex disturbance. Concerning the simplified model, several observed signals are firstly selected as output variables which can well represent the system response caused by the disturbances. A reduced-order model is utilized for designing the disturbance estimator. This is based on the following two considerations. The first is that the disturbance is assumed to be of a quasistatic nature. The other is based on the intuition that there exist a few dominant modes between the disturbances and the selected observed signals and that most of the non-dominant modes which remain may not affect the accuracy of the disturbance estimator. The reduced-order model is furtherly transformed to a single-output model using a linear combination of the output signals, where the standard procedure of the structural identification is evaded. The parameters of the model thus transformed are calculated by the generalized least square method. As for the multiplex disturbance estimator, the Kalman filtering method is applied by compromising the following three items : (a) quick response to disturbance, (b) reduction of estimation error in the presence of observation noises, and (c) the elimination of cross-interference between the disturbances to the plant and the estimates from the Kalman filter. The effectiveness of the proposed method is verified through some computer experiments using a BWR plant simulator. (author)

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

Science.gov (United States)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

Synchronization in reduced-order of chaotic systems via control approaches based on high-order sliding-mode observer

Energy Technology Data Exchange (ETDEWEB)

Rodriguez, A. [Electrical Engineering Doctoral Program, Mechanical and Electrical Engineering Faculty, Autonomous University of Nuevo Leon, 66450 San Nicolas de los Garza, N.L. (Mexico)], E-mail: angelrdz@gmail.com; De Leon, J. [Electrical Engineering Doctoral Program, Mechanical and Electrical Engineering Faculty, Autonomous University of Nuevo Leon, 66450 San Nicolas de los Garza, N.L. (Mexico)], E-mail: drjleon@gmail.com; Fridman, L. [Department of Control, Division of Electrical Engineering, Engineering Faculty, National Autonomous University of Mexico, 04510 Mexico City (Mexico)], E-mail: lfridman@servidor.unam.mx

2009-12-15

The reduced-order synchronization problem of two chaotic systems (master-slave) with different dimension and relative degree is considered. A control scheme based on a high-order sliding-mode observer-identifier and a feedback state controller is proposed, where the trajectories of slave can be synchronized with a canonical projection of the master. Thus, the reduced-order synchronization is achieved in spite of master/slave mismatches. Simulation results are provided in order to illustrate the performance of the proposed synchronization scheme.

Synchronization in reduced-order of chaotic systems via control approaches based on high-order sliding-mode observer

International Nuclear Information System (INIS)

Rodriguez, A.; De Leon, J.; Fridman, L.

2009-01-01

The reduced-order synchronization problem of two chaotic systems (master-slave) with different dimension and relative degree is considered. A control scheme based on a high-order sliding-mode observer-identifier and a feedback state controller is proposed, where the trajectories of slave can be synchronized with a canonical projection of the master. Thus, the reduced-order synchronization is achieved in spite of master/slave mismatches. Simulation results are provided in order to illustrate the performance of the proposed synchronization scheme.

Reduced order modeling of flashing two-phase jets

Energy Technology Data Exchange (ETDEWEB)

Gurecky, William, E-mail: william.gurecky@utexas.edu; Schneider, Erich, E-mail: eschneider@mail.utexas.edu; Ballew, Davis, E-mail: davisballew@utexas.edu

2015-12-01

Highlights: • Accident simulation requires ability to quickly predict two-phase flashing jet's damage potential. • A reduced order modeling methodology informed by experimental or computational data is described. • Zone of influence volumes are calculated for jets of various upstream thermodynamic conditions. - Abstract: In the event of a Loss of Coolant Accident (LOCA) in a pressurized water reactor, the escaping coolant produces a highly energetic flashing jet with the potential to damage surrounding structures. In LOCA analysis, the goal is often to evaluate many break scenarios in a Monte Carlo style simulation to evaluate the resilience of a reactor design. Therefore, in order to quickly predict the damage potential of flashing jets, it is of interest to develop a reduced order model that relates the damage potential of a jet to the pressure and temperature upstream of the break and the distance from the break to a given object upon which the jet is impinging. This work presents framework for producing a Reduced Order Model (ROM) that may be informed by measured data, Computational Fluid Dynamics (CFD) simulations, or a combination of both. The model is constructed by performing regression analysis on the pressure field data, allowing the impingement pressure to be quickly reconstructed for any given upstream thermodynamic condition within the range of input data. The model is applicable to both free and fully impinging two-phase flashing jets.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

Science.gov (United States)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

A method for generating reduced-order combustion mechanisms that satisfy the differential entropy inequality

Science.gov (United States)

Ream, Allen E.; Slattery, John C.; Cizmas, Paul G. A.

2018-04-01

This paper presents a new method for determining the Arrhenius parameters of a reduced chemical mechanism such that it satisfies the second law of thermodynamics. The strategy is to approximate the progress of each reaction in the reduced mechanism from the species production rates of a detailed mechanism by using a linear least squares method. A series of non-linear least squares curve fittings are then carried out to find the optimal Arrhenius parameters for each reaction. At this step, the molar rates of production are written such that they comply with a theorem that provides the sufficient conditions for satisfying the second law of thermodynamics. This methodology was used to modify the Arrhenius parameters for the Westbrook and Dryer two-step mechanism and the Peters and Williams three-step mechanism for methane combustion. Both optimized mechanisms showed good agreement with the detailed mechanism for species mole fractions and production rates of most major species. Both optimized mechanisms showed significant improvement over previous mechanisms in minor species production rate prediction. Both optimized mechanisms produced no violations of the second law of thermodynamics.

Hybrid reduced order modeling for assembly calculations

Energy Technology Data Exchange (ETDEWEB)

Bang, Y.; Abdel-Khalik, H. S. [North Carolina State University, Raleigh, NC (United States); Jessee, M. A.; Mertyurek, U. [Oak Ridge National Laboratory, Oak Ridge, TN (United States)

2013-07-01

While the accuracy of assembly calculations has considerably improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This manuscript extends those works to coupled code systems as currently employed in assembly calculations. Numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system. (authors)

Application of Reduced Order Transonic Aerodynamic Influence Coefficient Matrix for Design Optimization

Science.gov (United States)

Pak, Chan-gi; Li, Wesley W.

2009-01-01

Supporting the Aeronautics Research Mission Directorate guidelines, the National Aeronautics and Space Administration [NASA] Dryden Flight Research Center is developing a multidisciplinary design, analysis, and optimization [MDAO] tool. This tool will leverage existing tools and practices, and allow the easy integration and adoption of new state-of-the-art software. Today s modern aircraft designs in transonic speed are a challenging task due to the computation time required for the unsteady aeroelastic analysis using a Computational Fluid Dynamics [CFD] code. Design approaches in this speed regime are mainly based on the manual trial and error. Because of the time required for unsteady CFD computations in time-domain, this will considerably slow down the whole design process. These analyses are usually performed repeatedly to optimize the final design. As a result, there is considerable motivation to be able to perform aeroelastic calculations more quickly and inexpensively. This paper will describe the development of unsteady transonic aeroelastic design methodology for design optimization using reduced modeling method and unsteady aerodynamic approximation. The method requires the unsteady transonic aerodynamics be represented in the frequency or Laplace domain. Dynamically linear assumption is used for creating Aerodynamic Influence Coefficient [AIC] matrices in transonic speed regime. Unsteady CFD computations are needed for the important columns of an AIC matrix which corresponded to the primary modes for the flutter. Order reduction techniques, such as Guyan reduction and improved reduction system, are used to reduce the size of problem transonic flutter can be found by the classic methods, such as Rational function approximation, p-k, p, root-locus etc. Such a methodology could be incorporated into MDAO tool for design optimization at a reasonable computational cost. The proposed technique is verified using the Aerostructures Test Wing 2 actually designed

Empirical Reduced-Order Modeling for Boundary Feedback Flow Control

Directory of Open Access Journals (Sweden)

Seddik M. Djouadi

2008-01-01

Full Text Available This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation- (PDE- based models in general. Specifically, the proper orthogonal decomposition (POD of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the Galerkin model. The rationale for doing so is that linear subspace approximations to exact submanifolds associated with nonlinear controllability and observability require only standard matrix manipulations utilizing simulation/experimental data. The proposed method uses a chirp signal as input to produce the output in the eigensystem realization algorithm (ERA. This method estimates the system's Markov parameters that accurately reproduce the output. Balanced truncation is used to show that model reduction is still effective on ERA produced approximated systems. The method is applied to a prototype convective flow on obstacle geometry. An H∞ feedback flow controller is designed based on the reduced model to achieve tracking and then applied to the full-order model with excellent performance.

Experimental verifications of a structural damage identification technique using reduced order finite-element model

Science.gov (United States)

Li, Rui; Zhou, Li; Yang, Jann N.

2010-04-01

An objective of the structural health monitoring system is to identify the state of the structure and to detect the damage when it occurs. Analysis techniques for the damage identification of structures, based on vibration data measured from sensors, have received considerable attention. Recently, a new damage tracking technique, referred to as the adaptive quadratic sum-square error (AQSSE) technique, has been proposed, and simulation studies demonstrated that the AQSSE technique is quite effective in identifying structural damages. In this paper, the adaptive quadratic sumsquare error (AQSSE) along with the reduced-order finite-element method is proposed to identify the damages of complex structures. Experimental tests were conducted to verify the capability of the proposed damage detection approach. A series of experimental tests were performed using a scaled cantilever beam subject to the white noise and sinusoidal excitations. The capability of the proposed reduced-order finite-element based adaptive quadratic sum-square error (AQSSE) method in detecting the structural damage is demonstrated by the experimental results.

How can we strengthen students’ social relations in order to reduce school dropout?

DEFF Research Database (Denmark)

Ingholt, Liselotte; Sørensen, Betina Bang; Andersen, Susan

2015-01-01

on ethnographic methods, including 22 qualitative interviews with students 17-19 years old and fieldwork with participant observations at four vocational schools over 40 days, including informal interviews and discussion meetings with managers, teachers, counselors and students. As part of the fieldwork, four......BACKGROUND: This article describes the rationale and contents of an intervention program aimed at strengthening students' social relations in order to reduce dropout from vocational schools in Denmark. Taking its theoretical cue from the concept of 'social participation', a qualitative study...... was performed to investigate the specific relationships between the social environment within the schools and the institutional structures in order to analyse reasons for school dropout and their relation to well-being, cigarette smoking and substance use. METHODS: The development study was based...

Stable reduced-order models of generalized dynamical systems using coordinate-transformed Arnoldi algorithms

Energy Technology Data Exchange (ETDEWEB)

Silveira, L.M.; Kamon, M.; Elfadel, I.; White, J. [Massachusetts Inst. of Technology, Cambridge, MA (United States)

1996-12-31

Model order reduction based on Krylov subspace iterative methods has recently emerged as a major tool for compressing the number of states in linear models used for simulating very large physical systems (VLSI circuits, electromagnetic interactions). There are currently two main methods for accomplishing such a compression: one is based on the nonsymmetric look-ahead Lanczos algorithm that gives a numerically stable procedure for finding Pade approximations, while the other is based on a less well characterized Arnoldi algorithm. In this paper, we show that for certain classes of generalized state-space systems, the reduced-order models produced by a coordinate-transformed Arnoldi algorithm inherit the stability of the original system. Complete Proofs of our results will be given in the final paper.

Reduced Order Modeling in General Relativity

Science.gov (United States)

Tiglio, Manuel

2014-03-01

Reduced Order Modeling is an emerging yet fast developing filed in gravitational wave physics. The main goals are to enable fast modeling and parameter estimation of any detected signal, along with rapid matched filtering detecting. I will focus on the first two. Some accomplishments include being able to replace, with essentially no lost of physical accuracy, the original models with surrogate ones (which are not effective ones, that is, they do not simplify the physics but go on a very different track, exploiting the particulars of the waveform family under consideration and state of the art dimensional reduction techniques) which are very fast to evaluate. For example, for EOB models they are at least around 3 orders of magnitude faster than solving the original equations, with physically equivalent results. For numerical simulations the speedup is at least 11 orders of magnitude. For parameter estimation our current numbers are about bringing ~100 days for a single SPA inspiral binary neutron star Bayesian parameter estimation analysis to under a day. More recently, it has been shown that the full precessing problem for, say, 200 cycles, can be represented, through some new ideas, by a remarkably compact set of carefully chosen reduced basis waveforms (~10-100, depending on the accuracy requirements). I will highlight what I personally believe are the challenges to face next in this subarea of GW physics and where efforts should be directed. This talk will summarize work in collaboration with: Harbir Antil (GMU), Jonathan Blackman (Caltech), Priscila Canizares (IoA, Cambridge, UK), Sarah Caudill (UWM), Jonathan Gair (IoA. Cambridge. UK), Scott Field (UMD), Chad R. Galley (Caltech), Frank Herrmann (Germany), Han Hestahven (EPFL, Switzerland), Jason Kaye (Brown, Stanford & Courant). Evan Ochsner (UWM), Ricardo Nochetto (UMD), Vivien Raymond (LIGO, Caltech), Rory Smith (LIGO, Caltech) Bela Ssilagyi (Caltech) and MT (UMD & Caltech).

The Telegraph Equation and Its Solution by Reduced Differential Transform Method

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2013-01-01

Full Text Available One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM. Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

A Modified AH-FDTD Unconditionally Stable Method Based on High-Order Algorithm

Directory of Open Access Journals (Sweden)

Zheng Pan

2017-01-01

Full Text Available The unconditionally stable method, Associated-Hermite FDTD, has attracted more and more attentions in computational electromagnetic for its time-frequency compact property. Because of the fewer orders of AH basis needed in signal reconstruction, the computational efficiency can be improved further. In order to further improve the accuracy of the traditional AH-FDTD, a high-order algorithm is introduced. Using this method, the dispersion error induced by the space grid can be reduced, which makes it possible to set coarser grid. The simulation results show that, on the condition of coarse grid, the waveforms obtained from the proposed method are matched well with the analytic result, and the accuracy of the proposed method is higher than the traditional AH-FDTD. And the efficiency of the proposed method is higher than the traditional FDTD method in analysing 2D waveguide problems with fine-structure.

Efficiency of High Order Spectral Element Methods on Petascale Architectures

KAUST Repository

Hutchinson, Maxwell; Heinecke, Alexander; Pabst, Hans; Henry, Greg; Parsani, Matteo; Keyes, David E.

2016-01-01

High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.

Efficiency of High Order Spectral Element Methods on Petascale Architectures

KAUST Repository

Hutchinson, Maxwell

2016-06-14

High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.

Extreme learning machine for reduced order modeling of turbulent geophysical flows

Science.gov (United States)

San, Omer; Maulik, Romit

2018-04-01

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition-based reduced order models for quasistationary geophysical turbulent flows. An extreme learning machine concept is introduced for computing an eddy-viscosity closure dynamically to incorporate the effects of the truncated modes. We consider a four-gyre wind-driven ocean circulation problem as our prototype setting to assess the performance of the proposed data-driven approach. Our framework provides a significant reduction in computational time and effectively retains the dynamics of the full-order model during the forward simulation period beyond the training data set. Furthermore, we show that the method is robust for larger choices of time steps and can be used as an efficient and reliable tool for long time integration of general circulation models.

Static aeroelastic analysis including geometric nonlinearities based on reduced order model

Directory of Open Access Journals (Sweden)

Changchuan Xie

2017-04-01

Full Text Available This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM. The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM. Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

Parametric Methods for Order Tracking Analysis

DEFF Research Database (Denmark)

Nielsen, Jesper Kjær; Jensen, Tobias Lindstrøm

2017-01-01

Order tracking analysis is often used to find the critical speeds at which structural resonances are excited by a rotating machine. Typically, order tracking analysis is performed via non-parametric methods. In this report, however, we demonstrate some of the advantages of using a parametric method...

Computational design of patterned interfaces using reduced order models

International Nuclear Information System (INIS)

Vattre, A.J.; Abdolrahim, N.; Kolluri, K.; Demkowicz, M.J.

2014-01-01

Patterning is a familiar approach for imparting novel functionalities to free surfaces. We extend the patterning paradigm to interfaces between crystalline solids. Many interfaces have non-uniform internal structures comprised of misfit dislocations, which in turn govern interface properties. We develop and validate a computational strategy for designing interfaces with controlled misfit dislocation patterns by tailoring interface crystallography and composition. Our approach relies on a novel method for predicting the internal structure of interfaces: rather than obtaining it from resource-intensive atomistic simulations, we compute it using an efficient reduced order model based on anisotropic elasticity theory. Moreover, our strategy incorporates interface synthesis as a constraint on the design process. As an illustration, we apply our approach to the design of interfaces with rapid, 1-D point defect diffusion. Patterned interfaces may be integrated into the microstructure of composite materials, markedly improving performance. (authors)

Reduced-Order Modeling of 3D Rayleigh-Benard Turbulent Convection

Science.gov (United States)

Hassanzadeh, Pedram; Grover, Piyush; Nabi, Saleh

2017-11-01

Accurate Reduced-Order Models (ROMs) of turbulent geophysical flows have broad applications in science and engineering; for example, to study the climate system or to perform real-time flow control/optimization in energy systems. Here we focus on 3D Rayleigh-Benard turbulent convection at the Rayleigh number of 106 as a prototype for turbulent geophysical flows, which are dominantly buoyancy driven. The purpose of the study is to evaluate and improve the performance of different model reduction techniques using this setting. One-dimensional ROMs for horizontally averaged temperature are calculated using several methods. Specifically, the Linear Response Function (LRF) of the system is calculated from a large DNS dataset using Dynamic Mode Decomposition (DMD) and Fluctuation-Dissipation Theorem (FDT). The LRF is also calculated using the Green's function method of Hassanzadeh and Kuang (2016, J. Atmos. Sci.), which is based on using numerous forced DNS runs. The performance of these LRFs in estimating the system's response to weak external forcings or controlling the time-mean flow are compared and contrasted. The spectral properties of the LRFs and the scaling of the accuracy with the length of the dataset (for the data-driven methods) are also discussed.

Strategies for Reduced-Order Models in Uncertainty Quantification of Complex Turbulent Dynamical Systems

Science.gov (United States)

Qi, Di

applied in the training phase for calibrating model errors to achieve optimal imperfect model parameters; and total statistical energy dynamics are introduced to improve the model sensitivity in the prediction phase especially when strong external perturbations are exerted. The validity of reduced-order models for predicting statistical responses and intermittency is demonstrated on a series of instructive models with increasing complexity, including the stochastic triad model, the Lorenz '96 model, and models for barotropic and baroclinic turbulence. The skillful low-order modeling methods developed here should also be useful for other applications such as efficient algorithms for data assimilation.

A Reduced Order Model to Predict Transient Flows around Straight Bladed Vertical Axis Wind Turbines

Directory of Open Access Journals (Sweden)

Soledad Le Clainche

2018-03-01

Full Text Available We develop a reduced order model to represent the complex flow behaviour around vertical axis wind turbines. First, we simulate vertical axis turbines using an accurate high order discontinuous Galerkin–Fourier Navier–Stokes Large Eddy Simulation solver with sliding meshes and extract flow snapshots in time. Subsequently, we construct a reduced order model based on a high order dynamic mode decomposition approach that selects modes based on flow frequency. We show that only a few modes are necessary to reconstruct the flow behaviour of the original simulation, even for blades rotating in turbulent regimes. Furthermore, we prove that an accurate reduced order model can be constructed using snapshots that do not sample one entire turbine rotation (but only a fraction of it, which reduces the cost of generating the reduced order model. Additionally, we compare the reduced order model based on the high order Navier–Stokes solver to fast 2D simulations (using a Reynolds Averaged Navier–Stokes turbulent model to illustrate the good performance of the proposed methodology.

A Generalized Runge-Kutta Method of order three

DEFF Research Database (Denmark)

Thomsen, Per Grove

2002-01-01

The report presents a numerical method for the solution of stiff systems of ODE's and index one DAE's. The type of method is a 4- stage Generalized Linear Method that is reformulated in a special Semi Implicit Runge Kutta Method of SDIRK type. Error estimation is by imbedding a method of order 4...... based on the same stages as the method and the coefficients are selected for ease of implementation. The method has 4 stages and the stage-order is 2. For purposes of generating dense output and for initializing the iteration in the internal stages a continuous extension is derived. The method is A......-stable and we present the region of absolute stability and the order star of the order 3 method that is used for computing the solution....

Simplified Predictive Models for CO₂ Sequestration Performance Assessment: Research Topical Report on Task #4 - Reduced-Order Method (ROM) Based Models

Energy Technology Data Exchange (ETDEWEB)

Mishra, Srikanta; Jin, Larry; He, Jincong; Durlofsky, Louis

2015-06-30

Reduced-order models provide a means for greatly accelerating the detailed simulations that will be required to manage CO₂ storage operations. In this work, we investigate the use of one such method, POD-TPWL, which has previously been shown to be effective in oil reservoir simulation problems. This method combines trajectory piecewise linearization (TPWL), in which the solution to a new (test) problem is represented through a linearization around the solution to a previously-simulated (training) problem, with proper orthogonal decomposition (POD), which enables solution states to be expressed in terms of a relatively small number of parameters. We describe the application of POD-TPWL for CO₂-water systems simulated using a compositional procedure. Stanford’s Automatic Differentiation-based General Purpose Research Simulator (AD-GPRS) performs the full-order training simulations and provides the output (derivative matrices and system states) required by the POD-TPWL method. A new POD-TPWL capability introduced in this work is the use of horizontal injection wells that operate under rate (rather than bottom-hole pressure) control. Simulation results are presented for CO₂ injection into a synthetic aquifer and into a simplified model of the Mount Simon formation. Test cases involve the use of time-varying well controls that differ from those used in training runs. Results of reasonable accuracy are consistently achieved for relevant well quantities. Runtime speedups of around a factor of 370 relative to full- order AD-GPRS simulations are achieved, though the preprocessing needed for POD-TPWL model construction corresponds to the computational requirements for about 2.3 full-order simulation runs. A preliminary treatment for POD-TPWL modeling in which test cases differ from training runs in terms of geological parameters (rather than well controls) is also presented. Results in this case involve only small differences between

Robust simulation of buckled structures using reduced order modeling

International Nuclear Information System (INIS)

Wiebe, R.; Perez, R.A.; Spottswood, S.M.

2016-01-01

Lightweight metallic structures are a mainstay in aerospace engineering. For these structures, stability, rather than strength, is often the critical limit state in design. For example, buckling of panels and stiffeners may occur during emergency high-g maneuvers, while in supersonic and hypersonic aircraft, it may be induced by thermal stresses. The longstanding solution to such challenges was to increase the sizing of the structural members, which is counter to the ever present need to minimize weight for reasons of efficiency and performance. In this work we present some recent results in the area of reduced order modeling of post- buckled thin beams. A thorough parametric study of the response of a beam to changing harmonic loading parameters, which is useful in exposing complex phenomena and exercising numerical models, is presented. Two error metrics that use but require no time stepping of a (computationally expensive) truth model are also introduced. The error metrics are applied to several interesting forcing parameter cases identified from the parametric study and are shown to yield useful information about the quality of a candidate reduced order model. Parametric studies, especially when considering forcing and structural geometry parameters, coupled environments, and uncertainties would be computationally intractable with finite element models. The goal is to make rapid simulation of complex nonlinear dynamic behavior possible for distributed systems via fast and accurate reduced order models. This ability is crucial in allowing designers to rigorously probe the robustness of their designs to account for variations in loading, structural imperfections, and other uncertainties. (paper)

Robust simulation of buckled structures using reduced order modeling

Science.gov (United States)

Wiebe, R.; Perez, R. A.; Spottswood, S. M.

2016-09-01

Lightweight metallic structures are a mainstay in aerospace engineering. For these structures, stability, rather than strength, is often the critical limit state in design. For example, buckling of panels and stiffeners may occur during emergency high-g maneuvers, while in supersonic and hypersonic aircraft, it may be induced by thermal stresses. The longstanding solution to such challenges was to increase the sizing of the structural members, which is counter to the ever present need to minimize weight for reasons of efficiency and performance. In this work we present some recent results in the area of reduced order modeling of post- buckled thin beams. A thorough parametric study of the response of a beam to changing harmonic loading parameters, which is useful in exposing complex phenomena and exercising numerical models, is presented. Two error metrics that use but require no time stepping of a (computationally expensive) truth model are also introduced. The error metrics are applied to several interesting forcing parameter cases identified from the parametric study and are shown to yield useful information about the quality of a candidate reduced order model. Parametric studies, especially when considering forcing and structural geometry parameters, coupled environments, and uncertainties would be computationally intractable with finite element models. The goal is to make rapid simulation of complex nonlinear dynamic behavior possible for distributed systems via fast and accurate reduced order models. This ability is crucial in allowing designers to rigorously probe the robustness of their designs to account for variations in loading, structural imperfections, and other uncertainties.

A Reduced-Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography

Science.gov (United States)

Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Zeng, Wenzhi; Zhang, Yonggen; Sun, Fangqiang; Shi, Liangsheng

2018-03-01

Hydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (nd) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.

Identification of the reduced order models of a BWR reactor

International Nuclear Information System (INIS)

Hernandez S, A.

2004-01-01

The present work has as objective to analyze the relative stability of a BWR type reactor. It is analyzed that so adaptive it turns out to identify the parameters of a model of reduced order so that this it reproduces a condition of given uncertainty. This will take of a real fact happened in the La Salle plant under certain operation conditions of power and flow of coolant. The parametric identification is carried out by means of an algorithm of recursive least square and an Output Error model (Output Error), measuring the output power of the reactor when the instability is present, and considering that it is produced by a change in the reactivity of the system in the same way that a sign of type step. Also it is carried out an analytic comparison of the relative stability, analyzing two types of answers: the original answer of the uncertainty of the reactor vs. the obtained response identifying the parameters of the model of reduced order, reaching the conclusion that it is very viable to adapt a model of reduced order to study the stability of a reactor, under the only condition to consider that the dynamics of the reactivity is of step type. (Author)

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

International Nuclear Information System (INIS)

Zhao Shan; Wei, G.W.

2004-01-01

This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite-difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 and 12 are achieved, respectively, in 1D and 2D. Detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain method and the local spectral time-domain method, to cope with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high-order schemes could be over 2000 times more efficient than their fourth-order versions in 2D. In conclusion, the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high-order schemes for numerical solution of time-domain Maxwell's equations with material interfaces

Reduced order surrogate modelling (ROSM) of high dimensional deterministic simulations

Science.gov (United States)

Mitry, Mina

Often, computationally expensive engineering simulations can prohibit the engineering design process. As a result, designers may turn to a less computationally demanding approximate, or surrogate, model to facilitate their design process. However, owing to the the curse of dimensionality, classical surrogate models become too computationally expensive for high dimensional data. To address this limitation of classical methods, we develop linear and non-linear Reduced Order Surrogate Modelling (ROSM) techniques. Two algorithms are presented, which are based on a combination of linear/kernel principal component analysis and radial basis functions. These algorithms are applied to subsonic and transonic aerodynamic data, as well as a model for a chemical spill in a channel. The results of this thesis show that ROSM can provide a significant computational benefit over classical surrogate modelling, sometimes at the expense of a minor loss in accuracy.

Reducing the ordering temperature of CoPt nanoparticles by B additive

Energy Technology Data Exchange (ETDEWEB)

Khemjeen, Yutthaya [Materials Science and Nanotechnology Program, Faculty of Science, Khon Kaen University, Khon Kaen 40002 (Thailand); Pinitsoontorn, Supree, E-mail: psupree@kku.ac.th; Chompoosor, Apiwat [Department of Physics, Faculty of Science, Khon Kaen University, Khon Kaen 40002 (Thailand); Integrated Nanotechnology Research Center, Khon Kaen University, Khon Kaen 40002 (Thailand); Nanotec-KKU Center of Excellence on Advanced Nanomaterials for Energy Production and Storage, Khon Kaen University, Khon Kaen 40002 (Thailand); Maensiri, Santi [School of Physics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000 (Thailand)

2014-08-07

We reported the effect of boron addition on magnetic properties and structure of CoPt nanoparticles prepared by a polyol method. The magnetic property measurement showed that the CoPt-B sample exhibited a much larger coercivity compared to the sample without B additive at the same annealing temperature. Transmission electron microscopy and energy dispersive X-ray spectroscopy revealed that the average particle size was about 2 nm for the as-synthesized sample with the ratio of Co and Pt close to 1:1. After annealing, the particle sizes increased but the composition was maintained. The phase transformation of the nanoparticles versus temperature was investigated using a combination of X-ray diffraction and in-situ X-ray absorption analysis. It was shown that the phase transition temperature at which the nanoparticles change from the disordered A1 phase to the ordered L1{sub 0} phase occurs at temperature of 600 °C. We concluded that boron additives could reduce the ordering temperature of CoPt of about 100 °C.

Vortex network community based reduced-order force model

Science.gov (United States)

Gopalakrishnan Meena, Muralikrishnan; Nair, Aditya; Taira, Kunihiko

2017-11-01

We characterize the vortical wake interactions by utilizing network theory and cluster-based approaches, and develop a data-inspired unsteady force model. In the present work, the vortical interaction network is defined by nodes representing vortical elements and the edges quantified by induced velocity measures amongst the vortices. The full vorticity field is reduced to a finite number of vortical clusters based on network community detection algorithm, which serves as a basis for a skeleton network that captures the essence of the wake dynamics. We use this reduced representation of the wake to develop a data-inspired reduced-order force model that can predict unsteady fluid forces on the body. The overall formulation is demonstrated for laminar flows around canonical bluff body wake and stalled flow over an airfoil. We also show the robustness of the present network-based model against noisy data, which motivates applications towards turbulent flows and experimental measurements. Supported by the National Science Foundation (Grant 1632003).

A rational repeating template method for synthesis of 2D hexagonally ordered mesoporous precious metals.

Science.gov (United States)

Takai, Azusa; Doi, Yoji; Yamauchi, Yusuke; Kuroda, Kazuyuki

2011-03-01

A repeating template method is presented for the synthesis of mesoporous metals with 2D hexagonal mesostructures. First, a silica replica (i.e., silica nanorods arranged periodically) is prepared by using 2D hexagonally ordered mesoporous carbon as the template. After that, the obtained silica replica is used as the second template for the preparation of mesoporous ruthenium. After the ruthenium species are introduced into the silica replica, the ruthenium species are then reduced by a vapor-infiltration method by using the reducing agent dimethylamine borane. After the ruthenium deposition, the silica is chemically removed. Analysis by transmission and scanning electron microscopies, a nitrogen-adsorption-desorption isotherm, and small-angle X-ray scattering revealed that the mesoporous ruthenium had a 2D hexagonal mesostructure, although the mesostructural ordering is decreased compared to that of the original mesoporous carbon template. This method is widely applicable to other metal systems. By changing the metal species introduced into the silica replica, several mesoporous metals (palladium and platinum) can be synthesized. Ordered mesoporous ruthenium and palladium, which are not easily attainable by the soft-templating methods, can be prepared. This study has overcome the composition variation limitations of the soft-templating method. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Governor Design for a Hydropower Plant with an Upstream Surge Tank by GA-Based Fuzzy Reduced-Order Sliding Mode

Directory of Open Access Journals (Sweden)

Chang Xu

2015-11-01

Full Text Available This paper investigates governor design by reduced-order sliding mode for a hydropower plant with an upstream surge tank. The governing system is made up of a tunnel, a surge tank, a penstock, a wicket gate and servomechanism, a governor, a hydro-turbine and a grid. Concerning the components of the governing system, their mathematic models are established. Then, these models are interconnected to simulate the governing system. From the viewpoint of state space in modern control theory, the governing system is partially observed, which challenges the governor design. By introducing an additional state variable, the control method of reduced-order sliding mode is proposed, where the governor design is based on a reduced-order governing system. Since the governor is applied to the original governing system, the system stability is analyzed by means of the small gain theorem. An genetic algorithm is employed to search a group of parameters of the predefined sliding surface, and a fuzzy inference system is utilized to decrease the chattering problem. Some numerical simulations are illustrated to verify the feasibility and robustness of the control method.

A high-order time-accurate interrogation method for time-resolved PIV

International Nuclear Information System (INIS)

Lynch, Kyle; Scarano, Fulvio

2013-01-01

A novel method is introduced for increasing the accuracy and extending the dynamic range of time-resolved particle image velocimetry (PIV). The approach extends the concept of particle tracking velocimetry by multiple frames to the pattern tracking by cross-correlation analysis as employed in PIV. The working principle is based on tracking the patterned fluid element, within a chosen interrogation window, along its individual trajectory throughout an image sequence. In contrast to image-pair interrogation methods, the fluid trajectory correlation concept deals with variable velocity along curved trajectories and non-zero tangential acceleration during the observed time interval. As a result, the velocity magnitude and its direction are allowed to evolve in a nonlinear fashion along the fluid element trajectory. The continuum deformation (namely spatial derivatives of the velocity vector) is accounted for by adopting local image deformation. The principle offers important reductions of the measurement error based on three main points: by enlarging the temporal measurement interval, the relative error becomes reduced; secondly, the random and peak-locking errors are reduced by the use of least-squares polynomial fits to individual trajectories; finally, the introduction of high-order (nonlinear) fitting functions provides the basis for reducing the truncation error. Lastly, the instantaneous velocity is evaluated as the temporal derivative of the polynomial representation of the fluid parcel position in time. The principal features of this algorithm are compared with a single-pair iterative image deformation method. Synthetic image sequences are considered with steady flow (translation, shear and rotation) illustrating the increase of measurement precision. An experimental data set obtained by time-resolved PIV measurements of a circular jet is used to verify the robustness of the method on image sequences affected by camera noise and three-dimensional motions. In

Adding-point strategy for reduced-order hypersonic aerothermodynamics modeling based on fuzzy clustering

Science.gov (United States)

Chen, Xin; Liu, Li; Zhou, Sida; Yue, Zhenjiang

2016-09-01

Reduced order models(ROMs) based on the snapshots on the CFD high-fidelity simulations have been paid great attention recently due to their capability of capturing the features of the complex geometries and flow configurations. To improve the efficiency and precision of the ROMs, it is indispensable to add extra sampling points to the initial snapshots, since the number of sampling points to achieve an adequately accurate ROM is generally unknown in prior, but a large number of initial sampling points reduces the parsimony of the ROMs. A fuzzy-clustering-based adding-point strategy is proposed and the fuzzy clustering acts an indicator of the region in which the precision of ROMs is relatively low. The proposed method is applied to construct the ROMs for the benchmark mathematical examples and a numerical example of hypersonic aerothermodynamics prediction for a typical control surface. The proposed method can achieve a 34.5% improvement on the efficiency than the estimated mean squared error prediction algorithm and shows same-level prediction accuracy.

Field Method for Integrating the First Order Differential Equation

Institute of Scientific and Technical Information of China (English)

JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu

2007-01-01

An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.

The Matrix Element Method at Next-to-Leading Order

OpenAIRE

Campbell, John M.; Giele, Walter T.; Williams, Ciaran

2012-01-01

This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...

A Sharp-Interface Immersed Boundary Method with Improved Mass Conservation and Reduced Spurious Pressure Oscillations.

Science.gov (United States)

Seo, Jung Hee; Mittal, Rajat

2011-08-10

A method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods (IBMs) is proposed. By first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary, we adopt a cut-cell based approach to strictly enforce geometric conservation. In order to limit the complexity associated with the cut-cell method, the cut-cell based discretization is limited only to the pressure Poisson and velocity correction equations in the fractional-step method and the small-cell problem tackled by introducing a virtual cell-merging technique. The method is shown to retain all the desirable properties of the original finite-difference based IBM while at the same time, reducing pressure oscillations for moving boundaries by roughly an order of magnitude.

Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

OpenAIRE

Kumar, Sanjay

2018-01-01

In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

A Reduced-order NLTE Kinetic Model for Radiating Plasmas of Outer Envelopes of Stellar Atmospheres

Energy Technology Data Exchange (ETDEWEB)

Munafò, Alessandro [Aerospace Engineering Department, University of Illinois at Urbana-Champaign, 206A Talbot Lab., 104 S. Wright Street, Urbana, IL 61801 (United States); Mansour, Nagi N. [NASA Ames Research Center, Moffett Field, 94035 CA (United States); Panesi, Marco, E-mail: munafo@illinois.edu, E-mail: nagi.n.mansour@nasa.gov, E-mail: m.panesi@illinois.edu [Aerospace Engineering Department, University of Illinois at Urbana-Champaign, 306 Talbot Lab., 104 S. Wright Street, Urbana, IL 61801 (United States)

2017-04-01

The present work proposes a self-consistent reduced-order NLTE kinetic model for radiating plasmas found in the outer layers of stellar atmospheres. A detailed collisional-radiative kinetic mechanism is constructed by leveraging the most up-to-date set of ab initio and experimental data available in the literature. This constitutes the starting point for the derivation of a reduced-order model, obtained by lumping the bound energy states into groups. In order to determine the needed thermo-physical group properties, uniform and Maxwell–Boltzmann energy distributions are used to reconstruct the energy population of each group. Finally, the reduced set of governing equations for the material gas and the radiation field is obtained based on the moment method. Applications consider the steady flow across a shock wave in partially ionized hydrogen. The results clearly demonstrate that adopting a Maxwell–Boltzmann grouping allows, on the one hand, for a substantial reduction of the number of unknowns and, on the other, to maintain accuracy for both gas and radiation quantities. Also, it is observed that, when neglecting line radiation, the use of two groups already leads to a very accurate resolution of the photo-ionization precursor, internal relaxation, and radiative cooling regions. The inclusion of line radiation requires adopting just one additional group to account for optically thin losses in the α , β , and γ lines of the Balmer and Paschen series. This trend has been observed for a wide range of shock wave velocities.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

Science.gov (United States)

Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

2018-02-01

In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

Reduced order dynamic model for polysaccharides molecule attached to an atomic force microscope

International Nuclear Information System (INIS)

Tang Deman; Li Aiqin; Attar, Peter; Dowell, Earl H.

2004-01-01

A dynamic analysis and numerical simulation has been conducted of a polysaccharides molecular structure (a ten (10) single-α-D-glucose molecule chain) connected to a moving atomic force microscope (AFM). Sinusoidal base excitation of the AFM cantilevered beam is considered. First a linearized perturbation model is constructed for the complex polysaccharides molecular structure. Then reduced order (dynamic) models based upon a proper orthogonal decomposition (POD) technique are constructed using global modes for both the linearized perturbation model and for the full nonlinear model. The agreement between the original and reduced order models (ROM/POD) is very good even when only a few global modes are included in the ROM for either the linear case or for the nonlinear case. The computational advantage of the reduced order model is clear from the results presented

Reducing the first-order Doppler shift in a Sagnac interferometer

NARCIS (Netherlands)

Hannemann, S.; Salumbides, E.J.; Ubachs, W.M.G.

2007-01-01

We demonstrate a technique to reduce first-order Doppler shifts in crossed atomic/molecular and laser beam setups by aligning two counterpropagating laser beams as part of a Sagnac interferometer. Interference fringes on the exit port of the interferometer reveal minute deviations from perfect

Identification of reduced-order model for an aeroelastic system from flutter test data

Directory of Open Access Journals (Sweden)

Wei Tang

2017-02-01

Full Text Available Recently, flutter active control using linear parameter varying (LPV framework has attracted a lot of attention. LPV control synthesis usually generates controllers that are at least of the same order as the aeroelastic models. Therefore, the reduced-order model is required by synthesis for avoidance of large computation cost and high-order controller. This paper proposes a new procedure for generation of accurate reduced-order linear time-invariant (LTI models by using system identification from flutter testing data. The proposed approach is in two steps. The well-known poly-reference least squares complex frequency (p-LSCF algorithm is firstly employed for modal parameter identification from frequency response measurement. After parameter identification, the dominant physical modes are determined by clear stabilization diagrams and clustering technique. In the second step, with prior knowledge of physical poles, the improved frequency-domain maximum likelihood (ML estimator is presented for building accurate reduced-order model. Before ML estimation, an improved subspace identification considering the poles constraint is also proposed for initializing the iterative procedure. Finally, the performance of the proposed procedure is validated by real flight flutter test data.

A REVIEW OF ORDER PICKING IMPROVEMENT METHODS

Directory of Open Access Journals (Sweden)

Johan Oscar Ong

2014-09-01

Full Text Available As a crucial and one of the most important parts of warehousing, order picking often raises discussion between warehousing professionals, resulting in various studies aiming to analyze how order picking activity can be improved from various perspective. This paper reviews various past researches on order picking improvement, and the various methods those studies analyzed or developed. This literature review is based on twenty research articles on order picking improvement viewed from four different perspectives: Automation (specifically, stock-to-picker system, storage assignment policy, order batching, and order picking sequencing. By reviewing these studies, we try to identify the most prevalent order picking improvement approach to order picking improvement. Keywords: warehousing; stock-to-picker; storage assignment; order batching; order picking sequencing; improvement

A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring [PowerPoint

Energy Technology Data Exchange (ETDEWEB)

Roettgen, Dan [Wisc; Seeger, Benjamin [Stuttgart; Tai, Wei Che [Washington; Baek, Seunghun [Michigan; Dossogne, Tilan [Liege; Allen, Matthew S [Wisc; Kuether, Robert J.; Brake, Matthew Robert; Mayes, Randall L.

2016-01-01

Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.

Formulation of a reduced order model of the climatic system by combining classical simulation methods with artificial intelligence techniques

Science.gov (United States)

Bounceur, Nabila; Crucifix, Michel

2010-05-01

The climate is a multivariable dynamic complex system, governed by equations which are strongly nonlinear. The space-time modes of climatic variability extend on a very broad scale and constitute a major difficulty to represent this variability over long time-scales. It is generally decided to separate the dynamics of the slow components (ice sheets, carbon cycle, deep oceans) which have a time scale of about thousand of years and more, from those of the fast components (atmosphere, mixed layer, earth and ice surface) for which the time scale is for about some years. In this framework, the time-evolution of the slow components depends on the statistics of the fast components, and the latter are controlled by the slow components and the external forcing particularly astronomical ones characterised by the variation of the orbital parameters: Obliquity, precession and eccentricity. The statistics of the fast components of the climate could in principle be estimated with a general circulation model of the atmosphere and ocean. However, the demand on computing resources would be far too excessive. Given the complexity of the climatic system, the great number of dynamic equations which govern it and its degree of nonlinearity we are interested in the statistical reduction rather than an analytical one. The order reduction problem is equivalent to approximator construction. We will focus on neural networks because they constitute very powerful estimators in presence of non-linearity. The training of this network would be done using the output of the climate model of intermediate complexity "LoveClim" developed and available in the Institute of Astronomy and Geophysics G.Lemaître in Belgium as a first step of statistical reduction. The output of the model are first reduced using different methods of reduction order going from linear ones as principal component analysis (PCA) and empirical orthogonal functions (EOF) to non linear ones as Non Linear Principal component

REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI

Directory of Open Access Journals (Sweden)

O. Burlayenko

2018-04-01

Full Text Available Using a reduced isotropic crystal model the relationship between the fourth-order elastic moduli of an isotropic medium and the independent components of the fourth-order elastic moduli tensor of real crystals of various crystal systems is found. To calculate the coefficients of these relations, computer algebra systems Redberry and Mathematica for working with high order tensors in the symbolic and explicit form were used, in light of the overly complex computation. In an isotropic medium, there are four independent fourth order elastic moduli. This is due to the presence of four invariants for an eighth-rank tensor in the three-dimensional space, that has symmetries over the pairs of indices. As an example, the moduli of elasticity of an isotropic medium corresponding to certain crystals of cubic system are given (LiF, NaCl, MgO, CaF2. From the obtained results it can be seen that the reduced isotropic crystal model can be most effectively applied to high-symmetry crystal systems.

Performance of a reduced-order FSI model for flow-induced vocal fold vibration

Science.gov (United States)

Luo, Haoxiang; Chang, Siyuan; Chen, Ye; Rousseau, Bernard; PhonoSim Team

2017-11-01

Vocal fold vibration during speech production involves a three-dimensional unsteady glottal jet flow and three-dimensional nonlinear tissue mechanics. A full 3D fluid-structure interaction (FSI) model is computationally expensive even though it provides most accurate information about the system. On the other hand, an efficient reduced-order FSI model is useful for fast simulation and analysis of the vocal fold dynamics, which can be applied in procedures such as optimization and parameter estimation. In this work, we study performance of a reduced-order model as compared with the corresponding full 3D model in terms of its accuracy in predicting the vibration frequency and deformation mode. In the reduced-order model, we use a 1D flow model coupled with a 3D tissue model that is the same as in the full 3D model. Two different hyperelastic tissue behaviors are assumed. In addition, the vocal fold thickness and subglottal pressure are varied for systematic comparison. The result shows that the reduced-order model provides consistent predictions as the full 3D model across different tissue material assumptions and subglottal pressures. However, the vocal fold thickness has most effect on the model accuracy, especially when the vocal fold is thin.

Reduced Order Model Implementation in the Risk-Informed Safety Margin Characterization Toolkit

International Nuclear Information System (INIS)

Mandelli, Diego; Smith, Curtis L.; Alfonsi, Andrea; Rabiti, Cristian; Cogliati, Joshua J.; Talbot, Paul W.; Rinaldi, Ivan; Maljovec, Dan; Wang, Bei; Pascucci, Valerio; Zhao, Haihua

2015-01-01

The RISMC project aims to develop new advanced simulation-based tools to perform Probabilistic Risk Analysis (PRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermo-hydraulic behavior of the reactor primary and secondary systems but also external events temporal evolution and components/system ageing. Thus, this is not only a multi-physics problem but also a multi-scale problem (both spatial, µm-mm-m, and temporal, ms-s-minutes-years). As part of the RISMC PRA approach, a large amount of computationally expensive simulation runs are required. An important aspect is that even though computational power is regularly growing, the overall computational cost of a RISMC analysis may be not viable for certain cases. A solution that is being evaluated is the use of reduce order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RICM analysis computational cost by decreasing the number of simulations runs to perform and employ surrogate models instead of the actual simulation codes. This report focuses on the use of reduced order modeling techniques that can be applied to any RISMC analysis to generate, analyze and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (µs instead of hours/days). We apply reduced order and surrogate modeling techniques to several RISMC types of analyses using RAVEN and RELAP-7 and show the advantages that can be gained.

Reduced Order Model Implementation in the Risk-Informed Safety Margin Characterization Toolkit

Energy Technology Data Exchange (ETDEWEB)

Mandelli, Diego [Idaho National Lab. (INL), Idaho Falls, ID (United States); Smith, Curtis L. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Alfonsi, Andrea [Idaho National Lab. (INL), Idaho Falls, ID (United States); Rabiti, Cristian [Idaho National Lab. (INL), Idaho Falls, ID (United States); Cogliati, Joshua J. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Talbot, Paul W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Rinaldi, Ivan [Idaho National Lab. (INL), Idaho Falls, ID (United States); Maljovec, Dan [Idaho National Lab. (INL), Idaho Falls, ID (United States); Wang, Bei [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pascucci, Valerio [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhao, Haihua [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2015-09-01

The RISMC project aims to develop new advanced simulation-based tools to perform Probabilistic Risk Analysis (PRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermo-hydraulic behavior of the reactor primary and secondary systems but also external events temporal evolution and components/system ageing. Thus, this is not only a multi-physics problem but also a multi-scale problem (both spatial, µm-mm-m, and temporal, ms-s-minutes-years). As part of the RISMC PRA approach, a large amount of computationally expensive simulation runs are required. An important aspect is that even though computational power is regularly growing, the overall computational cost of a RISMC analysis may be not viable for certain cases. A solution that is being evaluated is the use of reduce order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RICM analysis computational cost by decreasing the number of simulations runs to perform and employ surrogate models instead of the actual simulation codes. This report focuses on the use of reduced order modeling techniques that can be applied to any RISMC analysis to generate, analyze and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (µs instead of hours/days). We apply reduced order and surrogate modeling techniques to several RISMC types of analyses using RAVEN and RELAP-7 and show the advantages that can be gained.

Higher-Order Integral Equation Methods in Computational Electromagnetics

DEFF Research Database (Denmark)

Jørgensen, Erik; Meincke, Peter

Higher-order integral equation methods have been investigated. The study has focused on improving the accuracy and efficiency of the Method of Moments (MoM) applied to electromagnetic problems. A new set of hierarchical Legendre basis functions of arbitrary order is developed. The new basis...

Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order

KAUST Repository

Hadjimichael, Yiannis

2013-07-23

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.

Strong Stability Preserving Explicit Runge--Kutta Methods of Maximal Effective Order

KAUST Repository

Hadjimichael, Yiannis; Macdonald, Colin B.; Ketcheson, David I.; Verner, James H.

2013-01-01

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge--Kutta methods. Relative to classical Runge--Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods---like classical order five methods---require the use of nonpositive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge--Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.

Reduced Order Modeling of Combustion Instability in a Gas Turbine Model Combustor

Science.gov (United States)

Arnold-Medabalimi, Nicholas; Huang, Cheng; Duraisamy, Karthik

2017-11-01

Hydrocarbon fuel based propulsion systems are expected to remain relevant in aerospace vehicles for the foreseeable future. Design of these devices is complicated by combustion instabilities. The capability to model and predict these effects at reduced computational cost is a requirement for both design and control of these devices. This work focuses on computational studies on a dual swirl model gas turbine combustor in the context of reduced order model development. Full fidelity simulations are performed utilizing URANS and Hybrid RANS-LES with finite rate chemistry. Following this, data decomposition techniques are used to extract a reduced basis representation of the unsteady flow field. These bases are first used to identify sensor locations to guide experimental interrogations and controller feedback. Following this, initial results on developing a control-oriented reduced order model (ROM) will be presented. The capability of the ROM will be further assessed based on different operating conditions and geometric configurations.

Benchmarking with high-order nodal diffusion methods

International Nuclear Information System (INIS)

Tomasevic, D.; Larsen, E.W.

1993-01-01

Significant progress in the solution of multidimensional neutron diffusion problems was made in the late 1970s with the introduction of nodal methods. Modern nodal reactor analysis codes provide significant improvements in both accuracy and computing speed over earlier codes based on fine-mesh finite difference methods. In the past, the performance of advanced nodal methods was determined by comparisons with fine-mesh finite difference codes. More recently, the excellent spatial convergence of nodal methods has permitted their use in establishing reference solutions for some important bench-mark problems. The recent development of the self-consistent high-order nodal diffusion method and its subsequent variational formulation has permitted the calculation of reference solutions with one node per assembly mesh size. In this paper, we compare results for four selected benchmark problems to those obtained by high-order response matrix methods and by two well-known state-of-the-art nodal methods (the open-quotes analyticalclose quotes and open-quotes nodal expansionclose quotes methods)

Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters

Energy Technology Data Exchange (ETDEWEB)

Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Purba, Victor [University of Minnesota; Jafarpour, Saber [University of California Santa-Barbara; Bullo, Francesco [University of California Santa-Barbara; Dhople, Sairaj V. [University of Minnesota

2017-08-21

Next-generation power networks will contain large numbers of grid-connected inverters satisfying a significant fraction of system load. Since each inverter model has a relatively large number of dynamic states, it is impractical to analyze complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model with lumped parameters for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. We show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as any individual inverter in the system. Numerical simulations validate the reduced-order model.

Model's sparse representation based on reduced mixed GMsFE basis methods

Energy Technology Data Exchange (ETDEWEB)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn [Institute of Mathematics, Hunan University, Changsha 410082 (China); Li, Qiuqi, E-mail: qiuqili@hnu.edu.cn [College of Mathematics and Econometrics, Hunan University, Changsha 410082 (China)

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

Science.gov (United States)

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

Hybrid Reduced Order Modeling Algorithms for Reactor Physics Calculations

Science.gov (United States)

Bang, Youngsuk

hybrid ROM algorithms which can be readily integrated into existing methods and offer higher computational efficiency and defendable accuracy of the reduced models. For example, the snapshots ROM algorithm is hybridized with the range finding algorithm to render reduction in the state space, e.g. the flux in reactor calculations. In another implementation, the perturbation theory used to calculate first order derivatives of responses with respect to parameters is hybridized with a forward sensitivity analysis approach to render reduction in the parameter space. Reduction at the state and parameter spaces can be combined to render further reduction at the interface between different physics codes in a multi-physics model with the accuracy quantified in a similar manner to the single physics case. Although the proposed algorithms are generic in nature, we focus here on radiation transport models used in support of the design and analysis of nuclear reactor cores. In particular, we focus on replacing the traditional assembly calculations by ROM models to facilitate the generation of homogenized cross-sections for downstream core calculations. The implication is that assembly calculations could be done instantaneously therefore precluding the need for the expensive evaluation of the few-group cross-sections for all possible core conditions. Given the generic natures of the algorithms, we make an effort to introduce the material in a general form to allow non-nuclear engineers to benefit from this work.

New Efficient Fourth Order Method for Solving Nonlinear Equations

Directory of Open Access Journals (Sweden)

Farooq Ahmad

2013-12-01

Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

Science.gov (United States)

Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

2013-08-01

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

Fast solution of neutron diffusion problem by reduced basis finite element method

International Nuclear Information System (INIS)

Chunyu, Zhang; Gong, Chen

2018-01-01

Highlights: •An extremely efficient method is proposed to solve the neutron diffusion equation with varying the cross sections. •Three orders of speedup is achieved for IAEA benchmark problems. •The method may open a new possibility of efficient high-fidelity modeling of large scale problems in nuclear engineering. -- Abstract: For the important applications which need carry out many times of neutron diffusion calculations such as the fuel depletion analysis and the neutronics-thermohydraulics coupling analysis, fast and accurate solutions of the neutron diffusion equation are demanding but necessary. In the present work, the certified reduced basis finite element method is proposed and implemented to solve the generalized eigenvalue problems of neutron diffusion with variable cross sections. The order reduced model is built upon high-fidelity finite element approximations during the offline stage. During the online stage, both the k eff and the spatical distribution of neutron flux can be obtained very efficiently for any given set of cross sections. Numerical tests show that a speedup of around 1100 is achieved for the IAEA two-dimensional PWR benchmark problem and a speedup of around 3400 is achieved for the three-dimensional counterpart with the fission cross-sections, the absorption cross-sections and the scattering cross-sections treated as parameters.

Hybrid RANS-LES using high order numerical methods

Science.gov (United States)

Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael

2017-11-01

Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

A family of high-order gas-kinetic schemes and its comparison with Riemann solver based high-order methods

Science.gov (United States)

Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun

2018-03-01

Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The advantage of this kind of space-time separation approach is the easy implementation and stability enhancement by introducing more middle stages. However, the nth-order time accuracy needs no less than n stages for the RK method, which can be very time and memory consuming due to the reconstruction at each stage for a high order method. On the other hand, the multi-stage multi-derivative (MSMD) method can be used to achieve the same order of time accuracy using less middle stages with the use of the time derivatives of the flux function. For traditional Riemann solver based CFD methods, the lack of time derivatives in the flux function prevents its direct implementation of the MSMD method. However, the gas kinetic scheme (GKS) provides such a time accurate evolution model. By combining the second-order or third-order GKS flux functions with the MSMD technique, a family of high order gas kinetic methods can be constructed. As an extension of the previous 2-stage 4th-order GKS, the 5th-order schemes with 2 and 3 stages will be developed in this paper. Based on the same 5th-order WENO reconstruction, the performance of gas kinetic schemes from the 2nd- to the 5th-order time accurate methods will be evaluated. The results show that the 5th-order scheme can achieve the theoretical order of accuracy for the Euler equations, and present accurate Navier-Stokes solutions as well due to the coupling of inviscid and viscous terms in the GKS formulation. In comparison with Riemann solver based 5th-order RK method, the high order GKS has advantages in terms of efficiency, accuracy, and robustness, for all test cases. The 4th- and 5th-order GKS have the same robustness as the 2nd-order scheme for the capturing of discontinuous solutions. The current high order MSMD GKS is a

An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

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Eman S. Alaidarous

2013-01-01

Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

Science.gov (United States)

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling

KAUST Repository

Ruzziconi, Laura

2013-06-10

We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.

Semiorders, Intervals Orders and Pseudo Orders Preference Structures in Multiple Criteria Decision Aid Methods

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Fernández Barberis, Gabriela

2013-06-01

Full Text Available During the last decades, an important number of Multicriteria Decision Aid Methods (MCDA has been proposed to help the decision maker to select the best compromise alternative. Meanwhile, the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations family of outranking method and their applications has attracted much attention from academics and practitioners. In this paper, an extension of these methods is presented, consisting of analyze its functioning under New Preference Structures (NPS. The preference structures taken into account are, namely: semiorders, intervals orders and pseudo orders. These structures outstandingly improve the modelization as they give more flexibility, amplitude and certainty at the preferences formulation, since they tend to abandon the Complete Transitive Comparability Axiom of Preferences in order to substitute it by the Partial Comparability Axiom of Preferences. It must be remarked the introduction of Incomparability relations to the analysis and the consideration of preference structures that accept the Indifference intransitivity. The NPS incorporation is carried out in three phases that the PROMETHEE Methodology takes in: preference structure enrichment, dominance relation enrichment and outranking relation exploitation for decision aid, in order to finally arrive at solving the alternatives ranking problem through the PROMETHEE I or the PROMETHEE II utilization, according to whether a partial ranking or a complete one, is respectively required under the NPS

An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

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Mohammad Maleki

2012-01-01

Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

A new time–space domain high-order finite-difference method for the acoustic wave equation

KAUST Repository

Liu, Yang; Sen, Mrinal K.

2009-01-01

A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

A new time–space domain high-order finite-difference method for the acoustic wave equation

KAUST Repository

Liu, Yang

2009-12-01

A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

Deterministic factor analysis: methods of integro-differentiation of non-integral order

Directory of Open Access Journals (Sweden)

Valentina V. Tarasova

2016-12-01

Full Text Available Objective to summarize the methods of deterministic factor economic analysis namely the differential calculus and the integral method. nbsp Methods mathematical methods for integrodifferentiation of nonintegral order the theory of derivatives and integrals of fractional nonintegral order. Results the basic concepts are formulated and the new methods are developed that take into account the memory and nonlocality effects in the quantitative description of the influence of individual factors on the change in the effective economic indicator. Two methods are proposed for integrodifferentiation of nonintegral order for the deterministic factor analysis of economic processes with memory and nonlocality. It is shown that the method of integrodifferentiation of nonintegral order can give more accurate results compared with standard methods method of differentiation using the first order derivatives and the integral method using the integration of the first order for a wide class of functions describing effective economic indicators. Scientific novelty the new methods of deterministic factor analysis are proposed the method of differential calculus of nonintegral order and the integral method of nonintegral order. Practical significance the basic concepts and formulas of the article can be used in scientific and analytical activity for factor analysis of economic processes. The proposed method for integrodifferentiation of nonintegral order extends the capabilities of the determined factorial economic analysis. The new quantitative method of deterministic factor analysis may become the beginning of quantitative studies of economic agents behavior with memory hereditarity and spatial nonlocality. The proposed methods of deterministic factor analysis can be used in the study of economic processes which follow the exponential law in which the indicators endogenous variables are power functions of the factors exogenous variables including the processes

Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

Lagrange-Noether method for solving second-order differential equations

Institute of Scientific and Technical Information of China (English)

Wu Hui-Bin; Wu Run-Heng

2009-01-01

The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

Method to render second order beam optics programs symplectic

International Nuclear Information System (INIS)

Douglas, D.; Servranckx, R.V.

1984-10-01

We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs

Probabilistic error bounds for reduced order modeling

Energy Technology Data Exchange (ETDEWEB)

Abdo, M.G.; Wang, C.; Abdel-Khalik, H.S., E-mail: abdo@purdue.edu, E-mail: wang1730@purdue.edu, E-mail: abdelkhalik@purdue.edu [Purdue Univ., School of Nuclear Engineering, West Lafayette, IN (United States)

2015-07-01

Reduced order modeling has proven to be an effective tool when repeated execution of reactor analysis codes is required. ROM operates on the assumption that the intrinsic dimensionality of the associated reactor physics models is sufficiently small when compared to the nominal dimensionality of the input and output data streams. By employing a truncation technique with roots in linear algebra matrix decomposition theory, ROM effectively discards all components of the input and output data that have negligible impact on reactor attributes of interest. This manuscript introduces a mathematical approach to quantify the errors resulting from the discarded ROM components. As supported by numerical experiments, the introduced analysis proves that the contribution of the discarded components could be upper-bounded with an overwhelmingly high probability. The reverse of this statement implies that the ROM algorithm can self-adapt to determine the level of the reduction needed such that the maximum resulting reduction error is below a given tolerance limit that is set by the user. (author)

A method for handlebars ballast calculation in order to reduce vibrations transmissibility in walk behind tractors

Directory of Open Access Journals (Sweden)

Angelo Fabbri

2017-06-01

Full Text Available Walk behind tractors have some advantages over other agricultural machines, such as the cheapness and the easy to use, however the driver is exposed to high level of vibrations transmitted from handles to hand-arm system and to shoulders. The vibrations induce discomfort and early fatigue to the operator. In order to control the vibration transmissibility, a ballast mass may be added to the handles. Even if the determination of the appropriate ballast mass is a critical point in the handle design. The aim of this research was to study the influence of the handle mass modification, on the dynamic structure behaviour. Modal frequencies and subsequent transmissibility calculated by using an analytical approach and a finite elements model, were compared. A good agreement between the results obtained by the two methods was found (average percentage difference calculated on natural frequencies equal to 5.8±3.8%. Power tillers are made generally by small or medium-small size manufacturers that have difficulties in dealing with finite element codes or modal analysis techniques. As a consequence, the proposed analytical method could be used to find the optimal ballast mass in a simple and economic way, without experimental tests or complex finite element codes. A specific and very simple software or spreadsheet, developed on the base of the analytical method here discussed, could effectively to help the manufacturers in the handlebar design phase. The choice of the correct elastic mount, the dimensioning of the guide members and the ballast mass could be considerably simplified.

Cheap arbitrary high order methods for single integrand SDEs

DEFF Research Database (Denmark)

Debrabant, Kristian; Kværnø, Anne

2017-01-01

For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order $p_d$ we obtain methods converging in the mean-square and weak sense with order $\\lfloor p_d/2\\rfloor$. The reason is that the B-series...

First-order Convex Optimization Methods for Signal and Image Processing

DEFF Research Database (Denmark)

Jensen, Tobias Lindstrøm

2012-01-01

In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple...

Reduced-Order Structure-Preserving Model for Parallel-Connected Three-Phase Grid-Tied Inverters: Preprint

Energy Technology Data Exchange (ETDEWEB)

Johnson, Brian B [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Purba, Victor [University of Minnesota; Jafarpour, Saber [University of California, Santa Barbara; Bullo, Francesco [University of California, Santa Barbara; Dhople, Sairaj [University of Minnesota

2017-08-31

Given that next-generation infrastructures will contain large numbers of grid-connected inverters and these interfaces will be satisfying a growing fraction of system load, it is imperative to analyze the impacts of power electronics on such systems. However, since each inverter model has a relatively large number of dynamic states, it would be impractical to execute complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. That is, we show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as an individual inverter in the paralleled system. Numerical simulations validate the reduced-order models.

Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes

Science.gov (United States)

2013-01-01

elastic deformation, has been the subject of intensive study and has been treated in a number of textbooks , including Refs. 9–11, as well as review...simulations, which can be quite computationally-intensive. Reduced-order models (ROMs) o er a solution to these competing demands of accuracy and e ciency...regimes, from subsonic to hypersonic ight. The correction factor term allows the ROM to be accurate over a range of vehicle elastic modal deformation

Reduced-order modeling (ROM) for simulation and optimization powerful algorithms as key enablers for scientific computing

CERN Document Server

Milde, Anja; Volkwein, Stefan

2018-01-01

This edited monograph collects research contributions and addresses the advancement of efficient numerical procedures in the area of model order reduction (MOR) for simulation, optimization and control. The topical scope includes, but is not limited to, new out-of-the-box algorithmic solutions for scientific computing, e.g. reduced basis methods for industrial problems and MOR approaches for electrochemical processes. The target audience comprises research experts and practitioners in the field of simulation, optimization and control, but the book may also be beneficial for graduate students alike. .

Convergency analysis of the high-order mimetic finite difference method

Energy Technology Data Exchange (ETDEWEB)

Lipnikov, Konstantin [Los Alamos National Laboratory; Veiga Da Beirao, L [UNIV DEGLI STUDI; Manzini, G [NON LANL

2008-01-01

We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.

A high-order SPH method by introducing inverse kernels

Directory of Open Access Journals (Sweden)

Le Fang

2017-02-01

Full Text Available The smoothed particle hydrodynamics (SPH method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square (LS and Moving-Least-Square (MLS methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.

First-order transitions and the multihistogram method

International Nuclear Information System (INIS)

Bhanot, G.; Lippert, T.; Schilling, K.; Ueberholz, P.

1992-01-01

We describe how the multihistogram method can be used to get reliable results from simulations in the critical region of first-order transitions even in the presence of severe hysteresis effects. (orig.)

New high order FDTD method to solve EMC problems

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N. Deymier

2015-10-01

Full Text Available In electromagnetic compatibility (EMC context, we are interested in developing new ac- curate methods to solve efficiently and accurately Maxwell’s equations in the time domain. Indeed, usual methods such as FDTD or FVTD present im- portant dissipative and/or dispersive errors which prevent to obtain a good numerical approximation of the physical solution for a given industrial scene unless we use a mesh with a very small cell size. To avoid this problem, schemes like the Discontinuous Galerkin (DG method, based on higher order spa- tial approximations, have been introduced and stud- ied on unstructured meshes. However the cost of this kind of method can become prohibitive accord- ing to the mesh used. In this paper, we first present a higher order spatial approximation method on carte- sian meshes. It is based on a finite element ap- proach and recovers at the order 1 the well-known Yee’s schema. Next, to deal with EMC problem, a non-oriented thin wire formalism is proposed for this method. Finally, several examples are given to present the benefits of this new method by compar- ison with both Yee’s schema and DG approaches.

Gaussian-2 theory using reduced Moller--Plesset orders

International Nuclear Information System (INIS)

Curtiss, L.A.; Raghavachari, K.; Pople, J.A.

1993-01-01

Two variations of Gaussian-2 (G2) theory are presented. In the first, referred to as G2 (MP2) theory, the basis-set-extension energy corrections are obtained at the 2nd order Moller--Plesset (MP2) level and in the second, referred to as G2(MP3) theory, they are obtained at the MP3 level. The methods are tested out on the set of 125 systems used for validation of G2 theory [J. Chem Phys. 94, 7221 (1991)]. The average absolute deviation of the G2(MP2) and G2(MP3) theories from experiment are 1.58 and 1.52 kcal/mol, respectively, compared to 1.21 kcal/mol for G2 theory. The new methods provide significant savings in computational time and disk storage

Control-oriented reduced order modeling of dipteran flapping flight

Science.gov (United States)

Faruque, Imraan

Flying insects achieve flight stabilization and control in a manner that requires only small, specialized neural structures to perform the essential components of sensing and feedback, achieving unparalleled levels of robust aerobatic flight on limited computational resources. An engineering mechanism to replicate these control strategies could provide a dramatic increase in the mobility of small scale aerial robotics, but a formal investigation has not yet yielded tools that both quantitatively and intuitively explain flapping wing flight as an "input-output" relationship. This work uses experimental and simulated measurements of insect flight to create reduced order flight dynamics models. The framework presented here creates models that are relevant for the study of control properties. The work begins with automated measurement of insect wing motions in free flight, which are then used to calculate flight forces via an empirically-derived aerodynamics model. When paired with rigid body dynamics and experimentally measured state feedback, both the bare airframe and closed loop systems may be analyzed using frequency domain system identification. Flight dynamics models describing maneuvering about hover and cruise conditions are presented for example fruit flies (Drosophila melanogaster) and blowflies (Calliphorids). The results show that biologically measured feedback paths are appropriate for flight stabilization and sexual dimorphism is only a minor factor in flight dynamics. A method of ranking kinematic control inputs to maximize maneuverability is also presented, showing that the volume of reachable configurations in state space can be dramatically increased due to appropriate choice of kinematic inputs.

Non-intrusive reduced order modeling of nonlinear problems using neural networks

Science.gov (United States)

Hesthaven, J. S.; Ubbiali, S.

2018-06-01

We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approximate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the Latin hypercube sampling (LHS) and the Levenberg-Marquardt (LM) training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy.

A reduced-order representation of the Schrödinger equation

Directory of Open Access Journals (Sweden)

Ming-C. Cheng

2016-09-01

Full Text Available A reduced-order-based representation of the Schrödinger equation is investigated for electron wave functions in semiconductor nanostructures. In this representation, the Schrödinger equation is projected onto an eigenspace described by a small number of basis functions that are generated from the proper orthogonal decomposition (POD. The approach substantially reduces the numerical degrees of freedom (DOF’s needed to numerically solve the Schrödinger equation for the wave functions and eigenstate energies in a quantum structure and offers an accurate solution as detailed as the direct numerical simulation of the Schrödinger equation. To develop such an approach, numerical data accounting for parametric variations of the system are used to perform decomposition in order to generate the POD eigenvalues and eigenvectors for the system. This approach is applied to develop POD models for single and multiple quantum well structure. Errors resulting from the approach are examined in detail associated with the selected numerical DOF’s of the POD model and quality of data used for generation of the POD eigenvalues and basis functions. This study investigates the fundamental concepts of the POD approach to the Schrödinger equation and paves a way toward developing an efficient modeling methodology for large-scale multi-block simulation of quantum nanostructures.

Hybrid High-Order methods for finite deformations of hyperelastic materials

Science.gov (United States)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

Higher order polynomial expansion nodal method for hexagonal core neutronics analysis

International Nuclear Information System (INIS)

Jin, Young Cho; Chang, Hyo Kim

1998-01-01

A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy

Reduced-Order Models for Load Management in the Power Grid

Science.gov (United States)

Alizadeh, Mahnoosh

In recent years, considerable research efforts have been directed towards designing control schemes that can leverage the inherent flexibility of electricity demand that is not tapped into in today's electricity markets. It is expected that these control schemes will be carried out by for-profit entities referred to as aggregators that operate at the edge of the power grid network. While the aggregator control problem is receiving much attention, more high-level questions of how these aggregators should plan their market participation, interact with the main grid and with each other, remain rather understudied. Answering these questions requires a large-scale model for the aggregate flexibility that can be harnessed from the a population of customers, particularly for residences and small businesses. The contribution of this thesis towards this goal is divided into three parts: In Chapter 3, a reduced-order model for a large population of heterogeneous appliances is provided by clustering load profiles that share similar degrees of freedom together. The use of such reduced-order model for system planning and optimal market decision making requires a foresighted approximation of the number of appliances that will join each cluster. Thus, Chapter 4 provides a systematic framework to generate such forecasts for the case of Electric Vehicles, based on real-world battery charging data. While these two chapters set aside the economic side that is naturally involved with participation in demand response programs and mainly focus on the control problem, Chapter 5 is dedicated to the study of optimal pricing mechanisms in order to recruit heterogeneous customers in a demand response program in which an aggregator can directly manage their appliances' load under their specified preferences. Prices are proportional to the wholesale market savings that can result from each recruitment event.

Methods for compressible fluid simulation on GPUs using high-order finite differences

Science.gov (United States)

Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer

2017-08-01

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

Science.gov (United States)

Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

2017-03-01

Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Order statistics & inference estimation methods

CERN Document Server

Balakrishnan, N

1991-01-01

The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A co

Second-Order Learning Methods for a Multilayer Perceptron

International Nuclear Information System (INIS)

Ivanov, V.V.; Purehvdorzh, B.; Puzynin, I.V.

1994-01-01

First- and second-order learning methods for feed-forward multilayer neural networks are studied. Newton-type and quasi-Newton algorithms are considered and compared with commonly used back-propagation algorithm. It is shown that, although second-order algorithms require enhanced computer facilities, they provide better convergence and simplicity in usage. 13 refs., 2 figs., 2 tabs

Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

KAUST Repository

Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel

2015-01-01

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search

Reduced Order Modeling Methods for Turbomachinery Design

Science.gov (United States)

2009-03-01

and Ma- terials Conference, May 2006. [45] A. Gelman , J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis. New York, NY: Chapman I& Hall...Macian- Juan , and R. Chawla, “A statistical methodology for quantif ca- tion of uncertainty in best estimate code physical models,” Annals of Nuclear En

Numerov iteration method for second order integral-differential equation

International Nuclear Information System (INIS)

Zeng Fanan; Zhang Jiaju; Zhao Xuan

1987-01-01

In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics

Multilevel Fast Multipole Method for Higher Order Discretizations

DEFF Research Database (Denmark)

Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

2014-01-01

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....

Recursive regularization step for high-order lattice Boltzmann methods

Science.gov (United States)

Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre

2017-09-01

A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.

A Novel Method for Decoding Any High-Order Hidden Markov Model

Directory of Open Access Journals (Sweden)

Fei Ye

2014-01-01

Full Text Available This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.

Notification: Implementation of Executive Order 13771, “Reducing Regulation and Controlling Regulatory Costs”

Science.gov (United States)

Project #OA&E-FY18-0177, April 10, 2018. The OIG plans to begin preliminary research on the Office of the Administrator's Office of Policy implementation of Executive Order 13771, Reducing Regulation and Controlling Regulatory Costs.

Bilinear reduced order approximate model of parabolic distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed

2015-07-01

This paper proposes a novel, low dimensional and accurate approximate model for the distributed parabolic solar collector, by means of a modified gaussian interpolation along the spatial domain. The proposed reduced model, taking the form of a low dimensional bilinear state representation, enables the reproduction of the heat transfer dynamics along the collector tube for system analysis. Moreover, presented as a reduced order bilinear state space model, the well established control theory for this class of systems can be applied. The approximation efficiency has been proven by several simulation tests, which have been performed considering parameters of the Acurex field with real external working conditions. Model accuracy has been evaluated by comparison to the analytical solution of the hyperbolic distributed model and its semi discretized approximation highlighting the benefits of using the proposed numerical scheme. Furthermore, model sensitivity to the different parameters of the gaussian interpolation has been studied.

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2012-09-20

The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered

A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

Directory of Open Access Journals (Sweden)

Sufia Zulfa Ahmad

2016-01-01

Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

Method and container for reducing pertechnetate

International Nuclear Information System (INIS)

Ruddock, C.F.

1980-01-01

A method of reducing the pertechnetate in TcO 4 - comprises mixing together an aqueous solution of pertechnetate, e.g. the eluant from a technetium generator, metallic tin or an alloy thereof as a reducing agent for the pertechnetate, and a soluble salt of a metal below tin in the electrochemical series, e.g. copper, as an activator for the tin metal reducing agent. A complexing agent for the reduced technetium or a colloid stabiliser may also be included. The pH is preferably 3 to 12. Also claimed is a closed container containing the tin reducing agent, the activator, and the complexant or colloid stabiliser if used, preferably in a freeze-dried sterile state, to which the pertechnetate solution may be added. (author)

Reduced order model of draft tube flow

International Nuclear Information System (INIS)

Rudolf, P; Štefan, D

2014-01-01

Swirling flow with compact coherent structures is very good candidate for proper orthogonal decomposition (POD), i.e. for decomposition into eigenmodes, which are the cornerstones of the flow field. Present paper focuses on POD of steady flows, which correspond to different operating points of Francis turbine draft tube flow. Set of eigenmodes is built using a limited number of snapshots from computational simulations. Resulting reduced order model (ROM) describes whole operating range of the draft tube. ROM enables to interpolate in between the operating points exploiting the knowledge about significance of particular eigenmodes and thus reconstruct the velocity field in any operating point within the given range. Practical example, which employs axisymmetric simulations of the draft tube flow, illustrates accuracy of ROM in regions without vortex breakdown together with need for higher resolution of the snapshot database close to location of sudden flow changes (e.g. vortex breakdown). ROM based on POD interpolation is very suitable tool for insight into flow physics of the draft tube flows (especially energy transfers in between different operating points), for supply of data for subsequent stability analysis or as an initialization database for advanced flow simulations

Comparison of three methods to reduce energy density. Effects on daily energy intake.

Science.gov (United States)

Williams, Rachel A; Roe, Liane S; Rolls, Barbara J

2013-07-01

Reductions in food energy density can decrease energy intake, but it is not known if the effects depend on the way that energy density is reduced. We investigated whether three methods of reducing energy density (decreasing fat, increasing fruit and vegetables, and adding water) differed in their effects on energy intake across the day. In a crossover design, 59 adults ate breakfast, lunch, and dinner in the laboratory once a week for 4 weeks. Across conditions, the entrées were either standard in energy density or were reduced in energy density by 20% using one of the three methods. Each meal included a manipulated entrée along with unmanipulated side dishes, and all foods were consumed ad libitum. Reducing the energy density of entrées significantly decreased daily energy intake compared to standard entrées (mean intake 2667 ± 77 kcal/day; 11,166 ± 322 kJ/day). The mean decrease was 396 ± 44 kcal/day (1658 ± 184 kJ/day) when fat was reduced, 308 ± 41 kcal/day (1290 ± 172 kJ/day) when fruit and vegetables were increased, and 230 ± 35 kcal/day (963 ± 147 kJ/day) when water was added. Daily energy intake was lower when fat was decreased compared to the other methods. These findings indicate that a variety of diet compositions can be recommended to reduce overall dietary energy density in order to moderate energy intake. Copyright © 2013 Elsevier Ltd. All rights reserved.

A Fifth Order Hybrid Linear Multistep method For the Direct Solution ...

African Journals Online (AJOL)

A linear multistep hybrid method (LMHM)with continuous coefficients isconsidered and directly applied to solve third order initial and boundary value problems (IBVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 5) which are combined as simultaneous numerical ...

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid

2012-01-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan

2012-08-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Overlay control methodology comparison: field-by-field and high-order methods

Science.gov (United States)

Huang, Chun-Yen; Chiu, Chui-Fu; Wu, Wen-Bin; Shih, Chiang-Lin; Huang, Chin-Chou Kevin; Huang, Healthy; Choi, DongSub; Pierson, Bill; Robinson, John C.

2012-03-01

Overlay control in advanced integrated circuit (IC) manufacturing is becoming one of the leading lithographic challenges in the 3x and 2x nm process nodes. Production overlay control can no longer meet the stringent emerging requirements based on linear composite wafer and field models with sampling of 10 to 20 fields and 4 to 5 sites per field, which was the industry standard for many years. Methods that have emerged include overlay metrology in many or all fields, including the high order field model method called high order control (HOC), and field by field control (FxFc) methods also called correction per exposure. The HOC and FxFc methods were initially introduced as relatively infrequent scanner qualification activities meant to supplement linear production schemes. More recently, however, it is clear that production control is also requiring intense sampling, similar high order and FxFc methods. The added control benefits of high order and FxFc overlay methods need to be balanced with the increased metrology requirements, however, without putting material at risk. Of critical importance is the proper control of edge fields, which requires intensive sampling in order to minimize signatures. In this study we compare various methods of overlay control including the performance levels that can be achieved.

Sparsity enabled cluster reduced-order models for control

Science.gov (United States)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids

Science.gov (United States)

Cheng, Jian; Zhang, Fan; Liu, Tiegang

2018-06-01

In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23,24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.

Using the Electronic Medical Record to Reduce Unnecessary Ordering of Coagulation Studies for Patients with Chest Pain

Directory of Open Access Journals (Sweden)

Jeremiah S. Hinson

2017-02-01

Full Text Available Introduction: Our goal was to reduce ordering of coagulation studies in the emergency department (ED that have no added value for patients presenting with chest pain. We hypothesized this could be achieved via implementation of a stopgap measure in the electronic medical record (EMR. Methods: We used a pre and post quasi-experimental study design to evaluate the impact of an EMRbased intervention on coagulation study ordering for patients with chest pain. A simple interactive prompt was incorporated into the EMR of our ED that required clinicians to indicate whether patients were on anticoagulation therapy prior to completion of orders for coagulation studies. Coagulation order frequency was measured via detailed review of randomly sampled encounters during two-month periods before and after intervention. We classified existing orders as clinically indicated or non-value added. Order frequencies were calculated as percentages, and we assessed differences between groups by chi-square analysis. Results: Pre-intervention, 73.8% (76/103 of patients with chest pain had coagulation studies ordered, of which 67.1% (51/76 were non-value added. Post-intervention, 38.5% (40/104 of patients with chest pain had coagulation studies ordered, of which 60% (24/40 were non-value added. There was an absolute reduction of 35.3% (95% confidence interval [CI]: 22.7%, 48.0% in the total ordering of coagulation studies and 26.4% (95% CI: 13.8%, 39.0% in non-value added order placement. Conclusion: Simple EMR-based interactive prompts can serve as effective deterrents to indiscriminate ordering of diagnostic studies. [West J Emerg Med. 2017;18(2267-269.

A high-order Petrov-Galerkin method for the Boltzmann transport equation

International Nuclear Information System (INIS)

Pain, C.C.; Candy, A.S.; Piggott, M.D.; Buchan, A.; Eaton, M.D.; Goddard, A.J.H.; Oliveira, C.R.E. de

2005-01-01

We describe a new Petrov-Galerkin method using high-order terms to introduce dissipation in a residual-free formulation. The method is developed following both a Taylor series analysis and a variational principle, and the result has much in common with traditional Petrov-Galerkin, Self Adjoint Angular Flux (SAAF) and Even Parity forms of the Boltzmann transport equation. In addition, we consider the subtleties in constructing appropriate boundary conditions. In sub-grid scale (SGS) modelling of fluids the advantages of high-order dissipation are well known. Fourth-order terms, for example, are commonly used as a turbulence model with uniform dissipation. They have been shown to have superior properties to SGS models based upon second-order dissipation or viscosity. Even higher-order forms of dissipation (e.g. 16.-order) can offer further advantages, but are only easily realised by spectral methods because of the solution continuity requirements that these higher-order operators demand. Higher-order operators are more effective, bringing a higher degree of representation to the solution locally. Second-order operators, for example, tend to relax the solution to a linear variation locally, whereas a high-order operator will tend to relax the solution to a second-order polynomial locally. The form of the dissipation is also important. For example, the dissipation may only be applied (as it is in this work) in the streamline direction. While for many problems, for example Large Eddy Simulation (LES), simply adding a second or fourth-order dissipation term is a perfectly satisfactory SGS model, it is well known that a consistent residual-free formulation is required for radiation transport problems. This motivated the consideration of a new Petrov-Galerkin method that is residual-free, but also benefits from the advantageous features that SGS modelling introduces. We close with a demonstration of the advantages of this new discretization method over standard Petrov

Identification of fractional order systems using modulating functions method

KAUST Repository

Liu, Dayan

2013-06-01

The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

Reduced order generalized integrators with phase compensation for three-phase active power filter

DEFF Research Database (Denmark)

Xie, Chuan; Li, Kai; Zhao, Xin

2017-01-01

-order generalized integrators (SOGIs) are utilized to achieve those objectives. However, it will increase the computational burden due to calculation of the multiple paralleled SOGIs. To overcome this issue, phase compensated reduced order generalized integrator (ROGI) is proposed in this paper. Compared...... paralleled ROGIs in positive and negative resonant frequencies. Moreover, the controller parameters are designed and optimized by means of Nyquist diagrams and sensitivity functions in z-domain for directly digital implementation. Finally, the laboratory tests of APF are performed to validate the feasibility...

Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles

International Nuclear Information System (INIS)

Bohm, A.; Loewe, M.; Maxson, S.; Patuleanu, P.; Puentmann, C.; Gadella, M.

1997-01-01

In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z R =E R -iΓ/2 leads to r generalized eigenvectors of order k=0,1,hor-ellipsis,r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E R -iΓ/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher-order poles, the microphysical state obeys a purely exponential decay law. copyright 1997 American Institute of Physics

Calibration Method to Eliminate Zeroth Order Effect in Lateral Shearing Interferometry

Science.gov (United States)

Fang, Chao; Xiang, Yang; Qi, Keqi; Chen, Dawei

2018-04-01

In this paper, a calibration method is proposed which eliminates the zeroth order effect in lateral shearing interferometry. An analytical expression of the calibration error function is deduced, and the relationship between the phase-restoration error and calibration error is established. The analytical results show that the phase-restoration error introduced by the calibration error is proportional to the phase shifting error and zeroth order effect. The calibration method is verified using simulations and experiments. The simulation results show that the phase-restoration error is approximately proportional to the phase shift error and zeroth order effect, when the phase shifting error is less than 2° and the zeroth order effect is less than 0.2. The experimental result shows that compared with the conventional method with 9-frame interferograms, the calibration method with 5-frame interferograms achieves nearly the same restoration accuracy.

On the POD based reduced order modeling of high Reynolds flows

Science.gov (United States)

Behzad, Fariduddin; Helenbrook, Brian; Ahmadi, Goodarz

2012-11-01

Reduced-order modeling (ROM) of a high Reynolds fluid flow using the proper orthogonal decomposition (POD) was studied. Particular attention was given to incompressible, unsteady flow over a two-dimensional NACA0015 airfoil. The Reynolds number is 105 and the angle of attacked of the airfoil is 12°. For DNS solution, hp-finite element method is employed to drive flow samples from which the POD modes are extracted. Particular attention is paid on two issues. First, the stability of POD-ROM resimulation of the turbulent flow is studied. High Reynolds flow contains a lot of fluctuating modes. So, to reach a certain amount of error, more POD modes are needed and the effect of truncation of POD modes is more important. Second, the role of convergence rate on the results of POD. Due to complexity of the flow, convergence of the governing equations is more difficult and the influences of weak convergence appear in the results of POD-ROM. For each issue, the capability of the POD-ROM is assessed in terms of predictions quality of times upon which the POD model was derived. The results are compared with DNS solution and the accuracy and efficiency of different cases are evaluated.

Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

International Nuclear Information System (INIS)

Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

2005-01-01

In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The overall technical objective of the Phase I effort is to develop a nonlinear aeroelastic solver utilizing the FUN3D generated nonlinear aerodynamic Reduced Order...

Method of reducing zirconium

International Nuclear Information System (INIS)

Megy, J.A.

1980-01-01

A method was developed for making nuclear-grade zirconium from a zirconium compound, which ismore economical than previous methods since it uses aluminum as the reductant metal rather than the more expensive magnesium. A fused salt phase containing the zirconium compound to be reduced is first prepared. The fused salt phase is then contacted with a molten metal phase which contains aluminum and zinc. The reduction is effected by mutual displacment. Aluminum is transported from the molten metal phase to the fused salt phase, replacing zirconium in the salt. Zirconium is transported from the fused salt phase to the molten metal phase. The fused salt phase and the molten metal phase are then separated, and the solvent metal and zirconium are separated by distillation or other means. (DN)

Modal-based reduced-order model of BWR out-of phase instabilities

International Nuclear Information System (INIS)

Turso, J.A.; Edwards, R.M.; March-Leuba, J.

1995-01-01

For the past 40 yr, reduced-order modeling of boiling water reactor (BWR) dynamic behavior has been accomplished by several researchers. These models have been primarily concerned with providing insight into the so-called corewide neutron flux oscillation, where the power at each radial location in the core oscillates in unison. This is generally considered to be an illustration of the fundamental neutronic mode excited by the core thermal hydraulics. The time dependence of the fundamental mode is typically described by the point-kinetics equations, with one or more delayed-neutron groups. Thermal-hydraulic excitation of the first azimuthal harmonic mode, the so-called out-of-phase (OOP) instability, has been observed in operating BWRs. The temporal behavior of a low-order model of this phenomenon can be characterized using the modal point-kinetics formulation developed in this paper

Simulation of local instabilities with the use of reduced order models

International Nuclear Information System (INIS)

Dykin, V.; Demaziere, C.; Lange, C.; Hennig, D.

2011-01-01

The development of an advanced reduced order model (ROM) with four heated channels, taking into account local, regional and core-wide oscillations, is described. The ROM contains three sub-models: a neutron-kinetic model (describing neutron transport), a thermal- hydraulic model (describing the coolant flow) and a heat transfer model (describing heat transfer between the fuel and the coolant). All these three models are coupled to each other, using two feedback mechanisms: void feedback and doppler feedback. Each of the sub-models is described by a set of reduced ordinary differential equations, derived from the corresponding time space-dependent partial differential equations by using different types of approximations and mathematical techniques. All three models were developed from past ROMs and, subsequently, were modified in order to fit the purpose of our investigations. One of the novelties of the present ROM is that it takes into account the effect of the first three neutronic modes, namely the fundamental, the first and the second azimuthal modes, as well as the effect of local oscillations on these modes. In order to have a proper representation of both azimuthal modes, a four heated channel ROM was developed. Another modification, compared to earlier work, is the determination of the coupling reactivity coefficients for both void fraction and fuel temperature, which were calculated explicitly by evaluating cross-section perturbations with the help of the SIMULATE-3 and the CORESIM codes. The ROM was thereafter applied to a channel instability event that occurred at the Swedish Forsmark-1 BWR in 1996/1997. The time signals for each of the modes were generated from the ROM and compared with the measurements, performed at the plant. Some qualitative comparison between the ROM and the measurements was made. The results could bear some significance in understanding the instability event and its coupling mechanism to core-wide oscillations. (author)

Methods for studying short-range order in solid binary solutions

International Nuclear Information System (INIS)

Beranger, Gerard

1969-12-01

The short range order definition and its characteristic parameters are first recalled. The different methods to study the short range order are then examined: X ray diffusion, electrical resistivity, specific heat and thermoelectric power, neutron diffraction, electron spin resonance, study of thermodynamic and mechanical properties. The theory of the X ray diffraction effects due to short range order and the subsequent experimental method are emphasized. The principal results obtained from binary Systems, by the different experimental techniques, are reported and briefly discussed. The Au-Cu, Li-Mg, Au-Ni and Cu-Zn Systems are moreover described. (author) [fr

High-order dynamic lattice method for seismic simulation in anisotropic media

Science.gov (United States)

Hu, Xiaolin; Jia, Xiaofeng

2018-03-01

The discrete particle-based dynamic lattice method (DLM) offers an approach to simulate elastic wave propagation in anisotropic media by calculating the anisotropic micromechanical interactions between these particles based on the directions of the bonds that connect them in the lattice. To build such a lattice, the media are discretized into particles. This discretization inevitably leads to numerical dispersion. The basic lattice unit used in the original DLM only includes interactions between the central particle and its nearest neighbours; therefore, it represents the first-order form of a particle lattice. The first-order lattice suffers from numerical dispersion compared with other numerical methods, such as high-order finite-difference methods, in terms of seismic wave simulation. Due to its unique way of discretizing the media, the particle-based DLM no longer solves elastic wave equations; this means that one cannot build a high-order DLM by simply creating a high-order discrete operator to better approximate a partial derivative operator. To build a high-order DLM, we carry out a thorough dispersion analysis of the method and discover that by adding more neighbouring particles into the lattice unit, the DLM will yield different spatial accuracy. According to the dispersion analysis, the high-order DLM presented here can adapt the requirement of spatial accuracy for seismic wave simulations. For any given spatial accuracy, we can design a corresponding high-order lattice unit to satisfy the accuracy requirement. Numerical tests show that the high-order DLM improves the accuracy of elastic wave simulation in anisotropic media.

Reduced order models inertial manifold and global bifurcations: searching instability boundaries in nuclear power systems

International Nuclear Information System (INIS)

Suarez Antola, R.

2009-01-01

In the framework of an analytic or numerical model of a BWR power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behaviour of this nonlinear system, and then a classification of the different solution types concerning their relation with the operational safety of the power plant, by distributing the different solution types in relation with the exclusion region of the power-flow map. Then the goal is to obtain the best attainable qualitative and quantitative global picture of plant dynamics. To do this, the construction and the analysis of the so called reduced order models (Rom) seems a necessary step. A reduced order model results after the full system of coupled nonlinear partial differential equations of the plant is reduced to a system of coupled nonlinear ordinary differential equations

Block Hybrid Collocation Method with Application to Fourth Order Differential Equations

Directory of Open Access Journals (Sweden)

Lee Ken Yap

2015-01-01

Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian

2014-08-17

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

KAUST Repository

Parsani, Matteo

2012-01-01

Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.

Reduced-order aeroelastic model for limit-cycle oscillations in vortex-dominated unsteady airfoil flows

Science.gov (United States)

Suresh Babu, Arun Vishnu; Ramesh, Kiran; Gopalarathnam, Ashok

2017-11-01

In previous research, Ramesh et al. (JFM,2014) developed a low-order discrete vortex method for modeling unsteady airfoil flows with intermittent leading edge vortex (LEV) shedding using a leading edge suction parameter (LESP). LEV shedding is initiated using discrete vortices (DVs) whenever the Leading Edge Suction Parameter (LESP) exceeds a critical value. In subsequent research, the method was successfully employed by Ramesh et al. (JFS, 2015) to predict aeroelastic limit-cycle oscillations in airfoil flows dominated by intermittent LEV shedding. When applied to flows that require large number of time steps, the computational cost increases due to the increasing vortex count. In this research, we apply an amalgamation strategy to actively control the DV count, and thereby reduce simulation time. A pair each of LEVs and TEVs are amalgamated at every time step. The ideal pairs for amalgamation are identified based on the requirement that the flowfield in the vicinity of the airfoil is least affected (Spalart, 1988). Instead of placing the amalgamated vortex at the centroid, we place it at an optimal location to ensure that the leading-edge suction and the airfoil bound circulation are conserved. Results of the initial study are promising.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

Science.gov (United States)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For

Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

Science.gov (United States)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

Singular perturbations introduction to system order reduction methods with applications

CERN Document Server

Shchepakina, Elena; Mortell, Michael P

2014-01-01

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...

Analysis of gear reducer housing using the finite element method

Science.gov (United States)

Miklos, I. Zs; Miklos, C. C.; Alic, C. I.; Raţiu, S.

2018-01-01

The housing is an important component in the construction of gear reducers, having the role of fixing the relative position of the shafts and toothed wheels. At the same time, the housing takes over, via the bearings, the shaft loads resulting when the toothed wheel is engaging another toothed mechanism (i.e. power transmission through belts or chains), and conveys them to the foundation on which it is anchored. In this regard, in order to ensure the most accurate gearing, a high stiffness of the housing is required. In this paper, we present the computer-aided 3D modelling of the housing (in cast version) of a single stage cylindrical gear reducer, using the Autodesk Inventor Professional software, on the principle of constructive sizing. For the housing resistance calculation, we carried out an analysis using the Autodesk Simulation Mechanical software to apply the finite element method, based on the actual loads, as well as a comparative study of the stress and strain distribution, for several tightening values of the retaining bolts that secure the cover and the foundation housing.

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

International Nuclear Information System (INIS)

Batou, A.; Soize, C.; Brie, N.

2013-01-01

Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading

Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

Energy Technology Data Exchange (ETDEWEB)

Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)

2013-09-15

Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.

Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan

2015-02-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

A Fuel-Sensitive Reduced-Order Model (ROM) for Piston Engine Scaling Analysis

Science.gov (United States)

2017-09-29

of high Reynolds number nonreacting and reacting JP-8 sprays in a constant pressure flow vessel with a detailed chemistry approach . J Energy Resour...for rapid grid generation applied to in-cylinder diesel engine simulations. Society of Automotive Engineers ; 2007 Apr. SAE Technical Paper No.: 2007...ARL-TR-8172 ● Sep 2017 US Army Research Laboratory A Fuel-Sensitive Reduced-Order Model (ROM) for Piston Engine Scaling Analysis

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

Formal Solutions for Polarized Radiative Transfer. II. High-order Methods

Energy Technology Data Exchange (ETDEWEB)

Janett, Gioele; Steiner, Oskar; Belluzzi, Luca, E-mail: gioele.janett@irsol.ch [Istituto Ricerche Solari Locarno (IRSOL), 6605 Locarno-Monti (Switzerland)

2017-08-20

When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al., emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost.

Linear and nonlinear stability analysis in BWRs applying a reduced order model

Energy Technology Data Exchange (ETDEWEB)

Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

2016-09-15

Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

Linear and nonlinear stability analysis in BWRs applying a reduced order model

International Nuclear Information System (INIS)

Olvera G, O. A.; Espinosa P, G.; Prieto G, A.

2016-09-01

Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

Operator ordering in quantum optics theory and the development of Dirac's symbolic method

International Nuclear Information System (INIS)

Fan Hongyi

2003-01-01

We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented. (review article)

Higher order methods for burnup calculations with Bateman solutions

International Nuclear Information System (INIS)

Isotalo, A.E.; Aarnio, P.A.

2011-01-01

Highlights: → Average microscopic reaction rates need to be estimated at each step. → Traditional predictor-corrector methods use zeroth and first order predictions. → Increasing predictor order greatly improves results. → Increasing corrector order does not improve results. - Abstract: A group of methods for burnup calculations solves the changes in material compositions by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates. This requires predicting representative averages for the one-group cross-sections and flux during each step, which is usually done using zeroth and first order predictions for their time development in a predictor-corrector calculation. In this paper we present the results of using linear, rather than constant, extrapolation on the predictor and quadratic, rather than linear, interpolation on the corrector. Both of these are done by using data from the previous step, and thus do not affect the stepwise running time. The methods were tested by implementing them into the reactor physics code Serpent and comparing the results from four test cases to accurate reference results obtained with very short steps. Linear extrapolation greatly improved results for thermal spectra and should be preferred over the constant one currently used in all Bateman solution based burnup calculations. The effects of using quadratic interpolation on the corrector were, on the other hand, predominantly negative, although not enough so to conclusively decide between the linear and quadratic variants.

Package Equivalent Reactor Networks as Reduced Order Models for Use with CAPE-OPEN Compliant Simulation

Energy Technology Data Exchange (ETDEWEB)

Meeks, E.; Chou, C. -P.; Garratt, T.

2013-03-31

Engineering simulations of coal gasifiers are typically performed using computational fluid dynamics (CFD) software, where a 3-D representation of the gasifier equipment is used to model the fluid flow in the gasifier and source terms from the coal gasification process are captured using discrete-phase model source terms. Simulations using this approach can be very time consuming, making it difficult to imbed such models into overall system simulations for plant design and optimization. For such system-level designs, process flowsheet software is typically used, such as Aspen Plus® [1], where each component where each component is modeled using a reduced-order model. For advanced power-generation systems, such as integrated gasifier/gas-turbine combined-cycle systems (IGCC), the critical components determining overall process efficiency and emissions are usually the gasifier and combustor. Providing more accurate and more computationally efficient reduced-order models for these components, then, enables much more effective plant-level design optimization and design for control. Based on the CHEMKIN-PRO and ENERGICO software, we have developed an automated methodology for generating an advanced form of reduced-order model for gasifiers and combustors. The reducedorder model offers representation of key unit operations in flowsheet simulations, while allowing simulation that is fast enough to be used in iterative flowsheet calculations. Using high-fidelity fluiddynamics models as input, Reaction Design’s ENERGICO® [2] software can automatically extract equivalent reactor networks (ERNs) from a CFD solution. For the advanced reduced-order concept, we introduce into the ERN a much more detailed kinetics model than can be included practically in the CFD simulation. The state-of-the-art chemistry solver technology within CHEMKIN-PRO allows that to be accomplished while still maintaining a very fast model turn-around time. In this way, the ERN becomes the basis for

Investigation of the density wave oscillation in ocean motions with reduced order models

International Nuclear Information System (INIS)

Yan, B.H.; Li, R.

2018-01-01

Highlights: •The parameter about the degree of instability is defined. •The results are in satisfactory agreement with experimental results. •The effect of ocean motions on DWO is analyzed quantitatively. •The results are of good universality and generality. -- Abstract: The two phase flow instability is an important phenomenon in nuclear power and thermal systems. In the research and design of small modular reactor, the effect of ocean motions on the two phase flow instability should be evaluated. In this work, the density wave oscillation in a uniformly heated channel in ocean motions is investigated with reduced order model by transforming the partial differential equations to ordinary differential equations. This kind of frequency domain method is complementary to the time domain analysis with system codes, not as alternatives. The parameter about the degree of instability is defined for the quantitative analysis of two phase flow instability. The results are in satisfactory agreement with experimental results. The effect of ocean motions on density wave oscillation in a uniformly heated channel is analyzed quantitatively. The parametric study is also carried out.

Probabilistic method/techniques of evaluation/modeling that permits to optimize/reduce the necessary resources

International Nuclear Information System (INIS)

Florescu, G.; Apostol, M.; Farcasiu, M.; Luminita Bedreaga, M.; Nitoi, M.; Turcu, I.

2004-01-01

Fault tree/event tree modeling approach is widely used in modeling and behavior simulation of nuclear structures, systems and components (NSSCs), during different condition of operation. Evaluation of NSSCs reliability, availability, risk or safety, during operation, by using probabilistic techniques, is also largely used. Development of computer capabilities offered new possibilities for large NSSCs models designing, processing and using. There are situations where large, complex and correct NSSC models are desired to be associated with rapid results/solutions/decisions or with multiple processing in order to obtain specific results. Large fault/event trees are hardly to be developed, reviewed and processed. During operation of NSSCs, the time, especially, is an important factor in taking decision. The paper presents a probabilistic method that permits evaluation/modeling of NSSCs and intents to solve the above problems by adopting appropriate techniques. The method is stated for special applications and is based on specific PSA analysis steps, information, algorithms, criteria and relations, in correspondence with the fault tree/event tree modeling and similar techniques, in order to obtain appropriate results for NSSC model analysis. Special classification of NSSCs is stated in order to reflect aspects of use of the method. Also the common reliability databases are part of information necessary to complete the analysis process. Special data and information bases contribute to state the proposed method/techniques. The paper also presents the specific steps of the method, its applicability, the main advantages and problems to be furthermore studied. The method permits optimization/reducing of resources used to perform the PSA activities. (author)

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

Science.gov (United States)

Fink, P. W.; Wilton, D. R.; Dobbins, J. A.

2002-01-01

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required

Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations

International Nuclear Information System (INIS)

Wang Haifeng; Popov, Pavel P.; Pope, Stephen B.

2010-01-01

We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes.

Higher-order schemes for the Laplace transformation method for parabolic problems

KAUST Repository

Douglas, C.

2011-01-01

In this paper we solve linear parabolic problems using the three stage noble algorithms. First, the time discretization is approximated using the Laplace transformation method, which is both parallel in time (and can be in space, too) and extremely high order convergent. Second, higher-order compact schemes of order four and six are used for the the spatial discretization. Finally, the discretized linear algebraic systems are solved using multigrid to show the actual convergence rate for numerical examples, which are compared to other numerical solution methods. © 2011 Springer-Verlag.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

Directory of Open Access Journals (Sweden)

Gang Chen

2012-01-01

Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

Two new solutions to the third-order symplectic integration method

International Nuclear Information System (INIS)

Iwatsu, Reima

2009-01-01

Two new solutions are obtained for the symplecticity conditions of explicit third-order partitioned Runge-Kutta time integration method. One of them has larger stability limit and better dispersion property than the Ruth's method.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Reduced Order Models for Dynamic Behavior of Elastomer Damping Devices

Science.gov (United States)

Morin, B.; Legay, A.; Deü, J.-F.

2016-09-01

In the context of passive damping, various mechanical systems from the space industry use elastomer components (shock absorbers, silent blocks, flexible joints...). The material of these devices has frequency, temperature and amplitude dependent characteristics. The associated numerical models, using viscoelastic and hyperelastic constitutive behaviour, may become computationally too expensive during a design process. The aim of this work is to propose efficient reduced viscoelastic models of rubber devices. The first step is to choose an accurate material model that represent the viscoelasticity. The second step is to reduce the rubber device finite element model to a super-element that keeps the frequency dependence. This reduced model is first built by taking into account the fact that the device's interfaces are much more rigid than the rubber core. To make use of this difference, kinematical constraints enforce the rigid body motion of these interfaces reducing the rubber device model to twelve dofs only on the interfaces (three rotations and three translations per face). Then, the superelement is built by using a component mode synthesis method. As an application, the dynamic behavior of a structure supported by four hourglass shaped rubber devices under harmonic loads is analysed to show the efficiency of the proposed approach.

A second-order unconstrained optimization method for canonical-ensemble density-functional methods

Science.gov (United States)

Nygaard, Cecilie R.; Olsen, Jeppe

2013-03-01

A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.

A reduced-order vortex model of three-dimensional unsteady non-linear aerodynamics

Science.gov (United States)

Eldredge, Jeff D.

2014-11-01

Rapid, large-amplitude maneuvers of low aspect ratio wings are inherent to biologically-inspired flight. These give rise to unsteady phenomena associated with the interactions among the coherent structures shed from wing edges. The objective of this work is to distill these phenomena into a low-order physics-based dynamical model. The model is based on interconnected vortex loops, composed of linear segments between a small number of vertices. Thus, the dynamics of the fluid are reduced to tracking the evolution of the vertices, whose motions are determined from the velocity field induced by the loops and wing motion. The feature that distinguishes this method from previous treatments is that the vortex loops, analogous to point vortices in our two-dimensional model, have time-varying strength. That is, the flux of vorticity from the wing is concentrated in the constituent segments. Chains of interconnected loops can be shed from any edge of the wing. The evolution equation for the loop vertices is based on the impulse matching principle developed in previous work. We demonstrate the model in various maneuvers, including impulse starts of low aspect ratio wings, oscillatory pitching, etc., and compare with experimental results and high-fidelity simulations where applicable. This work was supported by AFOSR under Award FA9550-11-1-0098.

Fourth-order perturbative extension of the single-double excitation coupled-cluster method

International Nuclear Information System (INIS)

Derevianko, Andrei; Emmons, Erik D.

2002-01-01

Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed

Reduced-order modellin for high-pressure transient flow of hydrogen-natural gas mixture

Science.gov (United States)

Agaie, Baba G.; Khan, Ilyas; Alshomrani, Ali Saleh; Alqahtani, Aisha M.

2017-05-01

In this paper the transient flow of hydrogen compressed-natural gas (HCNG) mixture which is also referred to as hydrogen-natural gas mixture in a pipeline is numerically computed using the reduced-order modelling technique. The study on transient conditions is important because the pipeline flows are normally in the unsteady state due to the sudden opening and closure of control valves, but most of the existing studies only analyse the flow in the steady-state conditions. The mathematical model consists in a set of non-linear conservation forms of partial differential equations. The objective of this paper is to improve the accuracy in the prediction of the HCNG transient flow parameters using the Reduced-Order Modelling (ROM). The ROM technique has been successfully used in single-gas and aerodynamic flow problems, the gas mixture has not been done using the ROM. The study is based on the velocity change created by the operation of the valves upstream and downstream the pipeline. Results on the flow characteristics, namely the pressure, density, celerity and mass flux are based on variations of the mixing ratio and valve reaction and actuation time; the ROM computational time cost advantage are also presented.

Frequency-domain reduced order models for gravitational waves from aligned-spin compact binaries

International Nuclear Information System (INIS)

Pürrer, Michael

2014-01-01

Black-hole binary coalescences are one of the most promising sources for the first detection of gravitational waves. Fast and accurate theoretical models of the gravitational radiation emitted from these coalescences are highly important for the detection and extraction of physical parameters. Spinning effective-one-body models for binaries with aligned-spins have been shown to be highly faithful, but are slow to generate and thus have not yet been used for parameter estimation (PE) studies. I provide a frequency-domain singular value decomposition-based surrogate reduced order model that is thousands of times faster for typical system masses and has a faithfulness mismatch of better than ∼0.1% with the original SEOBNRv1 model for advanced LIGO detectors. This model enables PE studies up to signal-to-noise ratios (SNRs) of 20 and even up to 50 for total masses below 50 M ⊙ . This paper discusses various choices for approximations and interpolation over the parameter space that can be made for reduced order models of spinning compact binaries, provides a detailed discussion of errors arising in the construction and assesses the fidelity of such models. (paper)

High-order multi-implicit spectral deferred correction methods for problems of reactive flow

International Nuclear Information System (INIS)

Bourlioux, Anne; Layton, Anita T.; Minion, Michael L.

2003-01-01

Models for reacting flow are typically based on advection-diffusion-reaction (A-D-R) partial differential equations. Many practical cases correspond to situations where the relevant time scales associated with each of the three sub-processes can be widely different, leading to disparate time-step requirements for robust and accurate time-integration. In particular, interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection. The numerical strategy introduced in this paper is a general procedure to account for this time-scale disparity. The proposed methods are high-order multi-implicit generalizations of spectral deferred correction methods (MISDC methods), constructed for the temporal integration of A-D-R equations. Spectral deferred correction methods compute a high-order approximation to the solution of a differential equation by using a simple, low-order numerical method to solve a series of correction equations, each of which increases the order of accuracy of the approximation. The key feature of MISDC methods is their flexibility in handling several sub-processes implicitly but independently, while avoiding the splitting errors present in traditional operator-splitting methods and also allowing for different time steps for each process. The stability, accuracy, and efficiency of MISDC methods are first analyzed using a linear model problem and the results are compared to semi-implicit spectral deferred correction methods. Furthermore, numerical tests on simplified reacting flows demonstrate the expected convergence rates for MISDC methods of orders three, four, and five. The gain in efficiency by independently controlling the sub-process time steps is illustrated for nonlinear problems, where reaction and diffusion are much stiffer than advection. Although the paper focuses on this specific time-scales ordering, the generalization to any ordering combination is straightforward

Generalized Reduced Order Modeling of Aeroservoelastic Systems

Science.gov (United States)

Gariffo, James Michael

Transonic aeroelastic and aeroservoelastic (ASE) modeling presents a significant technical and computational challenge. Flow fields with a mixture of subsonic and supersonic flow, as well as moving shock waves, can only be captured through high-fidelity CFD analysis. With modern computing power, it is realtively straightforward to determine the flutter boundary for a single structural configuration at a single flight condition, but problems of larger scope remain quite costly. Some such problems include characterizing a vehicle's flutter boundary over its full flight envelope, optimizing its structural weight subject to aeroelastic constraints, and designing control laws for flutter suppression. For all of these applications, reduced-order models (ROMs) offer substantial computational savings. ROM techniques in general have existed for decades, and the methodology presented in this dissertation builds on successful previous techniques to create a powerful new scheme for modeling aeroelastic systems, and predicting and interpolating their transonic flutter boundaries. In this method, linear ASE state-space models are constructed from modal structural and actuator models coupled to state-space models of the linearized aerodynamic forces through feedback loops. Flutter predictions can be made from these models through simple eigenvalue analysis of their state-transition matrices for an appropriate set of dynamic pressures. Moreover, this analysis returns the frequency and damping trend of every aeroelastic branch. In contrast, determining the critical dynamic pressure by direct time-marching CFD requires a separate run for every dynamic pressure being analyzed simply to obtain the trend for the critical branch. The present ROM methodology also includes a new model interpolation technique that greatly enhances the benefits of these ROMs. This enables predictions of the dynamic behavior of the system for flight conditions where CFD analysis has not been explicitly

Numerical methods of higher order of accuracy for incompressible flows

Czech Academy of Sciences Publication Activity Database

Kozel, K.; Louda, Petr; Příhoda, Jaromír

2010-01-01

Roč. 80, č. 8 (2010), s. 1734-1745 ISSN 0378-4754 Institutional research plan: CEZ:AV0Z20760514 Keywords : higher order methods * upwind methods * backward-facing step Subject RIV: BK - Fluid Dynamics Impact factor: 0.812, year: 2010

Ordered particles versus ordered pointers in the hybrid ordered plasma simulation (HOPS) code

International Nuclear Information System (INIS)

Anderson, D.V.; Shumaker, D.E.

1993-01-01

From a computational standpoint, particle simulation calculations for plasmas have not adapted well to the transitions from scalar to vector processing nor from serial to parallel environments. They have suffered from inordinate and excessive accessing of computer memory and have been hobbled by relatively inefficient gather-scatter constructs resulting from the use of indirect indexing. Lastly, the many-to-one mapping characteristic of the deposition phase has made it difficult to perform this in parallel. The authors' code sorts and reorders the particles in a spatial order. This allows them to greatly reduce the memory references, to run in directly indexed vector mode, and to employ domain decomposition to achieve parallelization. The field model solves pre-maxwell equations by interatively implicit methods. The OSOP (Ordered Storage Ordered Processing) version of HOPS keeps the particle tables ordered by rebuilding them after each particle pushing phase. Alternatively, the RSOP (Random Storage Ordered Processing) version keeps a table of pointers ordered by rebuilding them. Although OSOP is somewhat faster than RSOP in tests on vector-parallel machines, it is not clear this advantage will carry over to massively parallel computers

An extended Kalman filter approach to non-stationary Bayesian estimation of reduced-order vocal fold model parameters.

Science.gov (United States)

Hadwin, Paul J; Peterson, Sean D

2017-04-01

The Bayesian framework for parameter inference provides a basis from which subject-specific reduced-order vocal fold models can be generated. Previously, it has been shown that a particle filter technique is capable of producing estimates and associated credibility intervals of time-varying reduced-order vocal fold model parameters. However, the particle filter approach is difficult to implement and has a high computational cost, which can be barriers to clinical adoption. This work presents an alternative estimation strategy based upon Kalman filtering aimed at reducing the computational cost of subject-specific model development. The robustness of this approach to Gaussian and non-Gaussian noise is discussed. The extended Kalman filter (EKF) approach is found to perform very well in comparison with the particle filter technique at dramatically lower computational cost. Based upon the test cases explored, the EKF is comparable in terms of accuracy to the particle filter technique when greater than 6000 particles are employed; if less particles are employed, the EKF actually performs better. For comparable levels of accuracy, the solution time is reduced by 2 orders of magnitude when employing the EKF. By virtue of the approximations used in the EKF, however, the credibility intervals tend to be slightly underpredicted.

Comprehensive evaluation of SNP identification with the Restriction Enzyme-based Reduced Representation Library (RRL method

Directory of Open Access Journals (Sweden)

Du Ye

2012-02-01

Full Text Available Abstract Background Restriction Enzyme-based Reduced Representation Library (RRL method represents a relatively feasible and flexible strategy used for Single Nucleotide Polymorphism (SNP identification in different species. It has remarkable advantage of reducing the complexity of the genome by orders of magnitude. However, comprehensive evaluation for actual efficacy of SNP identification by this method is still unavailable. Results In order to evaluate the efficacy of Restriction Enzyme-based RRL method, we selected Tsp 45I enzyme which covers 266 Mb flanking region of the enzyme recognition site according to in silico simulation on human reference genome, then we sequenced YH RRL after Tsp 45I treatment and obtained reads of which 80.8% were mapped to target region with an 20-fold average coverage, about 96.8% of target region was covered by at least one read and 257 K SNPs were identified in the region using SOAPsnp software. Compared with whole genome resequencing data, we observed false discovery rate (FDR of 13.95% and false negative rate (FNR of 25.90%. The concordance rate of homozygote loci was over 99.8%, but that of heterozygote were only 92.56%. Repeat sequences and bases quality were proved to have a great effect on the accuracy of SNP calling, SNPs in recognition sites contributed evidently to the high FNR and the low concordance rate of heterozygote. Our results indicated that repeat masking and high stringent filter criteria could significantly decrease both FDR and FNR. Conclusions This study demonstrates that Restriction Enzyme-based RRL method was effective for SNP identification. The results highlight the important role of bias and the method-derived defects represented in this method and emphasize the special attentions noteworthy.

High order spatial expansion for the method of characteristics applied to 3-D geometries

International Nuclear Information System (INIS)

Naymeh, L.; Masiello, E.; Sanchez, R.

2013-01-01

The method of characteristics is an efficient and flexible technique to solve the neutron transport equation and has been extensively used in two-dimensional calculations because it permits to deal with complex geometries. However, because of a very fast increase in storage requirements and number of floating operations, its direct application to three-dimensional routine transport calculations it is not still possible. In this work we introduce and analyze several modifications aimed to reduce memory requirements and to diminish the computing burden. We explore high-order spatial approximation, the use of intermediary trajectory-dependent flux expansions and the possibility of dynamic trajectory reconstruction from local tracking for typed subdomains. (authors)

Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

Directory of Open Access Journals (Sweden)

Huan-Yu Bi

2015-09-01

Full Text Available The Principle of Maximum Conformality (PMC eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I; the other, more recent, method (PMC-II uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e− and the Higgs partial width Γ(H→bb¯. Both methods lead to the same resummed (‘conformal’ series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

CFD simulations and reduced order modeling of a refrigerator compartment including radiation effects

International Nuclear Information System (INIS)

Bayer, Ozgur; Oskay, Ruknettin; Paksoy, Akin; Aradag, Selin

2013-01-01

Highlights: ► Free convection in a refrigerator is simulated including radiation effects. ► Heat rates are affected drastically when radiation effects are considered. ► 95% of the flow energy can be represented by using one spatial POD mode. - Abstract: Considering the engineering problem of natural convection in domestic refrigerator applications, this study aims to simulate the fluid flow and temperature distribution in a single commercial refrigerator compartment by using the experimentally determined temperature values as the specified constant wall temperature boundary conditions. The free convection in refrigerator applications is evaluated as a three-dimensional (3D), turbulent, transient and coupled non-linear flow problem. Radiation heat transfer mode is also included in the analysis. According to the results, taking radiation effects into consideration does not change the temperature distribution inside the refrigerator significantly; however the heat rates are affected drastically. The flow inside the compartment is further analyzed with a reduced order modeling method called Proper Orthogonal Decomposition (POD) and the energy contents of several spatial and temporal modes that exist in the flow are examined. The results show that approximately 95% of all the flow energy can be represented by only using one spatial mode

Nonlinear Parameter-Varying AeroServoElastic Reduced Order Model for Aerostructural Sensing and Control, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...

Near-optimal order-reduced control for A/C (air-conditioning) system of EVs (electric vehicles)

International Nuclear Information System (INIS)

Chiu, Chien-Chin; Tsai, Nan-Chyuan; Lin, Chun-Chi

2014-01-01

This work is aimed to investigate the regulation problem for thermal comfortableness and propose control strategies for cabin environment of EVs (electric vehicles) by constructing a reduced-scale A/C (air-conditioning) system which mainly consists of two modules: ECB (environmental control box) and AHU (air-handling unit). Temperature and humidity in the ECB can be regulated by AHU via cooling, heating, mixing air streams and adjusting speed of fans. To synthesize the near-optimal controllers, the mathematical model for the system thermodynamics is developed by employing the equivalent lumped heat capacity approach, energy/mass conservation principle and the heat transfer theories. In addition, from the clustering pattern of system eigenvalues, the thermodynamics of the interested system can evidently be characterized by two-time-scale property. That is, the studied system can be decoupled into two subsystems, slow mode and fast mode, by singular perturbation technique. As to the optimal control strategies for EVs, by taking thermal comfortableness, humidity and energy consumption all into account, a series of optimal controllers is synthesized on the base of the order-reduced thermodynamic model. The feedback control loop for the experimental test rig is examined and realized by the aid of the control system development kit dSPACE DS1104 and the commercial software MATLAB/Simulink. To sum up, the intensive computer simulations and experimental results verify that the performance of the near-optimal order-reduced control law is almost as superior as that of standard LQR (Linear-Quadratic Regulator). - Highlights: • A reduced-scale test rig for A/C (air-conditioning) system to imitate the temperature/humidity of cabin in EV (electric vehicle) is constructed. • The non-linear thermodynamic model of A/C system can be decoupled by singular perturbation technique. • The temperature/humidity in cabin is regulated to the desired values by proposed optimal

Combination of ray-tracing and the method of moments for electromagnetic radiation analysis using reduced meshes

Science.gov (United States)

Delgado, Carlos; Cátedra, Manuel Felipe

2018-05-01

This work presents a technique that allows a very noticeable relaxation of the computational requirements for full-wave electromagnetic simulations based on the Method of Moments. A ray-tracing analysis of the geometry is performed in order to extract the critical points with significant contributions. These points are then used to generate a reduced mesh, considering the regions of the geometry that surround each critical point and taking into account the electrical path followed from the source. The electromagnetic analysis of the reduced mesh produces very accurate results, requiring a fraction of the resources that the conventional analysis would utilize.

Enhanced ordering reduces electric susceptibility of liquids confined to graphene slit pores

Science.gov (United States)

Terrones, Jeronimo; Kiley, Patrick J.; Elliott, James A.

2016-01-01

The behaviours of a range of polar and non-polar organic liquids (acetone, ethanol, methanol, N-methyl-2-pyrrolidone (NMP), carbon tetrachloride and water) confined to 2D graphene nanochannels with thicknesses in the range of 4.5 Å to 40 Å were studied using classical molecular dynamics and hybrid density functional theory. All liquids were found to organise spontaneously into ordered layers parallel to the confining surfaces, with those containing polar molecules having their electric dipoles aligned parallel to such surfaces. In particular, monolayers of NMP showed remarkable in-plane ordering and low molecular mobility, suggesting the existence of a previously unknown 2D solid-like phase. Calculations for polar liquids showed dramatically reduced static permittivities normal to the confining surfaces; these changes are expected to improve electron tunnelling across the liquid films, modifying the DC electrical properties of immersed assemblies of carbon nanomaterials. PMID:27265098

Nonlinear Parameter-Varying AeroServoElastic Reduced Order Model for Aerostructural Sensing and Control, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate parameter-varying (PV), aeroservoelastic (ASE)...

Reducing variety in product solution spaces of engineer-to-order companies: The case of Novenco A/S

DEFF Research Database (Denmark)

Haug, Anders; Hvam, Lars; Mortensen, Niels Henrik

2013-01-01

by eliminating the product variety that do not create customer value. However, for Engineer-to-Order (ETO) companies, elimination of variety is particularly challenging, since it is about reducing variety in a complex product solution space, rather than just eliminating already produced product variants......Today many companies are experiencing increasing demands from customers for shorter delivery times and more competitive prices. In order to increase competitiveness from a price and time-to-market perspective, many companies initiate projects to reduce their internal product complexity....... To support ETO companies in achieving more efficient product solution spaces, this paper presents a procedure for reducing product solution spaces in ETO companies. The procedure is demonstrated through an action research study at the Danish ETO company, Novenco, which develops and manufactures heating...

High order spectral volume and spectral difference methods on unstructured grids

Science.gov (United States)

Kannan, Ravishekar

The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed

Pseudospectral collocation methods for fourth order differential equations

Science.gov (United States)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Numerical simulation of stratified shear flow using a higher order Taylor series expansion method

Energy Technology Data Exchange (ETDEWEB)

Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)

1995-09-01

A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.

Time-Frequency Analysis Using Warped-Based High-Order Phase Modeling

Directory of Open Access Journals (Sweden)

Ioana Cornel

2005-01-01

Full Text Available The high-order ambiguity function (HAF was introduced for the estimation of polynomial-phase signals (PPS embedded in noise. Since the HAF is a nonlinear operator, it suffers from noise-masking effects and from the appearance of undesired cross-terms when multicomponents PPS are analyzed. In order to improve the performances of the HAF, the multi-lag HAF concept was proposed. Based on this approach, several advanced methods (e.g., product high-order ambiguity function (PHAF have been recently proposed. Nevertheless, performances of these new methods are affected by the error propagation effect which drastically limits the order of the polynomial approximation. This phenomenon acts especially when a high-order polynomial modeling is needed: representation of the digital modulation signals or the acoustic transient signals. This effect is caused by the technique used for polynomial order reduction, common for existing approaches: signal multiplication with the complex conjugated exponentials formed with the estimated coefficients. In this paper, we introduce an alternative method to reduce the polynomial order, based on the successive unitary signal transformation, according to each polynomial order. We will prove that this method reduces considerably the effect of error propagation. Namely, with this order reduction method, the estimation error at a given order will depend only on the performances of the estimation method.

Reduced-order modelling of wind turbines

NARCIS (Netherlands)

Elkington, K.; Slootweg, J.G.; Ghandhari, M.; Kling, W.L.; Ackermann, T.

2012-01-01

In this chapter power system dynamics simulation(PSDS) isused to study the dynamics of large-scale power systems. It is necessary to incorporate models of wind turbine generating systems into PSDS software packages in order to analyse the impact of high wind power penetration on electrical power

International Conference on Spectral and High-Order Methods

CERN Document Server

Dumont, Ney; Hesthaven, Jan

2017-01-01

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Doppler Radar Vital Signs Detection Method Based on Higher Order Cyclostationary.

Science.gov (United States)

Yu, Zhibin; Zhao, Duo; Zhang, Zhiqiang

2017-12-26

Due to the non-contact nature, using Doppler radar sensors to detect vital signs such as heart and respiration rates of a human subject is getting more and more attention. However, the related detection-method research meets lots of challenges due to electromagnetic interferences, clutter and random motion interferences. In this paper, a novel third-order cyclic cummulant (TOCC) detection method, which is insensitive to Gaussian interference and non-cyclic signals, is proposed to investigate the heart and respiration rate based on continuous wave Doppler radars. The k -th order cyclostationary properties of the radar signal with hidden periodicities and random motions are analyzed. The third-order cyclostationary detection theory of the heart and respiration rate is studied. Experimental results show that the third-order cyclostationary approach has better estimation accuracy for detecting the vital signs from the received radar signal under low SNR, strong clutter noise and random motion interferences.

An efficient modularized sample-based method to estimate the first-order Sobol' index

International Nuclear Information System (INIS)

Li, Chenzhao; Mahadevan, Sankaran

2016-01-01

Sobol' index is a prominent methodology in global sensitivity analysis. This paper aims to directly estimate the Sobol' index based only on available input–output samples, even if the underlying model is unavailable. For this purpose, a new method to calculate the first-order Sobol' index is proposed. The innovation is that the conditional variance and mean in the formula of the first-order index are calculated at an unknown but existing location of model inputs, instead of an explicit user-defined location. The proposed method is modularized in two aspects: 1) index calculations for different model inputs are separate and use the same set of samples; and 2) model input sampling, model evaluation, and index calculation are separate. Due to this modularization, the proposed method is capable to compute the first-order index if only input–output samples are available but the underlying model is unavailable, and its computational cost is not proportional to the dimension of the model inputs. In addition, the proposed method can also estimate the first-order index with correlated model inputs. Considering that the first-order index is a desired metric to rank model inputs but current methods can only handle independent model inputs, the proposed method contributes to fill this gap. - Highlights: • An efficient method to estimate the first-order Sobol' index. • Estimate the index from input–output samples directly. • Computational cost is not proportional to the number of model inputs. • Handle both uncorrelated and correlated model inputs.

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem

2017-01-01

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a

Reduced-Order Direct Numerical Simulation of Solute Transport in Porous Media

Science.gov (United States)

Mehmani, Yashar; Tchelepi, Hamdi

2017-11-01

Pore-scale models are an important tool for analyzing fluid dynamics in porous materials (e.g., rocks, soils, fuel cells). Current direct numerical simulation (DNS) techniques, while very accurate, are computationally prohibitive for sample sizes that are statistically representative of the porous structure. Reduced-order approaches such as pore-network models (PNM) aim to approximate the pore-space geometry and physics to remedy this problem. Predictions from current techniques, however, have not always been successful. This work focuses on single-phase transport of a passive solute under advection-dominated regimes and delineates the minimum set of approximations that consistently produce accurate PNM predictions. Novel network extraction (discretization) and particle simulation techniques are developed and compared to high-fidelity DNS simulations for a wide range of micromodel heterogeneities and a single sphere pack. Moreover, common modeling assumptions in the literature are analyzed and shown that they can lead to first-order errors under advection-dominated regimes. This work has implications for optimizing material design and operations in manufactured (electrodes) and natural (rocks) porous media pertaining to energy systems. This work was supported by the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B).

Application of He's variational iteration method to the fifth-order boundary value problems

International Nuclear Information System (INIS)

Shen, S

2008-01-01

Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems

Nuclear material enrichment identification method based on cross-correlation and high order spectra

International Nuclear Information System (INIS)

Yang Fan; Wei Biao; Feng Peng; Mi Deling; Ren Yong

2013-01-01

In order to enhance the sensitivity of nuclear material identification system (NMIS) against the change of nuclear material enrichment, the principle of high order statistic feature is introduced and applied to traditional NMIS. We present a new enrichment identification method based on cross-correlation and high order spectrum algorithm. By applying the identification method to NMIS, the 3D graphs with nuclear material character are presented and can be used as new signatures to identify the enrichment of nuclear materials. The simulation result shows that the identification method could suppress the background noises, electronic system noises, and improve the sensitivity against enrichment change to exponential order with no system structure modification. (authors)

A general first-order global sensitivity analysis method

International Nuclear Information System (INIS)

Xu Chonggang; Gertner, George Zdzislaw

2008-01-01

Fourier amplitude sensitivity test (FAST) is one of the most popular global sensitivity analysis techniques. The main mechanism of FAST is to assign each parameter with a characteristic frequency through a search function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency. Although FAST has been widely applied, there are two limitations: (1) the aliasing effect among parameters by using integer characteristic frequencies and (2) the suitability for only models with independent parameters. In this paper, we synthesize the improvement to overcome the aliasing effect limitation [Tarantola S, Gatelli D, Mara TA. Random balance designs for the estimation of first order global sensitivity indices. Reliab Eng Syst Safety 2006; 91(6):717-27] and the improvement to overcome the independence limitation [Xu C, Gertner G. Extending a global sensitivity analysis technique to models with correlated parameters. Comput Stat Data Anal 2007, accepted for publication]. In this way, FAST can be a general first-order global sensitivity analysis method for linear/nonlinear models with as many correlated/uncorrelated parameters as the user specifies. We apply the general FAST to four test cases with correlated parameters. The results show that the sensitivity indices derived by the general FAST are in good agreement with the sensitivity indices derived by the correlation ratio method, which is a non-parametric method for models with correlated parameters

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

Science.gov (United States)

Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

2008-09-01

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

State reduced order models for the modelling of the thermal behavior of buildings

Energy Technology Data Exchange (ETDEWEB)

Menezo, Christophe; Bouia, Hassan; Roux, Jean-Jacques; Depecker, Patrick [Institute National de Sciences Appliquees de Lyon, Villeurbanne Cedex, (France). Centre de Thermique de Lyon (CETHIL). Equipe Thermique du Batiment]. E-mail: menezo@insa-cethil-etb.insa-lyon.fr; bouia@insa-cethil-etb.insa-lyon.fr; roux@insa-cethil-etb.insa-lyon.fr; depecker@insa-cethil-etb.insa-lyon.fr

2000-07-01

This work is devoted to the field of building physics and related to the reduction of heat conduction models. The aim is to enlarge the model libraries of heat and mass transfer codes through limiting the considerable dimensions reached by the numerical systems during the modelling process of a multizone building. We show that the balanced realization technique, specifically adapted to the coupling of reduced order models with the other thermal phenomena, turns out to be very efficient. (author)

RCS Leak Rate Calculation with High Order Least Squares Method

International Nuclear Information System (INIS)

Lee, Jeong Hun; Kang, Young Kyu; Kim, Yang Ki

2010-01-01

As a part of action items for Application of Leak before Break(LBB), RCS Leak Rate Calculation Program is upgraded in Kori unit 3 and 4. For real time monitoring of operators, periodic calculation is needed and corresponding noise reduction scheme is used. This kind of study was issued in Korea, so there have upgraded and used real time RCS Leak Rate Calculation Program in UCN unit 3 and 4 and YGN unit 1 and 2. For reduction of the noise in signals, Linear Regression Method was used in those programs. Linear Regression Method is powerful method for noise reduction. But the system is not static with some alternative flow paths and this makes mixed trend patterns of input signal values. In this condition, the trend of signal and average of Linear Regression are not entirely same pattern. In this study, high order Least squares Method is used to follow the trend of signal and the order of calculation is rearranged. The result of calculation makes reasonable trend and the procedure is physically consistence

A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids

Energy Technology Data Exchange (ETDEWEB)

McCorquodale, Peter; Colella, Phillip

2011-01-28

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.

Method for reducing snap in magnetic amplifiers

Science.gov (United States)

Fischer, R. L. E.; Word, J. L.

1968-01-01

Method of reducing snap in magnetic amplifiers uses a degenerative feedback circuit consisting of a resistor and a separate winding on a magnetic core. The feedback circuit extends amplifier range by allowing it to be used at lower values of output current.

Wavelet Methods for Solving Fractional Order Differential Equations

OpenAIRE

A. K. Gupta; S. Saha Ray

2014-01-01

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...

Examining Methods to Reduce Wall-Wetting under HCCI conditions

Energy Technology Data Exchange (ETDEWEB)

Van Erp, D.D.T.M.

2009-01-15

technique is used. The existing software was not capable to determine the LL in a reliable way from the Mie recordings for low gas temperatures and densities. Three major challenges have been observed. Firstly, long LL's result in a gradual decrease of the intensity at the end of the liquid core, which makes it impossible to point out a LL. Secondly, a streak in the recordings, due to a disturbance in the laser sheet, causes problems with the LL determination. Finally, liquid core lengths (for gas temperature and gas density lower than 800K and 5 kg/m{sup 3}) larger than the measurement domain are not possible to determine. A background intensity reduction method in combination with an alternative LL determination method are developed to overcome the first 2 challenges. The combination of both methods improves the reliability of the LL determination for low gas temperatures and densities. The liquid length reducing measures were tested in practice and analysed using the new software to extract the LL. It can be concluded that the fuel temperature has a minor effect on the LL for HCCI conditions. An increase in fuel pressure results in a minor increase of a few millimeters in LL. An injection duration in the order of 0.5 ms results in a LL reduction for a fuel pressure of 400 bar. Higher fuel pressures are not sensitive for short injection durations. A decrease in orifice diameter results in a significant reduction in LL, but the reduction is less than expected from the model.

A reduced order aerothermodynamic modeling framework for hypersonic vehicles based on surrogate and POD

OpenAIRE

Chen Xin; Liu Li; Long Teng; Yue Zhenjiang

2015-01-01

Aerothermoelasticity is one of the key technologies for hypersonic vehicles. Accurate and efficient computation of the aerothermodynamics is one of the primary challenges for hypersonic aerothermoelastic analysis. Aimed at solving the shortcomings of engineering calculation, computation fluid dynamics (CFD) and experimental investigation, a reduced order modeling (ROM) framework for aerothermodynamics based on CFD predictions using an enhanced algorithm of fast maximin Latin hypercube design ...

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer

LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

International Nuclear Information System (INIS)

Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

2015-01-01

This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

Estimation methods with ordered exposure subject to measurement error and missingness in semi-ecological design

Directory of Open Access Journals (Sweden)

Kim Hyang-Mi

2012-09-01

Full Text Available Abstract Background In epidemiological studies, it is often not possible to measure accurately exposures of participants even if their response variable can be measured without error. When there are several groups of subjects, occupational epidemiologists employ group-based strategy (GBS for exposure assessment to reduce bias due to measurement errors: individuals of a group/job within study sample are assigned commonly to the sample mean of exposure measurements from their group in evaluating the effect of exposure on the response. Therefore, exposure is estimated on an ecological level while health outcomes are ascertained for each subject. Such study design leads to negligible bias in risk estimates when group means are estimated from ‘large’ samples. However, in many cases, only a small number of observations are available to estimate the group means, and this causes bias in the observed exposure-disease association. Also, the analysis in a semi-ecological design may involve exposure data with the majority missing and the rest observed with measurement errors and complete response data collected with ascertainment. Methods In workplaces groups/jobs are naturally ordered and this could be incorporated in estimation procedure by constrained estimation methods together with the expectation and maximization (EM algorithms for regression models having measurement error and missing values. Four methods were compared by a simulation study: naive complete-case analysis, GBS, the constrained GBS (CGBS, and the constrained expectation and maximization (CEM. We illustrated the methods in the analysis of decline in lung function due to exposures to carbon black. Results Naive and GBS approaches were shown to be inadequate when the number of exposure measurements is too small to accurately estimate group means. The CEM method appears to be best among them when within each exposure group at least a ’moderate’ number of individuals have their

Hierarchically ordered macro-mesoporous ZnS microsphere with reduced graphene oxide supporter for a highly efficient photodegradation of methylene blue

Energy Technology Data Exchange (ETDEWEB)

Sookhakian, M., E-mail: m.sokhakian@gmail.com [Department of Physics, University of Malaya, Kuala Lumpur 50603 (Malaysia); Amin, Y.M. [Department of Physics, University of Malaya, Kuala Lumpur 50603 (Malaysia); Basirun, W.J. [Department of Chemistry, University of Malaya, Kuala Lumpur 50603 (Malaysia); Centre of Research in Nanotechnology and Catalysis (NanoCat), Institute of Postgraduate Studies, University Malaya, Kuala Lumpur 50603 (Malaysia)

2013-10-15

A facile one-pot method for the fabrication of high quality self-assembled hierarchically ordered macro-mesoporous ZnS microsphere–reduced graphene oxide (RGO) composite without the use of templates or surfactants is described. During the hydrothermal process, reduced graphene oxide (RGO) was loaded into the ZnS microsphere by in situ reduction of graphene oxide added in the self-assembly system. The morphology and structure of the as-prepared composites were confirmed by X-ray diffraction, high resolution transmission electron microscopy, energy dispersive X-ray analysis, Fourier transform infrared spectroscopy and Raman spectroscopy. Incorporation of reduced graphene oxide as an excellent electron-transporting material effectively suppresses the charge recombination. Hence, a significant enhancement in the photocatalytic efficiency for the photodegradation of methylene blue was observed with the ZnS–RGO composite, compared to the pure ZnS. Overall, this research results may lay down new vistas for the in situ fabrication of the ZnS–RGO composite as a highly efficient photocatalysis under visible-light irradiation and their applications in environmental protection.

Reduced NOX combustion method

International Nuclear Information System (INIS)

Delano, M.A.

1991-01-01

This patent describes a method for combusting fuel and oxidant to achieve reduced formation of nitrogen oxides. It comprises: It comprises: heating a combustion zone to a temperature at least equal to 1500 degrees F.; injecting into the heated combustion zone a stream of oxidant at a velocity within the range of from 200 to 1070 feet per second; injecting into the combustion zone, spaced from the oxidant stream, a fuel stream at a velocity such that the ratio of oxidant stream velocity to fuel stream velocity does not exceed 20; aspirating combustion gases into the oxidant stream and thereafter intermixing the aspirated oxidant stream and fuel stream to form a combustible mixture; combusting the combustible mixture to produce combustion gases for the aspiration; and maintaining the fuel stream substantially free from contact with oxidant prior to the intermixture with aspirated oxidant

Fast temperature optimization of multi-source hyperthermia applicators with reduced-order modeling of 'virtual sources'

International Nuclear Information System (INIS)

Cheng, K-S; Stakhursky, Vadim; Craciunescu, Oana I; Stauffer, Paul; Dewhirst, Mark; Das, Shiva K

2008-01-01

The goal of this work is to build the foundation for facilitating real-time magnetic resonance image guided patient treatment for heating systems with a large number of physical sources (e.g. antennas). Achieving this goal requires knowledge of how the temperature distribution will be affected by changing each source individually, which requires time expenditure on the order of the square of the number of sources. To reduce computation time, we propose a model reduction approach that combines a smaller number of predefined source configurations (fewer than the number of actual sources) that are most likely to heat tumor. The source configurations consist of magnitude and phase source excitation values for each actual source and may be computed from a CT scan based plan or a simplified generic model of the corresponding patient anatomy. Each pre-calculated source configuration is considered a 'virtual source'. We assume that the actual best source settings can be represented effectively as weighted combinations of the virtual sources. In the context of optimization, each source configuration is treated equivalently to one physical source. This model reduction approach is tested on a patient upper-leg tumor model (with and without temperature-dependent perfusion), heated using a 140 MHz ten-antenna cylindrical mini-annular phased array. Numerical simulations demonstrate that using only a few pre-defined source configurations can achieve temperature distributions that are comparable to those from full optimizations using all physical sources. The method yields close to optimal temperature distributions when using source configurations determined from a simplified model of the tumor, even when tumor position is erroneously assumed to be ∼2.0 cm away from the actual position as often happens in practical clinical application of pre-treatment planning. The method also appears to be robust under conditions of changing, nonlinear, temperature-dependent perfusion. The

Lattice Boltzmann flow simulations with applications of reduced order modeling techniques

KAUST Repository

Brown, Donald

2014-01-01

With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.

Managing Variety in Configure-to-Order Products - An Operational Method

DEFF Research Database (Denmark)

Myrodia, Anna; Hvam, Lars

2014-01-01

is to develop an operational method to analyze profitability of Configure-To-Order (CTO) products. The operational method consists of a four-step: analysis of product assortment, profitability analysis on configured products, market and competitor analysis and, product assortment scenarios analysis....... The proposed operational method is firstly developed based on both available literature and practitioners experience and subsequently tested on a company that produces CTO products. The results from this application are further discussed and opportunities for further research identified....

The response analysis of fractional-order stochastic system via generalized cell mapping method.

Science.gov (United States)

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

Lowest-order constrained variational method for simple many-fermion systems

International Nuclear Information System (INIS)

Alexandrov, I.; Moszkowski, S.A.; Wong, C.W.

1975-01-01

The authors study the potential energy of many-fermion systems calculated by the lowest-order constrained variational (LOCV) method of Pandharipande. Two simple two-body interactions are used. For a simple hard-core potential in a dilute Fermi gas, they find that the Huang-Yang exclusion correction can be used to determine a healing distance. The result is close to the older Pandharipande prescription for the healing distance. For a hard core plus attractive exponential potential, the LOCV result agrees closely with the lowest-order separation method of Moszkowski and Scott. They find that the LOCV result has a shallow minimum as a function of the healing distance at the Moszkowski-Scott separation distance. The significance of the absence of a Brueckner dispersion correction in the LOCV result is discussed. (Auth.)

Symplectic and trigonometrically fitted symplectic methods of second and third order

International Nuclear Information System (INIS)

Monovasilis, Th.; Simos, T.E.

2006-01-01

The numerical integration of Hamiltonian systems by symplectic and trigonometrically symplectic method is considered in this Letter. We construct new symplectic and trigonometrically symplectic methods of second and third order. We apply our new methods as well as other existing methods to the numerical integration of the harmonic oscillator, the 2D harmonic oscillator with an integer frequency ratio and an orbit problem studied by Stiefel and Bettis

Detecting Violations of Unidimensionality by Order-Restricted Inference Methods

Directory of Open Access Journals (Sweden)

Moritz eHeene

2016-03-01

Full Text Available The assumption of unidimensionality and quantitative measurement represents one of the key concepts underlying most of the commonly applied of item response models. The assumption of unidimensionality is frequently tested although most commonly applied methods have been shown having low power against violations of unidimensionality whereas the assumption of quantitative measurement remains in most of the cases only an (implicit assumption. On the basis of a simulation study it is shown that order restricted inference methods within a Markov Chain Monte Carlo framework can successfully be used to test both assumptions.

Composition between mecd and runge-Kutta algorithm method for large system of second order differential equations

International Nuclear Information System (INIS)

Supriyono; Miyoshi, T.

1997-01-01

NECD Method and runge-Kutta method for large system of second order ordinary differential equations in comparing algorithm. The paper introduce a extrapolation method used for solving the large system of second order ordinary differential equation. We call this method the modified extrapolated central difference (MECD) method. for the accuracy and efficiency MECD method. we compare the method with 4-th order runge-Kutta method. The comparison results show that, this method has almost the same accuracy as the 4-th order runge-Kutta method, but the computation time is about half of runge-Kutta. The MECD was declare by the author and Tetsuhiko Miyoshi of the Dept. Applied Science Yamaguchi University Japan

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

KAUST Repository

Guermond, J. L.

2010-09-17

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

KAUST Repository

Guermond, J. L.; Pasquetti, R.

2010-01-01

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

Spectrophotometric determination of chlorthalidone in pharmaceutical formulations using different order derivative methods

Directory of Open Access Journals (Sweden)

Narmeen S. Abdullah

2017-05-01

Full Text Available Simple, repaid and accurate zero-, first- and second-order derivative spectrophotometric methods have been developed for determination of chlorthalidone (CLT in commercially available tablets. Normal spectrophotometric scan (zero order shows maximum absorbance at 276 nm in methanol solution and a good linearity in the range of 10.0–75.0 μg/mL. Linear relations using first (D1 and second (D2 order derivative methods were obtained at 278 and 288 nm for D1 and 286 and 292 nm for D2.The calibration curves were constructed in the range of 1.0–25.0 μg/mL for D1 (R = 0.998 and D2 (R = 0.999. Different analytical validations were determined (accuracy, precision, specificity, recovery, stability and robustness to demonstrate its suitability for routine quality control labs. All the developed methods were successfully applied to a tablet formulation and the results were compared statistically with each other and with those obtained by the HPLC reference method.

Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

Science.gov (United States)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

Developing strategies to reduce the risk of hazardous materials transportation in iran using the method of fuzzy SWOT analysis

Directory of Open Access Journals (Sweden)

A. S. Kheirkhah

2009-12-01

Full Text Available An increase in hazardous materials transportation in Iran along with the industrial development and increase of resulted deadly accidents necessitate the development and implementation of some strategies to reduce these incidents. SWOT analysis is an efficient method for developing strategies, however, its structural problems, including a lack of prioritizing internal and external factors and inability to consider two sided factors reducing its performance in the situations where the number of internal and external factors affecting the risk of hazardous materials is relatively high and some factors are two sided in nature are presented in the article. Fuzzy SWOT analysis is a method the use of which helps with solving these problems and is the issue of employing an effective methodology. Also, the article compares the resulted strategies of the fuzzy method with the strategies developed following SWOT in order to show the relative supremacy of the new method.

Aligning Order Picking Methods, Incentive Systems, and Regulatory Focus to Increase Performance

NARCIS (Netherlands)

de Vries, J.; de Koster, R.; Stam, D.

2016-01-01

A controlled field experiment investigates order picking performance in terms of productivity. We examined three manual picker-to-parts order picking methods (parallel, zone, and dynamic zone picking) under two different incentive systems (competition-based vs. cooperation-based) for pickers with

Aligning order picking methods, incentive systems, and regulatory focus to increase performance

NARCIS (Netherlands)

J. de Vries (Jelle); M.B.M. de Koster (René); D.A. Stam (Daan)

2015-01-01

textabstractA unique controlled field experiment investigates order picking performance (in terms of productivity and quality). We examined three manual picker-to-parts order picking methods (parallel, zone, and dynamic zone picking) under two different incentive systems (competition- based versus

Scale Sensitivity and Question Order in the Contingent Valuation Method

OpenAIRE

Andersson, Henrik; Svensson, Mikael

2010-01-01

This study examines the effect on respondents' willingness to pay to reduce mortality risk by the order of the questions in a stated preference study. Using answers from an experiment conducted on a Swedish sample where respondents' cognitive ability was measured and where they participated in a contingent valuation survey, it was found that scale sensitivity is strongest when respondents are asked about a smaller risk reduction first ('bottom-up' approach). This contradicts some previous evi...

Household methods to reduce 137Cs contents of mushrooms

International Nuclear Information System (INIS)

Kostiainen, E.

2005-01-01

High radiocaesium contents in different species of mushrooms have been observed in areas contaminated by radiocaesium deposition after the Chernobyl accident in 1986. There has been no significant reduction in the 137 Cs contents of mushrooms during the past ten years, besides via radioactive decay. The internal radiation dose received via mushrooms can be reduced by processing mushrooms before consumption. Various household methods were studied to find out their efficiency to reduce 137 Cs contents of mushrooms. The methods tested were the same as normally used in cooking. The tests were made for the species of edible mushrooms widely consumed. The retention factors for the treatments tested were in most cases 0.2-0.3. The efficiency of treatments in reducing the 137 Cs contents increased with larger water volumes and prolonged treatment times

Reducing vibration transfer from power plants by active methods

Science.gov (United States)

Kiryukhin, A. V.; Milman, O. O.; Ptakhin, A. V.

2017-12-01

The possibility of applying the methods of active damping of vibration and pressure pulsations for reducing their transfer from power plants into the environment, the seating, and the industrial premises are considered. The results of experimental works implemented by the authors on the active broadband damping of vibration and dynamic forces after shock-absorption up to 15 dB in the frequency band up to 150 Hz, of water pressure pulsations in the pipeline up to 20 dB in the frequency band up to 600 Hz, and of spatial low-frequency air noise indoors of a diesel generator at discrete frequency up to 20 dB are presented. It is shown that a reduction of vibration transfer through a vibration-isolating junction (expansion joints) of pipelines with liquid is the most complicated and has hardly been developed so far. This problem is essential for vibration isolation of power equipment from the seating and the environment through pipelines with water and steam in the power and transport engineering, shipbuilding, and in oil and gas pipelines in pumping stations. For improving efficiency, reducing the energy consumption, and decreasing the overall dimensions of equipment, it is advisable to combine the work of an active system with passive damping means, the use of which is not always sufficient. The executive component of the systems of active damping should be placed behind the vibration isolators (expansion joints). It is shown that the existence of working medium and connection of vibration with pressure pulsations in existing designs of pipeline expansion joints lead to growth of vibration stiffness of the expansion joint with the environment by two and more orders as compared with the static stiffness and makes difficulties for using the active methods. For active damping of vibration transfer through expansion joints of pipelines with a liquid, it is necessary to develop expansion joint structures with minimal connection of vibrations and pulsations and minimal

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo

2008-12-20

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.

Kernel methods for interpretable machine learning of order parameters

Science.gov (United States)

Ponte, Pedro; Melko, Roger G.

2017-11-01

Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of supervised learning has come from employing neural networks as classifiers. Although very powerful, such algorithms suffer from a lack of interpretability, which is usually desired in scientific applications in order to associate learned features with physical phenomena. In this paper, we explore support vector machines (SVMs), which are a class of supervised kernel methods that provide interpretable decision functions. We find that SVMs can learn the mathematical form of physical discriminators, such as order parameters and Hamiltonian constraints, for a set of two-dimensional spin models: the ferromagnetic Ising model, a conserved-order-parameter Ising model, and the Ising gauge theory. The ability of SVMs to provide interpretable classification highlights their potential for automating feature detection in both synthetic and experimental data sets for condensed matter and other many-body systems.

A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem

International Nuclear Information System (INIS)

Pan Shaohua; Chen, J.-S.

2009-01-01

We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method

Business risks, functions, methods of assessment and ways to reduce risk

Directory of Open Access Journals (Sweden)

A.V. Mihalchuk

2015-06-01

Full Text Available For successful existence in a market economy entrepreneur have to take bold actions, and this increases the risk. The article describes the concept of entrepreneurship and business risk, positive and negative aspects of functions of risk in business. Therefore, it is necessary to assess the risk properly and be able to manage it to achieve the most effective results in the market. In market conditions the problem of assessing and accounting market becomes independent theoretical and practical significance as an important component of the theory and practice of management. Risk - a key element of business activities. Development of risk situations can lead to both the occurrence of adverse effects (losses, lost profits, and positive results for a company in the form of increased profit. This article describes: the concept of entrepreneurship, risk and business risks, characteristic of positive and negative aspects of risk functions in business, methods of assessment and risk reduction, shows formulae and examples you can use to assess risk in an enterprise. Analyzing already established methods of risk assessment a number of rules were proposed in order to reduce business risk.

Cosmology and the neutrino mass ordering

DEFF Research Database (Denmark)

Hannestad, Steen; Schwetz, Thomas

2016-01-01

We propose a simple method to quantify a possible exclusion of the inverted neutrino mass ordering from cosmological bounds on the sum of the neutrino masses. The method is based on Bayesian inference and allows for a calculation of the posterior odds of normal versus inverted ordering. We apply...... the method for a specific set of current data from Planck CMB data and large-scale structure surveys, providing an upper bound on the sum of neutrino masses of 0.14 eV at 95% CL. With this analysis we obtain posterior odds for normal versus inverted ordering of about 2:1. If cosmological data is combined...... with data from oscillation experiments the odds reduce to about 3:2. For an exclusion of the inverted ordering from cosmology at more than 95% CL, an accuracy of better than 0.02 eV is needed for the sum. We demonstrate that such a value could be reached with planned observations of large scale structure...

COMPANY AIKIDO – IT SEEMS TO BE A PRACTICAL METHOD TO REDUCE STRESS AND INCREASE A PERSON’S ENERGY

Directory of Open Access Journals (Sweden)

Andronicus TORP

2016-05-01

Full Text Available Companies are increasingly using methods such as massage, sports, mindfulness, etc. in order for example to improve employee well-being, reduce stress, or increase the energy level of the employees. This article examines, based on a case study, if Aikido may be a practical way to reduce stress and/or increase energy. The empirical study is based on measuring the energy and stress level of the practitioners before and after the practice of Aikido by the use of the ElectroPhotonic Imaging Device developed by Prof. Dr. Korotkov.

Concurrent hyperthermia estimation schemes based on extended Kalman filtering and reduced-order modelling.

Science.gov (United States)

Potocki, J K; Tharp, H S

1993-01-01

The success of treating cancerous tissue with heat depends on the temperature elevation, the amount of tissue elevated to that temperature, and the length of time that the tissue temperature is elevated. In clinical situations the temperature of most of the treated tissue volume is unknown, because only a small number of temperature sensors can be inserted into the tissue. A state space model based on a finite difference approximation of the bioheat transfer equation (BHTE) is developed for identification purposes. A full-order extended Kalman filter (EKF) is designed to estimate both the unknown blood perfusion parameters and the temperature at unmeasured locations. Two reduced-order estimators are designed as computationally less intensive alternatives to the full-order EKF. Simulation results show that the success of the estimation scheme depends strongly on the number and location of the temperature sensors. Superior results occur when a temperature sensor exists in each unknown blood perfusion zone, and the number of sensors is at least as large as the number of unknown perfusion zones. Unacceptable results occur when there are more unknown perfusion parameters than temperature sensors, or when the sensors are placed in locations that do not sample the unknown perfusion information.

An implicit second order numerical method for two-fluid models

International Nuclear Information System (INIS)

Toumi, I.

1995-01-01

We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)

A reduced-order filtering approach for 3D dynamical electrical impedance tomography

International Nuclear Information System (INIS)

Voutilainen, A; Lehikoinen, A; Vauhkonen, M; Kaipio, J P

2011-01-01

Recently, it has been shown that the state estimation approach to process tomography can provide estimates that are significantly better than (a sequence of) conventional stationary snapshot estimates. One of the main obstacles of the adoption of the recursive state estimation algorithms, most commonly different versions of the Kalman filter, is the computational complexity. This is due to both the required large dimension for the state variable and the need to use iterative versions of the Kalman filter in such cases in which there are large contrasts or varying background. In this paper, we propose to use a reduced-order representation for the state variable. In particular, we propose to use the proper orthogonal decomposition-related basis for the state. We consider a simulation study with fluctuating background conductivity, and, in particular, with fluctuating contact impedances. We compare the proposed approach to three different versions of the Kalman filter having different computational complexities. We show that this approach allows the reduction of the dimension of the problem approximately by an order of magnitude and yields essentially as accurate estimates as the most accurate traditional Kalman filter version, the iterated extended Kalman filter

Development of a Reduced-Order Three-Dimensional Flow Model for Thermal Mixing and Stratification Simulation during Reactor Transients

Energy Technology Data Exchange (ETDEWEB)

Hu, Rui

2017-09-03

Mixing, thermal-stratification, and mass transport phenomena in large pools or enclosures play major roles for the safety of reactor systems. Depending on the fidelity requirement and computational resources, various modeling methods, from the 0-D perfect mixing model to 3-D Computational Fluid Dynamics (CFD) models, are available. Each is associated with its own advantages and shortcomings. It is very desirable to develop an advanced and efficient thermal mixing and stratification modeling capability embedded in a modern system analysis code to improve the accuracy of reactor safety analyses and to reduce modeling uncertainties. An advanced system analysis tool, SAM, is being developed at Argonne National Laboratory for advanced non-LWR reactor safety analysis. While SAM is being developed as a system-level modeling and simulation tool, a reduced-order three-dimensional module is under development to model the multi-dimensional flow and thermal mixing and stratification in large enclosures of reactor systems. This paper provides an overview of the three-dimensional finite element flow model in SAM, including the governing equations, stabilization scheme, and solution methods. Additionally, several verification and validation tests are presented, including lid-driven cavity flow, natural convection inside a cavity, laminar flow in a channel of parallel plates. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the developed 3-D fluid model can perform very well for a wide range of flow problems.

Energy stable and high-order-accurate finite difference methods on staggered grids

Science.gov (United States)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Second-order particle-in-cell (PIC) computational method in the one-dimensional variable Eulerian mesh system

International Nuclear Information System (INIS)

Pyun, J.J.

1981-01-01

As part of an effort to incorporate the variable Eulerian mesh into the second-order PIC computational method, a truncation error analysis was performed to calculate the second-order error terms for the variable Eulerian mesh system. The results that the maximum mesh size increment/decrement is limited to be α(Δr/sub i/) 2 where Δr/sub i/ is a non-dimensional mesh size of the ith cell, and α is a constant of order one. The numerical solutions of Burgers' equation by the second-order PIC method in the variable Eulerian mesh system wer compared with its exact solution. It was found that the second-order accuracy in the PIC method was maintained under the above condition. Additional problems were analyzed using the second-order PIC methods in both variable and uniform Eulerian mesh systems. The results indicate that the second-order PIC method in the variable Eulerian mesh system can provide substantial computational time saving with no loss in accuracy

High order aberrations calculation of a hexapole corrector using a differential algebra method

Energy Technology Data Exchange (ETDEWEB)

Kang, Yongfeng, E-mail: yfkang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Zhao, Jingyi, E-mail: jingyi.zhao@foxmail.com [School of Science, Chang’an University, Xi’an 710064 (China); Tang, Tiantong [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China)

2017-02-21

A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.

Variational methods for high-order multiphoton processes

International Nuclear Information System (INIS)

Gao, B.; Pan, C.; Liu, C.; Starace, A.F.

1990-01-01

Methods for applying the variationally stable procedure for Nth-order perturbative transition matrix elements of Gao and Starace [Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] to multiphoton processes involving systems other than atomic H are presented. Three specific cases are discussed: one-electron ions or atoms in which the electron--ion interaction is described by a central potential; two-electron ions or atoms in which the electronic states are described by the adiabatic hyperspherical representation; and closed-shell ions or atoms in which the electronic states are described by the multiconfiguration Hartree--Fock representation. Applications are made to the dynamic polarizability of He and the two-photon ionization cross section of Ar

A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows

Science.gov (United States)

Zhou, Qiang; Fan, Liang-Shih

2014-07-01

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding

A Three Step Explicit Method for Direct Solution of Third Order ...

African Journals Online (AJOL)

This study produces a three step discrete Linear Multistep Method for Direct solution of third order initial value problems of ordinary differential equations of the form y'''= f(x,y,y',y''). Taylor series expansion technique was adopted in the development of the method. The differential system from the basis polynomial function to ...

A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows

Energy Technology Data Exchange (ETDEWEB)

Zhou, Qiang; Fan, Liang-Shih, E-mail: fan.1@osu.edu

2014-07-01

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered

On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools

Energy Technology Data Exchange (ETDEWEB)

Vermeire, B.C., E-mail: brian.vermeire@concordia.ca; Witherden, F.D.; Vincent, P.E.

2017-04-01

First- and second-order accurate numerical methods, implemented for CPUs, underpin the majority of industrial CFD solvers. Whilst this technology has proven very successful at solving steady-state problems via a Reynolds Averaged Navier–Stokes approach, its utility for undertaking scale-resolving simulations of unsteady flows is less clear. High-order methods for unstructured grids and GPU accelerators have been proposed as an enabling technology for unsteady scale-resolving simulations of flow over complex geometries. In this study we systematically compare accuracy and cost of the high-order Flux Reconstruction solver PyFR running on GPUs and the industry-standard solver STAR-CCM+ running on CPUs when applied to a range of unsteady flow problems. Specifically, we perform comparisons of accuracy and cost for isentropic vortex advection (EV), decay of the Taylor–Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a second-order configuration, and a third-order configuration, where the latter was recommended by CD-adapco for more effective computation of unsteady flow problems. Results from both PyFR and STAR-CCM+ demonstrate that third-order schemes can be more accurate than second-order schemes for a given cost e.g. going from second- to third-order, the PyFR simulations of the EV and TGV achieve 75× and 3× error reduction respectively for the same or reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake statistics significantly more accurately for only twice the cost. Moreover, advancing to higher-order schemes on GPUs with PyFR was found to offer even further accuracy vs. cost benefits relative to industry-standard tools.

On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools

Science.gov (United States)

Vermeire, B. C.; Witherden, F. D.; Vincent, P. E.

2017-04-01

First- and second-order accurate numerical methods, implemented for CPUs, underpin the majority of industrial CFD solvers. Whilst this technology has proven very successful at solving steady-state problems via a Reynolds Averaged Navier-Stokes approach, its utility for undertaking scale-resolving simulations of unsteady flows is less clear. High-order methods for unstructured grids and GPU accelerators have been proposed as an enabling technology for unsteady scale-resolving simulations of flow over complex geometries. In this study we systematically compare accuracy and cost of the high-order Flux Reconstruction solver PyFR running on GPUs and the industry-standard solver STAR-CCM+ running on CPUs when applied to a range of unsteady flow problems. Specifically, we perform comparisons of accuracy and cost for isentropic vortex advection (EV), decay of the Taylor-Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a second-order configuration, and a third-order configuration, where the latter was recommended by CD-adapco for more effective computation of unsteady flow problems. Results from both PyFR and STAR-CCM+ demonstrate that third-order schemes can be more accurate than second-order schemes for a given cost e.g. going from second- to third-order, the PyFR simulations of the EV and TGV achieve 75× and 3× error reduction respectively for the same or reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake statistics significantly more accurately for only twice the cost. Moreover, advancing to higher-order schemes on GPUs with PyFR was found to offer even further accuracy vs. cost benefits relative to industry-standard tools.

On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools

International Nuclear Information System (INIS)

Vermeire, B.C.; Witherden, F.D.; Vincent, P.E.

2017-01-01

First- and second-order accurate numerical methods, implemented for CPUs, underpin the majority of industrial CFD solvers. Whilst this technology has proven very successful at solving steady-state problems via a Reynolds Averaged Navier–Stokes approach, its utility for undertaking scale-resolving simulations of unsteady flows is less clear. High-order methods for unstructured grids and GPU accelerators have been proposed as an enabling technology for unsteady scale-resolving simulations of flow over complex geometries. In this study we systematically compare accuracy and cost of the high-order Flux Reconstruction solver PyFR running on GPUs and the industry-standard solver STAR-CCM+ running on CPUs when applied to a range of unsteady flow problems. Specifically, we perform comparisons of accuracy and cost for isentropic vortex advection (EV), decay of the Taylor–Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a second-order configuration, and a third-order configuration, where the latter was recommended by CD-adapco for more effective computation of unsteady flow problems. Results from both PyFR and STAR-CCM+ demonstrate that third-order schemes can be more accurate than second-order schemes for a given cost e.g. going from second- to third-order, the PyFR simulations of the EV and TGV achieve 75× and 3× error reduction respectively for the same or reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake statistics significantly more accurately for only twice the cost. Moreover, advancing to higher-order schemes on GPUs with PyFR was found to offer even further accuracy vs. cost benefits relative to industry-standard tools.

Physical principles underlying the experimental methods for studying the orientational order of liquid crystals

International Nuclear Information System (INIS)

Limmer, S.

1989-01-01

The basic physical principles underlying different experimental methods frequently used for the determination of orientational order parameters of liquid crystals are reviewed. The methods that are dealt with here include the anisotropy of the diamagnetic susceptibility, birefringence, linear dichroism, Raman scattering, fluorescence depolarization, electron paramagnetic resonance (EPR), and nuclear magnetic resonance (NMR). The fundamental assertions that can be obtained by the different methods as well as their advantages, drawbacks and limitations are inspected. Typical sources of uncertainties and inaccuracies are discussed. To quantitatively evaluate the experimental data with reference to the orientational order the general tensor formalism developed by Schmiedel was employed throughout according to which the order matrix comprises 25 real elements yet. Within this context the interplay of orientational ordering and molecular conformation is scrutinized. (author)

Reducing Unnecessary and Duplicate Ordering for Ovum and Parasite Examinations and Clostridium difficile PCR in Immunocompromised Patients by Using an Alert at the Time of Request in the Order Management System.

Science.gov (United States)

Otto, Caitlin C; Shuptar, Susan L; Milord, Philippe; Essick, Connor J; Nevrekar, Reshma; Granovsky, Svetlana L; Seo, Susan K; Babady, N Esther; Martin, Steven C; Tang, Yi-Wei; Pessin, Melissa S

2015-08-01

We implemented hospital information system (HIS) alerts to deter unnecessary test orders for ovum and parasite (O&P) exams and Clostridium difficile PCR. The HIS alerts decreased noncompliant O&P orders (orders after >72 h of hospitalization) from 49.8% to 30.9%, an overall decrease of 19%, and reduced noncompliant C. difficile PCR orders (orders <7 days after a previous positive result) from 30.6% to 19.2%, an overall decrease of 31.9%. Copyright © 2015, American Society for Microbiology. All Rights Reserved.

A Reduced-Order Model for Evaluating the Dynamic Response of Multilayer Plates to Impulsive Loads

Science.gov (United States)

2016-04-12

A REDUCED-ORDER MODEL FOR EVALUATING THE DYNAMIC RESPONSE OF MULTILAYER PLATES TO IMPULSIVE LOADS Weiran Jiang, Alyssa Bennett, Nickolas...innovative multilayer materials or structures to optimize the dynamic performance as a mechanism to absorb and spread energy from an impulsive load...models. • Optimizing the structural weight and levels of protection of the multilayer plates with a good combination of materials. Technical Approach 2016

Direct oxide reducing method

International Nuclear Information System (INIS)

Tokiwai, Moriyasu.

1995-01-01

Calcium oxides and magnetic oxides as wastes generated upon direct reduction are subjected to molten salt electrolysis, and reduced metallic calcium and magnesium are separated and recovered. Then calcium and magnesium are used recyclically as the reducing agent upon conducting direct oxide reduction. Even calcium oxides and magnesium oxides, which have high melting points and difficult to be melted usually, can be melted in molten salts of mixed fluorides or chlorides by molten-salt electrolysis. Oxides are decomposed by electrolysis, and oxygen is removed in the form of carbon monoxide, while the reduced metallic calcium and magnesium rise above the molten salts on the side of a cathode, and then separated. Since only carbon monoxide is generated as radioactive wastes upon molten salt electrolysis, the amount of radioactive wastes can be greatly reduced, and the amount of the reducing agent used can also be decreased remarkably. (N.H.)

Development and validation of different methods manipulating zero order and first order spectra for determination of the partially overlapped mixture benazepril and amlodipine: A comparative study

Science.gov (United States)

Hemdan, A.

2016-07-01

Three simple, selective, and accurate spectrophotometric methods have been developed and then validated for the analysis of Benazepril (BENZ) and Amlodipine (AML) in bulk powder and pharmaceutical dosage form. The first method is the absorption factor (AF) for zero order and amplitude factor (P-F) for first order spectrum, where both BENZ and AML can be measured from their resolved zero order spectra at 238 nm or from their first order spectra at 253 nm. The second method is the constant multiplication coupled with constant subtraction (CM-CS) for zero order and successive derivative subtraction-constant multiplication (SDS-CM) for first order spectrum, where both BENZ and AML can be measured from their resolved zero order spectra at 240 nm and 238 nm, respectively, or from their first order spectra at 214 nm and 253 nm for Benazepril and Amlodipine respectively. The third method is the novel constant multiplication coupled with derivative zero crossing (CM-DZC) which is a stability indicating assay method for determination of Benazepril and Amlodipine in presence of the main degradation product of Benazepril which is Benazeprilate (BENZT). The three methods were validated as per the ICH guidelines and the standard curves were found to be linear in the range of 5-60 μg/mL for Benazepril and 5-30 for Amlodipine, with well accepted mean correlation coefficient for each analyte. The intra-day and inter-day precision and accuracy results were well within the acceptable limits.

Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

2009-01-01

A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

Implementation of Kalman filter algorithm on models reduced using singular pertubation approximation method and its application to measurement of water level

Science.gov (United States)

Rachmawati, Vimala; Khusnul Arif, Didik; Adzkiya, Dieky

2018-03-01

The systems contained in the universe often have a large order. Thus, the mathematical model has many state variables that affect the computation time. In addition, generally not all variables are known, so estimations are needed to measure the magnitude of the system that cannot be measured directly. In this paper, we discuss the model reduction and estimation of state variables in the river system to measure the water level. The model reduction of a system is an approximation method of a system with a lower order without significant errors but has a dynamic behaviour that is similar to the original system. The Singular Perturbation Approximation method is one of the model reduction methods where all state variables of the equilibrium system are partitioned into fast and slow modes. Then, The Kalman filter algorithm is used to estimate state variables of stochastic dynamic systems where estimations are computed by predicting state variables based on system dynamics and measurement data. Kalman filters are used to estimate state variables in the original system and reduced system. Then, we compare the estimation results of the state and computational time between the original and reduced system.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Directory of Open Access Journals (Sweden)

Rahmatullah

2018-03-01

Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

The Adapted Ordering Method for Lie algebras and superalgebras and their generalizations

Energy Technology Data Exchange (ETDEWEB)

Gato-Rivera, Beatriz [Instituto de Matematicas y Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); NIKHEF-H, Kruislaan 409, NL-1098 SJ Amsterdam (Netherlands)

2008-02-01

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows us to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this paper we present the Adapted Ordering Method for general Lie algebras and superalgebras and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N = 2 and Ramond N = 1 superconformal algebras.

Characterization of Flow Dynamics and Reduced-Order Description of Experimental Two-Phase Pipe Flow

Science.gov (United States)

Viggiano, Bianca; SkjæRaasen, Olaf; Tutkun, Murat; Cal, Raul Bayoan

2017-11-01

Multiphase pipe flow is investigated using proper orthogonal decomposition for tomographic X-ray data, where holdup, cross sectional phase distributions and phase interface characteristics are obtained. Instantaneous phase fractions of dispersed flow and slug flow are analyzed and a reduced order dynamical description is generated. The dispersed flow displays coherent structures in the first few modes near the horizontal center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent structures that correspond to the cyclical formation and breakup of the slug in the first 10 modes. The reconstruction of the fields indicate that main features are observed in the low order dynamical descriptions utilizing less than 1 % of the full order model. POD temporal coefficients a1, a2 and a3 show interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow. These flows are highly applicable to petroleum transport pipelines, hydroelectric power and heat exchanger tubes to name a few. The mathematical representations obtained via proper orthogonal decomposition will deepen the understanding of fundamental multiphase flow characteristics.

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.

2017-07-25

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a system of linear algebraic equations of the unknowns. The statistical properties of the modulating functions solution are described in this paper. In addition, guidelines for choosing the number of modulating functions, which is an important design parameter, are provided. The effectiveness and robustness of the proposed method are shown through numerical simulations in both noise-free and noisy cases.

Methods of reducing non-specific adsorption in microfluidic biosensors

International Nuclear Information System (INIS)

Choi, Seokheun; Chae, Junseok

2010-01-01

Non-specific adsorption (NSA) of biomolecules is a persistent challenge in microfluidic biosensors. Microfluidic biosensors often have immobilized bioreceptors such as antibodies, enzymes, DNAs, etc, via linker molecules such as SAMs (self-assembled monolayers) to enhance immobilization. However, the linker molecules are very susceptible to NSA, causing false responses and decreasing sensitivity. In this paper, we present design methods to reduce the NSA of alkanethiol SAMs, which are popular linker molecules on microfluidic biosensors. Three design parameters were studied for two different chain-length SAMs (n = 2 and 10): (i) SAM incubation time, (ii) surface roughness [0.8 nm and 4.4 nm RMS (root mean square)] and (iii) gold crystal re-growth along (1 1 1) the target orientation. NSA was monitored by surface plasmon resonance (SPR). The results suggest that increased SAM incubation time reduces NSA, and that short-chain SAMs respond more favorably than the long-chain SAMs. Both SAMs were shown to be sensitive to surface roughness, and long-chain SAMs reduced NSA by 75%. Gold crystal re-growth along (1 1 1) the target orientation profoundly reduced NSA on the short-chain SAM. On a gold surface where surface roughness was 0.8 nm and there was strong directional alignment along the (1 1 1) gold crystal, final concentrations of nonspecifically bound proteins were 0.05 ng mm −2 (fibrinogen) and 0.075 ng mm −2 (lysozyme)—significantly lower than other known methods. The results show that optimizing three parameters (SAM incubation time, gold surface roughness and gold crystal orientation) improved SAM sensitivity for fibrinogen–anti-fibrinogen conjugates by a factor of 5 in 2.94 pM, suggesting that the methods are effective for reducing NSA in microfluidic biosensors.

Sparse Method for Direction of Arrival Estimation Using Denoised Fourth-Order Cumulants Vector.

Science.gov (United States)

Fan, Yangyu; Wang, Jianshu; Du, Rui; Lv, Guoyun

2018-06-04

Fourth-order cumulants (FOCs) vector-based direction of arrival (DOA) estimation methods of non-Gaussian sources may suffer from poor performance for limited snapshots or difficulty in setting parameters. In this paper, a novel FOCs vector-based sparse DOA estimation method is proposed. Firstly, by utilizing the concept of a fourth-order difference co-array (FODCA), an advanced FOCs vector denoising or dimension reduction procedure is presented for arbitrary array geometries. Then, a novel single measurement vector (SMV) model is established by the denoised FOCs vector, and efficiently solved by an off-grid sparse Bayesian inference (OGSBI) method. The estimation errors of FOCs are integrated in the SMV model, and are approximately estimated in a simple way. A necessary condition regarding the number of identifiable sources of our method is presented that, in order to uniquely identify all sources, the number of sources K must fulfill K ≤ ( M 4 - 2 M 3 + 7 M 2 - 6 M ) / 8 . The proposed method suits any geometry, does not need prior knowledge of the number of sources, is insensitive to associated parameters, and has maximum identifiability O ( M 4 ) , where M is the number of sensors in the array. Numerical simulations illustrate the superior performance of the proposed method.

A numerical study of the second-order wave excitation of ship springing by a higher-order boundary element method

Directory of Open Access Journals (Sweden)

Shao Yan-Lin

2014-12-01

Full Text Available This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.

Study on the method or reducing the operator's exposure dose from a C-Arm system

International Nuclear Information System (INIS)

Kim, Ki Sik; Song, Jong Nam; Kim, Seung Ok

2016-01-01

In this study, C-Arm equipment is being used as we intend to verify the exposure dose on the operator by the scattering rays during the operation of the C-Arm equipment and to provide an effective method of reducing the exposure dose. Exposure dose is less than the Over Tube method utilizes the C-arm equipment Under Tube the scheme, The result showed that the exposure dose on the operator decreased with a thicker shield, and as the operator moved away from the center line. Moreover, as the research time prolongated, the exposure dose increased, and among the three affixed location of the dosimeter, the most exposure dose was measured at gonadal, then followed by chest and thyroid. However, in consideration of the relationship between the operator and the patient, the distance cannot be increased infinitely and the research time cannot be decreased infinitely in order to reduce the exposure dose. Therefore, by changing the thickness of the radiation shield, the exposure dose on the operator was able to be reduced. If you are using a C-Arm equipment discomfort during surgery because the grounds that the procedure is neglected and close to the dose of radiation shielding made can only increase. Because a separate control room cannot be used for the C-Arm equipment due to its characteristic, the exposure dose on the operator needs to be reduced by reinforcing the shield through an appropriate thickness of radiation shield devices, such as apron, etc. during a treatment

An algorithm for solving initial value problems of third order ordinary ...

African Journals Online (AJOL)

Abstract. We propose an implicit multi-step method for the solution of initial value problems (IVPs) of third order ordinary differential equations (ODE) which does not require reducing the ODE to first order before solving. The development of the method is based on collocation of the differential system and interpolation of the ...

A comparison of high-order polynomial and wave-based methods for Helmholtz problems

Science.gov (United States)

Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien

2016-09-01

The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.

Method and apparatus for reducing the drag of flows over surfaces

Science.gov (United States)

Keefe, Laurence R. (Inventor)

1998-01-01

An apparatus, and its accompanying method, for reducing the drag of flows over a surface includes arrays of small disks and sensors. The arrays are embedded in the surface and may extend above, or be depressed below, the surface, provided they remain hydraulically smooth either when operating or when inactive. The disks are arranged in arrays of various shapes, and spaced according to the cruising speed of the vehicle on which the arrays are installed. For drag reduction at speeds of the order of 30 meters/second, preferred embodiments include disks that are 0.2 millimeter in diameter and spaced 0.4 millimeter apart. For drag reduction at speeds of the order of 300 meters/second, preferred embodiments include disks that are 0.045 millimeter in diameter and spaced 0.09 millimeter apart. Smaller and larger dimensions for diameter and spacing are also possible. The disks rotate in the plane of the surface, with their rotation axis substantially perpendicular to the surface. The rotating disks produce velocity perturbations parallel to the surface in the overlying boundary layer. The sensors sense the flow at the surface and connect to control circuitry that adjusts the rotation rates and duty cycles of the disks accordingly. Suction and blowing holes can be interspersed among, or made coaxial with, the disks for creating general three-component velocity perturbations in the near-surface region. The surface can be a flat, planar surface or a nonplanar surface, such as a triangular riblet surface. The present apparatus and method have potential applications in the field of aeronautics for improving performance and efficiency of commercial and military aircraft, and in other industries where drag is an obstacle, including gas and oil delivery through long-haul pipelines.

Weed-biocontrol insects reduce native-plant recruitment through second-order apparent competition.

Science.gov (United States)

Pearson, Dean E; Callaway, Ragan M

2008-09-01

Small-mammal seed predation is an important force structuring native-plant communities that may also influence exotic-plant invasions. In the intermountain West, deer mice (Peromyscus maniculatus) are prominent predators of native-plant seeds, but they avoid consuming seeds of certain widespread invasives like spotted knapweed (Centaurea maculosa). These mice also consume the biological-control insects Urophora spp. introduced to control C. maculosa, and this food resource substantially increases deer mouse populations. Thus, mice may play an important role in the invasion and management of C. maculosa through food-web interactions. We examined deer mouse seed predation and its effects on seedling emergence and establishment of a dominant native grass, Pseudoroegneria spicata, and forb, Balsamorhiza sagittata, in C. maculosa-invaded grasslands that were treated with herbicide to suppress C. maculosa or left untreated as controls. Deer mice readily took seeds of both native plants but removed 2-20 times more of the larger B. sagittata seeds than the smaller P. spicata seeds. Seed predation reduced emergence and establishment of both species but had greater impacts on B. sagittata. The intensity of seed predation corresponded with annual and seasonal changes in deer mouse abundance, suggesting that abundance largely determined mouse impacts on native-plant seeds. Accordingly, herbicide treatments that reduced mouse abundance by suppressing C. maculosa and its associated biocontrol food subsidies to mice also reduced seed predation and decreased the impact of deer mice on B. sagittata establishment. These results provide evidence that Urophora biocontrol agents may exacerbate the negative effects of C. maculosa on native plants through a form of second-order apparent competition-a biocontrol indirect effect that has not been previously documented. Herbicide suppressed C. maculosa and Urophora, reducing mouse populations and moderating seed predation on native plants

Method of reducing radioactivity in nuclear reactors

International Nuclear Information System (INIS)

Koshino, Yasuo

1987-01-01

Purpose: To prevent increase of radiation dose ratio in primary coolant circuit pipeways of nuclear reactor and reduce operators' exposure dose upon periodical inspection, etc. Method: β-diketone such as acetylacetone is added in a predetermined amount to reactor cooling water. β-diketone dissolves to catch metal ions and iron oxides as the main ingredient of cruds. The resultant β-diketone complex of metals is slightly water soluble neutron molecule, and the total metal amount in the reactor coolant is at a concentration of less than 10 ppb and completely dissolved in water. Accordingly, deposition of clads in the coolant to pipeways can be prevented thereby enabling to prevent the increase in the radiation dose ratio in the pipeways and thus reduce the operators' exposure dose. (Takahashi, M.)

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo; Kanschat, Guido; Schö tzau, Dominik

2008-01-01

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability

An accurate and efficient reliability-based design optimization using the second order reliability method and improved stability transformation method

Science.gov (United States)

Meng, Zeng; Yang, Dixiong; Zhou, Huanlin; Yu, Bo

2018-05-01

The first order reliability method has been extensively adopted for reliability-based design optimization (RBDO), but it shows inaccuracy in calculating the failure probability with highly nonlinear performance functions. Thus, the second order reliability method is required to evaluate the reliability accurately. However, its application for RBDO is quite challenge owing to the expensive computational cost incurred by the repeated reliability evaluation and Hessian calculation of probabilistic constraints. In this article, a new improved stability transformation method is proposed to search the most probable point efficiently, and the Hessian matrix is calculated by the symmetric rank-one update. The computational capability of the proposed method is illustrated and compared to the existing RBDO approaches through three mathematical and two engineering examples. The comparison results indicate that the proposed method is very efficient and accurate, providing an alternative tool for RBDO of engineering structures.

A self-ordered, body-centered tetragonal superlattice of SiGe nanodot growth by reduced pressure CVD

Science.gov (United States)

Yamamoto, Yuji; Zaumseil, Peter; Capellini, Giovanni; Schubert, Markus Andreas; Hesse, Anne; Albani, Marco; Bergamaschini, Roberto; Montalenti, Francesco; Schroeder, Thomas; Tillack, Bernd

2017-12-01

Self-ordered three-dimensional body-centered tetragonal (BCT) SiGe nanodot structures are fabricated by depositing SiGe/Si superlattice layer stacks using reduced pressure chemical vapor deposition. For high enough Ge content in the island (>30%) and deposition temperature of the Si spacer layers (T > 700 °C), we observe the formation of an ordered array with islands arranged in staggered position in adjacent layers. The in plane periodicity of the islands can be selected by a suitable choice of the annealing temperature before the Si spacer layer growth and of the SiGe dot volume, while only a weak influence of the Ge concentration is observed. Phase-field simulations are used to clarify the driving force determining the observed BCT ordering, shedding light on the competition between heteroepitaxial strain and surface-energy minimization in the presence of a non-negligible surface roughness.

Method of reducing radon levels in buildings

International Nuclear Information System (INIS)

Khajdarov, R.A.; Gapurova, O.U.; Khajdarov, R.R.

2004-01-01

Radon concentration can be reduced by using polymeric compositions which fill pores inside building materials and decrease the coefficient of permeation of radon atoms and water molecules in building materials (concrete, gypsum, etc.). Polymeric silico-organic compounds were investigated and selected as the chemicals to prevent radon seeping indoors. Gas (air, Ar, 222 Rn, H 2 O) permeability of concrete and gypsum after treatment with chemicals was examined. The effect of the cement and sand types, preliminary treatment with various chemicals, type of the polymeric silico-organic compounds, time between treatments, moisture of concrete, time between the preparation of chemicals and the treatment of concrete (ageing of chemicals), time between the treatment of concrete and testing (ageing of treated concrete) were examined. Surfaces of the samples were treated by spraying. The experiments gave evidence that the chosen method of treatment of the construction materials allows reducing the coefficient of gas permeability in 200 - 400 times. Treatment of the floor, walls and ceiling of the basement of 5 buildings reduced the radon concentration in the premises of the first floor from 400-600 Bq/m 3 to the background value of 17-20 Bq/m 3

A practical implementation of the higher-order transverse-integrated nodal diffusion method

International Nuclear Information System (INIS)

Prinsloo, Rian H.; Tomašević, Djordje I.; Moraal, Harm

2014-01-01

Highlights: • A practical higher-order nodal method is developed for diffusion calculations. • The method resolves the issue of the transverse leakage approximation. • The method achieves much superior accuracy as compared to standard nodal methods. • The calculational cost is only about 50% greater than standard nodal methods. • The method is packaged in a module for connection to existing nodal codes. - Abstract: Transverse-integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming of this approach is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work, an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher-order nodal methods developed some years ago. Further, a number of iteration schemes are developed around this consistent quadratic leakage approximation which yields accurate node average results in much improved calculational times. The most promising of these iteration schemes results from utilizing the consistent leakage approximation as a correction method to the standard quadratic leakage approximation. Numerical results are demonstrated on a set of benchmark problems and further applied to a realistic reactor problem, particularly the SAFARI-1 reactor, operating at Necsa, South Africa. The final optimal solution strategy is packaged into a standalone module which may simply be coupled to existing nodal diffusion codes

Household methods to reduce {sup 137}Cs contents of mushrooms

Energy Technology Data Exchange (ETDEWEB)

Kostiainen, E. [Radiation and Nuclear Safety Authority - STUK, Helsinki (Finland)

2005-09-15

High radiocaesium contents in different species of mushrooms have been observed in areas contaminated by radiocaesium deposition after the Chernobyl accident in 1986. There has been no significant reduction in the {sup 137}Cs contents of mushrooms during the past ten years, besides via radioactive decay. The internal radiation dose received via mushrooms can be reduced by processing mushrooms before consumption. Various household methods were studied to find out their efficiency to reduce {sup 137}Cs contents of mushrooms. The methods tested were the same as normally used in cooking. The tests were made for the species of edible mushrooms widely consumed. The retention factors for the treatments tested were in most cases 0.2-0.3. The efficiency of treatments in reducing the {sup 137}Cs contents increased with larger water volumes and prolonged treatment times.

Level set methods for detonation shock dynamics using high-order finite elements

Energy Technology Data Exchange (ETDEWEB)

Dobrev, V. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Grogan, F. C. [Univ. of California, San Diego, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, T. V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, R [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Tomov, V. Z. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-05-26

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two- and three-dimensional benchmark problems as well as applications to DSD.

Variable High Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows

Science.gov (United States)

Sjogreen, Bjoern; Yee, H. C.

2007-01-01

Flows containing steady or nearly steady strong shocks in parts of the flow field, and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme even under the multiblock grid or adaptive grid refinement framework. On one hand, sixth-order or higher shock-capturing methods are appropriate for unsteady turbulence with shocklets. On the other hand, lower order shock-capturing methods are more effective for strong steady shocks in terms of convergence. In order to minimize the shortcomings of low order and high order shock-capturing schemes for the subject flows,a multi- block overlapping grid with different orders of accuracy on different blocks is proposed. Test cases to illustrate the performance of the new solver are included.

Statistical methods for transverse beam position diagnostics with higher order modes in third harmonic 3.9 GHz superconducting accelerating cavities at FLASH

CERN Document Server

Zhang, P; Jones, R M

2014-01-01

Beam-excited higher order modes (HOM) can be used to provide beam diagnostics. Here we focus on 3.9 GHz superconducting accelerating cavities. In particular we study dipole mode excitation and its application to beam position determinations. In order to extract beam position information, linear regression can be used. Due to a large number of sampling points in the waveforms, statistical methods are used to effectively reduce the dimension of the system, such as singular value decomposition (SVD) and k-means clustering. These are compared with the direct linear regression (DLR) on the entire waveforms. A cross-validation technique is used to study the sample independent precisions of the position predictions given by these three methods. A RMS prediction error in the beam position of approximately 50 micron can be achieved by DLR and SVD, while k-means clustering suggests 70 micron.

Methods Reduce Cost, Enhance Quality of Nanotubes

Science.gov (United States)

2009-01-01

For all the challenges posed by the microgravity conditions of space, weight is actually one of the more significant problems NASA faces in the development of the next generation of U.S. space vehicles. For the Agency s Constellation Program, engineers at NASA centers are designing and testing new vessels as safe, practical, and cost-effective means of space travel following the eventual retirement of the space shuttle. Program components like the Orion Crew Exploration Vehicle, intended to carry astronauts to the International Space Station and the Moon, must be designed to specific weight requirements to manage fuel consumption and match launch rocket capabilities; Orion s gross liftoff weight target is about 63,789 pounds. Future space vehicles will require even greater attention to lightweight construction to help conserve fuel for long-range missions to Mars and beyond. In order to reduce spacecraft weight without sacrificing structural integrity, NASA is pursuing the development of materials that promise to revolutionize not only spacecraft construction, but also a host of potential applications on Earth. Single-walled carbon nanotubes are one material of particular interest. These tubular, single-layer carbon molecules - 100,000 of them braided together would be no thicker than a human hair - display a range of remarkable characteristics. Possessing greater tensile strength than steel at a fraction of the weight, the nanotubes are efficient heat conductors with metallic or semiconductor electrical properties depending on their diameter and chirality (the pattern of each nanotube s hexagonal lattice structure). All of these properties make the nanotubes an appealing material for spacecraft construction, with the potential for nanotube composites to reduce spacecraft weight by 50 percent or more. The nanotubes may also feature in a number of other space exploration applications, including life support, energy storage, and sensor technologies. NASA s various

A high order regularisation method for solving the Poisson equation and selected applications using vortex methods

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm

ring dynamics is presented based on the alignment of the vorticity vector with the principal axis of the strain rate tensor.A novel iterative implementation of the Brinkman penalisation method is introduced for the enforcement of a fluid-solid interface in re-meshed vortex methods. The iterative scheme...... is included to explicitly fulfil the kinematic constraints of the flow field. The high order, unbounded particle-mesh based vortex method is used to simulate the instability, transition to turbulence and eventual destruction of a single vortex ring. From the simulation data, a novel analysis on the vortex...

Variational formulation and projectional methods for the second order transport equation

International Nuclear Information System (INIS)

Borysiewicz, M.; Stankiewicz, R.

1979-01-01

Herein the variational problem for a second-order boundary value problem for the neutron transport equation is formulated. The projectional methods solving the problem are examined. The approach is compared with that based on the original untransformed form of the neutron transport equation

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

Directory of Open Access Journals (Sweden)

Navnit Jha

2014-04-01

Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

Reducing waste generation and radiation exposure by analytical method modification

International Nuclear Information System (INIS)

Ekechukwu, A.A.

1996-01-01

The primary goal of an analytical support laboratory has traditionally been to provide accurate data in a timely and cost effective fashion. Added to this goal is now the need to provide the same high quality data while generating as little waste as possible. At the Savannah River Technology Center (SRTC), we have modified and reengineered several methods to decrease generated waste and hence reduce radiation exposure. These method changes involved improving detection limits (which decreased the amount of sample required for analysis), decreasing reaction and analysis time, decreasing the size of experimental set-ups, recycling spent solvent and reagents, and replacing some methods. These changes had the additional benefits of reducing employee radiation exposure and exposure to hazardous chemicals. In all cases, the precision, accuracy, and detection limits were equal to or better than the replaced method. Most of the changes required little or no expenditure of funds. This paper describes these changes and discusses some of their applications

Study on Differential Algebraic Method of Aberrations up to Arbitrary Order for Combined Electromagnetic Focusing Systems

Institute of Scientific and Technical Information of China (English)

CHENG Min; TANG Tiantong; YAO Zhenhua; ZHU Jingping

2001-01-01

Differential algebraic method is apowerful technique in computer numerical analysisbased on nonstandard analysis and formal series the-ory. It can compute arbitrary high order derivativeswith excellent accuracy. The principle of differentialalgebraic method is applied to calculate high orderaberrations of combined electromagnetic focusing sys-tems. As an example, third-order geometric aberra-tion coefficients of an actual combined electromagneticfocusing system were calculated. The arbitrary highorder aberrations are conveniently calculated by dif-ferential algebraic method and the fifth-order aberra-tion diagrams are given.

A class of fully second order accurate projection methods for solving the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Liu Miaoer; Ren Yuxin; Zhang Hanxin

2004-01-01

In this paper, a continuous projection method is designed and analyzed. The continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the Navier-Stokes (N-S) equations in each time interval of a given time discretization. The local truncation error (LTE) analysis is applied to the continuous projection methods, which yields a sufficient condition for the continuous projection methods to be temporally second order accurate. Based on this sufficient condition, a fully second order accurate discrete projection method is proposed. A heuristic stability analysis is performed to this projection method showing that the present projection method can be stable. The stability of the present scheme is further verified through numerical experiments. The second order accuracy of the present projection method is confirmed by several numerical test cases

An interconnecting bus power optimization method combining interconnect wire spacing with wire ordering

International Nuclear Information System (INIS)

Zhu Zhang-Ming; Hao Bao-Tian; En Yun-Fei; Yang Yin-Tang; Li Yue-Jin

2011-01-01

On-chip interconnect buses consume tens of percents of dynamic power in a nanometer scale integrated circuit and they will consume more power with the rapid scaling down of technology size and continuously rising clock frequency, therefore it is meaningful to lower the interconnecting bus power in design. In this paper, a simple yet accurate interconnect parasitic capacitance model is presented first and then, based on this model, a novel interconnecting bus optimization method is proposed. Wire spacing is a process for spacing wires for minimum dynamic power, while wire ordering is a process that searches for wire orders that maximally enhance it. The method, i.e., combining wire spacing with wire ordering, focuses on bus dynamic power optimization with a consideration of bus performance requirements. The optimization method is verified based on various nanometer technology parameters, showing that with 50% slack of routing space, 25.71% and 32.65% of power can be saved on average by the proposed optimization method for a global bus and an intermediate bus, respectively, under a 65-nm technology node, compared with 21.78% and 27.68% of power saved on average by uniform spacing technology. The proposed method is especially suitable for computer-aided design of nanometer scale on-chip buses. (interdisciplinary physics and related areas of science and technology)

First-order design of geodetic networks using the simulated annealing method

Science.gov (United States)

Berné, J. L.; Baselga, S.

2004-09-01

The general problem of the optimal design for a geodetic network subject to any extrinsic factors, namely the first-order design problem, can be dealt with as a numeric optimization problem. The classic theory of this problem and the optimization methods are revised. Then the innovative use of the simulated annealing method, which has been successfully applied in other fields, is presented for this classical geodetic problem. This method, belonging to iterative heuristic techniques in operational research, uses a thermodynamical analogy to crystalline networks to offer a solution that converges probabilistically to the global optimum. Basic formulation and some examples are studied.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Science.gov (United States)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints

Directory of Open Access Journals (Sweden)

Xuewen Mu

2015-01-01

quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.

Index-aware model order reduction : LTI DAEs in electric networks

NARCIS (Netherlands)

Banagaaya, N.; Schilders, W.H.A.; Ali, G.; Tischendorf, C.

2014-01-01

Purpose Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues. Design/methodology/approach Most methods first do an index reduction before reducing a

Advanced airflow distribution methods for reducing exposure of indoor pollution

DEFF Research Database (Denmark)

Cao, Guangyu; Nielsen, Peter Vilhelm; Melikov, Arsen

2017-01-01

The adverse effect of various indoor pollutants on occupants’ health have been recognized. In public spaces flu viruses may spread from person to person by airflow generated by various traditional ventilation methods, like natural ventilation and mixing ventilation (MV Personalized ventilation (PV......) supplies clean air close to the occupant and directly into the breathing zone. Studies show that it improves the inhaled air quality and reduces the risk of airborne cross-infection in comparison with total volume (TV) ventilation. However, it is still challenging for PV and other advanced air distribution...... methods to reduce the exposure to gaseous and particulate pollutants under disturbed conditions and to ensure thermal comfort at the same time. The objective of this study is to analyse the performance of different advanced airflow distribution methods for protection of occupants from exposure to indoor...

Advanced airflow distribution methods for reducing exposure of indoor pollution

DEFF Research Database (Denmark)

Cao, Guangyu; Nielsen, Peter Vilhelm; Melikov, Arsen Krikor

methods to reduce the exposure to gaseous and particulate pollutants under disturbed conditions and to ensure thermal comfort at the same time. The objective of this study is to analyse the performance of different advanced airflow distribution methods for protection of occupants from exposure to indoor......The adverse effect of various indoor pollutants on occupants’ health have been recognized. In public spaces flu viruses may spread from person to person by airflow generated by various traditional ventilation methods, like natural ventilation and mixing ventilation (MV Personalized ventilation (PV......) supplies clean air close to the occupant and directly into the breathing zone. Studies show that it improves the inhaled air quality and reduces the risk of airborne cross-infection in comparison with total volume (TV) ventilation. However, it is still challenging for PV and other advanced air distribution...

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

Science.gov (United States)

Dyson, Rodger W.; Goodrich, John W.

2000-01-01

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

A non-linear reduced order methodology applicable to boiling water reactor stability analysis

International Nuclear Information System (INIS)

Prill, Dennis Paul

2013-01-01

Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

The higher order flux mapping method in large size PHWRs

International Nuclear Information System (INIS)

Kulkarni, A.K.; Balaraman, V.; Purandare, H.D.

1997-01-01

A new higher order method is proposed for obtaining flux map using single set of expansion mode. In this procedure, one can make use of the difference between predicted value of detector reading and their actual values for determining the strength of local fluxes around detector site. The local fluxes are arising due to constant perturbation changes (both extrinsic and intrinsic) taking place in the reactor. (author)

On method of solving third-order ordinary differential equations directly using Bernstein polynomials

Science.gov (United States)

Khataybeh, S. N.; Hashim, I.

2018-04-01

In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

Efficient nonrigid registration using ranked order statistics

DEFF Research Database (Denmark)

Tennakoon, Ruwan B.; Bab-Hadiashar, Alireza; de Bruijne, Marleen

2013-01-01

of research. In this paper we propose a fast and accurate non-rigid registration method for intra-modality volumetric images. Our approach exploits the information provided by an order statistics based segmentation method, to find the important regions for registration and use an appropriate sampling scheme......Non-rigid image registration techniques are widely used in medical imaging applications. Due to high computational complexities of these techniques, finding appropriate registration method to both reduce the computation burden and increase the registration accuracy has become an intense area...... to target those areas and reduce the registration computation time. A unique advantage of the proposed method is its ability to identify the point of diminishing returns and stop the registration process. Our experiments on registration of real lung CT images, with expert annotated landmarks, show...

The application of the mesh-free method in the numerical simulations of the higher-order continuum structures

Energy Technology Data Exchange (ETDEWEB)

Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia [School of Civil Engineering and Architecture, Zhongyuan University of Technology, Zhengzhou (China)

2016-06-08

This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe the special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.

Method of solution mining subsurface orebodies to reduce restoration activities

Energy Technology Data Exchange (ETDEWEB)

Hartman, G.J.

1984-01-24

A method of solution mining is claimed wherein a lixiviant containing both leaching and oxidizing agents is injected into the subsurface orebody. The composition of the lixiviant is changed by reducing the level of oxidizing agent to zero so that soluble species continue to be removed from the subsurface environment. This reduces the uranium level of the ground water aquifer after termination of the lixiviant injection.

Statistical methods for transverse beam position diagnostics with higher order modes in third harmonic 3.9 GHz superconducting accelerating cavities at FLASH

Energy Technology Data Exchange (ETDEWEB)

Zhang, Pei, E-mail: pei.zhang@desy.de [School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, D-22607 Hamburg (Germany); Cockcroft Institute of Science and Technology, Daresbury WA4 4AD (United Kingdom); Baboi, Nicoleta [Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, D-22607 Hamburg (Germany); Jones, Roger M. [School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL (United Kingdom); Cockcroft Institute of Science and Technology, Daresbury WA4 4AD (United Kingdom)

2014-01-11

Beam-excited higher order modes (HOMs) can be used to provide beam diagnostics. Here we focus on 3.9 GHz superconducting accelerating cavities. In particular we study dipole mode excitation and its application to beam position determinations. In order to extract beam position information, linear regression can be used. Due to a large number of sampling points in the waveforms, statistical methods are used to effectively reduce the dimension of the system, such as singular value decomposition (SVD) and k-means clustering. These are compared with the direct linear regression (DLR) on the entire waveforms. A cross-validation technique is used to study the sample independent precisions of the position predictions given by these three methods. A RMS prediction error in the beam position of approximately 50 μm can be achieved by DLR and SVD, while k-means clustering suggests 70 μm.

A high order multi-resolution solver for the Poisson equation with application to vortex methods

DEFF Research Database (Denmark)

Hejlesen, Mads Mølholm; Spietz, Henrik Juul; Walther, Jens Honore

A high order method is presented for solving the Poisson equation subject to mixed free-space and periodic boundary conditions by using fast Fourier transforms (FFT). The high order convergence is achieved by deriving mollified Green’s functions from a high order regularization function which...

A parametric model order reduction technique for poroelastic finite element models.

Science.gov (United States)

Lappano, Ettore; Polanz, Markus; Desmet, Wim; Mundo, Domenico

2017-10-01

This research presents a parametric model order reduction approach for vibro-acoustic problems in the frequency domain of systems containing poroelastic materials (PEM). The method is applied to the Finite Element (FE) discretization of the weak u-p integral formulation based on the Biot-Allard theory and makes use of reduced basis (RB) methods typically employed for parametric problems. The parametric reduction is obtained rewriting the Biot-Allard FE equations for poroelastic materials using an affine representation of the frequency (therefore allowing for RB methods) and projecting the frequency-dependent PEM system on a global reduced order basis generated with the proper orthogonal decomposition instead of standard modal approaches. This has proven to be better suited to describe the nonlinear frequency dependence and the strong coupling introduced by damping. The methodology presented is tested on two three-dimensional systems: in the first experiment, the surface impedance of a PEM layer sample is calculated and compared with results of the literature; in the second, the reduced order model of a multilayer system coupled to an air cavity is assessed and the results are compared to those of the reference FE model.

Identification of the reduced order models of a BWR reactor; Identificacion de modelos de orden reducido de un reactor BWR

Energy Technology Data Exchange (ETDEWEB)

Hernandez S, A. [UNAM, Laboratorio de Analisis de Ingenieria de Reactores Nucleares, DEPFI, Campus Morelos, en IMTA Jiutepec, Morelos (Mexico)]. e-mail: augusto@correo.unam.mx

2004-07-01

The present work has as objective to analyze the relative stability of a BWR type reactor. It is analyzed that so adaptive it turns out to identify the parameters of a model of reduced order so that this it reproduces a condition of given uncertainty. This will take of a real fact happened in the La Salle plant under certain operation conditions of power and flow of coolant. The parametric identification is carried out by means of an algorithm of recursive least square and an Output Error model (Output Error), measuring the output power of the reactor when the instability is present, and considering that it is produced by a change in the reactivity of the system in the same way that a sign of type step. Also it is carried out an analytic comparison of the relative stability, analyzing two types of answers: the original answer of the uncertainty of the reactor vs. the obtained response identifying the parameters of the model of reduced order, reaching the conclusion that it is very viable to adapt a model of reduced order to study the stability of a reactor, under the only condition to consider that the dynamics of the reactivity is of step type. (Author)

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

Science.gov (United States)

Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

2016-07-01

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free

Reduced-Order Dynamic Modeling, Fouling Detection, and Optimal Control of Solar-Powered Direct Contact Membrane Distillation

KAUST Repository

Karam, Ayman M.

2016-12-01

Membrane Distillation (MD) is an emerging sustainable desalination technique. While MD has many advantages and can be powered by solar thermal energy, its main drawback is the low water production rate. However, the MD process has not been fully optimized in terms of its manipulated and controlled variables. This is largely due to the lack of adequate dynamic models to study and simulate the process. In addition, MD is prone to membrane fouling, which is a fault that degrades the performance of the MD process. This work has three contributions to address these challenges. First, we derive a mathematical model of Direct Contact Membrane Distillation (DCMD), which is the building block for the next parts. Then, the proposed model is extended to account for membrane fouling and an observer-based fouling detection method is developed. Finally, various control strategies are implemented to optimize the performance of the DCMD solar-powered process. In part one, a reduced-order dynamic model of DCMD is developed based on lumped capacitance method and electrical analogy to thermal systems. The result is an electrical equivalent thermal network to the DCMD process, which is modeled by a system of nonlinear differential algebraic equations (DAEs). This model predicts the water-vapor flux and the temperature distribution along the module length. Experimental data is collected to validate the steady-state and dynamic responses of the proposed model, with great agreement demonstrated in both. The second part proposes an extension of the model to account for membrane fouling. An adaptive observer for DAE systems is developed and convergence proof is presented. A method for membrane fouling detection is then proposed based on adaptive observers. Simulation results demonstrate the performance of the membrane fouling detection method. Finally, an optimization problem is formulated to maximize the process efficiency of a solar-powered DCMD. The adapted method is known as Extremum

Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

Science.gov (United States)

Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad

2018-03-01

An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.

Effectiveness of methods for reducing acrylamide in bakery products.

Science.gov (United States)

Sadd, Peter A; Hamlet, Colin G; Liang, Li

2008-08-13

Pilot-scale bread, biscuit, and cracker doughs have been baked to assess how well recipe changes could reduce acrylamide in commercial bakery products. Removing ammonium-based raising agents was beneficial in biscuits. In doughs, long yeast fermentations were an effective way of reducing asparagine levels and hence acrylamide. At moderate fermentation times fructose levels increased, but the yeast later absorbed this, so the net effect on acrylamide was beneficial. Metal ions such as calcium reduced acrylamide when added as the carbonate or chloride. Hence, the fortification of flour with calcium carbonate, over and above its natural mineral content, has an additional benefit. However, some other possible methods of adding calcium to bakery doughs, for example, via the permitted preservative calcium propionate, were not beneficial. Amino acid addition to doughs gave modest reductions in acrylamide. Lowering the dough pH reduced acrylamide, but at the expense of higher levels of other process contaminants such as 3-monochloropropane-1,2-diol (3-MCPD).

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

Energy Technology Data Exchange (ETDEWEB)

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn [School of Information Science and Technology, ShanghaiTech University, Shanghai 200031 (China); Lin, Guang, E-mail: guanglin@purdue.edu [Department of Mathematics & School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States)

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Evaluation of methods for available Zn in four soil orders in Costa Rica

International Nuclear Information System (INIS)

Molina, E.; Bornemisza, E.

2001-01-01

Analytical methods for available Zn determination were evaluated on four soil orders in Costa Rica (Ultisols, Vertisols, Inceptisols and Andisols) with 25 samples for each; using the following extract solutions : Modified Olsen, Mehlich 3, Modified Morgan , DTPA and HCI. The Zn levels obtained depended on the chemical characteristics of the extracting solutions. The highest levels were obtained with HCI, except for the Vertisols. The solutions with EDTA (Modified Olsen and Mehlich 3), extracted intermediate levels of Zn, while the method using DTPA (Modified Morgan and DTPA) gave the lowest Zn values . In most of the cases, significant values of correlation were obtained between the 5 extraction methods; so for individual soil orders, or comparing all 100 soils. The highest correlation coefficients for extractable Zn were found for the Mehlich 3, Modified Morgan and DTPA. The correlations were consistent for the 4 orders, which indicate that they are adaptable to different soils, a useful characteristic for these methods. The Modified Olsen was the most efficient extractor in slightly acis soils (Vertisols and Inceptisols). The HCI extracted very high Zn levels, which are probably not related to plant available forms. It is concluded that the Mehlich 3, Modified Morgan and DTPA solutions are probably adequate for available Zn determination and might present an alternative to substitute the generally used Modified Olsen solution in Costa Rica. (Author) [es

REGULAR METHOD FOR SYNTHESIS OF BASIC BENT-SQUARES OF RANDOM ORDER

Directory of Open Access Journals (Sweden)

A. V. Sokolov

2016-01-01

Full Text Available The paper is devoted to the class construction of the most non-linear Boolean bent-functions of any length N = 2k (k = 2, 4, 6…, on the basis of their spectral representation – Agievich bent squares. These perfect algebraic constructions are used as a basis to build many new cryptographic primitives, such as generators of pseudo-random key sequences, crypto graphic S-boxes, etc. Bent-functions also find their application in the construction of C-codes in the systems with code division multiple access (CDMA to provide the lowest possible value of Peak-to-Average Power Ratio (PAPR k = 1, as well as for the construction of error-correcting codes and systems of orthogonal biphasic signals. All the numerous applications of bent-functions relate to the theory of their synthesis. However, regular methods for complete class synthesis of bent-functions of any length N = 2k are currently unknown. The paper proposes a regular synthesis method for the basic Agievich bent squares of any order n, based on a regular operator of dyadic shift. Classification for a complete set of spectral vectors of lengths (l = 8, 16, … based on a criterion of the maximum absolute value and set of absolute values of spectral components has been carried out in the paper. It has been shown that any spectral vector can be a basis for building bent squares. Results of the synthesis for the Agievich bent squares of order n = 8 have been generalized and it has been revealed that there are only 3 basic bent squares for this order, while the other 5 can be obtained with help the operation of step-cyclic shift. All the basic bent squares of order n = 16 have been synthesized that allows to construct the bent-functions of length N = 256. The obtained basic bent squares can be used either for direct synthesis of bent-functions and their practical application or for further research in order to synthesize new structures of bent squares of orders n = 16, 32, 64, …

Model order reduction techniques with applications in finite element analysis

CERN Document Server

Qu, Zu-Qing

2004-01-01

Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardware, simulations are often extremely computationally intensive and time-consuming when full-blown models are under consideration. The need to reduce the computational cost involved when dealing with high-order/many-degree-of-freedom models can be offset by adroit computation. In this light, model-reduction methods have become a major goal of simulation and modeling research. Model reduction can also ameliorate problems in the correlation of widely used finite-element analyses and test analysis models produced by excessive system complexity. Model Order Reduction Techniques explains and compares such methods focusing mainly on recent work in dynamic condensation techniques: - Compares the effectiveness of static, exact, dynamic, SEREP and iterative-dynamic condensation techniques in producing valid reduced-order mo...

Higher order multipoles and splines in plasma simulations

International Nuclear Information System (INIS)

Okuda, H.; Cheng, C.Z.

1978-01-01

The reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and the spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular the spline method may be useful in three-dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length. (Auth.)

Higher-order multipoles and splines in plasma simulations

International Nuclear Information System (INIS)

Okuda, H.; Cheng, C.Z.

1977-12-01

Reduction of spatial grid effects in plasma simulations has been studied numerically using higher order multipole expansions and spline method in one dimension. It is found that, while keeping the higher order moments such as quadrupole and octopole moments substantially reduces the grid effects, quadratic and cubic splines in general have better stability properties for numerical plasma simulations when the Debye length is much smaller than the grid size. In particular, spline method may be useful in three dimensional simulations for plasma confinement where the grid size in the axial direction is much greater than the Debye length

Reduced order modeling, statistical analysis and system identification for a bladed rotor with geometric mistuning

Science.gov (United States)

Vishwakarma, Vinod

Modified Modal Domain Analysis (MMDA) is a novel method for the development of a reduced-order model (ROM) of a bladed rotor. This method utilizes proper orthogonal decomposition (POD) of Coordinate Measurement Machine (CMM) data of blades' geometries and sector analyses using ANSYS. For the first time ROM of a geometrically mistuned industrial scale rotor (Transonic rotor) with large size of Finite Element (FE) model is generated using MMDA. Two methods for estimating mass and stiffness mistuning matrices are used a) exact computation from sector FE analysis, b) estimates based on POD mistuning parameters. Modal characteristics such as mistuned natural frequencies, mode shapes and forced harmonic response are obtained from ROM for various cases, and results are compared with full rotor ANSYS analysis and other ROM methods such as Subset of Nominal Modes (SNM) and Fundamental Model of Mistuning (FMM). Accuracy of MMDA ROM is demonstrated with variations in number of POD features and geometric mistuning parameters. It is shown for the aforementioned case b) that the high accuracy of ROM studied in previous work with Academic rotor does not directly translate to the Transonic rotor. Reasons for such mismatch in results are investigated and attributed to higher mistuning in Transonic rotor. Alternate solutions such as estimation of sensitivities via least squares, and interpolation of mass and stiffness matrices on manifolds are developed, and their results are discussed. Statistics such as mean and standard deviations of forced harmonic response peak amplitude are obtained from random permutations, and are shown to have similar results as those of Monte Carlo simulations. These statistics are obtained and compared for 3 degree of freedom (DOF) lumped parameter model (LPM) of rotor, Academic rotor and Transonic rotor. A state -- estimator based on MMDA ROM and Kalman filter is also developed for offline or online estimation of harmonic forcing function from

Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

[Discussion on ideological concept implied in traditional reinforcing and reducing method of acupuncture].

Science.gov (United States)

Li, Suyun; Zhao, Jingsheng

2017-11-12

The forming and development of traditional reinforcing and reducing method of acupuncture was rooted in traditional culture of China, and was based on the ancients' special understanding of nature, life and diseases, therefore its principle and methods were inevitably influenced by philosophy culture and medicine concept at that time. With deep study on Inner Canon of Huangdi and representative reinforcing and reducing method of acupuncture, the implied ideological concept, including contradiction view and profit-loss view in ancient dialectic, yin-yang balance theory, concept of life flow, monophyletic theory of qi , theory of existence of disease-evil, yin - yang astrology theory, theory of inter-promotion of five elements, were summarized and analyzed. The clarified and systematic understanding on guiding ideology of reinforcing and reducing method of acupuncture could significantly promote the understanding on principle, method, content and manipulation.

Mixed first- and second-order transport method using domain decomposition techniques for reactor core calculations

International Nuclear Information System (INIS)

Girardi, E.; Ruggieri, J.M.

2003-01-01

The aim of this paper is to present the last developments made on a domain decomposition method applied to reactor core calculations. In this method, two kind of balance equation with two different numerical methods dealing with two different unknowns are coupled. In the first part the two balance transport equations (first order and second order one) are presented with the corresponding following numerical methods: Variational Nodal Method and Discrete Ordinate Nodal Method. In the second part, the Multi-Method/Multi-Domain algorithm is introduced by applying the Schwarz domain decomposition to the multigroup eigenvalue problem of the transport equation. The resulting algorithm is then provided. The projection operators used to coupled the two methods are detailed in the last part of the paper. Finally some preliminary numerical applications on benchmarks are given showing encouraging results. (authors)

The reduced basis method for the electric field integral equation

International Nuclear Information System (INIS)

Fares, M.; Hesthaven, J.S.; Maday, Y.; Stamm, B.

2011-01-01

We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.

Compositional modeling of three-phase flow with gravity using higher-order finite element methods

KAUST Repository

Moortgat, Joachim

2011-05-11

A wide range of applications in subsurface flow involve water, a nonaqueous phase liquid (NAPL) or oil, and a gas phase, such as air or CO2. The numerical simulation of such processes is computationally challenging and requires accurate compositional modeling of three-phase flow in porous media. In this work, we simulate for the first time three-phase compositional flow using higher-order finite element methods. Gravity poses complications in modeling multiphase processes because it drives countercurrent flow among phases. To resolve this issue, we propose a new method for the upwinding of three-phase mobilities. Numerical examples, related to enhanced oil recovery and carbon sequestration, are presented to illustrate the capabilities of the proposed algorithm. We pay special attention to challenges associated with gravitational instabilities and take into account compressibility and various phase behavior effects, including swelling, viscosity changes, and vaporization. We find that the proposed higher-order method can capture sharp solution discontinuities, yielding accurate predictions of phase boundaries arising in computational three-phase flow. This work sets the stage for a broad extension of the higher-order methods for numerical simulation of three-phase flow for complex geometries and processes.

Reduced Numerical Approximation of Reduced Fluid-Structure Interaction Problems With Applications in Hemodynamics

Directory of Open Access Journals (Sweden)

Claudia M. Colciago

2018-06-01

Full Text Available This paper deals with fast simulations of the hemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical discretisation. The resulting method is both accurate and computationally cheap. This goal is achieved by means of two levels of reduction: first, we describe the model equations with a reduced mathematical formulation which allows to write the fluid-structure interaction problem as a Navier-Stokes system with non-standard boundary conditions; second, we employ numerical reduction techniques to further and drastically lower the computational costs. The non standard boundary condition is of a generalized Robin type, with a boundary mass and boundary stiffness terms accounting for the arterial wall compliance. The numerical reduction is obtained coupling two well-known techniques: the proper orthogonal decomposition and the reduced basis method, in particular the greedy algorithm. We start by reducing the numerical dimension of the problem at hand with a proper orthogonal decomposition and we measure the system energy with specific norms; this allows to take into account the different orders of magnitude of the state variables, the velocity and the pressure. Then, we introduce a strategy based on a greedy procedure which aims at enriching the reduced discretization space with low offline computational costs. As application, we consider a realistic hemodynamics problem with a perturbation in the boundary conditions and we show the good performances of the reduction techniques presented in the paper. The results obtained with the numerical reduction algorithm are compared with the one obtained by a standard finite element method. The gains obtained in term of CPU time are of three orders of magnitude.

An Iterative Regularization Method for Identifying the Source Term in a Second Order Differential Equation

Directory of Open Access Journals (Sweden)

Fairouz Zouyed

2015-01-01

Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

A method for simultaneously counterbalancing condition order and assignment of stimulus materials to conditions.

Science.gov (United States)

Zeelenberg, René; Pecher, Diane

2015-03-01

Counterbalanced designs are frequently used in the behavioral sciences. Studies often counterbalance either the order in which conditions are presented in the experiment or the assignment of stimulus materials to conditions. Occasionally, researchers need to simultaneously counterbalance both condition order and stimulus assignment to conditions. Lewis (1989; Behavior Research Methods, Instruments, & Computers 25:414-415, 1993) presented a method for constructing Latin squares that fulfill these requirements. The resulting Latin squares counterbalance immediate sequential effects, but not remote sequential effects. Here, we present a new method for generating Latin squares that simultaneously counterbalance both immediate and remote sequential effects and assignment of stimuli to conditions. An Appendix is provided to facilitate implementation of these Latin square designs.

A method of reducing background fluctuation in tunable diode laser absorption spectroscopy

Science.gov (United States)

Yang, Rendi; Dong, Xiaozhou; Bi, Yunfeng; Lv, Tieliang

2018-03-01

Optical interference fringe is the main factor that leads to background fluctuation in gas concentration detection based on tunable diode laser absorption spectroscopy. The interference fringes are generated by multiple reflections or scatterings upon optical surfaces in optical path and make the background signal present an approximated sinusoidal oscillation. To reduce the fluctuation of the background, a method that combines dual tone modulation (DTM) with vibration reflector (VR) is proposed in this paper. The combination of DTM and VR can make the unwanted periodic interference fringes to be averaged out and the effectiveness of the method in reducing background fluctuation has been verified by simulation and real experiments in this paper. In the detection system based on the proposed method, the standard deviation (STD) value of the background signal is decreased to 0.0924 parts per million (ppm), which is reduced by a factor of 16 compared with that of wavelength modulation spectroscopy. The STD value of 0.0924 ppm corresponds to the absorption of 4 . 328 × 10-6Hz - 1 / 2 (with effective optical path length of 4 m and integral time of 0.1 s). Moreover, the proposed method presents a better stable performance in reducing background fluctuation in long time experiments.

Origin of how steam rockets can reduce space transport cost by orders of magnitude

International Nuclear Information System (INIS)

Zuppero, A.; Larson, T.K.; Schnitzler, B.G.; Rice, J.W.; Hill, T.J.; Richins, W.D.; Parlier, L.; Werner, J.E.

1999-01-01

A brief sketch shows the origin of why and how thermal rocket propulsion has the unique potential to dramatically reduce the cost of space transportation for most inner solar system missions of interest. Orders of magnitude reduction in cost are apparently possible when compared to all processes requiring electrolysis for the production of rocket fuels or propellants and to all electric propulsion systems. An order of magnitude advantage can be attributed to rocket propellant tank factors associated with storing water propellant, compared to cryogenic liquids. An order of magnitude can also be attributed to the simplicity of the extraction and processing of ice on the lunar surface, into an easily stored, non-cryogenic rocket propellant (water). A nuclear heated thermal rocket can deliver thousands of times its mass to Low Earth Orbit from the Lunar surface, providing the equivalent to orders of magnitude drop in launch cost for mass in Earth orbit. Mass includes water ice. These cost reductions depend (exponentially) on the mission delta-v requirements being less than about 6 km/s, or about 3 times the specific velocity of steam rockets (2 km/s, from Isp 200 sec). Such missions include: from the lunar surface to Low Lunar Orbit, (LLO), from LLO to lunar escape, from Low Earth Orbit (LEO) to Geosynchronous Orbit (GEO), from LEO to Earth Escape, from LEO to Mars Transfer Orbit, from LLO to GEO, missions returning payloads from about 10% of the periodic comets using propulsive capture to orbits around Earth itself, and fast, 100 day missions from Lunar Escape to Mars. All the assertions depend entirely and completely on the existence of abundant, nearly pure ice at the permanently dark North and South Poles of the Moon. copyright 1999 American Institute of Physics

Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

Directory of Open Access Journals (Sweden)

Muhammad Aslam Noor

2008-01-01

Full Text Available We apply the variational iteration method using He's polynomials (VIMHP for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

Method of moments solution of volume integral equations using higher-order hierarchical Legendre basis functions

DEFF Research Database (Denmark)

Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter

2004-01-01

An efficient higher-order method of moments (MoM) solution of volume integral equations is presented. The higher-order MoM solution is based on higher-order hierarchical Legendre basis functions and higher-order geometry modeling. An unstructured mesh composed of 8-node trilinear and/or curved 27...... of magnitude in comparison to existing higher-order hierarchical basis functions. Consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement with the analytical Mie series solution for a dielectric sphere as well as with results obtained...

Hamiltonian formulation of theory with higher order derivatives

International Nuclear Information System (INIS)

Gitman, D.M.; Lyakhovich, S.L.; Tyutin, I.V.

1983-01-01

A method of ''hamiltonization'' of a special theory with higher order derivatives is described. In a nonspecial case the result coincides with the known Ostrogradsky formulation. It is shown that in the nonspecial theory the lagrange equations of motion are reduced to the normal form

A comparison of high-order explicit Runge–Kutta, extrapolation, and deferred correction methods in serial and parallel

KAUST Repository

Ketcheson, David I.

2014-06-13

We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four through twelve, including both serial and parallel implementations. We cast extrapolation and deferred correction methods as fixed-order Runge–Kutta methods, providing a natural framework for the comparison. The stability and accuracy properties of the methods are analyzed by theoretical measures, and these are compared with the results of numerical tests. In serial, the eighth-order pair of Prince and Dormand (DOP8) is most efficient. But other high-order methods can be more efficient than DOP8 when implemented in parallel. This is demonstrated by comparing a parallelized version of the wellknown ODEX code with the (serial) DOP853 code. For an N-body problem with N = 400, the experimental extrapolation code is as fast as the tuned Runge–Kutta pair at loose tolerances, and is up to two times as fast at tight tolerances.

A review on power reducing methods of neural recording amplifiers

Directory of Open Access Journals (Sweden)

samira mehdipour

2016-10-01

Full Text Available Implantable multi-channel neural recording Microsystems comprise a large number of neural amplifiers, that can affect the overall power consumption and chip area of the analog part of the system.power, noise, size and dc offset are the main challenge faced by designers. Ideally the output of the opamp should be at zero volts when the inputs are grounded.In reality the input terminals are at slightly different dc potentials.The input offset voltage is defined as the voltage that must be applied between the two input terminals of the opamp to obtain zero volts at the output. Amplifier must have capability to reject this dc offset. First method that uses a capacitor feedback network with ac coupling of input devices to reject the offset is very popular in designs.very small low-cutoff frequency.The second method employs a closed-loop resistive feedback and electrode capacitance to form a highpass filter.Moreover,The third method adopts the symmetric floating resistor the feedback path of low noise amplifier to achieve low-frequency cutoff and rejects DC offset voltage. .In some application we can use folded cascade topology.The telescopic topology is a good candidate in terms of providing large gain and phase margin while dissipating small power. the cortical VLSI neuron model reducing power consumption of circuits.Power distribution is the best way to reduce power, noise and silicon area. The total power consumption of the amplifier array is reduced by applying the partial OTA sharing technique. The silicon area is reduced as a benefit of sharing the bulky capacitor.

Study on the method or reducing the operator's exposure dose from a C-Arm system

Energy Technology Data Exchange (ETDEWEB)

Kim, Ki Sik; Song, Jong Nam [Dept. of Radiological Science, Dongshin University, Naju (Korea, Republic of); Kim, Seung Ok [Dept. of Radiology, Catholic Kwangdong Universty International ST.Mary' s Hospital, Incheon (Korea, Republic of)

2016-12-15

In this study, C-Arm equipment is being used as we intend to verify the exposure dose on the operator by the scattering rays during the operation of the C-Arm equipment and to provide an effective method of reducing the exposure dose. Exposure dose is less than the Over Tube method utilizes the C-arm equipment Under Tube the scheme, The result showed that the exposure dose on the operator decreased with a thicker shield, and as the operator moved away from the center line. Moreover, as the research time prolongated, the exposure dose increased, and among the three affixed location of the dosimeter, the most exposure dose was measured at gonadal, then followed by chest and thyroid. However, in consideration of the relationship between the operator and the patient, the distance cannot be increased infinitely and the research time cannot be decreased infinitely in order to reduce the exposure dose. Therefore, by changing the thickness of the radiation shield, the exposure dose on the operator was able to be reduced. If you are using a C-Arm equipment discomfort during surgery because the grounds that the procedure is neglected and close to the dose of radiation shielding made can only increase. Because a separate control room cannot be used for the C-Arm equipment due to its characteristic, the exposure dose on the operator needs to be reduced by reinforcing the shield through an appropriate thickness of radiation shield devices, such as apron, etc. during a treatment.

Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model

Science.gov (United States)

Ushijima, Timothy T.; Yeh, William W.-G.

2013-10-01

An optimal experimental design algorithm is developed to select locations for a network of observation wells that provide maximum information about unknown groundwater pumping in a confined, anisotropic aquifer. The design uses a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. The formulated optimization problem is non-convex and contains integer variables necessitating a combinatorial search. Given a realistic large-scale model, the size of the combinatorial search required can make the problem difficult, if not impossible, to solve using traditional mathematical programming techniques. Genetic algorithms (GAs) can be used to perform the global search; however, because a GA requires a large number of calls to a groundwater model, the formulated optimization problem still may be infeasible to solve. As a result, proper orthogonal decomposition (POD) is applied to the groundwater model to reduce its dimensionality. Then, the information matrix in the full model space can be searched without solving the full model. Results from a small-scale test case show identical optimal solutions among the GA, integer programming, and exhaustive search methods. This demonstrates the GA's ability to determine the optimal solution. In addition, the results show that a GA with POD model reduction is several orders of magnitude faster in finding the optimal solution than a GA using the full model. The proposed experimental design algorithm is applied to a realistic, two-dimensional, large-scale groundwater problem. The GA converged to a solution for this large-scale problem.

The Impact of Order Source Misattribution on Computerized Provider Order Entry (CPOE) Performance Metrics

Science.gov (United States)

Gellert, George A.; Catzoela, Linda; Patel, Lajja; Bruner, Kylynn; Friedman, Felix; Ramirez, Ricardo; Saucedo, Lilliana; Webster, S. Luke; Gillean, John A.

2017-01-01

Background One strategy to foster adoption of computerized provider order entry (CPOE) by physicians is the monthly distribution of a list identifying the number and use rate percentage of orders entered electronically versus on paper by each physician in the facility. Physicians care about CPOE use rate reports because they support the patient safety and quality improvement objectives of CPOE implementation. Certain physician groups are also motivated because they participate in contracted financial and performance arrangements that include incentive payments or financial penalties for meeting (or failing to meet) a specified CPOE use rate target. Misattribution of order sources can hinder accurate measurement of individual physician CPOE use and can thereby undermine providers’ confidence in their reported performance, as well as their motivation to utilize CPOE. Misattribution of order sources also has significant patient safety, quality, and medicolegal implications. Objective This analysis sought to evaluate the magnitude and sources of misattribution among hospitalists with high CPOE use and, if misattribution was found, to formulate strategies to prevent and reduce its recurrence, thereby ensuring the integrity and credibility of individual and facility CPOE use rate reporting. Methods A detailed manual order source review and validation of all orders issued by one hospitalist group at a midsize community hospital was conducted for a one-month study period. Results We found that a small but not dismissible percentage of orders issued by hospitalists—up to 4.18 percent (95 percent confidence interval, 3.84–4.56 percent) per month—were attributed inaccurately. Sources of misattribution by department or function were as follows: nursing, 42 percent; pharmacy, 38 percent; laboratory, 15 percent; unit clerk, 3 percent; and radiology, 2 percent. Order management and protocol were the most common correct order sources that were incorrectly attributed

Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

International Nuclear Information System (INIS)

Suarez-Antola, Roberto; Ministerio de Industria, Energia y Mineria, Montevideo

2011-01-01

One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

KAUST Repository

Abdulle, Assyr

2012-01-01

© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

Application of the Arbitrarily High Order Method to Coupled Electron Photon Transport

International Nuclear Information System (INIS)

Duo, Jose Ignacio

2004-01-01

This work is about the application of the Arbitrary High Order Nodal Method to coupled electron photon transport.A Discrete Ordinates code was enhanced and validated which permited to evaluate the advantages of using variable spatial development order per particle.The results obtained using variable spatial development and adaptive mesh refinement following an a posteriori error estimator are encouraging.Photon spectra for clinical accelerator target and, dose and charge depositio profiles are simulated in one-dimensional problems using cross section generated with CEPXS code.Our results are in good agreement with ONELD and MCNP codes

OPTICON: Pro-Matlab software for large order controlled structure design

Science.gov (United States)

Peterson, Lee D.

1989-01-01

A software package for large order controlled structure design is described and demonstrated. The primary program, called OPTICAN, uses both Pro-Matlab M-file routines and selected compiled FORTRAN routines linked into the Pro-Matlab structure. The program accepts structural model information in the form of state-space matrices and performs three basic design functions on the model: (1) open loop analyses; (2) closed loop reduced order controller synthesis; and (3) closed loop stability and performance assessment. The current controller synthesis methods which were implemented in this software are based on the Generalized Linear Quadratic Gaussian theory of Bernstein. In particular, a reduced order Optimal Projection synthesis algorithm based on a homotopy solution method was successfully applied to an experimental truss structure using a 58-state dynamic model. These results are presented and discussed. Current plans to expand the practical size of the design model to several hundred states and the intention to interface Pro-Matlab to a supercomputing environment are discussed.

Reduced Vlasov-Maxwell simulations

International Nuclear Information System (INIS)

Helluy, P.; Navoret, L.; Pham, N.; Crestetto, A.

2014-01-01

The Maxwell-Vlasov system is a fundamental model in physics. It can be applied to plasma simulations, charged particles beam, astrophysics, etc. The unknowns are the electromagnetic field, solution to the Maxwell equations and the distribution function, solution to the Vlasov equation. In this paper we review two different numerical methods for Vlasov-Maxwell simulations. The first method is based on a coupling between a Discontinuous Galerkin (DG) Maxwell solver and a Particle-In-Cell (PIC) Vlasov solver. The second method only uses a DG approach for the Vlasov and Maxwell equations. The Vlasov equation is first reduced to a space-only hyperbolic system thanks to the finite-element method. The two numerical methods are implemented using OpenCL in order to achieve high performance on recent Graphic Processing Units (GPU). We obtained interesting speedups, but we also observe that the PIC method is the most expensive part of the computation. Therefore we propose another fully Eulerian approach. Thanks to a decomposition of the distribution function on velocity basis functions, we obtain a reduced Vlasov model, which appears to be a hyperbolic system of conservation laws written only in the (x,t) space. We can thus adapt very easily our DG solver to the reduced model

An integrated control method for a wind farm to reduce frequency deviations in a small power system

International Nuclear Information System (INIS)

Kaneko, Toshiaki; Uehara, Akie; Senjyu, Tomonobu; Yona, Atsushi; Urasaki, Naomitsu

2011-01-01

Output power of wind turbine generator (WTG) is not constant and fluctuates due to wind speed changes. To reduce the adverse effects of the power system introducing WTGs, there are several published reports on output power control of WTGs detailing various researches based on pitch angle control, variable speed wind turbines, energy storage systems, and so on. In this context, this paper presents an integrated control method for a WF to reduce frequency deviations in a small power system. In this study, the WF achieves the frequency control with two control schemes: load estimation and short-term ahead wind speed prediction. For load estimation in the small power system, a minimal-order observer is used as disturbance observer. The estimated load is utilized to determine the output power command of the WF. To regulate the output power command of the WF according to wind speed changing, short-term ahead wind speed is predicted by using least-squares method. The predicted wind speed adjusts the output power command of the WF as a multiplying factor with fuzzy reasoning. By means of the proposed method, the WF can operate according to the wind and load conditions. In the WF system, each output power of the WTGs is controlled by regulating each pitch angle. For increasing acquisition power of the WF, a dispatch control method also is proposed. In the pitch angle control system of each WTG, generalized predictive control (GPC) is applied to enhance the control performance. Effectiveness of the proposed method is verified by the numerical simulations.

Structure of the first order reduced density matrix in three electron systems: A generalized Pauli constraints assisted study.

Science.gov (United States)

Theophilou, Iris; Lathiotakis, Nektarios N; Helbig, Nicole

2018-03-21

We investigate the structure of the one-body reduced density matrix of three electron systems, i.e., doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use configuration interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e., the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in reduced density matrix functional theory minimization schemes, when generalized Pauli constraints (GPCs) are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned."

Structure of the first order reduced density matrix in three electron systems: A generalized Pauli constraints assisted study

Science.gov (United States)

Theophilou, Iris; Lathiotakis, Nektarios N.; Helbig, Nicole

2018-03-01

We investigate the structure of the one-body reduced density matrix of three electron systems, i.e., doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use configuration interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e., the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in reduced density matrix functional theory minimization schemes, when generalized Pauli constraints (GPCs) are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned."

High Order Finite Element Method for the Lambda modes problem on hexagonal geometry

International Nuclear Information System (INIS)

Gonzalez-Pintor, S.; Ginestar, D.; Verdu, G.

2009-01-01

A High Order Finite Element Method to approximate the Lambda modes problem for reactors with hexagonal geometry has been developed. This method is based on the expansion of the neutron flux in terms of the modified Dubiner's polynomials on a triangular mesh. This mesh is fixed and the accuracy of the method is improved increasing the degree of the polynomial expansions without the necessity of remeshing. The performance of method has been tested obtaining the dominant Lambda modes of different 2D reactor benchmark problems.

Higher order Godunov methods for general systems of hyperbolic conservation laws

International Nuclear Information System (INIS)

Bell, J.B.; Colella, P.; Trangenstein, J.A.

1989-01-01

We describe an extension of higher order Godunov methods to general systems of hyperbolic conservation laws. This extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields. The method constructs an approximation of the Riemann problem from local wave information. A generalization of the Engquist--Osher flux for systems is then used to compute a numerical flux based on this approximation. This numerical flux replaces the Godunov numerical flux in the algorithm, thereby eliminating the need for a global Riemann problem solution. The additional modifications to the Godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail. The method is applied to some simple model problems for which the glocal analytic structure is known. The method is also applied to the black-oil model for multiphase flow in petroleum reservoirs. copyright 1989 Academic Press, Inc

High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations

Science.gov (United States)

Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime; Demkowicz, Leszek

2018-04-01

This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in that all the weight of the derivatives lies in the test space, while most of the trial space can be chosen as copies of $L^2$-discretizations that have no need to be continuous across adjacent elements. Additionally, the test spaces are broken along the mesh interfaces. This allows one to construct conforming polygonal finite element methods, termed here as PolyDPG methods, by defining most spaces by restriction of a bounding triangle or box to the polygonal element. The only variables that require nontrivial compatibility across elements are the so-called interface or skeleton variables, which can be defined directly on the element boundaries. Unlike other high-order polygonal methods, PolyDPG methods do not require ad hoc stabilization terms thanks to the crafted stability of the DPG methodology. A proof of convergence of the form $h^p$ is provided and corroborated through several illustrative numerical examples. These include polygonal meshes with $n$-sided convex elements and with highly distorted concave elements, as well as the modeling of discontinuous material properties along an arbitrary interface that cuts a uniform grid. Since PolyDPG methods have a natural a posteriori error estimator a polygonal adaptive strategy is developed and compared to standard adaptivity schemes based on constrained hanging nodes. This work is also accompanied by an open-source $\\texttt{PolyDPG}$ software supporting polygonal and conventional elements.

RDTM solution of Caputo time fractional-order hyperbolic telegraph equation

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2013-03-01

Full Text Available In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE. The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM. The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.

The impact of computerized physician order entry on prescription orders: A quasi-experimental study in Iran

Science.gov (United States)

Khammarnia, Mohammad; Sharifian, Roxana; Zand, Farid; Barati, Omid; Keshtkaran, Ali; Sabetian, Golnar; Shahrokh, , Nasim; Setoodezadeh, Fatemeh

2017-01-01

Background: One way to reduce medical errors associated with physician orders is computerized physician order entry (CPOE) software. This study was conducted to compare prescription orders between 2 groups before and after CPOE implementation in a hospital. Methods: We conducted a before-after prospective study in 2 intensive care unit (ICU) wards (as intervention and control wards) in the largest tertiary public hospital in South of Iran during 2014 and 2016. All prescription orders were validated by a clinical pharmacist and an ICU physician. The rates of ordering the errors in medical orders were compared before (manual ordering) and after implementation of the CPOE. A standard checklist was used for data collection. For the data analysis, SPSS Version 21, descriptive statistics, and analytical tests such as McNemar, chi-square, and logistic regression were used. Results: The CPOE significantly decreased 2 types of errors, illegible orders and lack of writing the drug form, in the intervention ward compared to the control ward (p< 0.05); however, the 2 errors increased due to the defect in the CPOE (p< 0.001). The use of CPOE decreased the prescription errors from 19% to 3% (p= 0.001), However, no differences were observed in the control ward (p<0.05). In addition, more errors occurred in the morning shift (p< 0.001). Conclusion: In general, the use of CPOE significantly reduced the prescription errors. Nonetheless, more caution should be exercised in the use of this system, and its deficiencies should be resolved. Furthermore, it is recommended that CPOE be used to improve the quality of delivered services in hospitals. PMID:29445698

The impact of computerized physician order entry on prescription orders: A quasi-experimental study in Iran.

Science.gov (United States)

Khammarnia, Mohammad; Sharifian, Roxana; Zand, Farid; Barati, Omid; Keshtkaran, Ali; Sabetian, Golnar; Shahrokh, Nasim; Setoodezadeh, Fatemeh

2017-01-01

Background: One way to reduce medical errors associated with physician orders is computerized physician order entry (CPOE) software. This study was conducted to compare prescription orders between 2 groups before and after CPOE implementation in a hospital. Methods: We conducted a before-after prospective study in 2 intensive care unit (ICU) wards (as intervention and control wards) in the largest tertiary public hospital in South of Iran during 2014 and 2016. All prescription orders were validated by a clinical pharmacist and an ICU physician. The rates of ordering the errors in medical orders were compared before (manual ordering) and after implementation of the CPOE. A standard checklist was used for data collection. For the data analysis, SPSS Version 21, descriptive statistics, and analytical tests such as McNemar, chi-square, and logistic regression were used. Results: The CPOE significantly decreased 2 types of errors, illegible orders and lack of writing the drug form, in the intervention ward compared to the control ward (p< 0.05); however, the 2 errors increased due to the defect in the CPOE (p< 0.001). The use of CPOE decreased the prescription errors from 19% to 3% (p= 0.001), However, no differences were observed in the control ward (p<0.05). In addition, more errors occurred in the morning shift (p< 0.001). Conclusion: In general, the use of CPOE significantly reduced the prescription errors. Nonetheless, more caution should be exercised in the use of this system, and its deficiencies should be resolved. Furthermore, it is recommended that CPOE be used to improve the quality of delivered services in hospitals.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian

2016-07-26

Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian; Yang, Chao; Sun, Shuyu

2016-01-01

Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative

OpenAIRE

Erkinjon Karimov; Sardor Pirnafasov

2017-01-01

In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

Method of applying single higher order polynomial basis function over multiple domains

CSIR Research Space (South Africa)

Lysko, AA

2010-03-01

Full Text Available A novel method has been devised where one set of higher order polynomial-based basis functions can be applied over several wire segments, thus permitting to decouple the number of unknowns from the number of segments, and so from the geometrical...

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

Directory of Open Access Journals (Sweden)

Heinz Toparkus

2014-04-01

Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

Methods for Engineering Sulfate Reducing Bacteria of the Genus Desulfovibrio

Energy Technology Data Exchange (ETDEWEB)

Chhabra, Swapnil R; Keller, Kimberly L.; Wall, Judy D.

2011-03-15

Sulfate reducing bacteria are physiologically important given their nearly ubiquitous presence and have important applications in the areas of bioremediation and bioenergy. This chapter provides details on the steps used for homologous-recombination mediated chromosomal manipulation of Desulfovibrio vulgaris Hildenborough, a well-studied sulfate reducer. More specifically, we focus on the implementation of a 'parts' based approach for suicide vector assembly, important aspects of anaerobic culturing, choices for antibiotic selection, electroporation-based DNA transformation, as well as tools for screening and verifying genetically modified constructs. These methods, which in principle may be extended to other sulfate-reducing bacteria, are applicable for functional genomics investigations, as well as metabolic engineering manipulations.

Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter

Energy Technology Data Exchange (ETDEWEB)

Stetzel, KD; Aldrich, LL; Trimboli, MS; Plett, GL

2015-03-15

This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables. (C) 2014 Elsevier B.V. All rights reserved.

Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

Managing concrete bridges: Methods for reducing costs and user inconveniences

DEFF Research Database (Denmark)

Goltermann, Per

2005-01-01

The paper presents experiences from modern bridge maintenance management, which has been forced to develop new and cost-efficient approaches in order to cope with the increase in overall deterioration of the aging bridge stock, the growing requirements to accessibility and the decreasing budgets...... situations often postpone or reduce the repair and rehabilitation activities required in critical parts of the structure. The paper will present some cases, where these approaches have been used on existing concrete bridges and explain how these experiences can be applied on other types of structures...

SUN-RAH: a nucleoelectric BWR university simulator based in reduced order models

International Nuclear Information System (INIS)

Morales S, J.B.; Lopez R, A.; Sanchez B, A.; Sanchez S, R.; Hernandez S, A.

2003-01-01

The development of a simulator that allows to represent the dynamics of a nucleo electric central, with nuclear reactor of the BWR type, using reduced order models is presented. These models present the characteristics defined by the dominant poles of the system (1) and most of those premature operation transitories in a power station can be reproduced with considerable fidelity if the models are identified with data of plant or references of a code of better estimate like RAMONA, TRAC (2) or RELAP. The models of the simulator are developments or own simplifications starting from the physical laws and retaining the main terms. This work describes the objective of the project and the general specifications of the University student of Nucleo electric simulator with Boiling Water Reactor type (SUN-RAH) as well as the finished parts that fundamentally are the nuclear reactor, the one of steam supply (NSSS), the plant balance (BOP), the main controllers of the plant and the implemented graphic interfaces. The pendent goals as well as the future developments and applications of SUN-RAH are described. (Author)

Progress Report on SAM Reduced-Order Model Development for Thermal Stratification and Mixing during Reactor Transients

Energy Technology Data Exchange (ETDEWEB)

Hu, R. [Argonne National Lab. (ANL), Argonne, IL (United States)

2017-09-01

This report documents the initial progress on the reduced-order flow model developments in SAM for thermal stratification and mixing modeling. Two different modeling approaches are pursued. The first one is based on one-dimensional fluid equations with additional terms accounting for the thermal mixing from both flow circulations and turbulent mixing. The second approach is based on three-dimensional coarse-grid CFD approach, in which the full three-dimensional fluid conservation equations are modeled with closure models to account for the effects of turbulence.

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Directory of Open Access Journals (Sweden)

Zhen Chen

2017-03-01

Full Text Available An unconditionally stable thermal lattice Boltzmann method (USTLBM is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE through Chapman–Enskog (C-E expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM. Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

Comparison of the methods for discrete approximation of the fractional-order operator

Directory of Open Access Journals (Sweden)

Zborovjan Martin

2003-12-01

Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.

One Improvement Method of Reducing Duration Directly to Solve Time-Cost Tradeoff Problem

Science.gov (United States)

Jian-xun, Qi; Dedong, Sun

Time and cost are two of the most important factors for project plan and schedule management, and specially, time-cost tradeoff problem is one classical problem in project scheduling, which is also a difficult problem. Methods of solving the problem mainly contain method of network flow and method of mending the minimal cost. Thereinto, for the method of mending the minimal cost is intuitionistic, convenient and lesser computation, these advantages make the method being used widely in practice. But disadvantage of the method is that the result of each step is optimal but the terminal result maybe not optimal. In this paper, firstly, method of confirming the maximal effective quantity of reducing duration is designed; secondly, on the basis of above method and the method of mending the minimal cost, the main method of reducing duration directly is designed to solve time-cost tradeoff problem, and by analyzing validity of the method, the method could obtain more optimal result for the problem.

Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

Energy Technology Data Exchange (ETDEWEB)

Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.u, E-mail: rsuarez@ucu.edu.u [Universidad Catolica del Uruguay, Montevideo (Uruguay). Fac. de Ingenieria y Tecnologias. Dept. de Matematica; Ministerio de Industria, Energia y Mineria, Montevideo (Uruguay). Direccion General de Secretaria

2011-07-01

One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)

Application of the MOVE algorithm for the identification of reduced order models of a core of a BWR type reactor

International Nuclear Information System (INIS)

Victoria R, M.A.; Morales S, J.B.

2005-01-01

Presently work is applied the modified algorithm of the ellipsoid of optimal volume (MOVE) to a reduced order model of 5 differential equations of the core of a boiling water reactor (BWR) with the purpose of estimating the parameters that model the dynamics. The viability is analyzed of carrying out an analysis that calculates the global dynamic parameters that determine the stability of the system and the uncertainty of the estimate. The modified algorithm of the ellipsoid of optimal volume (MOVE), is a method applied to the parametric identification of systems, in particular to the estimate of groups of parameters (PSE for their initials in English). It is looked for to obtain the ellipsoid of smaller volume that guarantees to contain the real value of the parameters of the model. The PSE MOVE is a recursive identification method that can manage the sign of noise and to ponder it, the ellipsoid represents an advantage due to its easy mathematical handling in the computer, the results that surrender are very useful for the design of Robust Control since to smaller volume of the ellipsoid, better is in general the performance of the system to control. The comparison with other methods presented in the literature to estimate the reason of decline (DR) of a BWR is presented. (Author)

Adaptive grouping for the higher-order multilevel fast multipole method

DEFF Research Database (Denmark)

Borries, Oscar Peter; Jørgensen, Erik; Meincke, Peter

2014-01-01

An alternative parameter-free adaptive approach for the grouping of the basis function patterns in the multilevel fast multipole method is presented, yielding significant memory savings compared to the traditional Octree grouping for most discretizations, particularly when using higher-order basis...... functions. Results from both a uniformly and nonuniformly meshed scatterer are presented, showing how the technique is worthwhile even for regular meshes, and demonstrating that there is no loss of accuracy in spite of the large reduction in memory requirements and the relatively low computational cost....

Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

Energy Technology Data Exchange (ETDEWEB)

Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

2006-01-01

Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

Obstetric outcomes in reduced and non-reduced twin pregnancies. A single hospital experience

Directory of Open Access Journals (Sweden)

UmmKulthoum E. AlShelaly

2015-09-01

Full Text Available Objectives: To compare pregnancy outcomes between high-order multiple pregnancies resulting from assisted reproductive technology (ART reduced to twins and non-reduced pregnancies, and to evaluate indications for using ART. Methods: This is a descriptive retrospective review of women with high-order multiple pregnancies reduced to twin carried out at the Department of Obstetrics & Gynecology, King Faisal Specialist Hospital & Research Center, Riyadh, Saudi Arabia between December 2010 and December 2013. The control group consisted of subjects with twin pregnancies who received their fertility treatment at the same hospital during the same period. Results: One hundred and twelve women were included in this study. Of women reaching fetal viability, significantly more women delivered before the thirtieth week in the study group (50% versus 12%, p<0.004. Miscarriage/delivery prior to fetal viability, chorioamnionitis, and preterm premature rupture of membranes were statistically higher in the study group. A total of 83% of the miscarriages in the study group were in women carrying 4 or more fetuses initially, and 50% of women in the study group were multiparous with no clear indication for fertility treatment. Conclusion: Although fetal reduction is a safe procedure, it is associated with complications. Primary prevention of high-order multiple pregnancy is recommended.

Efficient response spectrum analysis of a reactor using Model Order Reduction

International Nuclear Information System (INIS)

Oh, Jin Ho; Choi, Jin Bok; Ryu, Jeong Soo

2012-01-01

A response spectrum analysis (RSA) has been widely used to evaluate the structural integrity of various structural components in the nuclear industry. However, solving the large and complex structural systems numerically using the RSA requires a considerable amount of computational resources and time. To overcome this problem, this paper proposes the RSA based on the model order reduction (MOR) technique achieved by applying a projection from a higher order to a lower order space using Krylov subspaces generated by the Arnoldi algorithm. The dynamic characteristics of the final reduced system are almost identical with those of the full system by matching the moments of the reduced system with those of the full system up to the required nth order. It is remarkably efficient in terms of computation time and does not require a global system. Numerical examples demonstrate that the proposed method saves computational costs effectively, and provides a reduced system framework that predicts the accurate responses of a global system

Compiler-Directed Transformation for Higher-Order Stencils

Energy Technology Data Exchange (ETDEWEB)

Basu, Protonu [Univ. of Utah, Salt Lake City, UT (United States); Hall, Mary [Univ. of Utah, Salt Lake City, UT (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, Leonid [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Colella, Phillip [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2015-07-20

As the cost of data movement increasingly dominates performance, developers of finite-volume and finite-difference solutions for partial differential equations (PDEs) are exploring novel higher-order stencils that increase numerical accuracy and computational intensity. This paper describes a new compiler reordering transformation applied to stencil operators that performs partial sums in buffers, and reuses the partial sums in computing multiple results. This optimization has multiple effect son improving stencil performance that are particularly important to higher-order stencils: exploits data reuse, reduces floating-point operations, and exposes efficient SIMD parallelism to backend compilers. We study the benefit of this optimization in the context of Geometric Multigrid (GMG), a widely used method to solvePDEs, using four different Jacobi smoothers built from 7-, 13-, 27-and 125-point stencils. We quantify performance, speedup, andnumerical accuracy, and use the Roofline model to qualify our results. Ultimately, we obtain over 4× speedup on the smoothers themselves and up to a 3× speedup on the multigrid solver. Finally, we demonstrate that high-order multigrid solvers have the potential of reducing total data movement and energy by several orders of magnitude.

BIRTH ORDER AMONG NORTHERN INDIAN MEDICAL STUDENTS

Directory of Open Access Journals (Sweden)

Vinay Agarwal

2011-12-01

Full Text Available Background: Birth order is claimed to be linked with academic achievement. However, many scientists do not accept it. Objective: To assess the association of birth order in North Indian medical students with number of attempts to cross the competition bar. Study design: Cross sectional study. Setting and participation: M.B.B.S. 1st year students of L.L.R.M. Medical College, Meerut. Statistical analysis used: Chi Square test. Methods: Enquiry of Birth order and number of attempts to crack the medical entrance examination from responded 360 medical students among 494 students admitted during 2005 – 2010. Results: The study revealed insignificant relationship between ages of entrance in medical college in both sexes. of 360 students responded 37% students were of first Birth order. Among those admitted in first attempt, 67% students were of first birth order and proportion of success in first attempt reduced with increasing birth order. Conclusion: Birth Order strongly influences academic achievements.