WorldWideScience
 
 
1

The Best Finite-Difference Scheme for the Helmholtz Equation  

Directory of Open Access Journals (Sweden)

Full Text Available The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on several examples.

T. Zhanlav; V. Ulziibayar

2012-01-01

2

Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations  

International Nuclear Information System (INIS)

[en] A new finite difference scheme on a non-uniform staggered grid in cylindrical coordinates is proposed for incompressible flow. The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is satisfied. A novel pole treatment is also introduced, where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole. The pole singularity is removed properly using analytical and numerical techniques. The kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates. The pole treatment is verified for inviscid pipe flow. Mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow

2004-07-01

3

Semigroup stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We develop a simple energy method to prove the stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems. In particular we extend to several space dimensions a crucial result by Goldberg and Tadmor. This allows us to give two conditions on the discretized...

Coulombel, Jean-Francois; Gloria, Antoine

4

Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime  

Energy Technology Data Exchange (ETDEWEB)

Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection.

Zumbusch, G, E-mail: gerhard.zumbusch@uni-jena.d [Institut fuer Angewandte Mathematik, Friedrich-Schiller-Universitaet Jena, 07743 Jena (Germany)

2009-09-07

5

ADI finite difference schemes for option pricing in the Heston model with correlation  

CERN Document Server

This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional convection-diffusion-reaction equation is the presence of a mixed spatial-derivative term, which stems from the correlation between the two underlying stochastic processes for the asset price and its variance. Semi-discretization of the Heston PDE, using finite difference schemes on a non-uniform grid, gives rise to large systems of stiff ordinary differential equations. For the effective numerical solution of these systems, standard implicit time-stepping methods are often not suitable anymore, and tailored time-discretization methods are required. In the present paper, we investigate four splitting schemes of the Alternating Direction Implicit (ADI) type: the Douglas scheme, the Craig & Sneyd scheme, the Modified Craig & Sneyd scheme, and the Hundsdorfer & Verwer sch...

Hout, K J in 't

2008-01-01

6

Finite Difference Schemes for . . . That Inherit Energy Conservation Or Dissipation Property  

UK PubMed Central (United Kingdom)

We propose a new procedure to design finite difference schemes thatinherit the energy conservation or dissipation property from nonlinearpartial differential equations, such as the Korteweg-de Vries equationand the Cahn-Hilliard equation. The most important feature of ourprocedure is a rigorous discretization of variational derivatives usingsummation by parts.The inherited properties are satisfied exactly. Because of this we canexpect that derived schemes are numerically stable and yield solutionsconverging to PDE solutions. We proved the stability and convergenceof the scheme for the Cahn-Hilliard equation, and numerically verifiedthe inheritance of the energy conservation and dissipation properties forKdV eq. and Cahn-Hilliard eq.Key words. finite difference method, energy conservation, energy dissipation,KdV equation, Cahn-Hilliard equationAMS subject classification. 65M06This work is partially supported by Grant-in-Aid of the Ministry of Education, Science,Sport...

Daisuke Furihata

7

Finite difference scheme for parabolic problems on composite grids with refinement in time and space  

Energy Technology Data Exchange (ETDEWEB)

Finite difference schemes for transient convection-diffusion problems on grids with local refinement in time and space are constructed and studied. The construction utilizes a modified upwind approximation and linear interpolation at the slave nodes. The proposed schemes are implicit of backward Euler type and unconditionally stable. Error analysis is presented in the maximum norm, and convergence estimates are derived for smooth solutions. Optimal approximation results for ratios between the spatial and time discretization parameters away from the CFL condition are shown. Finally, numerical examples illustrating the theory are given.

Ewing, R.E.; Lazarov, R.D.; Vassilev, T. (Texas A and M Univ., College Station, TX (United States))

1994-12-01

8

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case  

International Nuclear Information System (INIS)

[en] Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax-Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc

1000-01-00

9

ADI finite difference schemes for the Heston-Hull-White PDE  

CERN Document Server

In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider the Heston-Hull-White model with arbitrary correlation factors, with time-dependent mean-reversion levels, with short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. In addition, both European-style call options and up-and-out call options are considered. It is shown through extensive tests that ADI schemes, with a proper choice of their parameters, perform very well in all situations - in terms of stability, accuracy and efficiency.

Haentjens, Tinne

2011-01-01

10

A Nonstandard Finite Difference Scheme for SIS Epidemic Model with Delay: Stability and Bifurcation Analysis  

Directory of Open Access Journals (Sweden)

Full Text Available A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the linearized system, we can provide the stable regions in the appropriate parameter plane. It is shown that the conditions for those equilibria to be asymptotically stable are consistent with the continuous model for any size of numerical time-step. Furthermore, we also establish the existence of Neimark-Sacker bifurcation (also called Hopf bifurcation for map) which is controlled by the time delay. The analytical results are confirmed by some numerical simulations.

Agus Suryanto

2012-01-01

11

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains  

Science.gov (United States)

Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.

Fisher, Travis C.; Carpenter, Mark H.

2013-11-01

12

A finite difference scheme for time dependent eddy currents in tokamaks  

International Nuclear Information System (INIS)

The paper reports a finite difference scheme for time dependent eddy currents, which result from plasma disruption, in tokamaks. The potential formulation employed in the present work is that of the T - ? approach, and the numerical scheme is based on a finite difference solution of the potential equations in toroidal co-ordinates. The code is written in ALgol 68. Preliminary results using the scheme are presented. (UK).

1986-01-01

13

Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics  

CERN Document Server

In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vecto...

Christlieb, Andrew J; Tang, Qi

2013-01-01

14

Localized solutions for the finite difference semi-discretization of the wave equation  

CERN Multimedia

We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along the corresponding bi-characteristic rays of Geometric Optics with a group velocity arbitrarily close to zero. Our analysis is motivated by control theoretical issues. In particular, the continuous wave equation has the so-called observability property: for a sufficiently large time, the total energy of its solutions can be estimated in terms of the energy concentrated in the exterior of a compact set. This fails to be true, uniformly on the mesh-size parameter, for the semi-discrete schemes and the observability constant blows-up at an arbitrarily large polynomial order. Our contribution consists in providing a rigorous derivation of those wave packets and in analyzing their behavior near that ray, by taking into account the subtle added dispersive effects that the numerical...

Marica, Aurora-Mihaela; 10.1016/j.crma.2010.03.020

2010-01-01

15

A conservative, skew-symmetric Finite Difference Scheme for the compressible Navier--Stokes Equations  

CERN Document Server

We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical damping. In contrast to other skew-symmetric schemes no special averaging procedures are needed. Instead, the scheme builds purely on point-wise operations and derivatives. Any explicit and central derivative can be used, permitting high order and great freedom to optimize the scheme otherwise. This also allows the simple adaption of existing finite difference schemes to improve their stability and damping properties.

Reiss, Julius

2013-01-01

16

A Stable, Convergent, Conservative and Linear Finite Difference Scheme for the Cahn-Hilliard Equation  

UK PubMed Central (United Kingdom)

We propose a stable, convergent, conservative and linear finite difference scheme to solve numerically the Cahn-Hilliard equation. Its most essential property is to realize both linearity and stability. In addition to them, we show the uniqueness, existence and the convergence of the solution to the scheme. Numerical examples demonstrate the effectiveness of the proposed scheme.

Daisuke Furihata; Takayasu Matsuo

17

Invariant meshless discretization schemes  

CERN Document Server

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a way of associating invariant functions to non-invariant functions. An invariant meshless approximation of a nonlinear diffusion equation is constructed. Comparative numerical tests with a non-invariant meshless scheme are presented. These tests yield that invariant meshless schemes can lead to substantially improved numerical solutions compared to numerical solutions generated by non-invariant meshless schemes.

Bihlo, Alexander

2012-01-01

18

A finite difference scheme for a degenerated diffusion equation arising in microbial ecology  

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference scheme is presented for a density-dependent diffusion equation that arises in the mathematical modelling of bacterial biofilms. The peculiarity of the underlying model is that it shows degeneracy as the dependent variable vanishes, as well as a singularity as the dependent variable approaches its a priori known upper bound. The first property leads to a finite speed of interface propagation if the initial data have compact support, while the second one introduces counter-acting super diffusion. This squeezing property of this model leads to steep gradients at the interface. Moving interface problems of this kind are known to be problematic for classical numerical methods and introduce non-physical and non-mathematical solutions. The proposed method is developed to address this observation. The central idea is a non-local (in time) representation of the diffusion operator. It can be shown that the proposed method is free of oscillations at the interface, that the discrete interface satisfies a discrete version of the continuous interface condition and that the effect of interface smearing is quantitatively small.

Hermann J. Eberl; Laurent Demaret

2007-01-01

19

Stable higher order finite-difference schemes for stellar pulsation calculations  

CERN Multimedia

Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach fourth order accuracy on eigenfunctions. Although this is a simple and robust approach, a number of drawbacks exist thus making fourth order schemes desirable. A robust and simple finite-difference scheme, which can easily be implemented in either 1D or 2D stellar pulsation codes is therefore required. Aims: One of the difficulties in setting up higher order finite-difference schemes for stellar pulsations is the so-called mesh-drift instability. Current ways of dealing with this defect include introducing artificial viscosity or applying a staggered grids approach. However these remedies are not well-suited to eigenvalue problems, especially those involving non-dissipative systems, because they unduly change the spectrum of the operator, introduce supplementary free parameter...

Reese, D R

2013-01-01

20

Optimal convergence rate of the explicit finite difference scheme for American option valuation  

Science.gov (United States)

An optimal convergence rate O([Delta]x) for an explicit finite difference scheme for a variational inequality problem is obtained under the stability condition using completely PDE methods. As a corollary, a binomial tree scheme of an American put option (where ) is convergent unconditionally with the rate O(([Delta]t)1/2).

Hu, Bei; Liang, Jin; Jiang, Lishang

2009-08-01

 
 
 
 
21

On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems  

Directory of Open Access Journals (Sweden)

Full Text Available We give some results concerning the real-interpolation method and finite differences. Next, we apply them to estimate the resolvents of finite-difference discretizations of Dirichlet boundary value problems for elliptic equations in space dimensions one and two in analogs of spaces of continuous and Hölder continuous functions. Such results were employed to study finite-difference discretizations of parabolic equations.

Davide Guidetti; Sergei Piskarev

2003-01-01

22

On non-standard finite difference schemes for initial value problems in ordinary differential equations  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we present the theory of non-standard finite difference schemes which can be used to solve some initial value problems in ordinary differential equations. Methods of construction and mode of implementation of these methods are also discussed. We also examine the stability properties o...

Ibijola, E.A.; Lubuma, Jean M.-S.; Ade-Ibijola, O.A.

23

A finite difference method for estimating second order parameter sensitivities of discrete stochastic chemical reaction networks.  

UK PubMed Central (United Kingdom)

We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of the perturbed processes that yields a much lower variance than existing methods, thereby drastically lowering the computational complexity required to solve a given problem. Further, the method is simple to implement and will also prove useful in any setting in which continuous time Markov chains are used to model dynamics, such as population processes. We expect the new method to be useful in the context of optimization algorithms that require knowledge of the Hessian.

Wolf ES; Anderson DF

2012-12-01

24

Lie group invariant finite difference schemes for the neutron diffusion equation  

Energy Technology Data Exchange (ETDEWEB)

Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.

Jaegers, P.J.

1994-06-01

25

2D numerical simulation of the MEP energy-transport model with a finite difference scheme  

International Nuclear Information System (INIS)

A finite difference scheme of Scharfetter-Gummel type is used to simulate a consistent energy-transport model for electron transport in semiconductors devices, free of any fitting parameters, formulated on the basis of the maximum entropy principle. Simulations of silicon n+-n-n+ diodes, 2D-MESFET and 2D-MOSFET and comparisons with the results obtained by a direct simulation of the Boltzmann transport equation and with other energy-transport models, known in the literature, show the validity of the model and the robustness of the numerical scheme

2007-02-10

26

Accelerated direct semiclassical molecular dynamics using a compact finite difference Hessian scheme.  

Science.gov (United States)

This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator. PMID:23406107

Ceotto, Michele; Zhuang, Yu; Hase, William L

2013-02-01

27

Accelerated direct semiclassical molecular dynamics using a compact finite difference Hessian scheme.  

UK PubMed Central (United Kingdom)

This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator.

Ceotto M; Zhuang Y; Hase WL

2013-02-01

28

Pseudospectral versus finite-difference schemes in the numerical integration of stochastic models of surface growth.  

UK PubMed Central (United Kingdom)

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi, and Zhang model (KPZ) and the Lai, Das Sarma, and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in earlier numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.

Gallego R; Castro M; López JM

2007-11-01

29

Pseudospectral versus finite-difference schemes in the numerical integration of stochastic models of surface growth.  

Science.gov (United States)

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi, and Zhang model (KPZ) and the Lai, Das Sarma, and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in earlier numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model. PMID:18233637

Gallego, Rafael; Castro, Mario; López, Juan M

2007-11-20

30

Optimally Accurate Second-Order Time-Domain Finite-Difference Scheme for Acoustic, Electromagnetic, and Elastic Wave Modeling  

Directory of Open Access Journals (Sweden)

Full Text Available Numerical methods are extremely useful in solving real-life problems with complex materials and geometries. However, numerical methods in the time domain suffer from artificial numerical dispersion. Standard numerical techniques which are second-order in space and time, like the conventional Finite Difference 3-point (FD3) method, Finite-Difference Time-Domain (FDTD) method, and Finite Integration Technique (FIT) provide estimates of the error of discretized numerical operators rather than the error of the numerical solutions computed using these operators. Here optimally accurate time-domain FD operators which are second-order in time as well as in space are derived. Optimal accuracy means the greatest attainable accuracy for a particular type of scheme, e.g., second-order FD, for some particular grid spacing. The modified operators lead to an implicit scheme. Using the first order Born approximation, this implicit scheme is transformed into a two step explicit scheme, namely predictor-corrector scheme. The stability condition (maximum time step for a given spatial grid interval) for the various modified schemes is roughly equal to that for the corresponding conventional scheme. The modified FD scheme (FDM) attains reduction of numerical dispersion almost by a factor of 40 in 1-D case, compared to the FD3, FDTD, and FIT. The CPU time for the FDM scheme is twice of that required by the FD3 method. The simulated synthetic data for a 2-D P-SV (elastodynamics) problem computed using the modified scheme are 30 times more accurate than synthetics computed using a conventional scheme, at a cost of only 3.5 times as much CPU time. The FDM is of particular interest in the modeling of large scale (spatial dimension is more or equal to one thousand wave lengths or observation time interval is very high compared to reference time step) wave propagation and scattering problems, for instance, in ultrasonic antenna and synthetic scattering data modeling for Non-Destructive Testing (NDT) applications, where other standard numerical methods fail due to numerical dispersion effects. The possibility of extending this method to staggered grid approach is also discussed. The numerical FD3, FDTD, FIT, and FDM results are compared against analytical solutions.

C. Bommaraju; R. Marklein; P. K. Chinta

2005-01-01

31

Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves  

CERN Multimedia

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature of this method is the way in which these fictitious values are calculated. They are based on boundary conditions and compatibility conditions satisfied by the successive spatial derivatives of the solution, up to a given order that depends on the spatial accuracy of the integration scheme adopted. Since the work is mostly done during the preprocessing step, the extra computational cost is negligible. Stress-free conditions can be designed at any arbitrary order without any numerical instability, as numerically checked. Using 10 grid nodes per minimal S-wavelength with a propagation distance of 50 wavelengths yields highly accurate results. With 5 grid ...

Lombard, Bruno; Gélis, Céline; Virieux, Jean

2007-01-01

32

A block interface flux reconstruction method for numerical simulation with high order finite difference scheme  

Science.gov (United States)

Overlap grid is usually used in numerical simulation of flow with complex geometry by high order finite difference scheme. It is difficult to generate overlap grid and the connectivity information between adjacent blocks, especially when interpolation is required for non-coincident overlap grids. In this study, an interface flux reconstruction (IFR) method is proposed for numerical simulation using high order finite difference scheme with multi-block structured grids. In this method the neighboring blocks share a common face, and the fluxes on each block are matched to set the boundary conditions for each interior block. Therefore this method has the promise of allowing discontinuous grids on either side of an interior block interface. The proposed method is proven to be stable for 7-point central DRP scheme coupled with 4-point and 5-point boundary closure schemes, as well as the 4th order compact scheme coupled with 3rd order boundary closure scheme. Four problems are numerically solved with the developed code to validate the interface flux reconstruction method in this study. The IFR method coupled with the 4th order DRP scheme or compact scheme is validated to be 4th order accuracy with one and two dimensional waves propagation problems. Two dimensional pulse propagation in mean flow is computed with wavy mesh to demonstrate the ability of the proposed method for non-uniform grid. To demonstrate the ability of the proposed method for complex geometry, sound scattering by two cylinders is simulated and the numerical results are compared with the analytical data. It is shown that the numerical results agree well with the analytical data. Finally the IFR method is applied to simulate viscous flow pass a cylinder at Reynolds number 150 to show its capability for viscous problem. The computed pressure coefficient on the cylinder surface, the frequency of vortex shedding, the lift and drag coefficients are presented. The numerical results are compared with the data of other researchers, and a good agreement is obtained. The validations imply that the proposed IFR method is accurate and effective for inviscid and viscous problems with complex geometry.

Gao, Junhui

2013-05-01

33

Fuzzy logic to improve efficiency of finite element and finite difference schemes  

Energy Technology Data Exchange (ETDEWEB)

This paper explores possible applications of logic in the areas of finite element and finite difference methods applied to engineering design problems. The application of fuzzy logic to both front-end selection of computational options and within the numerical computation itself are proposed. Further, possible methods of overcoming these limitations through the application of methods are explored. Decision strategy is a fundamental limitation in performing finite element calculations, such as selecting the optimum coarseness of the grid, numerical integration algorithm, element type, implicit versus explicit schemes, and the like. This is particularly true of novice analysts who are confronted with a myriad of choices in performing a calculation. The advantage of having the myriad of options available to the analyst is, however, that it improves and optimizes the design process if the appropriate ones are selected. Unfortunately, the optimum choices are not always apparent and only through the process of elimination or prior extensive experience can the optimum choices or combination of choices be selected. The knowledge of expert analysts could be integrated into a fuzzy ``front-end`` rule-based package to optimize the design process. The use of logic to capture the heuristic and human knowledge for selecting optimum solution strategies sets the framework for these proposed strategies.

Garcia, M.D. [Los Alamos National Lab., NM (United States); Heger, A.S. [New Mexico Univ., Albuquerque, NM (United States)

1994-05-01

34

Landing-gear noise prediction using high-order finite difference schemes  

Science.gov (United States)

Aerodynamic noise from a generic two-wheel landing-gear model is predicted by a CFD/FW-H hybrid approach. The unsteady flow-field is computed using a compressible Navier-Stokes solver based on high-order finite difference schemes and a fully structured grid. The calculated time history of the surface pressure data is used in an FW-H solver to predict the far-field noise levels. Both aerodynamic and aeroacoustic results are compared to wind tunnel measurements and are found to be in good agreement. The far-field noise was found to vary with the 6th power of the free-stream velocity. Individual contributions from three components, i.e. wheels, axle and strut of the landing-gear model are also investigated to identify the relative contribution to the total noise by each component. It is found that the wheels are the dominant noise source in general. Strong vortex shedding from the axle is the second major contributor to landing-gear noise. This work is part of Airbus LAnding Gear nOise database for CAA validatiON (LAGOON) program with the general purpose of evaluating current CFD/CAA and experimental techniques for airframe noise prediction.

Liu, Wen; Wook Kim, Jae; Zhang, Xin; Angland, David; Caruelle, Bastien

2013-07-01

35

On behavior of preconditioned methods for a class of compact finite difference schemes in solution of hyperbolic equations  

Directory of Open Access Journals (Sweden)

Full Text Available In this article, for a class of linear systems arising from the compact finite difference schemes, we apply Krylov subspace methods in combination the ADI, BLAGE,... preconditioners. We consider our scheme in solution of hyperbolic equations  subject to appropriate initial and Dirichlet boundary conditions, where  is constant. We show, the BLAGE preconditioner is extremely effective in achieving optimal convergence rates. Numerical results performed on model problems to confirm the efficiency of our approach.

M.M. Arabshahi

2012-01-01

36

Isotropic finite-differences  

International Nuclear Information System (INIS)

New finite-differences, called isotropic finite-differences, where the lowest order error terms are without any directional bias, are proposed. An accurate simulation of 6-fold symmetric dendritic solidification is presented using a numerical scheme based on these finite-differences.

2004-11-20

37

Invariant Discretization Schemes Using Evolution-Projection Techniques  

Directory of Open Access Journals (Sweden)

Full Text Available Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for non-invariant schemes of the heat equation in computational coordinates. We propose a new methodology for handling moving discretization grids which are generally indispensable for invariant numerical schemes. The idea is to use the invariant grid equation, which determines the locations of the grid point at the next time level only for a single integration step and then to project the obtained solution to the regular grid using invariant interpolation schemes. This guarantees that the scheme is invariant and allows one to work on the simpler stationary grids. The discretization errors of the invariant schemes are established and their convergence rates are estimated. Numerical tests are carried out to shed some light on the numerical properties of invariant discretization schemes using the proposed evolution-projection strategy.

Alexander Bihlo; Jean-Christophe Nave

2013-01-01

38

Locally exact modifications of discrete gradient schemes  

CERN Multimedia

Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying classical discrete gradient schemes. Modifications of this kind are found for any discrete gradient.

Cie?li?ski, Jan L

2013-01-01

39

On the Equivalence of the Digital Waveguide and FDTD Finite Difference Schemes  

CERN Document Server

It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variables in a DW simulation. Since boundary conditions and initial values are more intuitively transparent in the DW formulation, the simple means of converting back and forth can be useful in initializing and constructing boundaries for FDTD simulations.

Smith, J O

2004-01-01

40

Numerical pricing of options using high-order compact finite difference schemes  

Science.gov (United States)

We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.

Tangman, D. Y.; Gopaul, A.; Bhuruth, M.

2008-09-01

 
 
 
 
41

Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes  

Scientific Electronic Library Online (English)

Full Text Available Abstract in english We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the or (more) iginal non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order) and implicit compact-difference (fourth-order) formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid) is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved.

Duque-Daza, Carlos; Lockerby, Duncan; Galeano, Carlos

2011-12-01

42

An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation  

Science.gov (United States)

The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations.

Zhan, Ge; Pestana, Reynam C.; Stoffa, Paul L.

2013-04-01

43

Simulation of three-dimensional waveguide discontinuities by a full-vector mode-matching method based on finite-difference schemes.  

UK PubMed Central (United Kingdom)

A rigorous full-vector analysis based on the finite-difference mode-matching method is presented for three-dimensional optical wave propagation problems. The computation model is facilitated by a perfectly matched layer (PML) terminated with a perfectly reflecting boundary condition (PRB). The complex modes including both the guided and the radiation fields of the three-dimensional waveguide with arbitrary index profiles are computed by a finite-difference scheme. The method is applied to and validated by the analysis of the facet reflectivity of a buried waveguide and the power exchange of a periodically loaded dielectric waveguide polarization rotator.

Mu J; Huang WP

2008-10-01

44

Upwind Finite Difference Schemes for the Computation of Traveltime in Transversely Isotropic Media with Vertical Symmetry Axis  

UK PubMed Central (United Kingdom)

We apply our general mathematical formulations of finite difference schemesfor the computation of traveltime and amplitude in inhomogeneous anisotropicmedia to the transversely isotropic media with vertical symmetry axis (VTI).The Hamilton-Jacobi equation for the downgoing qP wave is given in termsof Thomsen parameters and a second order Essentially Nonoscillatory(ENO)Hamilton-Jacobi solver is applied to get the viscosity solution (the first-arrivaltraveltime field) on a regular grid.Numerical experiments (2D and 3D) and testson the isotropic and an anisotropic Marmousi model show that our approach isefficient and accurate.IntroductionAnisotropic traveltime computations play an important role in many methodsof seismic data processing, such as anisotropic DMO and anisotropic migration(Tsvankin, 1995; Alkhalifah, 1996; Anderson, 1996). These traveltimes are oftencomputed by ray tracing (Cerveny, 1972);and because depth and surface points areusually distributed on a regular...

Jian L. Qian; William W. Symes

45

Numerical Stability of Explicit Runge-Kutta Finite Difference Schemes for the Nonlinear Schr\\"odinger Equation  

CERN Multimedia

Linearized numerical stability bounds for solving the nonlinear time-dependent Schr\\"odinger equation (NLSE) are shown. The bounds are computed for the fourth-order Runge-Kutta scheme in time and both second-order and fourth-order central differencing in space. Results are given for Dirichlet, modulus-squared Dirichlet, Laplacian-zero, and periodic boundary conditions for one, two, and three dimensions. Our approach is to use standard Runge-Kutta linear stability theory, treating the nonlinearity of the NLSE as a constant. The required bounds on the eigenvalues of the scheme matrices are found analytically when possible, and otherwise estimated using the Gershgorin circle theorem.

Caplan, Ronald M

2011-01-01

46

On discretization schemes for stochastic evolution equations  

CERN Multimedia

Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.

Gy"ongy, I; Gy\\"{o}ngy, Istvan; Millet, Annie

2005-01-01

47

On discretization schemes for stochastic evolution equations  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.

Gyöngy, Istvan; Millet, Annie

48

Optimized Discretization Schemes For Brain Images  

Directory of Open Access Journals (Sweden)

Full Text Available In medical image processing active contour method is the important technique in segmenting human organs. Geometric deformable curves known as levelsets are widely used in segmenting medical images. In this modeling , evolution of the curve is described by the basic lagrange pde expressed as a function of space and time. This pde can be solved either using continuous functions or discrete numerical methods.This paper deals with the application of numerical methods like finite diffefence and TVd-RK methods for brain scans. The stability and accuracy of these methods are also discussed. This paper also deals with the more accurate higher order non-linear interpolation techniques like ENO and WENO in reconstructing the brain scans like CT,MRI,PET and SPECT is considered.

USHA RANI.N,; DR.P.V.SUBBAIAH; Dr.D.Venkata Rao

2011-01-01

49

Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.  

UK PubMed Central (United Kingdom)

In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed.

Guo Z; Zhao TS

2003-06-01

50

Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.  

Science.gov (United States)

In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed. PMID:16241382

Guo, Zhaoli; Zhao, T S

2003-06-26

51

Discrete-time interacting quantum walks and quantum Hash schemes  

Science.gov (United States)

Through introducing discrete-time quantum walks on the infinite line and on circles, we present a kind of two-particle interacting quantum walk which has two kinds of interactions. We investigate the characteristics of this kind of quantum walk and the time evolution of the two particles. Then we put forward a kind of quantum Hash scheme based on two-particle interacting quantum walks and discuss their feasibility and security. The security of this kind of quantum Hash scheme relies on the infinite possibilities of the initial state rather than the algorithmic complexity of hard problems, which will greatly enhance the security of the Hash schemes.

Li, Dan; Zhang, Jie; Guo, Fen-Zhuo; Huang, Wei; Wen, Qiao-Yan; Chen, Hui

2013-03-01

52

A Transport Acceleration Scheme for Multigroup Discrete Ordinates with Upscattering  

International Nuclear Information System (INIS)

We have developed a modification of the two-grid upscatter acceleration scheme of Adams and Morel. The modified scheme uses a low-angular-order discrete ordinates equation to accelerate Gauss-Seidel multigroup iteration. This modification ensures that the scheme does not suffer from consistency problems that can affect diffusion-accelerated methods in multidimensional, multimaterial problems. The new transport two-grid scheme is very simple to implement for different spatial discretizations because it uses the same transport operator. The scheme has also been demonstrated to be very effective on three-dimensional, multimaterial problems. On simple one-dimensional graphite and heavy-water slabs modeled in three dimensions with reflecting boundary conditions, we see reductions in the number of Gauss-Seidel iterations by factors of 75 to 1000. We have also demonstrated the effectiveness of the new method on neutron well-logging problems. For forward problems, the new acceleration scheme reduces the number of Gauss-Seidel iterations by more than an order of magnitude with a corresponding reduction in the run time. For adjoint problems, the speedup is not as dramatic, but the new method still reduces the run time by greater than a factor of 6.

2010-07-01

53

Energy levels of interacting curved nanomagnets in a frustrated geometry: increasing accuracy when using finite difference methods.  

UK PubMed Central (United Kingdom)

The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore the resulting computed properties of lattices of interacting curved nanomagnets. In this paper, we detail these effects for the multi-axis kagome lattice. Using the OOMMF finite difference method, we propose an alternative way of discretizing the nanomagnet shape via a variable moment per cell scheme. This method is shown to be efficient in reducing discretization effects.

Riahi H; Montaigne F; Rougemaille N; Canals B; Lacour D; Hehn M

2013-07-01

54

Energy levels of interacting curved nanomagnets in a frustrated geometry: increasing accuracy when using finite difference methods.  

Science.gov (United States)

The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore the resulting computed properties of lattices of interacting curved nanomagnets. In this paper, we detail these effects for the multi-axis kagome lattice. Using the OOMMF finite difference method, we propose an alternative way of discretizing the nanomagnet shape via a variable moment per cell scheme. This method is shown to be efficient in reducing discretization effects. PMID:23803392

Riahi, H; Montaigne, F; Rougemaille, N; Canals, B; Lacour, D; Hehn, M

2013-06-26

55

On the accuracy and efficiency of finite difference solutions for nonlinear waves  

DEFF Research Database (Denmark)

We consider the relative accuracy and efficiency of low- and high-order finite difference discretizations of the exact potential flow problem for nonlinear water waves. The continuous differential operators are replaced by arbitrary order finite difference schemes on a structured but non-uniform grid. Time-integration is performed using a fourth-order Runge-Kutta scheme. The linear accuracy, stability and convergence properties of the method are analyzed in two-dimensions, and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as providing an optimal balance between accuracy and complexity for practical purposes.

Bingham, Harry B.

2006-01-01

56

Time step and mesh size dependencies in the heat conduction solution of a semi-implicit, finite difference scheme for transient two-phase flow  

Energy Technology Data Exchange (ETDEWEB)

This report examines, and establishes the causes of, previously identified time step and mesh size dependencies. These dependencies were observed in the solution of a coupled system of heat conduction and fluid flow equations as used in the TRAC-PF1/MOD1 computer code. The report shows that a significant time step size dependency can arise in calculations of the quenching of a previously unwetted surface. The cause of this dependency is shown to be the explicit evaluation, and subsequent smoothing of the term which couples the heat transfer and fluid flow equations. An axial mesh size dependency is also identified, but this is very much smaller than the time step size dependency. The report concludes that the time step size dependency represents a potential limitation on the use of large time step sizes for types of calculation discussed. This limitation affects the present TRAC-PF-1/MOD1 computer code and may similarly affect other semi-implicit finite difference codes that employ similar techniques. It is likely to be of greatest significance in codes where multi-step techniques are used to allow the use of large time steps.

O' Mahoney, R. (AEA Technology, Winfrith (United Kingdom))

1992-04-01

57

Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography. Revision 2.  

Science.gov (United States)

This Recommendation specifies key-establishment schemes based on the discrete logarithm problem over finite fields and elliptic curves, including several variations of Diffie-Hellman and Menezes-Qu-Vanstone(MQV) key establishment schemes.

A. Roginsky E. Barker L. Chen M. Smid

2013-01-01

58

Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography.  

Science.gov (United States)

This Recommendation specifies key-establishment schemes based on the discrete logarithm problem over finite fields and elliptic curves, including several variations of Diffie-Hellman and Menezes-Qu-Vanstone(MQV) key establishment schemes.

A. Roginsky E. Barker L. Chen M. Smid

2013-01-01

59

Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow  

International Nuclear Information System (INIS)

We consider the approximation scheme to the American call option via the discrete Morse semiflow, which is a minimizing scheme of a time semi-discretized variational functional. In this paper we obtain a rate of convergence of approximate solutions and the convergence of approximate free boundaries. We mainly apply the theory of variational inequalities and that of viscosity solutions to prove our results.

2011-01-01

60

Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow  

Energy Technology Data Exchange (ETDEWEB)

We consider the approximation scheme to the American call option via the discrete Morse semiflow, which is a minimizing scheme of a time semi-discretized variational functional. In this paper we obtain a rate of convergence of approximate solutions and the convergence of approximate free boundaries. We mainly apply the theory of variational inequalities and that of viscosity solutions to prove our results.

Ishii, Katsuyuki, E-mail: ishii@maritime.kobe-u.ac.jp [Kobe University, Graduate School of Maritime Sciences (Japan); Omata, Seiro, E-mail: omata@kenroku.kanazawa-u.ac.jp [Kanazawa University, School of Mathematics and Physics, Institute of Science and Engineering (Japan)

2011-12-15

 
 
 
 
61

Finite Difference Method of Modelling Groundwater Flow  

Directory of Open Access Journals (Sweden)

Full Text Available In this study, finite difference method is used to solve the equations that govern groundwater flow to obtain flow rates, flow direction and hydraulic heads through an aquifer. The aim therefore is to discuss the principles of Finite Difference Method and its applications in groundwater modelling. To achieve this, a rectangular grid is overlain an aquifer in order to obtain an exact solution. Initial and boundary conditions are then determined. By discretizing the system into grids and cells that are small compared to the entire aquifer, exact solutions are obtained. A flow chart of the computational algorithm for particle tracking is also developed. Results show that under a steady-state flow with no recharge, pathlines coincide with streamlines. It is also found that the accuracy of the numerical solution by Finite Difference Method is largely dependent on initial particle distribution and number of particles assigned to a cell. It is therefore concluded that Finite Difference Method can be used to predict the future direction of flow and particle location within a simulation domain.

Magnus.U. Igboekwe; N. J. Achi

2011-01-01

62

High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves  

DEFF Research Database (Denmark)

The incompressible Euler equations are solved with a free surface, the position of which is captured by applying an Eulerian kinematic boundary condition. The solution strategy follows that of [1, 2], applying a coordinate-transformation to obtain a time-constant spatial computational domain which is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied implicitly, at the end of each time stage, by constructing the pressure from a discrete Poisson equation, derived from the discrete continuity and momentum equations and taking the time-dependent physical domain into account. An efficient preconditionedDefect Correction (DC) solution of the discrete Poisson equation for the pressure is presented, in which the preconditioning step is based on an order-multigrid formulation with a direct solution on the lowest order-level. This ensures fast convergence of the DC method with a computational effort which scales linearly with the problem size. Results obtained with a two-dimensional implementation of the model are compared with highly accurate stream function solutions to the nonlinear wave problem, which show the approximately expected convergence rates and a clear advantage of using high-order finite difference schemes in combination with the Euler equations.

Christiansen, Torben Robert Bilgrav; Bingham, Harry B.

2012-01-01

63

A New Signature Scheme Based on Factoring and Discrete Logarithm Problems  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In 1994, He and Kiesler proposed a digital signature scheme which was based on the factoring and the discrete logarithm problem both. Same year, Shimin-Wei modi?ed the He-Kiesler signature scheme. In this paper, we propose an improvement of Shimin-Wei signature scheme based on factorization and disc...

Swati Verma; Birendra Kumar Sharma

64

A New Signature Scheme Based on Factoring and Discrete Logarithm Problems  

Directory of Open Access Journals (Sweden)

Full Text Available In 1994, He and Kiesler proposed a digital signature scheme which was based on the factoring and the discrete logarithm problem both. Same year, Shimin-Wei modi?ed the He-Kiesler signature scheme. In this paper, we propose an improvement of Shimin-Wei signature scheme based on factorization and discrete logarithm problem both with di?erent parameters and using a collision-free one-way hash function. In our opinion, our scheme is more secure than the earlier one.

Swati Verma; Birendra Kumar Sharma

2012-01-01

65

Convergence of discrete duality finite volume schemes for the cardiac bidomain model  

CERN Document Server

We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.

Andreianov, Boris; Karlsen, Kenneth H; Pierre, Charles

2010-01-01

66

Grid cell distortion and MODFLOW's integrated finite-difference numerical solution.  

UK PubMed Central (United Kingdom)

The ground water flow model MODFLOW inherently implements a nongeneralized integrated finite-difference (IFD) numerical scheme. The IFD numerical scheme allows for construction of finite-difference model grids with curvilinear (piecewise linear) rows. The resulting grid comprises model cells in the shape of trapezoids and is distorted in comparison to a traditional MODFLOW finite-difference grid. A version of MODFLOW-88 (herein referred to as MODFLOW IFD) with the code adapted to make the one-dimensional DELR and DELC arrays two dimensional, so that equivalent conductance between distorted grid cells can be calculated, is described. MODFLOW IFD is used to inspect the sensitivity of the numerical head and velocity solutions to the level of distortion in trapezoidal grid cells within a converging radial flow domain. A test problem designed for the analysis implements a grid oriented such that flow is parallel to columns with converging widths. The sensitivity analysis demonstrates MODFLOW IFD's capacity to numerically derive a head solution and resulting intercell volumetric flow when the internal calculation of equivalent conductance accounts for the distortion of the grid cells. The sensitivity of the velocity solution to grid cell distortion indicates criteria for distorted grid design. In the radial flow test problem described, the numerical head solution is not sensitive to grid cell distortion. The accuracy of the velocity solution is sensitive to cell distortion with error <1% if the angle between the nonparallel sides of trapezoidal cells is <12.5 degrees. The error of the velocity solution is related to the degree to which the spatial discretization of a curve is approximated with piecewise linear segments. Curvilinear finite-difference grid construction adds versatility to spatial discretization of the flow domain. MODFLOW-88's inherent IFD numerical scheme and the test problem results imply that more recent versions of MODFLOW 2000, with minor modifications, have the potential to make use of a curvilinear grid.

Romero DM; Silver SE

2006-11-01

67

A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative  

CERN Multimedia

A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method.

Sousa, Ercília

2011-01-01

68

A New Digital Signature Scheme Based on Factoring and Discrete Logarithms  

Directory of Open Access Journals (Sweden)

Full Text Available Problem statement: A digital signature scheme allows one to sign an electronic message and later the produced signature can be validated by the owner of the message or by any verifier. Most of the existing digital signature schemes were developed based on a single hard problem like factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. Although these schemes appear secure, one day in a near future they may be exploded if one finds a solution of the single hard problem. Approach: To overcome this problem, in this study, we proposed a new signature scheme based on multiple hard problems namely factoring and discrete logarithms. We combined the two problems into both signing and verifying equations such that the former depends on two secret keys whereas the latter depends on two corresponding public keys. Results: The new scheme was shown to be secure against the most five considering attacks for signature schemes. The efficiency performance of our scheme only requires 1203Tmul+Th time complexity for signature generation and 1202Tmul+Th time complexity for verification generation and this magnitude of complexity is considered minimal for multiple hard problems-like signature schemes. Conclusions: The new signature scheme based on multiple hard problems provides longer and higher security level than that scheme based on one problem. This is because no enemy can solve multiple hard problems simultaneously.

E. S. Ismail; N. M.F. Tahat; R. R. Ahmad

2008-01-01

69

MATHEMATICAL MODELING OF FINANCIAL PYRAMID SCHEME. PART 2. DISCRETE MODELS ?????????????? ????????????? ???????????? ?????????? ?????????. ????? 2. ?????????? ??????  

Directory of Open Access Journals (Sweden)

Full Text Available This article analyzes the changes in the number of cases of various clients of the pyramid and the establishment of the basic rules of the pyramid schemes based on discrete models. The article is also a continuation of previous work [1], which had formulas to simulate the amount collected by the pyramid scheme

Kovalenko A. V.; Urtenov M. K.; Chagarov R. H.

2012-01-01

70

A splitting higher order scheme with discrete transparent boundary conditions for the Schr\\"odinger equation in a semi-infinite parallelepiped  

CERN Multimedia

An initial-boundary value problem for the $n$-dimensional ($n\\geq 2$) time-dependent Schr\\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we first construct higher order scheme with splitting space averages having much better spectral properties for $n\\geq 3$. Next we apply the Strang-type splitting with respect to the potential and, third, construct discrete transparent boundary conditions (TBC). For the resulting method, the uniqueness of solution and the unconditional uniform in time $L^2$-stability (in particular, $L^2$-conservativeness) are proved. Owing to the splitting, an effective direct algorithm using FFT (in the coordinate directions perpendicular to the leading axis of the parallelepiped) is applicable for general potential. Numerical results on the 2D tunnel effect for a P\\"{o}schl-Teller-like potential-barrier and a rectangular potential-well are also included.

Ducomet, Bernard; Romanova, Alla

2013-01-01

71

A comparison of spatial discretization schemes for differential solution methods of the radiative transfer equation  

International Nuclear Information System (INIS)

[en] A comparison of discretization schemes required to evaluate the radiation intensity at the cell faces of a control volume in differential solution methods of the radiative transfer equation is presented. Several schemes developed using the normalized variable diagram and the total variation diminishing formalisms are compared along with essentially non-oscillatory schemes and genuinely multidimensional schemes. The calculations were carried out using the discrete ordinates method, but the analysis is equally valid for the finite-volume method. It is shown that the S schemes of the genuinely multidimensional family perform quite well, particularly in problems with discontinuous radiation intensity fields. However, they are time consuming, and so they do not always become more attractive regarding the trade-off between accuracy and computational requirements, in comparison with other high-order schemes that, although being less accurate, are also more economical

2008-01-01

72

Original Signer's Forgery Attacks on Discrete Logarithm Based Proxy Signature Schemes  

Directory of Open Access Journals (Sweden)

Full Text Available A proxy signature scheme enables a proxy signer to sign messages on behalf of the original signer. In this paper, we demonstrate that a number of discrete logarithm based proxy signature schemes are vulnerable to an original signer's forgery attack. In this attack, a malicious original signer can impersonate a proxy signer and produce a forged proxy signature on a message. A third party will incorrectly believe that the proxy signer was responsible for generating the proxy signature. This contradicts the strong unforgeability property that is required of proxy signatures schemes. We show six proxy signature schemes vulnerable to this attack including Lu et al.'s proxy blind multi-signature scheme, Xue and Cao's proxy blind signature scheme, Fu et al. and Gu et al.'s anonymous proxy signature schemes, Dai et al. and Huang et al.'s nominative proxy signature schemes are all insecure against the original signer's forgery.

Tianjie Cao; Xianping Mao

2007-01-01

73

Novel Two-Scale Discretization Schemes for Lagrangian Hydrodynamics  

Energy Technology Data Exchange (ETDEWEB)

In this report we propose novel higher order conservative schemes of discontinuous Galerkin (or DG) type for the equations of gas dynamics in Lagrangian coordinates suitable for general unstructured finite element meshes. The novelty of our approach is in the formulation of two-scale non-oscillatory function recovery procedures utilizing integral moments of the quantities of interest (pressure and velocity). The integral moments are computed on a primary mesh (cells or zones) which defines our original scale that governs the accuracy of the schemes. In the non-oscillatory smooth function recovery procedures, we introduce a finer mesh which defines the second scale. Mathematically, the recovery can be formulated as nonlinear energy functional minimization subject to equality and nonlinear inequality constraints. The schemes are highly accurate due to both the embedded (local) mesh refinement features as well as the ability to utilize higher order integral moments. The new DG schemes seem to offer an alternative to currently used artificial viscosity techniques and limiters since the two-scale recovery procedures aim at resolving these issues. We report on some preliminary tests for the lowest order case, and outline some possible future research directions.

Vassilevski, P

2008-05-29

74

COMPARISON OF THE ACCURACY OF VARIOUS SPATIAL DISCRETIZATION SCHEMES OF THE DISCRETE ORDINATES EQUATIONS IN 2D CARTESIAN GEOMETRY  

Energy Technology Data Exchange (ETDEWEB)

We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.

Sebastian Schunert; Yousry Y. Azmy; Damien Fournier

2011-05-01

75

Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case  

Science.gov (United States)

Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well.

Guo, Zhaoli; Xu, Kun; Wang, Ruijie

2013-09-01

76

Spatial parallelism of a 3D finite difference, velocity-stress elastic wave propagation code  

Energy Technology Data Exchange (ETDEWEB)

Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, finite difference simulations for 3D elastic wave propagation are expensive. The authors model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.

Minkoff, S.E.

1999-12-01

77

Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation  

Directory of Open Access Journals (Sweden)

Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

Walter H. Aschbacher

2009-01-01

78

On implicit and explicit discretization schemes for parabolic SPDEs in any dimension  

CERN Document Server

We study the speed of convergence of the explicit and implicit space-time discretization schemes of the solution $u(t,x)$ to a parabolic partial differential equation in any dimension perturbed by a space-correlated Gaussian noise. The coefficients only depend on $u(t,x)$ and the influence of the correlation on the speed is observed.

Millet, A; Millet, Annie; Morien, Pierre-Luc

2006-01-01

79

On implicit and explicit discretization schemes for parabolic SPDEs in any dimension  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study the speed of convergence of the explicit and implicit space-time discretization schemes of the solution $u(t,x)$ to a parabolic partial differential equation in any dimension perturbed by a space-correlated Gaussian noise. The coefficients only depend on $u(t,x)$ and the influence of the co...

Millet, Annie; Morien, Pierre-Luc

80

Accurate convergent finite difference approximations for viscosity solutions of the elliptic Monge-Amp\\`ere partial differential equation  

CERN Document Server

The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear Partial Differential Equations (PDEs) such as the elliptic Monge-Amp\\`ere equation. The approximation theory of Barles-Souganidis [Barles and Souganidis, Asymptotic Anal., 4 (1999) 271-283] requires that numerical schemes be monotone (or elliptic in the sense of [Oberman, SIAM J. Numer. Anal, 44 (2006) 879-895]. But such schemes have limited accuracy. In this article, we establish a convergence result for nearly monotone schemes. This allows us to construct finite difference discretizations of arbitrarily high-order. We demonstrate that the higher accuracy is achieved when solutions are sufficiently smooth. In addition, the filtered scheme provides a natural detection principle for singularities. We employ this framework to construct a formally second-order scheme for the Monge-Amp\\`ere equation and present computational results on smooth and singular solutions.

Froese, Brittany D

2012-01-01

 
 
 
 
81

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.  

UK PubMed Central (United Kingdom)

A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.

Liu H; Valocchi AJ; Zhang Y; Kang Q

2013-01-01

82

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows  

Science.gov (United States)

A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.

Liu, Haihu; Valocchi, Albert J.; Zhang, Yonghao; Kang, Qinjun

2013-01-01

83

A high-order Nystrom discretization scheme for boundary integral equations defined on rotationally symmetric surfaces  

CERN Multimedia

A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e.g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting...

Young, P; Martinsson, P G

2012-01-01

84

A new transport discretization scheme for arbitrary spatial meshes in XY geometry  

Energy Technology Data Exchange (ETDEWEB)

We introduce a new spatial discretization scheme for transport on arbitrary spatial grids in XY geometry. Our arbitrary'' spatial grid is composed of arbitrarily-connected polygons, each of which may have an arbitrary number of sides. We begin our derivation by imposing particle balance on every corner'' of each cell (Consequently, we call our scheme the corner-balance (CB) method.) We complete the derivation by introducing simple closure formulas that relate volume-averaged unknowns to surface-averaged unknowns in each corner. We discuss the relationship of the new scheme to discontinuous finite-element methods and to multiple-balance methods. We demonstrate that on simple grids, the method reduces to very robust schemes that have been studied previously. We discuss the theoretical performance of the method in the thick diffusion limit, and provide numerical results for that limit. We present additional numerical results from simple problems that test the new scheme in other limits. Finally, we offer some concluding remarks about the method. 9 refs., 6 figs.

Adams, M.L.

1991-01-18

85

Extension of functions with bounded finite differences  

CERN Document Server

We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original function's finite differences.

Duarte, P

2008-01-01

86

Reduction of the spatial discretization error in the method of characteristics using the diamond-difference scheme  

International Nuclear Information System (INIS)

[en] In this paper, the diamond-difference (DD) scheme, which is commonly used in discrete-ordinate codes, is applied to the method of characteristics (MOC) to reduce the spatial discretization error of the flat flux approximation. Smaller spatial discretization error allows coarser background mesh division, which leads to smaller computational burden. Some theoretical considerations on the DD scheme are discussed to clarify the strength of this method. An absorption cross section weighted DD scheme (AWDD), which utilizes macroscopic absorption cross section to set the weight, is also discussed. The DD and AWDD schemes are implemented to AEGIS, which is a lattice physics code based on MOC. Then the AEGIS code is applied to two different benchmark problems whose spatial discretization errors are large. The calculation results indicate that from the viewpoint of spatial discretization error, the AWDD scheme is superior to the conventional MOC in which the step characteristics approximation is commonly used. Since incorporation of the AWDD scheme to current MOC codes is very simple, it will be a good candidate of spatial discretization method for MOC codes. (author)

2006-01-01

87

A parallel adaptive finite difference algorithm for petroleum reservoir simulation  

Energy Technology Data Exchange (ETDEWEB)

Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)

Hoang, Hai Minh

2005-07-01

88

A modified semi--implict Euler-Maruyama Scheme for finite element discretization of SPDEs  

CERN Multimedia

We consider the numerical approximation of a general second order semi-linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new scheme using in time a linear functional of the noise with a semi-implicit Euler-Maruyama method and in space we analyse a finite element method although extension to finite differences or finite volumes would be possible. We consider noise that is white in time and either in $H^1$ or $H^2$ in space. We give the convergence proofs in the root mean square $L^{2}$ norm for a diffusion reaction equation and in root mean square $H^{1}$ norm in the presence of advection. We examine the regularity of the initial data, the regularity of the noise and errors from projecting the noise. We present numerical results for a linear reaction diffusion equatio in two dimensions as well as a nonlinear example of two-dimensional stochastic advection diffusion reaction equation. We see from both the analysis and numerics that we have bette...

Lord, Gabriel J

2010-01-01

89

An induced charge readout scheme incorporating image charge splitting on discrete pixels  

Energy Technology Data Exchange (ETDEWEB)

Top hat electrostatic analysers used in space plasma instruments typically use microchannel plates (MCPs) followed by discrete pixel anode readout for the angular definition of the incoming particles. Better angular definition requires more pixels/readout electronics channels but with stringent mass and power budgets common in space applications, the number of channels is restricted. We describe here a technique that improves the angular definition using induced charge and an interleaved anode pattern. The technique adopts the readout philosophy used on the CRRES and CLUSTER I instruments but has the advantages of the induced charge scheme and significantly reduced capacitance. Charge from the MCP collected by an anode pixel is inductively split onto discrete pixels whose geometry can be tailored to suit the scientific requirements of the instrument. For our application, the charge is induced over two pixels. One of them is used for a coarse angular definition but is read out by a single channel of electronics, allowing a higher rate handling. The other provides a finer angular definition but is interleaved and hence carries the expense of lower rate handling. Using the technique and adding four channels of electronics, a four-fold increase in the angular resolution is obtained. Details of the scheme and performance results are presented.

Kataria, D.O. E-mail: dok@mssl.ucl.ac.uk; Lapington, J.S

2003-11-01

90

Optimal Independent Encoding Schemes for Several Classes of Discrete Degraded Broadcast Channels  

CERN Multimedia

Let $X \\to Y \\to Z$ be a discrete memoryless degraded broadcast channel (DBC) with marginal transition probability matrices $T_{YX}$ and $T_{ZX}$. For any given input distribution $\\boldsymbol{q}$, and $H(Y|X) \\leq s \\leq H(Y)$, define the function $F^*_{T_{YX},T_{ZX}}(\\boldsymbol{q},s)$ as the infimum of $H(Z|U)$ with respect to all discrete random variables $U$ such that a) $H(Y|U) = s$, and b) $U$ and $Y,Z$ are conditionally independent given $X$. This paper studies the function $F^*$, its properties and its calculation. This paper then applies these results to several classes of DBCs including the broadcast Z channel, the input-symmetric DBC, which includes the degraded broadcast group-addition channel, and the discrete degraded multiplication channel. This paper provides independent encoding schemes and demonstrates that each achieve the boundary of the capacity region for the corresponding class of DBCs. This paper first represents the capacity region of the DBC $X \\to Y \\to Z$ with the function $F^*_{T...

Xie, Bike

2008-01-01

91

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.  

UK PubMed Central (United Kingdom)

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed.

Macías-Díaz JE; Macías S; Medina-Ramírez IE

2013-06-01

92

Wave Equation Simulation on Manifold using Discrete Exterior Calculus  

CERN Multimedia

Numerical simulation provides a effective tool for studying both the spatial and temporal nature of acoustic field on 3D or 4D timespace. The paper deals with the description of discrete exterior calculus scheme for the wave equation. This method can be directly implemented on manifold, which is the generation of finite difference time domain method from flat space to curved space.

Xie, Zheng; Ma, Bin; Shen, Qinghua

2009-01-01

93

The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain  

Science.gov (United States)

In this paper, for a class of fractional sub-diffusion equations on a space unbounded domain, firstly, exact artificial boundary conditions, which involve the time-fractional derivatives, are derived using the Laplace transform technique. Then the original problem on the space unbounded domain is reduced to the initial-boundary value problem on a space bounded domain. Secondly, an efficient finite difference approximation for the reduced initial-boundary problem on the space bounded domain is constructed. Different from the method of order reduction used in [37] for the fractional sub-diffusion equations on a space half-infinite domain, the presented difference scheme, which is more simple than that in the previous work, is developed using the direct discretization method, i.e. the approximate method of considering the governing equations at mesh points directly. The stability and convergence of the scheme with numerical accuracy O(?+h2) are proved by means of discrete energy method and Sobolev imbedding inequality, where ? is the order of time-fractional derivative in the governing equation, ? and h are the temporal stepsize and spatial stepsize, respectively. Thirdly, a compact difference scheme for the case of ??2/3 is derived with the truncation errors of fourth-order accuracy for interior points and third-order accuracy for boundary points, respectively. Then the global convergence order O(?+h4) of the compact difference scheme is proved. Finally, numerical experiments are used to verify the numerical accuracy and the efficiency of the obtained schemes.

Gao, Guang-hua; Sun, Zhi-zhong

2013-03-01

94

TWO STAGE DISCRETE TIME EXTENDED KALMAN FILTER SCHEME FOR MICRO AIR VEHICLE  

Directory of Open Access Journals (Sweden)

Full Text Available Navigation of Micro Air Vehicle (MAV) is one of the most challenging areas of twenty first century’s research. Micro Air Vehicle (MAV) is the miniaturized configuration of aircraft with a size of six inches in length and below the weight of hundred grams, which includes twenty grams of payload as well. Due to its small size, MAV is highly affected by the wind gust and therefore the navigation of Micro Air Vehicle (MAV) is very important because precise navigation is a very basic step for the control of the Micro Air Vehicle (MAV). This paper presents two stage cascaded discrete time Extended Kalman Filter while using INS/GPS based navigation. First stage of this scheme estimates the Euler angles of Micro Air Vehicle (MAV) whereas the second stage of this scheme estimates the position of Micro Air Vehicle (MAV) in terms of height, longitude and latitude. As the system is considered as non-linear, so Extended Kalman Filter is used. On-board sensors in first stage included MEMS Gyro, MEMS Accelerometer, MEMS Magnetometer whereas second stage includes GPS.

Sadia Riaz; Ali Usman

2012-01-01

95

A finite-difference lattice Boltzmann approach for gas microflows  

CERN Multimedia

Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB velocity-space discretizations based on the roots of full-range Hermite polynomials, using the nodes of a quadrature defined in the half-space permits a consistent treatment of kinetic boundary conditions. The possibilities of the proposed LB models are illustrated by studying the one-dimensional Couette flow and the two-dimensional driven cavity flow. Numerical and analytical results show an improved accuracy in finite Knudsen flows as compared with standard LB models.

Ghiroldi, G P

2013-01-01

96

On the finite-difference Schroedinger equation  

International Nuclear Information System (INIS)

[en] A finite-difference Schroedinger equation with an explicity time-dependent Hamiltonian is considered. Solutions are discussed for the case in which it is possible to assume that, during a certain time interval, a perturbation described by the operator V(t)=Vsup(0)(t) for 0(T acts upon the particle with a time-independent Hamiltonian Hsub(deg)

1976-12-04

97

Scheme for measuring experimentally the velocity of pilot waves and the discreteness of time  

International Nuclear Information System (INIS)

We consider the following two questions. Suppose that a quantum system suffers a change of the boundary condition or the potential at a given space location. Then (1)when will the wavefunction shows a response to this change at another location? And (2)how does the wavefunction changes?The answer to question (1) could reveal how a quantum system gets information on the boundary condition or the potential. Here we show that if the response takes place immediately, then it can allow superluminal signal transfer. Else if the response propagates in space with a finite velocity, then it could give a simple explanation why our world shows classicality on the macroscopic scale. Furthermore, determining the exact value of this velocity can either clarify the doubts on static experiments for testing Bell's inequality, or support the pilot-wave interpretation of quantum mechanics. We propose a feasible experimental scheme for measuring this velocity, which can be implemented with state-of-art technology, e.g., single-electron biprism interferometry.Question (2) is studied with a square-well potential model, and we find a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions. To solve the paradox, we predict that when a change of the potential occurs at a given space location, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore it gives a simple proof that time is discrete, with Planck time being the smallest unit. Combining with the answer to question (1), systems with a larger size and a slower velocity could have a larger unit of time, making it possible to test the discreteness of time experimentally. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.

2010-12-22

98

The discrete variational derivative method based on discrete differential forms  

Science.gov (United States)

As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice. Lately, Furihata and Matsuo have developed the so-called "discrete variational derivative method" that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems. On the other hand, the theories of discrete differential forms have received much attention recently. These theories provide a discrete analogue of the vector calculus on general meshes. In this paper, we show that the discrete variational derivative method and the discrete differential forms by Bochev and Hyman can be combined. Applications to the Cahn-Hilliard equation and the Klein-Gordon equation on triangular meshes are provided as demonstrations. We also show that the schemes for these equations are H1-stable under some assumptions. In particular, one for the nonlinear Klein-Gordon equation is obtained by combination of the energy conservation property and the discrete Poincaré inequality, which are the temporal and spacial structures that are preserved by the above methods.

Yaguchi, Takaharu; Matsuo, Takayasu; Sugihara, Masaaki

2012-05-01

99

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes  

CERN Multimedia

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.

Kovács, M; Lindgren, F

2012-01-01

100

Finite difference approximations for a class of non-local parabolic equations  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the original equation, and fully-implicit scheme also possesses strict monotonicity. It is also proved that finite difference solutions approach to zero as t→∞ exponentially. The numerical results of some examples are presented, which support our theoretical justifications.

Yanping Lin; Shuzhan Xu; Hong-Ming Yin

1997-01-01

 
 
 
 
101

Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods  

Energy Technology Data Exchange (ETDEWEB)

Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.

Kim, S. [Purdue Univ., West Lafayette, IN (United States)

1994-12-31

102

Finite-difference migration to zero offset  

Energy Technology Data Exchange (ETDEWEB)

Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.

Li, Jianchao.

1992-01-01

103

Finite-difference migration to zero offset  

Energy Technology Data Exchange (ETDEWEB)

Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.

Li, Jianchao

1992-07-01

104

Operational Method for Finite Difference Equations  

CERN Multimedia

In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and can be used to find the particular solution of the FDE. This work raises the possibility of developing new ways to expand the scope of the operational methods.

Merino, S

2011-01-01

105

Finite difference approximations for a class of non-local parabolic equations  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we study finite difference procedures for a class of parabolic equations with non-local boundary condition. The semi-implicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the ori...

Yanping Lin; Shuzhan Xu; Hong-Ming Yin

106

3D finite-difference seismic migration with parallel computers  

Energy Technology Data Exchange (ETDEWEB)

The ability to image complex geologies such as salt domes in the Gulf of Mexico and thrusts in mountainous regions is essential for reducing the risk associated with oil exploration. Imaging these structures, however, is computationally expensive as datasets can be terabytes in size. Traditional ray-tracing migration methods cannot handle complex velocity variations commonly found near such salt structures. Instead the authors use the full 3D acoustic wave equation, discretized via a finite difference algorithm. They reduce the cost of solving the apraxial wave equation by a number of numerical techniques including the method of fractional steps and pipelining the tridiagonal solves. The imaging code, Salvo, uses both frequency parallelism (generally 90% efficient) and spatial parallelism (65% efficient). Salvo has been tested on synthetic and real data and produces clear images of the subsurface even beneath complicated salt structures.

Ober, C.C.; Gjertsen, R.; Minkoff, S.; Womble, D.E.

1998-11-01

107

Finite difference methods for coupled flow interaction transport models  

Directory of Open Access Journals (Sweden)

Full Text Available Understanding chemical transport in blood flow involves coupling the chemical transport process with flow equations describing the blood and plasma in the membrane wall. In this work, we consider a coupled two-dimensional model with transient Navier-Stokes equation to model the blood flow in the vessel and Darcy's flow to model the plasma flow through the vessel wall. The advection-diffusion equation is coupled with the velocities from the flows in the vessel and wall, respectively to model the transport of the chemical. The coupled chemical transport equations are discretized by the finite difference method and the resulting system is solved using the additive Schwarz method. Development of the model and related analytical and numerical results are presented in this work.

Shelly McGee; Padmanabhan Seshaiyer

2009-01-01

108

Analysis of optical waveguide structures by use of a combined finite-difference/finite-difference time-domain method.  

UK PubMed Central (United Kingdom)

We present a method for full-wave characterization of optical waveguide structures. The method computes mode-propagation constants and cross-sectional field profiles from a straight forward discretization of Maxwell's equations. These modes are directly excited in a three-dimensional finite-difference time-domain simulation to obtain optical field transmission and reflection coefficients for arbitrary waveguide discontinuities. The implementation uses the perfectly-matched-layer technique to absorb both guided modes and radiated fields. A scattered-field formulation is also utilized to allow accurate determination of weak scattered-field strengths. Individual three-dimensional waveguide sections are cascaded by S-parameter analysis. A complete 10(4)-section Bragg resonator is successfully simulated with the method.

Wallace JW; Jensen MA

2002-03-01

109

Finite Difference Method of the Study on Radioactivities DispersionModeling in Environment of Ground  

International Nuclear Information System (INIS)

It has been resulted the mathematics equation as model of constructingthe computer algorithm deriving from the transport equation having been theform of radionuclides dispersion in the environment of ground as a result ofdiffusion and advection process. The derivation of mathematics equation usedthe finite difference method into three schemes, the explicit scheme,implicit scheme and Crank-Nicholson scheme. The computer algorithm then wouldbe used as the basic of making the software in case of making a monitoringsystem of automatic radionuclides dispersion on the area around the nuclearfacilities. By having the three schemes, so it would be, in choosing thesoftware system, able to choose the more approximate with the fact. (author)

2000-01-01

110

A New Conservative Difference Scheme for the General Rosenau-RLW Equation  

Directory of Open Access Journals (Sweden)

Full Text Available A new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable, and second-order convergent. Numerical examples show the efficiency of the scheme.

Zuo Jin-Ming; Zhang Yao-Ming; Zhang Tian-De; Chang Feng

2010-01-01

111

A composite Chebyshev finite difference method for nonlinear optimal control problems  

Science.gov (United States)

In this paper, a composite Chebyshev finite difference method is introduced and is successfully employed for solving nonlinear optimal control problems. The proposed method is an extension of the Chebyshev finite difference scheme. This method can be regarded as a non-uniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto points. The convergence of the method is established. The nice properties of hybrid functions are then used to convert the nonlinear optimal control problem into a nonlinear mathematical programming one that can be solved efficiently by a globally convergent algorithm. The validity and applicability of the proposed method are demonstrated through some numerical examples. The method is simple, easy to implement and yields very accurate results.

Marzban, H. R.; Hoseini, S. M.

2013-06-01

112

Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time  

CERN Document Server

We consider the problem of discretization for the $U(1)$-invariant nonlinear wave equations in any dimension. We show that the classical finite-difference scheme used by Strauss and Vazquez \\cite{MR0503140} conserves the positive-definite discrete analog of the energy and the discrete analog of the charge if the grid ratio is $dt/dx=1/\\sqrt{n}$, where $dt$ and $dx$ are the mesh sizes of the time and space variables and $n$ is the spatial dimension. We prove the existence and uniqueness of solutions to the discrete Cauchy problem. We use the energy conservation to obtain the a priori bounds for finite energy solutions, thus showing that the Strauss -- Vazquez finite-difference scheme for the nonlinear Klein-Gordon equation with positive nonlinear term in the Hamiltonian is unconditionally stable in this case.

Komech, Alexander

2010-01-01

113

A New Digital Signature Scheme Based on Factoring and Discrete Logarithms  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Problem statement: A digital signature scheme allows one to sign an electronic message and later the produced signature can be validated by the owner of the message or by any verifier. Most of the existing digital signature schemes were developed based on a single hard problem like factoring,...

E. S. Ismail; N. M.F. Tahat; R. R. Ahmad

114

Iterative solutions of finite difference diffusion equations  

International Nuclear Information System (INIS)

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

1981-01-01

115

Finite difference seismic modeling using staggered grid  

Energy Technology Data Exchange (ETDEWEB)

The seismic reflection exploration technique which is one of the geophysical methods for oil exploration became effectively to image the subsurface structure with rapid development of computer. As a tool to perform seismic inversion, seismic forward modeling program using ray tracing should be developed. In this study, we have developed the algorithm that is to calculate the travel time of the complex geological structure using ray tracing by subdividing the geologic model into triangular element (finite element) having the constant velocity. We can analytically calculate Jacobian with some information by this current ray tracing. With this Jacobian, we will develop new algorithm which is to obtain geological properties and to image the subsurface. Since the FEM (Finite Element Method) ray tracing we have developed goes well the inverse velocities structure, we can apply the inversion problem to complex geological model. We apply the staggered grid to seismic wave equation modeling which is well known in fluid dynamics and propagation modeling of electromagnetic wave. In seismic wave equation modeling using staggered grid, we can exactly understand variation of physical properties and waveform in FDM(finite difference method) wave equation because the source problem is simple. Since seismic wave equation modeling using staggered grid can be exactly represent variation of physical properties, it can be applied to reverse time migration for imaging the reflection event of seismic data in elastic media. (author). 11 refs., 12 figs.

Park, Geun Pil; Shin, Chang Soo [Korea Institute of Geology Mining and Materials, Taejon (Korea, Republic of)

1996-12-01

116

Multigroup Monte Carlo Reactor Calculation with Coarse Mesh Finite Difference Formulation for Real Variance Reduction  

Energy Technology Data Exchange (ETDEWEB)

The coarse mesh finite difference (CMFD) formulation has been applied to Monte Carlo (MC) simulations in order to mitigate the issue of large real variances of pin power tallies in full-core problems. In this work, a parallelized multigroup (MG) two-dimensional (2-D) MC code named PRIDE (Probabilistic Reactor Investigation with Discretized Energy), which is capable of handling lattices of square pin cells within which circular substructures can be modeled, has been developed as a tool for the investigations of the new method. In this code, a scheme to construct a CMFD linear system is based on the MC tallies of coarse mesh average fluxes and the net currents at coarse mesh interfaces. These tallies are accumulated over the MC cycles to get more stable CMFD solutions which are used for feedback to MC fission source distribution (FSD). The feedback scheme in this code employs a weight adjustment of fission source neutrons for the next MC cycle that is to reflect the global CMFD FSD into the MC FSD. The performance of CMFD feedback has been investigated in terms of the number of inactive cycles required for the convergence of FSD and also the reduction of real variances of local property tallies in active cycles. The applications to 2-D multigroup full-core pressurized water reactor problems have demonstrated that the MC FSD converges considerably faster and the real variances of pin powers are smaller by a factor of 4 with CMFD FSD feedback. It is also noted that the large real variances of pin powers are caused mainly by the global assembly-wise fluctuations of power distributions in a large core rather than local fluctuations.

Lee, Min-Jae [ORNL; Joo, Han Gyu [Seoul National University; Lee, Deokjung [ORNL; Smith, Kord [Studsvik Scandpower, Inc.

2010-01-01

117

An assessment of semi-discrete central schemes for hyperbolic conservation laws  

International Nuclear Information System (INIS)

High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in Z pinch physics. In this work, we describe initial efforts to develop a generalized 'black-box' conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between 'black-box' central schemes and the piecewise parabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both methods. However, PPM clearly outperforms the central schemes in terms of accuracy at a given grid resolution and the cost of additional complexity in the numerical flux functions. Overall we have observed that the finite volume schemes, implemented within a well-designed framework, are extremely efficient with (potentially) very low memory storage. Finally, we have found by computational experiment that second and third-order strong-stability preserving (SSP) time integration methods with the number of stages greater than the order provide a useful enhanced stability region. However, we observe that non-SSP and non-optimal SSP schemes with SSP factors less than one can still be very useful if used with time-steps below the standard CFL limit. The 'well-designed' integration schemes that we have examined appear to perform well in all instances where the time step is maintained below the standard physical CFL limit.

2003-01-01

118

A new family of (5,5)CC-4OC schemes applicable for unsteady Navier-Stokes equations  

Science.gov (United States)

A new family of implicit spatially fourth order accurate compact finite difference scheme has been proposed.The system of Navier-Stokes equations reduces to a diagonally dominant constant coefficients algebraic system.The family of schemes enjoys better resolution properties compared to other compact formulations.Linear stability analysis shows the schemes are unconditionally stable.The extension of the proposed discretization procedure to irregular domains and three dimensional cases has been discussed.

Sen, Shuvam

2013-10-01

119

Discrete Mechanics and Optimal Control: an Analysis  

CERN Multimedia

The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper is to directly discretize the variational description of the system's motion. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. We show that the DMOC approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The numerical performance of DMOC and its relationsh...

Ober-Bloebaum, S; Marsden, J E

2008-01-01

120

Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\\'ere equation  

CERN Document Server

The elliptic Monge-Amp\\`ere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Amp\\'ere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the nece...

Froese, Brittany D

2010-01-01

 
 
 
 
121

Using finite difference method to simulate casting thermal stress  

Directory of Open Access Journals (Sweden)

Full Text Available Thermal stress simulation can provide a scientific reference to eliminate defects such as crack, residual stress centralization and deformation etc., caused by thermal stress during casting solidification. To study the thermal stress distribution during casting process, a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method (FDM), namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete. A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process. Two practical verifications were carried out, and the results from simulation basically coincided with practical cases. The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress, and to predict the occurrence of hot tearing. Because heat transfer and stress analysis are all based on FDM, they can use the same FD model, which can avoid the matching process between different models, and hence reduce temperature-load transferring errors. This approach makes the simulation of fluid flow, heat transfer and stress analysis unify into one single model.

Liao Dunming; Zhang Bin; Zhou Jianxin

2011-01-01

122

Convergence of a numerical scheme for a coupled Schr\\"odinger--KdV system  

CERN Multimedia

We prove the convergence in a strong norm of a finite difference semi-discrete scheme approximating a coupled Schr\\"odinger--KdV system on a bounded domain. This system models the interaction of short and long waves. Since the energy estimates available in the continuous case do not carry over to the discrete setting, we rely on a suitably truncated problem which we prove reduces to the original one. We present some numerical examples to illustrate our convergence result.

Amorim, Paulo

2012-01-01

123

On discontinuous Galerkin for time integration in option pricing problems with adaptive finite differences in space  

Science.gov (United States)

The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.

von Sydow, Lina

2013-10-01

124

Minimal positive stencils in meshfree finite difference methods for the Poisson equation  

CERN Multimedia

Meshfree finite difference methods for the Poisson equation approximate the Laplace operator on a point cloud. Desirable are positive stencils, i.e. all neighbor entries are of the same sign. Classical least squares approaches yield large stencils that are in general not positive. We present an approach that yields stencils of minimal size, which are positive. We provide conditions on the point cloud geometry, so that positive stencils always exist. The new discretization method is compared to least squares approaches.

Seibold, Benjamin

2008-01-01

125

An Image Hiding Scheme Using 3D Sawtooth Map and Discrete Wavelet Transform  

Directory of Open Access Journals (Sweden)

Full Text Available An image encryption scheme based on the 3D sawtooth map is proposed in this paper. The 3D sawtooth map is utilized to generate chaotic orbits to permute the pixel positions and to generate pseudo-random gray value sequences to change the pixel gray values. The image encryption scheme is then applied to encrypt the secret image which will be imbedded in one host image. The encrypted secret image and the host image are transformed by the wavelet transform and then are merged in the frequency domain. Experimental results show that the stego-image looks visually identical to the original host one and the secret image can be effectively extracted upon image processing attacks, which demonstrates strong robustness against a variety of attacks.

Ruisong Ye; Wenping Yu

2012-01-01

126

Implicit-Explicit Runge-Kutta schemes for numerical discretization of optimal control problems  

CERN Multimedia

Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge-Kutta methods in the context of optimal control problems. The analysis of the schemes is based on the continuous optimality system. Using suitable transformations of the adjoint equation, order conditions up to order three are proven as well as the relation between adjoint schemes obtained through different transformations is investigated. Conditions for the IMEX Runge-Kutta methods to be symplectic are also derived. A numerical example illustrating the theoretical properties is presented.

Herty, Michael; Steffensen, Sonja

2012-01-01

127

Explicit Finite Difference Solution of Heat Transfer Problems of Fish Packages in Precooling  

Directory of Open Access Journals (Sweden)

Full Text Available The present work aims at finding an optimized explicit finite difference scheme for the solution of problems involving pure heat transfer from the surfaces of Pangasius Sutchi fish samples suddenly exposed to a cooling environment. Regular shaped packages in the form of an infinite slab were considered and a generalized mathematical model was written in dimensionless form. An accurate sample of the data set was chosen from the experimental work and was used to seek an optimized scheme of solutions. A fully explicit finite difference scheme has been thoroughly studied from the viewpoint of stability, the required time for execution and precision. The characteristic dimension (half thickness) was divided into a number of divisions; n = 5, 10, 20, 50 and 100 respectively. All the possible options of dimensionless time (the Fourier number) increments were taken one by one to give the best convergence and truncation error criteria. The simplest explicit finite difference scheme with n = (10) and stability factor (Î?X)2/Î?Ï? = 2) was found to be reliable and accurate for prediction purposes."

A. S. Mokhtar; K. A. Abbas; M. M.H.M. Ahmad; S. M. Sapuan; A. O. Ashraf; M. A. Wan; B. Jamilah

2004-01-01

128

Calculation of critical flows by finite difference methods  

International Nuclear Information System (INIS)

The phenomenon of choking which is observed for compressible flows is mathematically interpreted as the characteristic determinant of the flow equations being zero. If it is computed by a finite difference method, it is shown that a flow rate blockage results from a property of the matrix of the linearized finite difference equations. This property is reducibility

1976-11-22

129

A Skin Tone Based Stenographic Scheme using Double Density Discrete Wavelet Transforms.  

Directory of Open Access Journals (Sweden)

Full Text Available Steganography is the art of concealing the existence of data in another transmission medium i.e. image, audio, video files to achieve secret communication. It does not replace cryptography but rather boosts the security using its obscurity features. In the proposed method Biometric feature (Skin tone region) is used to implement Steganography[1]. In our proposed method Instead of embedding secret data anywhere in image, it will be embedded in only skin tone region. This skin region provides excellent secure location for data hiding. So, firstly skin detection is performed using, HSV (Hue, Saturation, Value) color space in cover images. Thereafter, a region from skin detected area is selected, which is known as the cropped region. In this cropped region secret message is embedded using DD-DWT (Double Density Discrete Wavelet Transform). DD-DWT overcomes the intertwined shortcomings of DWT (like poor directional selectivity, Shift invariance, oscillations and aliasing)[2].optimal pixel adjustment process (OPA) is used to enhance the image quality of the stego-image. Hence the image obtained after embedding secret message (i.e. Stego image) is far more secure and has an acceptable range of PSNR. The proposed method is much better than the previous works both in terms of PSNR and robustness against various attacks (like Gaussian Noise, salt and pepper Noise, Speckle Noise, rotation, JPEG Compression, Cropping, and Contrast Adjustment etc.)

Varsha Gupta

2013-01-01

130

ADI FD schemes for the numerical solution of the three-dimensional Heston-Cox-Ingersoll-Ross PDE  

Science.gov (United States)

This paper deals with the numerical solution of the time-dependent, three-dimensional Heston-Cox-Ingersoll- Ross PDE, with all correlations nonzero, for the fair pricing of European call options. We apply a finite difference dis-cretization on non-uniform spatial grids and then numerically solve the semi-discrete system in time by using an Alternating Direction Implicit scheme. We show that this leads to a highly efficient and stable numerical solution method.

Haentjens, Tinne

2012-09-01

131

Finite difference methods for 1st Order in time, 2nd order in space, hyperbolic systems used in numerical relativity  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This thesis is concerned with the development of numerical methods using finite difference techniques for the discretization of initial value problems (IVPs) and initial boundary value problems (IBVPs) of certain hyperbolic systems which are first order in time and second order in space. This type o...

Chirvasa, Mihaela

132

A combined finite volume-finite element scheme for the discretization of strongly nonlinear convection-diffusion-reaction problems on nonmatching grids  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We propose and analyze a numerical scheme for nonlinear degenerate parabolic convection-diffusion-reaction equations in two or three space dimensions. We discretize the time evolution, convection, reaction, and sources terms on a given grid, which can be nonmatching and can contain nonconvex element...

Eymard, R.; Hilhorst, D.; Vohralik, M.

133

Stability analysis of single-phase thermosyphon loops by finite difference numerical methods  

International Nuclear Information System (INIS)

[en] In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs

1998-01-01

134

A new discretization scheme for the finite volume method, applied to the scalar wave propagation; Um novo esquema de discretizacao para o metodo de volumes finitos aplicado a propagacao de onda escalar  

Energy Technology Data Exchange (ETDEWEB)

The aim of this work was to present a new discretization scheme, to the finite volume method, applied to scalar wave propagation problem. The new scheme is compared to the traditional Central Difference scheme and Flux-Spline scheme by means of the two test problems. The results obtained showed that under the same grid, the new scheme provide a better approximation of the reference solutions, than the others two schemes. (author)

Santorio, Carlos Alexandre [Espirito Santo Univ., Vitoria, ES (Brazil). Programa de Pos-graduacao em Engenharia Mecanica]. E-mail: casantorio@terra.com.br; Oliveira, Paulo Cesar [Espirito Santo Univ., Alegre, ES (Brazil). Centro de Ciencias Agrarias. Dept. de Engenharia Rural]. E-mail: pacol@npd.ufes.br

2003-07-01

135

Optimization of plate thickness using finite different method  

International Nuclear Information System (INIS)

A finite difference numerical method of solving biharmonic equation is presented. The biharmonic equation and plate theory are used to solve a classical engineering problem involving the optimisation of plate thickness to minimise deformations and stresses in the plate. Matlab routines were developed to solve the resulting finite difference equations. The results from the finite difference method were compared with results obtained using ANSYS finite element formulation. Using the finite difference method, a plate thickness of 277 mm was obtained with a mesh size of 3 m and a plate thickness of 271 mm was obtained with a mesh size of 1 m., whiles using ANSYS finite element formulation, a plate thickness of 270 mm was obtained. The significance of these results is that, by using off-the-shelf general application tool and without resorting to expensive dedicated application tool, simple engineering problems could be solved. (au)

2008-01-01

136

Finite-difference solutions of the 3-D eikonal equation  

Energy Technology Data Exchange (ETDEWEB)

Prestack Kirchhoff depth migration requires the computation of traveltimes from surface source and receiver locations to subsurface image locations. In 3-D problems, computational efficiency becomes important. Finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference method for computing the first arrival traveltime by solving the eikonal equation has been developed in Cartesian coordinates. The method, which is unconditionally stable and computationally efficient, can handle instabilities due to caustics and provide information about head waves. The comparison of finite-difference solutions of the acoustic wave equation with the traveltime solutions from the eikonal equation in various structure models demonstrate that the method developed here can provide correct first arrival traveltime information even in areas of complex velocity structure.

Fei, Tong; Fehler, M.C.; Hildebrand, S.T. [Los Alamos National Lab., NM (United States)

1995-12-31

137

Hidden sl$_{2}$-algebra of finite-difference equations  

CERN Document Server

The connection between polynomial solutions of finite-difference equations and finite-dimensional representations of the sl_2-algebra is established. (Talk presented at the Wigner Symposium, Guadalajara, Mexico, August 1995; to be published in Proceedings)

Smirnov, Yu F; Smirnov, Yuri; Turbiner, Alexander

1995-01-01

138

Gain from a mixed finite-difference formulation for three-dimensional diffusion-theory neutronics  

Energy Technology Data Exchange (ETDEWEB)

The advantage of a mixed differencing scheme for representing the diffusion theory approximation to neutron transport in three-dimensional triangular-Z geometry is demonstrated for a fast reactor. Most of the early codes employed the mesh edge difference formulation as is used in the German D3E code. A mesh centered formulation was chosen for use on a routine basis with mesh points located at the centers of the finite difference elements instead of at the corners where the internal material interfaces intersect, the VENURE code being the latest to use this scheme. Results are presented for a fast reactor core problem modeling hexagonal assemblies.

Vondy, D.R.; Fowler, T.B.

1981-01-01

139

Gain from a mixed finite-difference formulation for three-dimensional diffusion-theory neutronics  

International Nuclear Information System (INIS)

The advantage of a mixed differencing scheme for representing the diffusion theory approximation to neutron transport in three-dimensional triangular-Z geometry is demonstrated for a fast reactor. Most of the early codes employed the mesh edge difference formulation as is used in the German D3E code. A mesh centered formulation was chosen for use on a routine basis with mesh points located at the centers of the finite difference elements instead of at the corners where the internal material interfaces intersect, the VENURE code being the latest to use this scheme. Results are presented for a fast reactor core problem modeling hexagonal assemblies

1981-12-04

140

Generalized Alternating-Direction Implicit Finite-Difference Time-Domain Method in Curvilinear Coordinate System  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is carried out by numerical experiments. The application in the modelling of the Electromagnetic Bandgap (EBG) structure has further demonstrated the advantage of the proposed method.

Wei Song; Yang Hao

2010-01-01

 
 
 
 
141

Finite difference solution for multigroup transport equation in r-z geometry by spherical harmonics method  

Energy Technology Data Exchange (ETDEWEB)

In the r-z geometry, a second order differential equation for spherical harmonics moments is derived, and for simplicity, it includes only higher order of scattering within a group. Using the finite difference approximation for this spherical harmonics equation, a multi-group transport code of a general order of approximation is developed. Sample calculations are carried out for external source problem in pure absorber, Gelberd's benchmark shielding problem of two groups, four groups criticality problem of fast reactor, and the results were compared with exact solution based on analytic method or with those obtained by discrete-ordinates method. It is shown that the present method gives more accurate results than the discrete-ordinates method in the reasonable computation time for shielding problems of the strong absorber because of the disappearance of the ray effect, although this spherical harmonics code requires more computer memory than the discrete-ordinates method. (author).

Yamamoto, Akio; Kobayashi, Keisuke (Kyoto Univ. (Japan). Faculty of Engineering)

1989-06-01

142

Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation  

Science.gov (United States)

In this paper, we propose a new conservative hybrid finite element-finite difference method for the Vlasov equation. The proposed methodology uses Strang splitting to decouple the nonlinear high dimensional Vlasov equation into two lower dimensional equations, which describe spatial advection and velocity acceleration/deceleration processes respectively. We then propose to use a semi-Lagrangian (SL) discontinuous Galerkin (DG) scheme (or Eulerian Runge-Kutta (RK) DG scheme with local time stepping) for spatial advection, and use a SL finite difference WENO for velocity acceleration/deceleration. Such hybrid method takes the advantage of DG scheme in its compactness and its ability in handling complicated spatial geometry; while takes the advantage of the WENO scheme in its robustness in resolving filamentation solution structures of the Vlasov equation. The proposed highly accurate methodology enjoys great computational efficiency, as it allows one to use relatively coarse phase space mesh due to the high order nature of the scheme. At the same time, the time step can be taken to be extra large in the SL framework. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and classical plasma problems, such as Landau damping and the two stream instability. Although we only tested 1D1V examples, the proposed method has the potential to be extended to problems with high spatial dimensions and complicated geometry. This constitutes our future research work.

Guo, Wei; Qiu, Jing-Mei

2013-02-01

143

A time domain finite-difference technique for oblique incidence of antiplane waves in heterogeneous dissipative media  

Directory of Open Access Journals (Sweden)

Full Text Available This paper deals with the antiplane wave propagation in a 2D heterogeneous dissipative medium with complex layer interfaces and irregular topography. The initial boundary value problem which represents the viscoelastic dynamics driving 2D antiplane wave propagation is formulated. The discretization scheme is based on the finite-difference technique. Our approach presents some innovative features. First, the introduction of the forcing term into the equation of motion offers the advantage of an easier handling of different inputs such as general functions of spatial coordinates and time. Second, in the case of a straight-line source, the symmetry of the incident plane wave allows us to solve the problem of oblique incidence simply by rotating the 2D model. This artifice reduces the oblique incidence to the vertical one. Third, the conventional rheological model of the generalized Maxwell body has been extended to include the stress-free boundary condition. For this reason we solve explicitly the stress-free boundary condition, not following the most popular technique called vacuum formalism. Finally, our numerical code has been constructed to model the seismic response of complex geological structures: real geological interfaces are automatically digitized and easily introduced in the input model. Three numerical applications are discussed. To validate our numerical model, the first test compares the results of our code with others shown in the literature. The second application rotates the input model to simulate the oblique incidence. The third one deals with a real high-complexity 2D geological structure.

A. Caserta

1998-01-01

144

Discrete conservation laws and the convergence of long time simulations of the mkdv equation  

Science.gov (United States)

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

145

Discrete spacetime and Lorentz invariance  

International Nuclear Information System (INIS)

The idea of discrete spacetime originates from the fundamental length of Heisenberg and the elementary domain of Yukawa. The concept of discrete spacetime is explained in brief. To transfer from continuous spacetime to discrete spacetime the differentials appearing in a theory should be replaced by finite differences. The quantum field theory on discrete spacetime is briefly reviewed. Finally it becomes clear how to conform the discrete spacetime to the special theory of relativity. (orig.)

1989-01-01

146

Minimal positive stencils in meshfree finite difference methods for the Poisson equation  

Science.gov (United States)

Meshfree finite difference methods for the Poisson equation approximate the Laplace operator on a point cloud. Desirable are positive stencils, i.e. all neighbor entries are of the same sign. Classical least squares approaches yield large stencils that are in general not positive. We present an approach that yields stencils of minimal size, which are positive. We provide conditions on the point cloud geometry, so that positive stencils always exist. The new discretization method is compared to least squares approaches in terms of accuracy and computational performance.

Seibold, B.

2008-12-01

147

Solution of transient transport equation by combining the LTSN and finite difference methods  

International Nuclear Information System (INIS)

[en] In this work, we present an approach to solve the time-dependent linear transport equation combining the LTSN and Finite Difference methods. The idea of this method consists of the discretization of the time variable of the angular flux using a simple Backward Difference Finite Method, transforming the transient problem at a set of stationary one-dimensional linear transport problems.The approximation SN of these problems is solved by the application of the LTSN method. Numerical results are presented and compared with the literature. (author)

2000-01-01

148

FINITE DIFFERENCE SIMULATION OF LOW CARBON STEEL MANUAL ARC WELDING  

Directory of Open Access Journals (Sweden)

Full Text Available This study discusses the evaluation and simulation of angular distortion in welding joints, and the ways of controlling and treating them, while welding plates of (low carbon steel) type (A-283-Gr-C) through using shielded metal arc welding. The value of this distortion is measured experimentally and the results are compared with the suggested finite difference method computer program. Time dependent temperature distributions are obtained using finite difference method. This distribution is used to obtain the shrinkage that causes the distortions accompanied with structural forces that act to modify these distortions. Results are compared with simple empirical models and experimental results. Different thickness of plates and welding parameters is manifested to illustrate its effect on angular distortions. Results revealed the more accurate results of finite difference method that match experimental results in comparison with empirical formulas. Welding parameters include number of passes, current, electrode type and geometry of the welding process.

Moneer H Al-Sa'ady; Mudar A Abdulsattar; Laith S Al-Khafagy

2011-01-01

149

Holistic finite differences ensure fidelity to Burger's equation  

CERN Multimedia

I analyse a generalised Burger's equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The trick to the application of centre manifold theory is to divide the physical domain into small elements by introducing insulating internal boundaries which are later removed. Burger's equation is used as an example to show how the concepts work in practise. The resulting finite difference models are shown to be significantly more accurate than conventional discretisations, particularly for highly nonlinear dynamics. This centre manifold approach treats the dynamical equations as a whole, not just as the sum of separate terms---it is holistic. The techniques developed here may be used to accurately model the nonlinear evolution of quite general spatio-temporal dynamical systems.

Roberts, A J

1999-01-01

150

A holistic finite difference approach models linear dynamics consistently  

CERN Multimedia

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of finite difference models under nonlinear and other perturbations on grids with finite spacing. For example, the advection-diffusion equation is found to be stably modelled for all advection speeds and all grid spacing. The theorems establish an extremely good form for the artificial internal boundary conditions that need to be introduced to apply centre manifold theory. When numerically solving nonlinear partial differential equations, this approach can be used to derive systematically finite difference models which automatically have excellent characteristics. Their good performance for finite grid spacing implies that fewer grid points may be used and consequently there will be less difficulties with stiff rapidly decaying modes in continuum problems.

Roberts, A J

2000-01-01

151

Compact finite difference method for American option pricing  

Science.gov (United States)

A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h[greater-or-equal, slanted]0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.

Zhao, Jichao; Davison, Matt; Corless, Robert M.

2007-09-01

152

A model-based fault-detection and prediction scheme for nonlinear multivariable discrete-time systems with asymptotic stability guarantees.  

UK PubMed Central (United Kingdom)

In this paper, a novel, unified model-based fault-detection and prediction (FDP) scheme is developed for nonlinear multiple-input-multiple-output (MIMO) discrete-time systems. The proposed scheme addresses both state and output faults by considering separate time profiles. The faults, which could be incipient or abrupt, are modeled using input and output signals of the system. The fault-detection (FD) scheme comprises online approximator in discrete time (OLAD) with a robust adaptive term. An output residual is generated by comparing the FD estimator output with that of the measured system output. A fault is detected when this output residual exceeds a predefined threshold. Upon detecting the fault, the robust adaptive terms and the OLADs are initiated wherein the OLAD approximates the unknown fault dynamics online while the robust adaptive terms help in ensuring asymptotic stability of the FD design. Using the OLAD outputs, a fault diagnosis scheme is introduced. A stable parameter update law is developed not only to tune the OLAD parameters but also to estimate the time to failure (TTF), which is considered as a first step for prognostics. The asymptotic stability of the FDP scheme enhances the detection and TTF accuracy. The effectiveness of the proposed approach is demonstrated using a fourth-order MIMO satellite system.

Thumati BT; Jagannathan S

2010-03-01

153

Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation  

Energy Technology Data Exchange (ETDEWEB)

Wave propagation phenomena are important in many DOE applications such as nuclear explosion monitoring, geophysical exploration, estimating ground motion hazards and damage due to earthquakes, non-destructive testing, underground facilities detection, and acoustic noise propagation. There are also future applications that would benefit from simulating wave propagation, such as geothermal energy applications and monitoring sites for carbon storage via seismic reflection techniques. In acoustics and seismology, it is of great interest to increase the frequency bandwidth in simulations. In seismic exploration, greater frequency resolution enables shorter wave lengths to be included in the simulations, allowing for better resolution in the seismic imaging. In nuclear explosion monitoring, higher frequency seismic waves are essential for accurate discrimination between explosions and earthquakes. When simulating earthquake induced motion of large structures, such as nuclear power plants or dams, increased frequency resolution is essential for realistic damage predictions. Another example is simulations of micro-seismic activity near geothermal energy plants. Here, hydro-fracturing induces many small earthquakes and the time scale of each event is proportional to the square root of the moment magnitude. As a result, the motion is dominated by higher frequencies for smaller seismic events. The above wave propagation problems are all governed by systems of hyperbolic partial differential equations in second order differential form, i.e., they contain second order partial derivatives of the dependent variables. Our general research theme in this project has been to develop numerical methods that directly discretize the wave equations in second order differential form. The obvious advantage of working with hyperbolic systems in second order differential form, as opposed to rewriting them as first order hyperbolic systems, is that the number of differential equations in the second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a low order method.

Petersson, N A; Sjogreen, B

2012-03-26

154

Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation  

International Nuclear Information System (INIS)

Wave propagation phenomena are important in many DOE applications such as nuclear explosion monitoring, geophysical exploration, estimating ground motion hazards and damage due to earthquakes, non-destructive testing, underground facilities detection, and acoustic noise propagation. There are also future applications that would benefit from simulating wave propagation, such as geothermal energy applications and monitoring sites for carbon storage via seismic reflection techniques. In acoustics and seismology, it is of great interest to increase the frequency bandwidth in simulations. In seismic exploration, greater frequency resolution enables shorter wave lengths to be included in the simulations, allowing for better resolution in the seismic imaging. In nuclear explosion monitoring, higher frequency seismic waves are essential for accurate discrimination between explosions and earthquakes. When simulating earthquake induced motion of large structures, such as nuclear power plants or dams, increased frequency resolution is essential for realistic damage predictions. Another example is simulations of micro-seismic activity near geothermal energy plants. Here, hydro-fracturing induces many small earthquakes and the time scale of each event is proportional to the square root of the moment magnitude. As a result, the motion is dominated by higher frequencies for smaller seismic events. The above wave propagation problems are all governed by systems of hyperbolic partial differential equations in second order differential form, i.e., they contain second order partial derivatives of the dependent variables. Our general research theme in this project has been to develop numerical methods that directly discretize the wave equations in second order differential form. The obvious advantage of working with hyperbolic systems in second order differential form, as opposed to rewriting them as first order hyperbolic systems, is that the number of differential equations in the second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a low order method.

2012-01-01

155

New Finite Difference Domain Decomposition Algorithms for Two-Dimensional Heat Equation  

Directory of Open Access Journals (Sweden)

Full Text Available The domain decomposition scheme is a high efficient and useful method which is widely used in the field of the finite difference parallel computing on parabolic equation. The natural method of parallel solution of the partial differential equation is to divide the solution area into several sub-regions and then independently calculate the problem of each sub-region. To solve the two-dimensional heat equation on parallel computers, we present new domain decomposition algorithms wherein the space domain is divided into two independent sub-regions along with x-axis or divided into four independent sub-regions along with the x-axis and y-axis. The values of the interface points between sub-domains are calculated by Du Fort-Frankel scheme. The values of the interior points are solved by the fully implicit scheme.

Yuanfeng Jin; Lijie Zhao; Jingyuan Li; Tinghuai Ma

2010-01-01

156

Finite Difference Weights Using The Modified Lagrange Interpolant  

CERN Multimedia

Let $z_{1},z_{2},\\ldots,z_{N}$ be a sequence of distinct grid points. A finite difference formula approximates the $m$-th derivative $f^{(m)}(0)$ as $\\sum w_{i}f\\left(z_{i}\\right)$, with $w_{i}$ being the weights. We give two algorithms for finding the weights $w_{i}$ either of which is an improvement of an algorithm of Fornberg (\\emph{Mathematics of Computation}, vol. 51 (1988), p. 699-706). The first algorithm, which we call the direct method, uses fewer arithmetic operations than that of Fornberg by a factor of $4/(5m+5)$. The order of accuracy of the finite difference formula for $f^{(m)}(0)$ with grid points $hz_{i}$, $1\\leq i\\leq N$, is typically $\\mathcal{O}\\left(h^{N-m}\\right)$. However, the most commonly used finite difference formulas have an order of accuracy that is higher than the typical. For instance, the centered difference approximation $\\left(f(h)-2f(0)+f(-h)\\right)/h^{2}$ to $f''(0)$ has an order of accuracy equal to $2$ not $1$ . Even unsymmetric finite difference formulas can have such bo...

Sadiq, Burhan

2011-01-01

157

Finite difference method for thermally expandable fluid transients  

International Nuclear Information System (INIS)

[en] In this paper we discuss equations that define a thermally expandable fluid transient. We then present a set of finite difference equations for the numerical solution of such transients, discuss their solvability, and investigate certain aspects involving the convergence of the numerical solution. Finally, we apply these ideas to a problem involving flow in the preheater section of a steam generator

1977-01-01

158

A FINITE DIFFERENCE SOLUTION OF NUCLEAR REACTOR KINETICS EQUATIONS  

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference first order integration formula for a set of ordinary differential equations has been developed. It has been shown that this formula gives better estimation of an error in the meaning of an Euclidean norm than those already known. The proposed method has been illustrated by examples. A special attention has been paid to nuclear reactor kinetics equations.

Micha? Podowski

1972-01-01

159

Finite difference time domain modelling of particle accelerators  

Energy Technology Data Exchange (ETDEWEB)

Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs.

Jurgens, T.G.; Harfoush, F.A.

1989-03-01

160

Grid cell distortion and MODFLOW's integrated finite-difference numerical solution.  

Science.gov (United States)

The ground water flow model MODFLOW inherently implements a nongeneralized integrated finite-difference (IFD) numerical scheme. The IFD numerical scheme allows for construction of finite-difference model grids with curvilinear (piecewise linear) rows. The resulting grid comprises model cells in the shape of trapezoids and is distorted in comparison to a traditional MODFLOW finite-difference grid. A version of MODFLOW-88 (herein referred to as MODFLOW IFD) with the code adapted to make the one-dimensional DELR and DELC arrays two dimensional, so that equivalent conductance between distorted grid cells can be calculated, is described. MODFLOW IFD is used to inspect the sensitivity of the numerical head and velocity solutions to the level of distortion in trapezoidal grid cells within a converging radial flow domain. A test problem designed for the analysis implements a grid oriented such that flow is parallel to columns with converging widths. The sensitivity analysis demonstrates MODFLOW IFD's capacity to numerically derive a head solution and resulting intercell volumetric flow when the internal calculation of equivalent conductance accounts for the distortion of the grid cells. The sensitivity of the velocity solution to grid cell distortion indicates criteria for distorted grid design. In the radial flow test problem described, the numerical head solution is not sensitive to grid cell distortion. The accuracy of the velocity solution is sensitive to cell distortion with error MODFLOW-88's inherent IFD numerical scheme and the test problem results imply that more recent versions of MODFLOW 2000, with minor modifications, have the potential to make use of a curvilinear grid. PMID:17087751

Romero, Dave M; Silver, Steven E

 
 
 
 
161

Esquema de discretização Flux-Spline aplicado à secagem, em meio poroso capilar/ Flux-Spline discretization scheme applied to drying in capillary porous media  

Scientific Electronic Library Online (English)

Full Text Available Abstract in portuguese Este trabalho foi desenvolvido com o objetivo de se apresentar a aplicação de um esquema de discretização mais eficiente para volumes finitos, denominado Flux-Spline utilizando-se, para tal, de dois casos de transporte difusivo de umidade e calor, através de um meio poroso capilar. Os resultados da solução numérica do sistema de equações formado pelas equações de Luikov mostram desempenho adequado do esquema para este tipo de problema, quando comparado ao tradicional esquema de diferença central e ao método da transformada integral. Abstract in english This study was conducted with the objective to present a more efficient discretization scheme to finite volumes method called Flux-Spline, utilising for the purpose two cases of pure diffusion in capillary porous media. The results of numerical simulation of the equations system formed by Luikov equations showed a good performance of the scheme in comparison to the Central Difference Scheme and Generalised Integral Transform Technique method.

Oliveira, Paulo C.; Lima, José L.

2003-04-01

162

The effect of various vertical discretization schemes and horizontal diffusion parameterization on the performance of a 3-D ocean model: the Black Sea case study  

Directory of Open Access Journals (Sweden)

Full Text Available Results of a sensitivity study are presented from various configurations of the NEMO ocean model in the Black Sea. The standard choices of vertical discretization, viz. z levels, s coordinates and enveloped s coordinates, all show their limitations in the areas of complex topography. Two new hybrid vertical coordinate schemes are presented: the "s-on-top-of-z" and its enveloped version. The hybrid grids use s coordinates or enveloped s coordinates in the upper layer, from the sea surface to the depth of the shelf break, and z-coordinates are set below this level. The study is carried out for a number of idealised and real world settings. The hybrid schemes help reduce errors generated by the standard schemes in the areas of steep topography. Results of sensitivity tests with various horizontal diffusion formulations are used to identify the optimum value of Smagorinsky diffusivity coefficient to best represent the mesoscale activity.

G. Shapiro; M. Luneva; J. Pickering; D. Storkey

2013-01-01

163

Discrete conservation laws and the convergence of long time simulations of the mKdV equation  

CERN Multimedia

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Gorria, Carlos; Vega, Luis

2011-01-01

164

Finite-difference modeling of seismological problems in magnitude estimation using body waves, surface waves, and seismic source imaging. Final report, 11 February 1985-10 February 1987  

Energy Technology Data Exchange (ETDEWEB)

Contents include: boundary conditions for arbitrary polygonal topography in a 2-d elastic finite-difference scheme for seismogram generation; teleseismic spectral and temporal m/sub 0/ and psi/sub infinity/ estimates for four French explosions in southern Sahara; scattering from near-source topography: teleseismic observations and numerical 2-d explosive line-source simulations; effects of local geologic structure on Yucca Flats, NTS, explosion waveforms: 2-dimensional linear finite-difference simulations; and finite-difference simulations of Rayleigh-wave scattering by 2-d rough topography.

McLaughlin, K.L.; Der, Z.A.; Jih, R.S.; Lees, A.C.; Anderson, L.M.

1987-03-01

165

3D electromagnetic modeling using staggered finite differences  

Energy Technology Data Exchange (ETDEWEB)

The method of finite differences has been employed to solve a variety of 3D electromagnetic (EM) forward problems arising in geophysical applications. Specific sources considered include dipolar and magnetotelluric (MT) field excitation in the frequency domain. In the forward problem, the EM fields are simulated using a vector Helmholtz equation for the electric field, which are approximated using finite differences on a staggered grid. To obtain the fields, a complex-symmetric matrix system of equations is assembled and iteratively solved using the quasi minimum method (QMR) method. Perfectly matched layer (PML) absorbing boundary conditions are included in the solution and are necessary to accurately simulate fields in propagation regime (frequencies > 10 MHZ). For frequencies approaching the static limit (< 10 KHz), the solution also includes a static-divergence correction, which is necessary to accurately simulate MT source fields and can be used to accelerate convergence for the dipolar source problem.

Newman, G.A.; Alumbaugh, D.L.

1997-06-01

166

Holistic projection of initial conditions onto a finite difference approximation  

CERN Document Server

Modern dynamical systems theory has previously had little to say about finite difference and finite element approximations of partial differential equations (Archilla, 1998). However, recently I have shown one way that centre manifold theory may be used to create and support the spatial discretisation of \\pde{}s such as Burgers' equation (Roberts, 1998a) and the Kuramoto-Sivashinsky equation (MacKenzie, 2000). In this paper the geometric view of a centre manifold is used to provide correct initial conditions for numerical discretisations (Roberts, 1997). The derived projection of initial conditions follows from the physical processes expressed in the PDEs and so is appropriately conservative. This rational approach increases the accuracy of forecasts made with finite difference models.

Roberts, A J

2001-01-01

167

Finite difference approach for modeling multispecies transport in porous media  

Directory of Open Access Journals (Sweden)

Full Text Available An alternative approach to the decomposition method for solving multispecies transport in porous media, coupled with first-order reactions has been proposed. The numerical solution is based on implicit finite difference method. The task of decoupling the coupled partial differential equations has been overcome in this method. The proposed approach is very much advantageous because of its simplicity and also can be adopted in situations where non linear processes are coupled with multi-species transport problems.

N.Natarajan; G. Suresh Kumar

2010-01-01

168

A 3-D A.D.I. finite difference modeling of acoustic wave equation  

Energy Technology Data Exchange (ETDEWEB)

The purpose of this study is to investigate the wave propagation in three dimensional acoustic media with the use of A.D.I. (Alternating Direction Implicit) finite-difference scheme of Lees operator splitting. The internal boundary condition is automatically satisfied in the present heterogeneous formulation in which the parameters can be given at each nodal point. Both Reynolds and Cerjan transparent boundary conditions are used for the treatment of the artificial external boundary. The differentiation operators are approximated to the fourth order in space and time. Three dimensional refraction, reflection, and diffraction events are clearly identified in the snapshots associated with the models of infinite half space, horizontal and sloping interfaces, and faults. Particularly, they conform with the two dimensional L.O.D.(Locally One Dimensional) implicit finite-difference modeling by Mufti. It is therefore concluded that the present A.D.I. scheme of Lees operator splitting can be an effective means of three dimensional numerical modeling of acoustic waves. (author). 12 refs., 15 figs.

Oh, Young Chul; Cho, Dong Heng [Inha Univ., Inchon (Korea, Republic of)

1995-06-01

169

COMESH - A corner mesh finite difference code to solve multigroup diffusion equations in multidimensions  

International Nuclear Information System (INIS)

A code called COMESH based on corner mesh finite difference scheme has been developed to solve multigroup diffusion theory equations. One can solve 1-D, 2-D or 3-D problems in Cartesian geometry and 1-D (r) or 2-D (r-z) problem in cylindrical geometry. On external boundary one can use either homogeneous Dirichlet (?-specified) or Neumann (?? specified) type boundary conditions or a linear combination of the two. Internal boundaries for control absorber simulations are also tackled by COMESH. Many an acceleration schemes like successive line over-relaxation, two parameter Chebyschev acceleration for fission source, generalised coarse mesh rebalancing etc., render the code COMESH a very fast one for estimating eigenvalue and flux/power profiles in any type of reactor core configuration. 6 refs. (author).

1987-01-01

170

Seismic imaging using finite-differences and parallel computers  

Energy Technology Data Exchange (ETDEWEB)

A key to reducing the risks and costs of associated with oil and gas exploration is the fast, accurate imaging of complex geologies, such as salt domes in the Gulf of Mexico and overthrust regions in US onshore regions. Prestack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar wave equation using finite differences. As part of an ongoing ACTI project funded by the US Department of Energy, a finite difference, 3-D prestack, depth migration code has been developed. The goal of this work is to demonstrate that massively parallel computers can be used efficiently for seismic imaging, and that sufficient computing power exists (or soon will exist) to make finite difference, prestack, depth migration practical for oil and gas exploration. Several problems had to be addressed to get an efficient code for the Intel Paragon. These include efficient I/O, efficient parallel tridiagonal solves, and high single-node performance. Furthermore, to provide portable code the author has been restricted to the use of high-level programming languages (C and Fortran) and interprocessor communications using MPI. He has been using the SUNMOS operating system, which has affected many of his programming decisions. He will present images created from two verification datasets (the Marmousi Model and the SEG/EAEG 3D Salt Model). Also, he will show recent images from real datasets, and point out locations of improved imaging. Finally, he will discuss areas of current research which will hopefully improve the image quality and reduce computational costs.

Ober, C.C. [Sandia National Labs., Albuquerque, NM (United States)

1997-12-31

171

Finite difference program for calculating hydride bed wall temperature profiles  

International Nuclear Information System (INIS)

A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis

1992-01-01

172

Finite-difference method of incompressible flows with rotation and moving boundary in a nonstaggered grid  

Energy Technology Data Exchange (ETDEWEB)

In this article a finite-difference solution method for simulating incompressible two-dimensional and axisymmetric flow problems with rotation and moving boundary is developed. In this method conservative governing equations are approximated by a vertex-based control-volume discretization in a nonstaggered grid. The solutions for velocity field and pressure are coupled in a similar manner to the SIMPLE family. Moving boundaries are solved step by step from the kinematic boundary condition, and the changing flow domain is fitted by a curvilinear coordinate system with updated grid. To avoid unrealistic distributions of velocity components and pressure, the Rhie-Chow interpolation is employed and the boundary value of pressure on solid surfaces is determined from the local mass conservation. The validation is carried out in simulating two-dimensional lid-driven square cavity flows and rotating coaxial disk flows with and without free surfaces.

Wu, J.; Rath, H.J. (Univ. of Bremen (Germany). Center of Applied Space Technology and Microgravity)

1994-09-01

173

Solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post-processing  

Energy Technology Data Exchange (ETDEWEB)

A coordinate transformation approach is described that enables pseudospectral methods to be applied efficiently to unsteady differential problems with steep solutions. The work is an extension of a method presented by Mulholland, Huang, and Sloan for the adaptive pseudospectral solution of steady problems. A coarse grid is generated by a moving mesh finite difference method that is based on equidistribution, and this grid is used to construct a time-dependent coordinate transformation. A sequence of spatial transformations may be generated at discrete points in time, or a single transformation may be generated as a continuous function of space and time. The differential problem is transformed by the coordinate transformation and then solved using a method that combines pseudospectral discretisation in space with a suitable integrator in time. Numerical results are presented for unsteady problems in one space dimension. 18 refs., 8 figs., 12 tabs.

Mulholland, L.S.; Qiu, Y.; Sloan, D.M. [Univ. of Strathclyde, Glasgow (United Kingdom)

1997-03-01

174

Finite difference analysis of curved deep beams on Winkler foundation  

Directory of Open Access Journals (Sweden)

Full Text Available This research deals with the linear elastic behavior of curved deep beams resting on elastic foundations with both compressional and frictional resistances. Timoshenko’s deep beam theory is extended to include the effect of curvature and the externally distributed moments under static conditions. As an application to the distributed moment generations, the problems of deep beams resting on elastic foundations with both compressional and frictional restraints have been investigated in detail. The finite difference method was used to represent curved deep beams and the results were compared with other methods to check the accuracy of the developed analysis. Several important parameters are incorporated in the analysis, namely, the vertical subgrade reaction, horizontal subgrade reaction, beam width, and also the effect of beam thickness to radius ratio on the deflections, bending moments, and shear forces. The computer program (CDBFDA) (Curved Deep Beam Finite Difference Analysis Program) coded in Fortran-77 for the analysis of curved deep beams on elastic foundations was formed. The results from this method are compared with other methods exact and numerical and check the accuracy of the solutions. Good agreements are found, the average percentages of difference for deflections and moments are 5.3% and 7.3%, respectively, which indicate the efficiency of the adopted method for analysis.

Adel A. Al-Azzawi; Ali S. Shaker

2011-01-01

175

Modeling of Surface Waves in a Fluid Saturated Poro-Elastic Medium under Initial Stress Using Time-Space Domain Higher Order Finite Difference Method  

Directory of Open Access Journals (Sweden)

Full Text Available In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).

Anjana P. Ghorai; R. Tiwary

2013-01-01

176

Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge  

International Nuclear Information System (INIS)

This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

1996-01-01

177

A coarse-mesh nodal method-diffusive-mesh finite difference method  

International Nuclear Information System (INIS)

[en] Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper

1994-01-01

178

Diagonally Staggered Grid for Elastodynamic Analysis Using the Finite-Difference Time-Domain Method  

Science.gov (United States)

A new diagonally staggered grid configuration is proposed for the finite-difference time-domain analysis of elastic wave fields. The structure of the grid is the same as a standard staggered grid, but the diagonals of the standard grid lie parallel to the coordinate axes of the field of analysis in this new configuration. Adopting this grid configuration allows a natural implementation of antisymmetric stress boundary conditions, as is required when implementing free boundaries for example. In implementing these boundary conditions no virtual lattice around the analysis region is required, and so free surfaces with complex boundary shapes are easily treated. To date, free boundaries have usually been treated using the zero-stress formulation (ZSF), the vacuum formulation (VCF), etc. The ZSF is relatively precise, but requires the creation of virtual grids in the vacuum region. On the other hand, the VCF does not require the use of virtual grids, but accuracy and stability are reduced relative to the ZSF. Also, other methods of free boundary implementation have some demerits. The validity of the diagonally staggered grid is confirmed by comparing the calculation results of the present scheme with those derived by existing finite-difference methods for a model test problem.

Sato, Masahiro

2007-07-01

179

Towards optimal DRP scheme for linear advection  

CERN Document Server

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building a new DRP scheme in the same time.

David, Claire

2008-01-01

180

Introduction of Hypermatrix and Operator Notation into a Discrete Mathematics Simulation Model of Malignant Tumour Response to Therapeutic Schemes In Vivo. Some Operator Properties  

Directory of Open Access Journals (Sweden)

Full Text Available The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.

Georgios S. Stamatakos; Dimitra D. Dionysiou

2009-01-01

 
 
 
 
181

The effect of various vertical discretization schemes and horizontal diffusion parameterisation on the performance of a 3-D ocean model: the Black Sea case study  

Directory of Open Access Journals (Sweden)

Full Text Available Results of a sensitivity study are presented from various configurations of the NEMO ocean model in the Black Sea. The standard choices of vertical discretization, viz. z-levels, s-coordinates and enveloped s-coordinates, all show their limitations in the areas of complex topography. Two new hydrid vertical coordinate schemes are presented: the "s-on-top-of-z" and its enveloped version. The hybrid grids use s-coordinates or enveloped s-coordinates in the upper layer, from the sea surface to the depth of the shelf break, and z-coordinates are set below this level. The study is carried out for a number of idealised and real world settings. The hybrid schemes help reduce errors generated by the standard schemes in the areas of steep topography. Results of sensitivity tests with various horizontal diffusion formulations show that the mesoscale activity is better captured with a significantly smaller value of Smagorinsky viscosity coefficient than it was previously suggested.

G. Shapiro; M. Luneva; J. Pickering; D. Storkey

2012-01-01

182

Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation  

CERN Multimedia

In this paper, a fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. We prove that our scheme is unconditional stable and $L^2$ error estimate for the linear case with the convergence rate $O(h^{k+1}+(\\Delta t)^2+(\\Delta t)^\\frac{\\alpha}{2}h^{k+1/2})$. Numerical examples are presented to show the efficiency and accuracy of our scheme.

Wei, Leilei

2012-01-01

183

Visualization of elastic wavefields computed with a finite difference code  

Energy Technology Data Exchange (ETDEWEB)

The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.

Larsen, S. [Lawrence Livermore National Lab., CA (United States); Harris, D.

1994-11-15

184

Finite-difference modeling of commercial aircraft using TSAR  

Energy Technology Data Exchange (ETDEWEB)

Future aircraft may have systems controlled by fiber optic cables, to reduce susceptibility to electromagnetic interference. However, the digital systems associated with the fiber optic network could still experience upset due to powerful radio stations, radars, and other electromagnetic sources, with potentially serious consequences. We are modeling the electromagnetic behavior of commercial transport aircraft in support of the NASA Fly-by-Light/Power-by-Wire program, using the TSAR finite-difference time-domain code initially developed for the military. By comparing results obtained from TSAR with data taken on a Boeing 757 at the Air Force Phillips Lab., we hope to show that FDTD codes can serve as an important tool in the design and certification of U.S. commercial aircraft, helping American companies to produce safe, reliable air transportation.

Pennock, S.T.; Poggio, A.J.

1994-11-15

185

Seven-point finite difference method for improved grid orientation performance in pattern steam floods  

Energy Technology Data Exchange (ETDEWEB)

This paper presents a novel seven-point finite difference approximation for simulations of adverse mobility ratio displacements. The method is based on partitioning of a two-dimensional flow domain into regular or nearly regular hexagons. The accuracy of the method for pattern steam floods of heavy oil reservoirs is compared to five- and nine-point approximations. For five-spot floods, the accuracy of the seven-point method is good and comparable to that of the nine-point scheme. For seven-spot floods, the seven-point method provides good numerical accuracy at substantially less computational work than five- or nine-point methods. For nine-spot floods, only the nine-point method is found to give accurate results. 16 references, 10 figures, 3 tables.

Pruess, K.; Bodvarsson, G.S.

1983-08-01

186

GPU Accelerated 2-D Staggered-grid Finite Difference Seismic Modelling  

Directory of Open Access Journals (Sweden)

Full Text Available The staggered-grid finite difference (FD) method demands significantly computational capability and is inefficient for seismic wave modelling in 2-D viscoelastic media on a single PC. To improve computation speedup, a graphic processing units (GPUs) accelerated method was proposed, for modern GPUs have now become ubiquitous in desktop computers and offer an excellent cost-to-performance-ratio parallelism. The geophysical model is decomposed into subdomains for PML absorbing conditions. The vertex and fragment processing are fully used to solve FD schemes in parallel and the latest updated frames are swapped in Framebuffer Object (FBO) attachments as inputs for the next simulation step. The seismic simulation program running on modern PCs provides significant speedup over a CPU implementation, which makes it possible to simulate realtime complex seismic propagation in high resolution of 2048*2048 gridsizes on low-cost PCs.

Zhangang Wang; Suping Peng; Tao Liu

2011-01-01

187

Depropagation and propagation simulation of the acoustic waves by using finite differences operators; Simulacao da propagacao e depropagacao de ondas acusticas usando operadores de diferencas finitas  

Energy Technology Data Exchange (ETDEWEB)

The numerical simulation of shot gathers over a (2D) velocity field, which corresponds to a model of Atlantic continental shelf, at the continental break area, using a typical model of the Brazilian Atlantic coast, suggested by PETROBRAS. The finite difference technique (FD) is used to solve the second derivatives in time and space of the acoustic wave equation, using fourth order operators to solve the spatial derivatives and second order operators to solve the time derivative. It is applied an explicitly scheme to calculate the pressure field values at a future instant. The use of rectangular mesh helps to generate data less noisy, since we can control better the numerical dispersion. The source functions (wavelets), as the first and the second derivatives of the gaussian function, are proper to generate synthetic seismograms with the FD method, because they allow an easy discretization. On the forward modeling, which is the simulation of wave fields, allows to control the stability limit of the method, wherever be the given velocity field, just employing compatible small values of the sample rate. The algorithm developed here, which uses only the FD technique, is able to perform the forward modeling, saving the image times, which can be used latter to perform the retropropagation of the wave field and thus migrate the source-gathers the reverse time extrapolation is able to test the used velocity model, and detect determine errors up to 5% on the used velocity model. (author)

Botelho, Marco A.B.; Santos, Roberto H.M. dos; Silva, Marcelo S. [Universidade Federal da Bahia (UFBA), Salvador, BA (Brazil). Centro de Pesquisa em Geofisica e Geologia

2004-07-01

188

Implementations of the optimal multigrid algorithm for the cell-centered finite difference on equilateral triangular grids  

Energy Technology Data Exchange (ETDEWEB)

A multigrid algorithm for the cell-centered finite difference on equilateral triangular grids for solving second-order elliptic problems is proposed. This finite difference is a four-point star stencil in a two-dimensional domain and a five-point star stencil in a three dimensional domain. According to the authors analysis, the advantages of this finite difference are that it is an O(h{sup 2})-order accurate numerical scheme for both the solution and derivatives on equilateral triangular grids, the structure of the scheme is perhaps the simplest, and its corresponding multigrid algorithm is easily constructed with an optimal convergence rate. They are interested in relaxation of the equilateral triangular grid condition to certain general triangular grids and the application of this multigrid algorithm as a numerically reasonable preconditioner for the lowest-order Raviart-Thomas mixed triangular finite element method. Numerical test results are presented to demonstrate their analytical results and to investigate the applications of this multigrid algorithm on general triangular grids.

Ewing, R.E.; Saevareid, O.; Shen, J. [Texas A& M Univ., College Station, TX (United States)

1994-12-31

189

FLUOMEG: a planar finite difference mesh generator for fluid flow problems with parallel boundaries  

International Nuclear Information System (INIS)

A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables

1980-01-01

190

Three-dimensional finite-difference lattice Boltzmann model and its application to inviscid compressible flows with shock waves  

Science.gov (United States)

In this paper, a three-dimensional (3D) finite-difference lattice Boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double-distribution-function approach. In the model, a density distribution function is adopted to model the flow field, while a total energy distribution function is adopted to model the temperature field. The discrete equilibrium density and total energy distribution functions are derived from the Hermite expansions of the continuous equilibrium distribution functions. The discrete velocity set is obtained by choosing the abscissae of a suitable Gauss-Hermite quadrature with sufficient accuracy. In order to capture the shock waves in compressible flows and improve the numerical accuracy and stability, an implicit-explicit finite-difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations. The model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1D to 3D. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

He, Ya-Ling; Liu, Qing; Li, Qing

2013-10-01

191

Comparison of measured and predicted thermal mixing tests using improved finite difference technique  

Energy Technology Data Exchange (ETDEWEB)

The numerical diffusion introduced by the use of upwind formulations in the finite difference solution of the flow and energy equations for thermal mixing problems (cold water injection after small break LOCA in a PWR) was examined. The relative importance of numerical diffusion in the flow equations, compared to its effect on the energy equation was demonstrated. The flow field equations were solved using both first order accurate upwind, and second order accurate differencing schemes. The energy equation was treated using the conventional upwind and a mass weighted skew upwind scheme. Results presented for a simple test case showed that, for thermal mixing problems, the numerical diffusion was most significant in the energy equation. The numerical diffusion effect in the flow field equations was much less significant. A comparison of predictions using the skew upwind and the conventional upwind with experimental data from a two dimensional thermal mixing text are presented. The use of the skew upwind scheme showed a significant improvement in the accuracy of the steady state predicted temperatures.

Hassan, Y.A. (Babcock and Wilcox Co., Lynchburg, VA (USA). Power Generation Div.); Rice, J.G. (Virginia Univ., Charlottesville (USA). Dept. of Mechanical and Aerospace Engineering); Kim, J.H. (Electric Power Research Inst., Palo Alto, CA (USA). Nuclear Power Div.)

1983-11-01

192

A Robust and Non-Blind Watermarking Scheme for Gray Scale Images Based on the Discrete Wavelet Transform Domain  

Science.gov (United States)

In this paper, a new adaptive watermarking algorithm is proposed for still image based on the wavelet transform. The two major applications for watermarking are protecting copyrights and authenticating photographs. Our robust watermarking [3] [22] is used for copyright protection owners. The main reason for protecting copyrights is to prevent image piracy when the provider distributes the image on the Internet. Embed watermark in low frequency band is most resistant to JPEG compression, blurring, adding Gaussian noise, rescaling, rotation, cropping and sharpening but embedding in high frequency is most resistant to histogram equalization, intensity adjustment and gamma correction. In this paper, we extend the idea to embed the same watermark in two bands (LL and HH bands or LH and HL bands) at the second level of Discrete Wavelet Transform (DWT) decomposition. Our generalization includes all the four bands (LL, HL, LH, and HH) by modifying coefficients of the all four bands in order to compromise between acceptable imperceptibility level and attacks' resistance.

Bakhouche, A.; Doghmane, N.

2008-06-01

193

An iterative ?-optimal control scheme for a class of discrete-time nonlinear systems with unfixed initial state.  

UK PubMed Central (United Kingdom)

In this paper, a finite horizon iterative adaptive dynamic programming (ADP) algorithm is proposed to solve the optimal control problem for a class of discrete-time nonlinear systems with unfixed initial state. A new ?-optimal control algorithm based on the iterative ADP approach is proposed that makes the performance index function iteratively converge to the greatest lower bound of all performance indices within an error ? in finite time. The convergence analysis of the proposed ADP algorithm in terms of performance index function and control policy is conducted. The optimal number of control steps can also be obtained by the proposed ?-optimal control algorithm for the unfixed initial state. Neural networks are used to approximate the performance index function, and compute the optimal control policy, respectively, for facilitating the implementation of the ?-optimal control algorithm. Finally, a simulation example is given to show the effectiveness of the proposed method.

Wei Q; Liu D

2012-08-01

194

Accuracy of the staggered-grid finite-difference method of the acoustic wave equation for marine seismic reflection modeling  

Science.gov (United States)

Seismic wave modeling is a cornerstone of geophysical data acquisition, processing, and interpretation, for which finite-difference methods are often applied. In this paper, we extend the velocity-pressure formulation of the acoustic wave equation to marine seismic modeling using the staggered-grid finite-difference method. The scheme is developed using a fourth-order spatial and a second-order temporal operator. Then, we define a stability coefficient (SC) and calculate its maximum value under the stability condition. Based on the dispersion relationship, we conduct a detailed dispersion analysis for submarine sediments in terms of the phase and group velocity over a range of angles, stability coefficients, and orders. We also compare the numerical solution with the exact solution for a P-wave line source in a homogeneous submarine model. Additionally, the numerical results determined by a Marmousi2 model with a rugged seafloor indicate that this method is sufficient for modeling complex submarine structures.

Qian, Jin; Wu, Shiguo; Cui, Ruofei

2013-01-01

195

The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A finite difference approximation for the Caputo fractional derivative of the 4-?, 1 < ? ? 2 order has been developed. A difference schemes for solving the Dirihlet’s problem of the Poisson’s equation with fractional derivatives has been applied and solved. Both the stability of difference pro...

Beibalaev V.D.; Meilanov R.P.

196

The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme.  

UK PubMed Central (United Kingdom)

In the hippocampus, oscillations in the theta and gamma frequency range occur together and interact in several ways, indicating that they are part of a common functional system. It is argued that these oscillations form a coding scheme that is used in the hippocampus to organize the readout from long-term memory of the discrete sequence of upcoming places, as cued by current position. This readout of place cells has been analyzed in several ways. First, plots of the theta phase of spikes vs. position on a track show a systematic progression of phase as rats run through a place field. This is termed the phase precession. Second, two cells with nearby place fields have a systematic difference in phase, as indicated by a cross-correlation having a peak with a temporal offset that is a significant fraction of a theta cycle. Third, several different decoding algorithms demonstrate the information content of theta phase in predicting the animal's position. It appears that small phase differences corresponding to jitter within a gamma cycle do not carry information. This evidence, together with the finding that principle cells fire preferentially at a given gamma phase, supports the concept of theta/gamma coding: a given place is encoded by the spatial pattern of neurons that fire in a given gamma cycle (the exact timing within a gamma cycle being unimportant); sequential places are encoded in sequential gamma subcycles of the theta cycle (i.e., with different discrete theta phase). It appears that this general form of coding is not restricted to readout of information from long-term memory in the hippocampus because similar patterns of theta/gamma oscillations have been observed in multiple brain regions, including regions involved in working memory and sensory integration. It is suggested that dual oscillations serve a general function: the encoding of multiple units of information (items) in a way that preserves their serial order. The relationship of such coding to that proposed by Singer and von der Malsburg is discussed; in their scheme, theta is not considered. It is argued that what theta provides is the absolute phase reference needed for encoding order. Theta/gamma coding therefore bears some relationship to the concept of "word" in digital computers, with word length corresponding to the number of gamma cycles within a theta cycle, and discrete phase corresponding to the ordered "place" within a word.

Lisman J

2005-01-01

197

The theta/gamma discrete phase code occuring during the hippocampal phase precession may be a more general brain coding scheme.  

Science.gov (United States)

In the hippocampus, oscillations in the theta and gamma frequency range occur together and interact in several ways, indicating that they are part of a common functional system. It is argued that these oscillations form a coding scheme that is used in the hippocampus to organize the readout from long-term memory of the discrete sequence of upcoming places, as cued by current position. This readout of place cells has been analyzed in several ways. First, plots of the theta phase of spikes vs. position on a track show a systematic progression of phase as rats run through a place field. This is termed the phase precession. Second, two cells with nearby place fields have a systematic difference in phase, as indicated by a cross-correlation having a peak with a temporal offset that is a significant fraction of a theta cycle. Third, several different decoding algorithms demonstrate the information content of theta phase in predicting the animal's position. It appears that small phase differences corresponding to jitter within a gamma cycle do not carry information. This evidence, together with the finding that principle cells fire preferentially at a given gamma phase, supports the concept of theta/gamma coding: a given place is encoded by the spatial pattern of neurons that fire in a given gamma cycle (the exact timing within a gamma cycle being unimportant); sequential places are encoded in sequential gamma subcycles of the theta cycle (i.e., with different discrete theta phase). It appears that this general form of coding is not restricted to readout of information from long-term memory in the hippocampus because similar patterns of theta/gamma oscillations have been observed in multiple brain regions, including regions involved in working memory and sensory integration. It is suggested that dual oscillations serve a general function: the encoding of multiple units of information (items) in a way that preserves their serial order. The relationship of such coding to that proposed by Singer and von der Malsburg is discussed; in their scheme, theta is not considered. It is argued that what theta provides is the absolute phase reference needed for encoding order. Theta/gamma coding therefore bears some relationship to the concept of "word" in digital computers, with word length corresponding to the number of gamma cycles within a theta cycle, and discrete phase corresponding to the ordered "place" within a word. PMID:16161035

Lisman, John

2005-01-01

198

A Non-Blind Watermarking Scheme for Gray Scale Images in Discrete Wavelet Transform Domain using Two Subbands  

Directory of Open Access Journals (Sweden)

Full Text Available Digital watermarking is the process to hide digital pattern directly into a digital content. Digital watermarking techniques are used to address digital rights management, protect information and conceal secrets. An invisible non-blind watermarking approach for gray scale images is proposed in this paper. The host image is decomposed into 3-levels using Discrete Wavelet Transform. Based on the parent-child relationship between the wavelet coefficients the Set Partitioning in Hierarchical Trees (SPIHT) compression algorithm is performed on the LH3, LH2, HL3 and HL2 subbands to find out the significant coefficients. The most significant coefficients of LH2 and HL2 bands are selected to embed a binary watermark image. The selected significant coefficients are modulated using Noise Visibility Function, which is considered as the best strength to ensure better imperceptibility. The approach is tested against various image processing attacks such as addition of noise, filtering, cropping, JPEG compression, histogram equalization and contrast adjustment. The experimental results reveal the high effectiveness of the method.

Abdur Shahid; Shahriar Badsha; Md. Rethwan Kabeer; Junaid Ahsan; Mufti Mahmud

2012-01-01

199

Assessment of linear finite-difference Poisson-Boltzmann solvers.  

UK PubMed Central (United Kingdom)

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications.

Wang J; Luo R

2010-06-01

200

Assessment of linear finite-difference Poisson-Boltzmann solvers.  

Science.gov (United States)

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

Wang, Jun; Luo, Ray

2010-06-01

 
 
 
 
201

A hybrid finite-difference and analytic element groundwater model.  

UK PubMed Central (United Kingdom)

Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.

Haitjema HM; Feinstein DT; Hunt RJ; Gusyev MA

2010-07-01

202

Partitioning a finite difference code for a local memory multiprocessor  

Energy Technology Data Exchange (ETDEWEB)

The TSAR code, a 3d finite difference EM model, was partitioned into parallel modules where each processor computed a subset of the 3d mesh. The multiprocessor was arranged in a square mesh of processors with the full range of one dimension in each processor and sub ranges in the other dimensions. Finding the range and checking for independence of array elements over those sub ranges is the main problem of partitioning. In addition with local memory multiprocessors, the array elements are distributed over the processors' local memory and a communications structure must be available which allows non-local elements to be assessed. Element communications must be fast enough or few enough to allow good utilization of the processor compute power. Automated partitioning was not available, but recent work provides some hope in this area. TSAR stands for Time-Domain Scattering and Response software that has been used for many years to model electric and magnetic waves in a three dimensional box. This code was partitioned to run on the SPRINT processor. SPRINT is a Systolic Processor with a Reconfigurable Interconnection Network of Transputers. It incorporates 64 floating point transputers. Results of this partitioning resulted in performance nearly equal to a CRAY XMP for identical problems. 4 refs., 3 figs.

Lawver, B.

1989-03-06

203

Simulation of heat pipe rapid transient performance using a multi-nodal implicit finite difference scheme  

International Nuclear Information System (INIS)

Heat pipes are being considered as a part of the thermal management system of many space crafts due to the fact that heat pipes are capable of passively transporting large amounts of thermal energy over considerable distances with essentially no temperature drop. Mathematical modeling of heat pipe performance has been developed for both transient and steady state modes: however, existing transient heat pipe models are of limited accuracy during vary rapid transients. The modeling of the response of the vapor region in the event of rapid transients (including frozen start-ups) has not been investigated fully. The purpose of this study is to model the performance of a screened wick heat pipe in rapid transient modes and to determine the limiting conditions under which the heat pipe will operate

1986-01-01

204

Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions  

Science.gov (United States)

An effective finite difference scheme is considered for solving the time fractional sub-diffusion equation with Neumann boundary conditions. A difference scheme combining the compact difference approach the spatial discretization and L1 approximation for the Caputo fractional derivative is proposed and analyzed. Although the spatial approximation order at the Neumann boundary is one order lower than that for interior mesh points, the unconditional stability and the global convergence order O(?+h4) in discrete L2 norm of the compact difference scheme are proved rigorously, where ? is the temporal grid size and h is the spatial grid size. Numerical experiments are included to support the theoretical results, and comparison with the related works are presented to show the effectiveness of our method.

Ren, Jincheng; Sun, Zhi-zhong; Zhao, Xuan

2013-01-01

205

Tradable Schemes  

CERN Document Server

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very elegant way, due to the fact that in our tradable based formulation there appear no drift terms in the PDE. We construct a mixed scheme based on this idea and apply it to price various types of arithmetic Asian options, as well as plain vanilla options (both european and american style) on stocks paying known cash dividends. We find prices which are accurate to $\\sim 0.1%$ in about 10ms on a Pentium 233MHz computer and to $\\sim 0.001%$ in a second. The scheme can also be used for market conform pricing, by fitting it to observed option prices.

Hoogland, Jiri Kamiel; Hoogland, Jiri; Neumann, Dimitri

2000-01-01

206

Discrete spectrum of the two-center problem of p bar He+ atomcule  

International Nuclear Information System (INIS)

[en] A discrete spectrum of the two-center Coulomb problem of p bar He+ system is studied. For solving this problem the finite-difference scheme of the 4th-order and the continuous analog of Newton's method are applied. The algorithm for calculation of eigenvalues and eigenfunctions with optimization of the parameter of the fractional-rational transformation of the quasiradial variable to a finite interval is developed. The specific behaviour of the solutions in a vicinity of the united and separated atoms is discussed

1999-01-01

207

Two-step finite difference methods for fluid transient analysis  

Science.gov (United States)

Transient-state flow of highly compressible fluid through closed flexible conduits with linearly elastic walls are described by a set of quasilinear, hyperbolic partial differential equations. These equations are transformed into canonical form in order to allow the application of Richtmyer's and MacCormack's two-step methods. Modifications of these methods are performed in order to solve these particular equations. These schemes yield conditional stable computation and second-order accuracy. The details of the numerical schemes and the treatment of the boundary conditions are presented. It is also shown that there exists no advantage in using these methods for transient-flow analysis when the nonlinear terms of the system are relatively insignificant.

Hsiao, R. C.; Rivera, M. P.

208

A comparison between the finite difference and nodal integral methods for the neutron diffusion equation  

International Nuclear Information System (INIS)

The lowest order Nodal Integral Method (NIM) which belongs to a large class of nodal methods, the Lawrence-Dorning class, is written in a five-point, weighted-difference form and contrasted against the edge-centered Finite Difference Method (FDM). The final equations for the two methods exhibit three differences: the NIM employs almost three times as many discrete-variables (which are node- and surface-averaged values of the flux) as the FDM; the spatial weights in the NIM include hyperbolic functions opposed to the algebraic weights in the FDM; the NIM explicitly imposes continuity of the net current across cell edges. A homogeneous model problem is devised to enable an analytical study of the numerical solutions accuracy. The analysis shows that on a given mesh the FDM calculated fundamental mode eigenvalue is more accurate than that calculated by the NIM. However, the NIM calculated flux distribution is more accurate, especially when the problem size is several times as thick as the diffusion length. Numerical results for a nonhomogeneous test problem indicate the very high accuracy of the NIM for fixed source problems in such cases. 18 refs., 1 fig., 1 tab

1991-05-02

209

Finite difference modelling of bulk high temperature superconducting cylindrical hysteresis machines  

International Nuclear Information System (INIS)

A mathematical model of the critical state based on averaged fluxon motion has been implemented to solve for the current and field distributions inside a high temperature superconducting hysteresis machine. The machine consists of a rotor made from a solid cylindrical single domain HTS placed in a perpendicular rotating field. The solution technique uses the finite difference approximation for a two-dimensional domain, discretized in cylindrical polar co-ordinates. The torque generated or equivalently the hysteresis loss in such a machine has been investigated using the model. It was found that to maximize the efficiency, the field needs to penetrate the rotor such that B0/?0JcR=0.56, where B0 is the applied field amplitude, Jc is the critical current density and R is the rotor radius. This corresponds to a penetration that is 27% greater than that which reaches the centre of the rotor. An examination of the torque density distributions across the rotor reveal that for situations where the field is less than optimal, a significant increase in the performance can be achieved by removing an inner cylinder from the rotor. (author)

2000-01-01

210

Convergence of a finite difference method for the KdV and modified KdV equations with $L^2$ data  

CERN Document Server

We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order (in space) stabilization term and a special conservative discretization of the nonlinear term. Convergence follows from a smoothing effect and energy estimates. We illustrate our results with numerical experiments, including a numerical investigation of an open problem related to uniqueness posed by Y. Tsutsumi.

Amorim, Paulo

2012-01-01

211

A Split-Step Scheme for the Incompressible Navier-Stokes  

Energy Technology Data Exchange (ETDEWEB)

We describe a split-step finite-difference scheme for solving the incompressible Navier-Stokes equations on composite overlapping grids. The split-step approach decouples the solution of the velocity variables from the solution of the pressure. The scheme is based on the velocity-pressure formulation and uses a method of lines approach so that a variety of implicit or explicit time stepping schemes can be used once the equations have been discretized in space. We have implemented both second-order and fourth-order accurate spatial approximations that can be used with implicit or explicit time stepping methods. We describe how to choose appropriate boundary conditions to make the scheme accurate and stable. A divergence damping term is added to the pressure equation to keep the numerical dilatation small. Several numerical examples are presented.

Henshaw, W; Petersson, N A

2001-06-12

212

Finite-difference and frequency-wavenumber modeling of seismic monopole sources and receivers in fluid-filled boreholes  

Energy Technology Data Exchange (ETDEWEB)

In borehole seismic experiments the presence of the borehole has a significant effect on observations. Unfortunately, including boreholes explicitly in modeling schemes excludes the use of some methods (e.g., frequency-wavenumber) and adds prohibitively to the cost of others (e.g., finite difference). To overcome this problem, the authors use the concept of an effective source/receiver array to replace the explicit representation of the borehole by a distributed seismic source/receiver. This method mimics the presence of the borehole at seismic frequencies under a wide variety of conditions without adding a significant computational cost. It includes the effects of dispersive and attenuative tube wave propagation, the generation of secondary sources at interfaces and caliper changes, and the generation of conical waves in low-velocity layers. Comparison with a finite-difference scheme with an explicit borehole representation validates the approach. The modeling method applied to a continuity logging geometry demonstrates that the presence of guided waves does not uniquely imply bed connectivity. Results for a single-well imaging geometry emphasize the dominance of the tube wave in the hydrophone synthetics and demonstrates the necessity of using clamped geophones for single-well experiments. The concept of an effective source/receiver array is an efficient way of including borehole phenomena in seismic modeling methods at minimal extra computational cost.

Kurkjian, A.L.; Coates, R.T. (Schlumberger Cambridge Research, Cambridge (United Kingdom)); White, J.E. (Colorado School of Mines, Golden, CO (United States). Dept. of Geophysics); Schmidt, H. (Massachusetts Inst. of Tech., Cambridge, MA (United States). Dept. of Ocean Engineering)

1994-07-01

213

A higher-order spatial FDTD scheme with CFS PML for 3D numerical simulation of wave propagation in cold plasma  

CERN Multimedia

A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are used to discretize Maxwell's curl equations and a uniaxial perfectly matched layer with the complex frequency-shifted equations is introduced to terminate the computational domain. A numerical dispersion study of second- and higher-order techniques is elaborated and their stability criteria are extracted for each scheme. Comparisons with analytical solutions verify the accuracy of the proposed methods and the low dispersion error of the higher-order schemes.

Prokopidis, Konstantinos P

2013-01-01

214

A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme  

Science.gov (United States)

We present a new finite-difference numerical method to solve the incompressible Navier-Stokes equations using a collocated discretization in space on a logically Cartesian grid. The method shares some common aspects with, and it was inspired by, the Box scheme. It uses centered second-order-accurate finite-difference approximations for the spatial derivatives combined with semi-implicit time integration. The proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity-pressure form of the equations. The continuity equation is enforced exactly (to machine accuracy) at the collocated locations, whereas the momentum equations are evaluated in a staggered manner. This formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure. The method shows uniform order of accuracy, both in space and time, for velocity and pressure. In addition, the skew-symmetric form of the non-linear advection term of the Navier-Stokes equations improves discrete conservation of kinetic energy in the inviscid limit, to within the order of the truncation error of the time integrator. The method has been formulated to accommodate different types of boundary conditions; fully periodic, periodic channel, inflow-outflow and lid-driven cavity; always ensuring global mass conservation. A novel aspect of this finite-difference formulation is the derivation of the discretization near boundaries using the weak form of the equations, as in the finite element method. The method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver. To assess the applicability of the new method presented in this paper, four realistic flow problems have been simulated and results are compared with those in the literature. These cases include a lid-driven cavity, backward-facing step, Kovasznay flow, and fully developed turbulent channel.

Ranjan, R.; Pantano, C.

2013-01-01

215

Efficient Solution of Maxwell's Equations Using the Nonuniform Orthogonal Finite Difference Time Domain Method  

Canada Institute for Scientific and Technical Information (Canada)

The Finite Difference Time Domain (FDTD) method is limited by memory requirements and computation time when applied to large problems, complicated geometries, or geometries with fine features. In this thesis, the nonuniform orthogonal FDTD method is presented and applied to a variety of electromagnetic problems. The nonuniform aspect of the method gives great flexibility in modeling complicated geometries with fine features. Furthermore, the variability of the mesh resolution also enables the user to move the boundaries of the computational domain farther away from the center of the problem without an undue increase in the number of cells. Most significantly, the orthogonality of the method preserves the speed of the conventional FDTD method. These three features of the nonuniform orthogonal FDTD method are demonstrated by means of numerical examples throughout the thesis. Grid dispersion error from the nonuniform mesh is analyzed and numerical examples are presented, demonstrating that small growth rates in mesh discretization lead to acceptably small errors. The issue of absorbing boundary conditions is addressed with the analysis and application of the dispersive boundary condition on nonuniform meshes. New techniques are also introduced for the efficient characterization of microstrip lines, microstrip discontinuities, and coupled microstrip structures using FDTD data. A local mesh refinement technique is introduced for planar perfect electric conductor, and is shown to be three times more accurate than the staircasing approximation. The versatility of the method is demonstrated by the analysis of a balun-fed folded dipole antenna, the characterization of the transition of grounded coplanar waveguide to microstrip line, and the study of fields in lossy layered media.

1995-01-01

216

The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution  

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference approximation for the Caputo fractional derivative of the 4-?, 1 < ? ? 2 order has been developed. A difference schemes for solving the Dirihlet’s problem of the Poisson’s equation with fractional derivatives has been applied and solved. Both the stability of difference problem in its right-side part and the convergence have been proved. A numerical example was developed by applying both the Liebman and the Monte-Carlo methods.

Beibalaev V.D.; Meilanov R.P.

2012-01-01

217

Vector analysis of bending waveguides by using a modified finite-difference method in a local cylindrical coordinate system.  

UK PubMed Central (United Kingdom)

A vector mode solver for bending waveguides by using a modified finite-difference (FD) method is developed in a local cylindrical coordinate system, where the perfectly matched layer absorbing boundary conditions are incorporated. Utilizing Taylor series expansion technique and continuity condition of the longitudinal field components, a standard matrix eigenvalue equation without the averaged index approximation approach for dealing with the discrete points neighboring the dielectric interfaces is obtained. Complex effective indexes and field distributions of leaky modes for a typical rib bending waveguide and a silicon wire bend are presented, and solutions accord well with those from the film mode matching method, which shows the validity and utility of the established method.

Xiao J; Sun X

2012-09-01

218

Vector analysis of bending waveguides by using a modified finite-difference method in a local cylindrical coordinate system.  

Science.gov (United States)

A vector mode solver for bending waveguides by using a modified finite-difference (FD) method is developed in a local cylindrical coordinate system, where the perfectly matched layer absorbing boundary conditions are incorporated. Utilizing Taylor series expansion technique and continuity condition of the longitudinal field components, a standard matrix eigenvalue equation without the averaged index approximation approach for dealing with the discrete points neighboring the dielectric interfaces is obtained. Complex effective indexes and field distributions of leaky modes for a typical rib bending waveguide and a silicon wire bend are presented, and solutions accord well with those from the film mode matching method, which shows the validity and utility of the established method. PMID:23037277

Xiao, Jinbiao; Sun, Xiaohan

2012-09-10

219

Compensating finite-difference errors in 3-D migration and modeling  

Energy Technology Data Exchange (ETDEWEB)

One-pass three-dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two-pass migration, in variable velocity media. Conventional one-pass 3-D migration, done with the method of finite-difference inline and crossline splitting, however, creates large errors in imaging complex structures due to paraxial wave-equation approximation of the one-way wave equation, inline-crossline splitting, and finite-difference grid dispersion. After analyzing the finite-difference errors in conventional 3-D poststack wave field extrapolation, the paper presents a method that compensates for the errors and yet still preserves the efficiency of the conventional finite-difference splitting method. For frequency-space 3-D finite-difference migration and modeling, the compensation operator is implemented using the phase-shift method, or phase-shift plus interpolation method, depending on the extent of lateral velocity variations. The compensation operator increases the accuracy of handling steep dips, suppresses the inline and crossline splitting error, and reduces finite-difference grid dispersions. Numerical calculations show that the quality of 3-D migration and 3-D modeling is improved significantly with the finite-difference error compensation method presented in this paper. 13 refs., 7 figs.

Li, Zhiming.

1990-09-01

220

Efficient Solution of Maxwell's Equations Using the Nonuniform Orthogonal Finite Difference Time Domain Method.  

Science.gov (United States)

The Finite Difference Time Domain (FDTD) method is limited by memory requirements and computation time when applied to large problems, complicated geometries, or geometries with fine features. In this thesis, the nonuniform orthogonal FDTD method is prese...

J. A. Svigelj

1995-01-01

 
 
 
 
221

Hybrid lattice-Boltzmann and finite-difference simulation of electroosmotic flow in a microchannel  

International Nuclear Information System (INIS)

A three-dimensional (3D) transient mathematical model is developed to simulate electroosmotic flows (EOFs) in a homogeneous, square cross-section microchannel, with and without considering the effects of axial pressure gradients. The general governing equations for electroosmotic transport are incompressible Navier-Stokes equations for fluid flow and the nonlinear Poisson-Boltzmann (PB) equation for electric potential distribution within the channel. In the present numerical approach, the hydrodynamic equations are solved using a lattice-Boltzmann (LB) algorithm and the PB equation is solved using a finite-difference (FD) method. The hybrid LB-FD numerical scheme is implemented on an iterative framework solving the system of coupled time-dependent partial differential equations subjected to the pertinent boundary conditions. Transient behavior of the EOF and effects due to the variations of different physicochemical parameters on the electroosmotic velocity profile are investigated. Transport characteristics for the case of combined electroosmotic- and pressure-driven microflows are also examined with the present model. For the sake of comparison, the cases of both favorable and adverse pressure gradients are considered. EOF behaviors of the non-Newtonian fluid are studied through implementation of the power-law model in the 3D LB algorithm devised for the fluid flow analysis. Numerical simulations reveal that the rheological characteristic of the fluid changes the EOF pattern to a considerable extent and can have significant consequences in the design of electroosmotically actuated bio-microfluidic systems. To improve the performance of the numerical solver, the proposed algorithm is implemented for parallel computing architectures and the overall parallel performance is found to improve with the number of processors.

2011-01-01

222

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows  

International Nuclear Information System (INIS)

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.

2010-08-20

223

Discretization of a model for the formation of longshore sand ridges  

Energy Technology Data Exchange (ETDEWEB)

This paper presents and evaluates the numerical solution of a coupled system of equations that arises in a model for the formation and evolution of three-dimensional longshore sand ridges. The model is based on the interaction between surficial or internal weakly nonlinear shallow-water waves, having weak spanwise spatial dependence, and the deformable bottom topography. The presentation of the details concerning the discretization of the model is primarily motivated by two facts: (1) The model involves equations for which little is known regarding its solutions, and (2) the predictor-corrector scheme presented here, which combines finite difference techniques and fixed-point methods, is simple, fast, and general enough to be used in the discretization of partial differential equations with local nonlinearities whose solutions are smooth.

Restrepo, J.M. [Argonne National Lab., IL (United States); Bona, J.L. [Pennsylvania State Univ., University Park, PA (United States) Mathmatics Dept.

1994-01-04

224

Remesh algorithms for the finite element and finite difference calculation of solid and fluid continuum mecahanics problems  

International Nuclear Information System (INIS)

In the lagrangian calculations of some nuclear reactor problems such as a bubble expansion in the core of a fast breeder reactor, the crash of an airplane on the external containment or the perforation of a concrete slab by a rigid missile, the mesh may become highly distorted. A remesh is then necessary to continue the calculation with precision and economy. Similarly, an eulerian calculation of a fluid volume bounded by lagrangian shells can be facilitated by a remesh scheme with continuously adapts the boundary of the eulerian domain to the lagrangian shell. This paper reviews available remesh algorithms for finite element and finite difference calculations of solid and fluid continuum mechanics problems, and presents an improved Finite Element Remesh Method which is independent of the quantities at the nodal points (NP) and the integration points (IP) and permits a restart with a new mesh. (orig.).

1979-08-21

225

Dependency of finite difference solutions on grid structures and turbulence models for cascade flows; Yokuretsu nagare no sabunkai ni oyobosu koshi kozo to ranryu model no eikyo no kento  

Energy Technology Data Exchange (ETDEWEB)

For cascade with a high turning and a large camber, it is difficult to impose grid orthogonality as well as point-to-point periodicity simultaneously on a single structured grid. In this study, the effects of periodic and non-periodic grids on finite difference solutions are investigated for two-dimensional transonic flows about rotor blades. The spatial derivatives of the Reynolds-averaged Navier-Stokes equations are discretized with central difference approximations and matrix dissipation models. The resulting system of equations is integrated in time with an explicit 2-stage Rational Runge-Kutta scheme. For turbulence closure, Baldwin-Lomax model, Baldwin-Barth model, and Spalart-Allmaras model are compared. The non-periodic grids have favorable resolutions for the shock system and the wake. The shock-induced production of the eddy-viscosity is remarkable in the Baldwin-Barth model. The Spalart-Allmaras model works well, even on the periodic grids, in comparison with the other models. 9 refs., 15 figs.

Omote, H.; Morinishi, K.; Satofuka, N. [Kyoto Inst. of Technology, Kyoto (Japan)

1998-09-25

226

FLUOMEG: a planar finite difference mesh generator for fluid flow problems with parallel boundaries. [In FORTRAN IV  

Energy Technology Data Exchange (ETDEWEB)

A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables.

Kleinstreuer, C.; Patterson, M.R.

1980-05-01

227

Choas and instabilities in finite difference approximations to nonlinear differential equations  

Energy Technology Data Exchange (ETDEWEB)

The numerical solution of time-dependent ordinary and partial differential equations by finite difference techniques is a common task in computational physics and engineering The rate equations for chemical kinetics in combustion modeling are an important example. They not only are nonlinear, but they tend to be stiff, which makes their solution a challenge for transient problems. We show that one must be very careful how such equations are solved In addition to the danger of large time-marching errors, there can be unphysical chaotic solutions that remain numerically stable for a range of time steps that depends on the particular finite difference method used We point out that the solutions of the finite difference equations converge to those of the differential equations only in the limit as the time step approaches zero for stable and consistent finite difference approximations The chaotic behavior observed for finite time steps in some nonlinear difference equations is unrelated to solutions of the differential equations, but is connected with the onset of numerical instabilities of the finite difference equations This behavior suggests that the use of the theory of chaos in nonlinear iterated maps may be useful in stability anlaysis of finite difference approximations to nonlinear differential equations, providing more stringent time step limits than the formal linear stability analysis that tests only for unbounded solutions This observation implies that apparently stable numerical solutions of nonlinear differential equations by finite difference techniques may in fact be contaminated (if not dominated) by nonphysical chaotic parasitic solutions that degrade the accuracy of the numerical solution We demonstrate this phenomenon with some solutions of the logistic equation and a simple two-dimensional computational fluid dynamics example

Cloutman, L. D., LLNL

1998-07-01

228

Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport  

Energy Technology Data Exchange (ETDEWEB)

Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitary variations in velocity and density, and can handle turning waves well. However, conventional finite-difference methods for solving the acousticwave equation suffer from numerical dispersion when too few samples per wavelength are used. Here, we present two flux-corrected transport (FCT) algorithms, one based the second-order equation and the other based on first-order wave equations derived from the second-order one. Combining the FCT technique with conventional finite-difference modeling or reverse-time wave extrapolation can ensure finite-difference solutions without numerical dispersion even for shock waves and impulsive sources. Computed two-dimensional migration images show accurate positioning of reflectors with greater than 90-degree dip. Moreover, application to real data shows no indication of numerical dispersion. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use of approximations of increasing order.

Fei, Tong; Larner, K.

1993-11-01

229

On the simulation of the energy transmission in the forbidden band-gap of a spatially discrete double sine-Gordon system  

CERN Multimedia

In this work, we present a numerical method to consistently approximate solutions of a spatially discrete, double sine-Gordon chain which considers the presence of external damping. In addition to the finite-difference scheme employed to approximate the solution of the difference-differential equations of the model under investigation, our method provides positivity-preserving schemes to approximate the local and the total energy of the system, in such way that the discrete rate of change of the total energy with respect to time provides a consistent approximation of the corresponding continuous rate of change. Simulations are performed, first of all, to assess the validity of the computational technique against known qualitative solutions of coupled sine-Gordon and coupled double sine-Gordon chains. Secondly, the method is used in the investigation of the phenomenon of nonlinear transmission of energy in double sine-Gordon systems; the qualitative effects of the damping coefficient on the occurrence of the n...

Macías-Díaz, J E

2011-01-01

230

Simulation of sonic waves along a borehole in a heterogeneous formation: Accelerating 2.5-D finite differences using [Py]OpenCL  

Science.gov (United States)

This paper presents an implementation of a 2.5-D finite-difference (FD) code to model acoustic full waveform monopole logging in cylindrical coordinates accelerated by using the new parallel computing devices (PCDs). For that purpose we use the industry open standard Open Computing Language (OpenCL) and an open-source toolkit called PyOpenCL. The advantage of OpenCL over similar languages is that it allows one to program a CPU (central processing unit) a GPU (graphics processing unit), or multiple GPUs and their interaction among them and with the CPU, or host device. We describe the code and give a performance test in terms of speed using six different computing devices under different operating systems. A maximum speedup factor over 34.2, using the GPU is attained when compared with the execution of the same program in parallel using a CPU quad-core. Furthermore, the results obtained with the finite differences are validated using the discrete wavenumber method (DWN) achieving a good agreement. To provide the Geoscience and the Petroleum Science communities with an open tool for numerical simulation of full waveform sonic logs that runs on the PCDs, the full implementation of the 2.5-D finite difference with PyOpenCL is included.

Iturrarán-Viveros, Ursula; Molero, Miguel

2013-07-01

231

Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation  

CERN Document Server

We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing insulating internal boundaries which are later removed. The Kuramoto-Sivashinsky equation is used as an example to show how holistic finite differences may be applied to fourth order, nonlinear, spatio-temporal dynamical systems. This novel centre manifold approach is holistic in the sense that it treats the dynamical equations as a whole, not just as the sum of separate terms.

MacKenzie, T

2000-01-01

232

Multidimensional finite difference electromagnetic modeling and inversion based on the balance method  

Science.gov (United States)

A new approach for multisource three-dimensional (3-D) finite-difference (FD) electromagnetic (EM) modeling in the frequency domain is introduced. This approach is based on the balance method, solves for the anomalous electric field and automatically takes into account the conservation law of Maxwell's equations. Also a new Dirichlet boundary condition, based on the quasi-analytical (QA) approximation/series, is proposed to truncate the FD modeling grid significantly without notable loss of computational accuracy. The developed 3-D FD modeling code can be used in different geophysical applications including magnetotelluric (MT), controlled source magnetotelluric (CSMT), airborne, and borehole EM methods in the frequency domain. The modeling results obtained by the new algorithm demonstrated good agreement with the respective integral equation solutions. Regularization methods search for a smooth or focused class of the geoelectrical models to invert for. The traditional approach has been to use smooth models to describe the conductivity distribution in the subsurface formations. A new method for two-dimensional (2-D) MT focusing inversion is developed. It approximates the conductivity distribution by models with blocky (focused) conductivity structures. The class (smooth or focused) of inverse models is chosen based on the objective of the survey and available geological information, and can be determined from inversion by selecting the corresponding stabilizing functional in the regularized objective functional subjected to minimization. This new method was applied to synthetic MT data, and MT field data collected for crustal imaging in Carrizo Plain, California and for mining exploration in Voisey's Bay, Canada. A novel algorithm for 3-D EM iterative migration is introduced. It does not require Frechet (Jacobian) matrix computation but rather the conjugate of Frechet matrix acting on the residual field using just one forward modeling run. This algorithm utilizes the 3-D FD method described above and the regularized conjugate gradient (RCG) scheme. In the framework of this approach, the 3-D FD forward modeling solution is computed three times per frequency in each iteration step. In the first forward solution, the FD forward operator is applied to compute the predicted field for a given conductivity distribution. The residual field is then computed by taking the difference between the observed and predicted data. In the second forward solution, the FD operator is utilized to migrate the residual field in the lower half-space using the adjoint operator. In the third forward solution, the FD operator is used to compute the optimal step of minimization. The practical effectiveness of the newly developed 3-D FD inversion technique is illustrated by inverting both synthetic data and field data of Voisey's Bay like geoelectrical model.

Mehanee, Salah Abdelraheem

233

The reliability of a finite-difference method for the solution of the inverse scattering problem  

International Nuclear Information System (INIS)

The properties and the applicability of the finite-difference method of Hooshyar and Razavy for the solution of the inverse scattering problem are studied. Testing the method for the reconstruction of potentials under realistic conditions leads to significant systematic differences between the reconstructed and the input potentials. The inversion procedure does not converge and exhibits a characteristic instability for small variations of the scattering input. Therefore, this finite-difference method appears to be unsuitable for the extraction of reliable potentials from experimental scattering data. (orig.).

1991-01-01

234

A Second Order Finite Difference Approximation for the Fractional Diffusion Equation  

Directory of Open Access Journals (Sweden)

Full Text Available We consider an approximation of one-dimensional fractional diffusion equation. We claim and show that the finite difference approximation obtained from the Grünwald-Letnikov formulation, often claimed to be of first order accuracy, is in fact a second order approximation of the fractional derivative at a point away from the grid points. We use this fact to device a second order accurate finite difference approximation for the fractional diffusion equation. The proposed method is also shown to be unconditionally stable. By this approach, we treat three cases of difference approximations in a unified setting. The results obtained are justified by numerical examples.

H. M. Nasir; B. L. K. Gunawardana; H. M. N. P. Abeyrathna

2013-01-01

235

Dispersion fitted finite difference method with applications to molecular quantum mechanics.  

Energy Technology Data Exchange (ETDEWEB)

An approach to finite difference approximation is presented based on the idea of fitting the dispersion relation up to a limiting accuracy. The resulting approximations to the second derivative can be more accurate than the standard, Lagrangian finite difference approximations by an order of magnitude or more. The locality of the methods makes them well suited to parallel computation, in contrast with pseudospectral methods. The approach is illustrated with application to a simple bound state problem and to a more challenging three dimensional reactive scattering problem.

Gray, S.; Goldfield, E.; Chemistry; Wayne State Univ.

2001-11-01

236

Flood routing using finite differences and the fourth order Runge-Kutta method  

International Nuclear Information System (INIS)

The Saint-Venant continuity and momentum equations are solved numerically by discretising the time variable using finite differences and then the Runge-Kutta method is employed to solve the resulting ODE. A model of the Rufiji river downstream on the proposed Stiegler Gourge Dam is used to provide numerical results for comparison. The present approach is found to be superior to an earlier analysis using finite differences in both space and time. Moreover, the steady and unsteady flow analyses give almost identical predictions for the stage downstream provided that the variations of the discharge and stage upstream are small. (author)

1984-01-01

237

Generalized finite element and finite differences methods for the Helmholtz problem  

International Nuclear Information System (INIS)

We briefly review the Quasi Optimal Finite Difference (QOFD) and Petrov-Galerkin finite element (QOPG) methods for the Helmholtz problem recently introduced in references [1] and [2], respectively, and extend these formulations to heterogeneous media and singular sources. Results of numerical experiments are presented illustrating the blended use of these methods on general meshes to take advantage of the lower cost and simplicity of the finite difference approach combined with the natural ability of the finite element method to deal with source terms, boundary and interface conditions.

2010-06-01

238

Modelagem Sísmica via métodos das diferenças finitas: caso da bacia do Amazonas/ Seismic Modeling by finites difference method: case of Amazon basin  

Scientific Electronic Library Online (English)

Full Text Available Abstract in portuguese Este trabalho tem por objetivo apresentar os resultados da modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações e múltiplas reflexões, tendo a Bacia do Amazonas como referência à modelagem. As condições de estabilidade e de fronteiras utilizadas no cálculo do campo de ondas sísmicas foram analisadas numericamente pelo método das diferenças finitas, visando melhor compreensão e controle da in (more) terpretação de dados sísmicos. A geologia da Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o Recente que atingem espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançam espessuras de centenas de metros e perfazem um volume total de aproximadamente 90000 Km³. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica o que impossibilita melhor interpretação dos horizontes refletores que se encontram abaixo destas soleiras. Para representar situações geológicas desse tipo foram usados um modelo (sintético) acústico de velocidades e um código computacional elaborado via método das diferenças finitas com aproximação de quarta ordem no espaço e no tempo da equação da onda. A aplicação dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas melhorou a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observada a influência significativa das reflexões múltiplas devido à camada de alta velocidade, isto provocou maior perda de energia e dificultou a interpretação dos alvos. Por esta razão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio. Abstract in english This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of di (more) abasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic) acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.

Fernandes, Lindemberg Lima; Cruz, João Carlos Ribeiro; Blanco, Claudio José Cavalcante; Barp, Ana Rosa Baganha

2009-03-01

239

Modelagem Sísmica via métodos das diferenças finitas: caso da bacia do Amazonas Seismic Modeling by finites difference method: case of Amazon basin  

Directory of Open Access Journals (Sweden)

Full Text Available Este trabalho tem por objetivo apresentar os resultados da modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações e múltiplas reflexões, tendo a Bacia do Amazonas como referência à modelagem. As condições de estabilidade e de fronteiras utilizadas no cálculo do campo de ondas sísmicas foram analisadas numericamente pelo método das diferenças finitas, visando melhor compreensão e controle da interpretação de dados sísmicos. A geologia da Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o Recente que atingem espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançam espessuras de centenas de metros e perfazem um volume total de aproximadamente 90000 Km³. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica o que impossibilita melhor interpretação dos horizontes refletores que se encontram abaixo destas soleiras. Para representar situações geológicas desse tipo foram usados um modelo (sintético) acústico de velocidades e um código computacional elaborado via método das diferenças finitas com aproximação de quarta ordem no espaço e no tempo da equação da onda. A aplicação dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas melhorou a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observada a influência significativa das reflexões múltiplas devido à camada de alta velocidade, isto provocou maior perda de energia e dificultou a interpretação dos alvos. Por esta razão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio.This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of diabasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic) acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.

Lindemberg Lima Fernandes; João Carlos Ribeiro Cruz; Claudio José Cavalcante Blanco; Ana Rosa Baganha Barp

2009-01-01

240

Stability and Dispersion Analysis of Battle--Lemarie-Based MRTD Schemes  

UK PubMed Central (United Kingdom)

The stability and dispersion performance of therecently developed Battle--Lemarie multiresolution time-domainschemes is investigated for different stencil sizes. The contributionof wavelets is enhanced and analytical expressions for themaximum allowable time step are derived. It is observed thatlarger stencils decrease the numerical phase error, making itsignificantly lower than finite-difference time domain for lowand medium discretizations. The addition of wavelets furtherimproves the dispersion performance for discretizations close tothe Nyquist limit, though it decreases the value of the maximumtime step, guaranteeing the stability of the scheme.I. INTRODUCTIONFINITE-DIFFERENCE time-domain (FDTD) numericaltechniques are widely used today for the analysis ofvarious microwave geometries and for the modeling ofelectromagnetic (EM) wave propagation. Though many ofthem are very simple to implement and can be easilyapplied to different topologies with remarkable accu...

Emmanouil M. Tentzeris; Robert L. Robertson; James F. Harvey; Linda P. B. Katehi

 
 
 
 
241

Application of the finite-difference time-domain (FDTD) method with local grid refinement to nanostructure design  

Science.gov (United States)

The Finite-Difference Time-Domain (FDTD) method is often a viable alternative to other computational methods used for the design of sub-wavelength components of photonic devices. We describe an FDTD based grid refinement method, which reduces the computational cell size locally, using a collection of nested rectangular grid patches. On each patch, a standard FDTD update of the electromagnetic fields is applied. At the coarse/fine grid interfaces the solution is interpolated, and consistent circulation of the fields is enforced on shared cell edges. Stability and accuracy of the scheme depend critically on the update scheme, space and time interpolation, and a proper implementation of flux conditions at mesh boundaries. Compared to the conformal grid refinement, the method enables better efficiency by using non-conformal grids around the region of interest and by refining both space and time dimensions, which leads to considerable savings in computation time. We discuss the advantages and shortcomings of the method and present its application to the problem of computation of a quality factor of a 3-D photonic crystal microcavity.

Zakharian, Aramais R.; Moloney, Jerome V.; Dineen, Colm; Brio, Moysey

2005-03-01

242

Comparison between a finite difference model (PUMA) and a finite element model (DELFIN) for simulation of the reactor of the atomic power plant of Atucha I  

International Nuclear Information System (INIS)

[en] The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs

1996-01-01

243

A Mathematical Description of the IDSA for Supernova Neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann's Equation  

CERN Multimedia

In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the \\emph{Isotropic Diffusion Source Approximation} (IDSA). Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized.

Berninger, Heiko; Gander, Martin; Liebendörfer, Mathias; Michaud, Jérôme; Vasset, Nicolas

2012-01-01

244

Applications of single mode extraction from finite difference time domain data  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A simple technique is described which is capable of providing considerable reductions in the computational demands of the finite difference time domain (FDTD) algorithm. It is shown that, by forming the inner product of the FDTD time domain data and the transverse field variation of the mode of inte...

Craddock, IJ; Paul, DL; Railton, CJ; Fletcher, PN; Dean, M

245

[Forecasting of biocenosis quantity in the open system with a finite difference model  

UK PubMed Central (United Kingdom)

A simple mathematical model for the dynamics of biocenosis in an open system was worked out. The model is based on the finite-difference presentation of experimental data. It also takes into account the past history of population development. The testing of the model proved its ability to forecast the density of populations in open systems.

Arzamastsev AA; Shindiapin AI; Andreev AA

2001-11-01

246

Comparison of finite differences and finite elements in the case of large fast power reactor  

International Nuclear Information System (INIS)

A large number of test calculations in two-dimension hexagonal geometry for different configurations of SUPER-PHENIX 1 type Fast Reactor have been performed to compare finite differences theory versus finite elements theory performances. At present, no definitive advantages were found for the application of the finite elements method to two dimensional hexagonal design calculations.

1981-04-24

247

Finite-difference time domain solution of light scattering by arbitrarily shaped particles and surfaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This chapter reviews the fundamental methods and some of the applications of the three-dimensional (3D) finite-difference time-domain (FDTD) technique for the modeling of light scattering by arbitrarily shaped dielectric particles and surfaces. The emphasis is on the details of the FDTD algorithms f...

Tanev, Stoyan; Sun, Wenbo

248

A Fractional Finite Difference Method for Solving the Fractional Poisson Equation Based on Shifted Grünwald Estimate  

Directory of Open Access Journals (Sweden)

Full Text Available In this study fractional Poisson equation is scrutinized through finite difference using shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of solution for the fractional Poisson equation are proved. Exact and numerical solution are constructed and compared. Then numerical result shows the efficiency of the proposed method.

Abdollah BORHANIFAR; Sohrab VALIZADEH

2013-01-01

249

Dispersion properties of non-radiating configurations: Finite-Difference Time-Domain modeling  

CERN Multimedia

A finite-difference time-domain (FDTD) numerical analysis is used to demonstrate that a toroidal solenoid, coaxial with an electric dipole, is a remarkable non-radiating configuration. It can be used to measure the dielectric permittivity of any ambient matter. It becomes a directional radiator at an interface between two dielectric media, depositing energy in the material with the highest polarizability.

Boardman, A D; Zheludev, N I; Fedotov, V A

2005-01-01

250

Accelerating a 3D finite-difference wave propagation code using GPU graphics cards  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We accelerate a three-dimensional finite-difference in the time domain (FDTD) wave propagation code by a factor between about 20 and 60 compared to a serial implementation using Graphics Processing Unit (GPU) computing on NVIDIA graphics cards with the CUDA programming language. We describe the impl...

Michéa, David; Komatitsch, Dimitri

251

Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry  

International Nuclear Information System (INIS)

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two steps for the analytical reconstruction of the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (SN) transport model in slab geometry. The first step of the algorithm is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the grid set up on the spatial domain. The second step is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the SN model. Numerical results are given so we can illustrate the accuracy of the two reconstruction techniques, as described in this paper.

2010-01-01

252

Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry  

Energy Technology Data Exchange (ETDEWEB)

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two steps for the analytical reconstruction of the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S{sub N}) transport model in slab geometry. The first step of the algorithm is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the grid set up on the spatial domain. The second step is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S{sub N} model. Numerical results are given so we can illustrate the accuracy of the two reconstruction techniques, as described in this paper.

Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.b [Programa de Pos-graduacao em Modelagem Computacional, Instituto Politecnico (IPRJ/UERJ), Rua Alberto Rangel s/n, 28630-050 Nova Friburgo, RJ (Brazil); Filho, Hermes Alves, E-mail: halves@iprj.uerj.b [Programa de Pos-graduacao em Modelagem Computacional, Instituto Politecnico (IPRJ/UERJ), Rua Alberto Rangel s/n, 28630-050 Nova Friburgo, RJ (Brazil); Platt, Gustavo M., E-mail: gmplatt@iprj.uerj.b [Programa de Pos-graduacao em Modelagem Computacional, Instituto Politecnico (IPRJ/UERJ), Rua Alberto Rangel s/n, 28630-050 Nova Friburgo, RJ (Brazil); Oliveira, Francisco Bruno S., E-mail: fbrunoso@uol.com.b [Programa de Pos-graduacao em Modelagem Computacional, Instituto Politecnico (IPRJ/UERJ), Rua Alberto Rangel s/n, 28630-050 Nova Friburgo, RJ (Brazil); Militao, Damiano S., E-mail: mestredam@yahoo.com.b [Programa de Pos-graduacao em Modelagem Computacional, Instituto Politecnico (IPRJ/UERJ), Rua Alberto Rangel s/n, 28630-050 Nova Friburgo, RJ (Brazil)

2010-11-15

253

Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory  

Energy Technology Data Exchange (ETDEWEB)

The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.

Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado

1997-10-01

254

Numerical schemes for three-dimensional irregular shape quantum dots over curvilinear coordinate systems  

International Nuclear Information System (INIS)

In this article, we present efficient and stable numerical schemes to simulate three-dimensional quantum dot with irregular shape, so that we can compute all the bound state energies and associated wave functions. A curvilinear coordinate system that fits the target quantum dot shape is first determined. Three finite difference discretizations of the Schroedinger equation are then developed on the original and the skewed curvilinear coordinate system. The resulting large-scale generalized eigenvalue systems are solved by a modified Jacobi-Davidson method. Intensive numerical experiments show that the scheme using both grid points on the original and skewed curvilinear coordinate system can converge to the eigenpairs quickly and stably with second-order accuracy.

2007-09-10

255

Techniques for improving computational speed in numerical simulation of casting thermal stress based on finite difference method  

Directory of Open Access Journals (Sweden)

Full Text Available Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational speed in numerical simulation of casting thermal stress based on FDM, one for handling of nonconstant material properties and the other for dealing with the various coefficients in discretization equations. The use of the two techniques has been discussed and an application in wave-guide casting is given. The results show that the computational speed is almost tripled and the computer storage needed is reduced nearly half compared with those of the original method without the new technologies. The stress results for the casting domain obtained by both methods that set the temperature steps to 0.1 ? and 10 ?, respectively are nearly the same and in good agreement with actual casting situation. It can be concluded that both handling the material properties as an assumption of stepwise profile and eliminating the repeated calculation are reliable and effective to improve computational speed, and applicable in heat transfer and fluid flow simulation.

Xue Xiang; Wang Yueping

2013-01-01

256

Wind Turbine Micrositing: Comparison of Finite Difference Method and Computational Fluid Dynamics  

Directory of Open Access Journals (Sweden)

Full Text Available For smooth and optimal operation of wind turbines the location of wind turbines in wind farm is critical. Parameters that need to be considered for micrositing of wind turbines are topographic effect and wind effect. The location under consideration for wind farm is Gharo, Sindh, Pakistan. Several techniques are being researched for finding the most optimal location for wind turbines. These techniques are based on linear and nonlinear mathematical models. In this paper wind pressure distribution and its effect on wind turbine on the wind farm are considered. This study is conducted to compare the mathematical model; Finite Difference Method with a computational fluid dynamics software results. Finally the results of two techniques are compared for micrositing of wind turbines and found that finite difference method is not applicable for wind turbine micrositing.

Samina Rajper; Imran Amin

2012-01-01

257

Adaptive Finite Difference Method with Non-uniform Timesteps for Fractional Diffusion Equations  

CERN Document Server

An adaptive implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to adapt the size of the timesteps to the behaviour of the solution in order to keep the numerical errors small without the penalty of a huge computational cost. The method is unconditionally stable and convergent. In fact, it is shown that consistency and stability implies convergence for a rather general class of fractional finite difference methods to which the present method belongs. The computational advantages of the present adaptive method against fixed step methods are illustrated by solving the problem of the dispersion of a flux of subdiffusive particles stemming from a point source.

Yuste, Santos B

2011-01-01

258

Implementation of compact finite-difference method to parabolized Navier-Stokes equations  

International Nuclear Information System (INIS)

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

2005-08-03

259

Implementation of compact finite-difference method to parabolized Navier-Stokes equations  

Energy Technology Data Exchange (ETDEWEB)

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

Esfahanian, V. [Univ. of Tehran, Mechanical Engineering Dept., Tehran (Iran, Islamic Republic of)]. E-mail: evahid@ut.ac.ir; Hejranfar, K. [Sharif Univ. of Technology, Aerospace Engineering Dept., Tehran (Iran, Islamic Republic of); Darian, H.M. [Univ. of Tehran, Mechanical Engineering Dept., Tehran (Iran, Islamic Republic of)

2005-07-01

260

A finite difference method with non-uniform timesteps for fractional diffusion equations  

Science.gov (United States)

An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the behavior of the solution in order to keep the numerical errors small without the penalty of a huge computational cost. The method is unconditionally stable and convergent. In fact, it is shown that consistency and stability implies convergence for a rather general class of fractional finite difference methods to which the present method belongs. The huge computational advantage of adaptive methods against fixed step methods for fractional diffusion equations is illustrated by solving the problem of the dispersion of a flux of subdiffusive particles stemming from a point source.

Yuste, Santos B.; Quintana-Murillo, Joaquín

2012-12-01

 
 
 
 
261

Hybrid multiple-relaxation-time lattice-Boltzmann finite-difference method for axisymmetric multiphase flows  

Science.gov (United States)

We propose a hybrid lattice-Boltzmann finite-difference method to simulate axisymmetric multiphase flows. The hydrodynamics is simulated by the lattice-Boltzmann equations with the multiple-relaxation-time (MRT) collision model and suitable forcing terms that account for the interfacial tension and axisymmetric effects. The interface dynamics is captured by the finite-difference solution of the convective Cahn-Hilliard equation. This method is applied to simulate a quiescent drop, an oscillating drop, a drop spreading on a dry surface and a drop accelerated by a constant body force. It is validated through comparisons of the computed results for these problems with analytical solutions or numerical solutions by other different methods. It is shown that the MRT-based method is able to handle more challenging cases than that with the single-relaxation-time collision model for axisymmetric multiphase flows due to its improved stability.

Huang, Jun-Jie; Huang, Haibo; Shu, Chang; Tian Chew, Yong; Wang, Shi-Long

2013-02-01

262

Hybrid multiple-relaxation-time lattice-Boltzmann finite-difference method for axisymmetric multiphase flows  

International Nuclear Information System (INIS)

We propose a hybrid lattice-Boltzmann finite-difference method to simulate axisymmetric multiphase flows. The hydrodynamics is simulated by the lattice-Boltzmann equations with the multiple-relaxation-time (MRT) collision model and suitable forcing terms that account for the interfacial tension and axisymmetric effects. The interface dynamics is captured by the finite-difference solution of the convective Cahn–Hilliard equation. This method is applied to simulate a quiescent drop, an oscillating drop, a drop spreading on a dry surface and a drop accelerated by a constant body force. It is validated through comparisons of the computed results for these problems with analytical solutions or numerical solutions by other different methods. It is shown that the MRT-based method is able to handle more challenging cases than that with the single-relaxation-time collision model for axisymmetric multiphase flows due to its improved stability. (paper)

1175-01-00

263

On Recursive Definition of the Green Function of Finite Difference and Differential Operators  

Science.gov (United States)

The possibility of recursive definition of the Green function of finite difference operators with constant coefficients is considered. New equations for the Green functions are found. In particular cases a representation for the Green functions in the form of a series of rational functions is obtained. Generalization for the case of differential operators is carried out. The general problems of the Green functions recursive definition are formulated.

Kabanovich, V. I.; Ermilov, A. N.; Kurbatov, A. M.

264

Transport and dispersion of pollutants in surface impoundments: a finite difference model  

Energy Technology Data Exchange (ETDEWEB)

A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.

Yeh, G.T.

1980-07-01

265

Transport and dispersion of pollutants in surface impoundments: a finite difference model  

International Nuclear Information System (INIS)

A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.

1980-01-01

266

The Classical Moment Problem as a Self-Adjoint Finite Difference Operator  

CERN Multimedia

This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Pade approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we obtain new results on the convergence of certain Pade approximants for series of Hamburger.

Simon, B

1998-01-01

267

RODCON: a finite difference heat conduction computer code in cylindrical coordinates  

International Nuclear Information System (INIS)

RODCON, a finite difference computer code, was developed to calculate the internal temperature distribution of the fuel rod simulator (FRS) for the Core Flow Test Loop (CFTL). RODCON solves the implicit, time-dependent forward-differencing heat transfer equation in 2-dimensional (Rtheta) cylindrical coordinates at an axial plane with user specified radial material zones and surface conditions at the FRS periphery. Symmetry of the boundary conditions of coolant bulk temperatures and film coefficients at the FRS periphery is not necessary

1980-09-19

268

RODCON: a finite difference heat conduction computer code in cylindrical coordinates  

Energy Technology Data Exchange (ETDEWEB)

RODCON, a finite difference computer code, was developed to calculate the internal temperature distribution of the fuel rod simulator (FRS) for the Core Flow Test Loop (CFTL). RODCON solves the implicit, time-dependent forward-differencing heat transfer equation in 2-dimensional (Rtheta) cylindrical coordinates at an axial plane with user specified radial material zones and surface conditions at the FRS periphery. Symmetry of the boundary conditions of coolant bulk temperatures and film coefficients at the FRS periphery is not necessary.

Conklin, J.C.

1980-09-16

269

Chebyshev pseudospectral solution of advection-diffusion equations with mapped finite difference preconditioning  

Energy Technology Data Exchange (ETDEWEB)

A new Chebyshev pseudo-spectral algorithm with finite difference preconditioning is proposed for the solution of advection-diffusion equations. A mapping technique is introduced which allows good convergence for any Peclet number both for one-dimensional and two-dimensional problems. Numerical results show that first-order Lagrange polynomials are the optimal mapping procedure for the one-dimensional problem and second-order Lagrange polynomials, for the two-dimensional one. 8 refs., 22 figs., 4 tabs.

Pinelli, A.; Benocci, C. (Von Karman Institute for Fluid Dynamics, Rhode-St-Genese (Belgium)); Deville, M. (Universite Catholique de Louvain, Louvain-La-Neuve (Belgium))

1994-05-01

270

HEATING5-JR: a finite difference computer program for nonlinear heat conduction problems  

International Nuclear Information System (INIS)

[en] Computer program HEATING5-JR is a revised version of HEATING5 which is a finite difference computer program used for the solution of multi-dimensional, nonlinear heat conduction problems. Pre- and post-processings for graphical representations of input data and calculation results of HEATING5 are avaiable in HEATING5-JR. The calculation equations, program descriptions and user instructions are presented. Several example problems are described in detail to demonstrate the use of the program. (author)

1983-01-01

271

A FINITE DIFFERENCE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS OF NEUTRON DIFFUSION  

Directory of Open Access Journals (Sweden)

Full Text Available Partial differential equations of neutron diffusion type have been reduced to a set of finite difference equations and an error of approximation in the meaning of an Euclidean norm has been investigated.The cases when the proposed method gives better estimation of error than other methods have been demonstrated.A special attentionhas been paid to the equations of thermal neutron diffusion in a nuclear reactor.

Micha? Podowski

1972-01-01

272

TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems  

International Nuclear Information System (INIS)

Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author).

1984-01-01

273

Finite-difference time-domain calculations of a liquid-crystal-based switchable Bragg grating.  

Science.gov (United States)

A polymer-wall-confined transmissive switchable liquid crystal grating is proposed and investigated by two-dimensional finite-difference time-domain optical calculation and liquid-crystal-director calculation, to our knowledge for the first time. The results show how to obtain optimized conditions for high diffraction efficiency by adjusting the liquid crystal parameters, grating geometric structure, and applied voltages. The light propagation direction and efficiency can be accurately calculated and visualized concurrently. PMID:15191189

Wang, Bin; Wang, Xinghua; Bos, Philip J

2004-06-01

274

Finite-difference time-domain calculations of a liquid-crystal-based switchable Bragg grating.  

UK PubMed Central (United Kingdom)

A polymer-wall-confined transmissive switchable liquid crystal grating is proposed and investigated by two-dimensional finite-difference time-domain optical calculation and liquid-crystal-director calculation, to our knowledge for the first time. The results show how to obtain optimized conditions for high diffraction efficiency by adjusting the liquid crystal parameters, grating geometric structure, and applied voltages. The light propagation direction and efficiency can be accurately calculated and visualized concurrently.

Wang B; Wang X; Bos PJ

2004-06-01

275

A finite difference solution of the regularized long-wave equation  

Directory of Open Access Journals (Sweden)

Full Text Available A linearized implicit finite difference method to obtain numerical solution of the one-dimensional regularized long-wave (RLW) equation is presented. The performance and the accuracy of the method are illustrated by solving three test examples of the problem: a single solitary wave, two positive solitary waves interaction, and an undular bore. The obtained results are presented and compared with earlier work.

S. Kutluay; A. Esen

2006-01-01

276

Efficient finite difference solutions to the time-dependent Schroedinger equation  

International Nuclear Information System (INIS)

The matrix elements of the exponential of a finite difference realization of the one-dimensional Laplacian are found exactly. This matrix is used to formulate an efficient algorithm for the numerical solution to the time-dependent quantum mechanical scattering of a single particle from a time-independent potential in one-space and one-time dimension. The method generalizes to high spatial dimensions, as well as to multiparticle problems. 8 refs.

1997-01-01

277

Modeling and Simulation of Hamburger Cooking Process Using Finite Difference and CFD Methods  

Directory of Open Access Journals (Sweden)

Full Text Available Unsteady-state heat transfer in hamburger cooking process was modeled using one dimensional finite difference (FD) and three dimensional computational fluid dynamic (CFD) models. A double-sided cooking system was designed to study the effect of pressure and oven temperature on the cooking process. Three different oven temperatures (114, 152, 204°C) and three different pressures (20, 332, 570 pa) were selected and 9 experiments were performed. Applying pressure to hamburger increases the contact area of hamburger with heating plate and hence the heat transfer rate to the hamburger was increased and caused the weight loss due to water evaporation and decreasing cooking time, while increasing oven temperature led to increasing weight loss and decreasing cooking time. CFD predicted results were in good agreement with the experimental results than the finite difference (FD) ones. But considering the long time needed for CFD model to simulate the cooking process (about 1 hour), using the finite difference model would be more economic.

J. Sargolzaei; M. Abarzani; R. Aminzadeh

2011-01-01

278

A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes.  

Science.gov (United States)

A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles. PMID:16140344

Trew, Mark L; Smaill, Bruce H; Bullivant, David P; Hunter, Peter J; Pullan, Andrew J

2005-09-06

279

An Improvement for the Locally One-Dimensional Finite-Difference Time-Domain Method  

Directory of Open Access Journals (Sweden)

Full Text Available To reduce the memory usage of computing, the locally one-dimensional reduced finite-difference time-domain method is proposed. It is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions, when the electric-field and magnetic-field are calculated with locally one-dimensional finite-difference time-domain (LOD-FDTD) method, and the concrete expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the LOD-FDTD method is combined with the reduced finite-difference time-domain (R-FDTD) method. In the proposed method, the memory requirement of LOD-R-FDTD is reduced by1/6 (3D case) of the memory requirement of LOD-FDTD averagely. The formulation is presented and the accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.

Xiuhai Jin; Pin Zhang; Yiwang Chen

2011-01-01

280

A mathematical description of the IDSA for supernova neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann’s equation  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the Isotropic Diffusion Source Approximation (IDSA) established in [6]. Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA in [6] for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized. Dans cet article, nous donnons une introduction à l’équation de Boltzmann pour le transport des neutrinos dans les modèles de supernovae à effondrement de cœur ainsi qu’une description détaillée de l’Isotropic Diffusion Source Approximation (IDSA) développée dans [6]. De plus, nous présentons le traitement numérique d’un modèle de Boltzmann simplifié basé sur une décomposition en temps de l’opérateur et sur un algorithme de volumes finis ainsi que l’adaptation de la discrétisation de l’IDSA de [6] à notre modèle. Les études de l’erreur de discrétisation faites sur le modèle de Boltzmann simplifié et sur l’IDSA montrent que les erreurs sont d’ordre un dans les deux cas. A l’aide d’un exemple numérique, nous comparons et interprétons en détail les deux modèles. Pour cet exemple, l’erreur de modélisation de l’IDSA par rapport au modèle de Boltzmann simplifié est déterminée numériquement et localisée.

Berninger Heiko; Frénod Emmanuel; Gander Martin J.; Liebendörfer Matthias; Michaud Jérôme; Vasset Nicolas

2013-01-01

 
 
 
 
281

Lattice operators from discrete hydrodynamics  

CERN Document Server

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive techniques to increase the convergence order. This provides a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators, which are expected to apply across a broad range of problems in computational physics.

Ramadugu, Rashmi; Adhikari, Ronojoy; Succi, Sauro; Ansumali, Santosh

2012-01-01

282

Finite difference approach on magnetohydrodynamic flow and heat transfer in a viscous incompressible fluid between two parallel porous plates  

Directory of Open Access Journals (Sweden)

Full Text Available This paper considers the magnetohydrodynamic flow and heat transfer in a viscous incompressible fluid between two parallel porous plates experiencing a discontinuous change in wall temperature. An explicit finite difference scheme has been employed to solve the coupled non-linear equations governing the flow. The flow phenomenon has been characterized by Hartmann number, suction Reynolds number, channel Reynolds number and Prandtl number. The effects of these parameters on the velocity and temperature distribution have been analyzed and the results are presented with the aid of figures. It is observed that a growing suction parameter R retards the velocity of the flow field both in MHD as well as non-MHD flow. The effect of increasing Hartmann number is to decrease the transverse component of velocity for both suction and injection and in absence of suction and injection, while it decreases the axial component of velocity up to the middle of the channel and beyond this the effect reverses. There is a sharp fluctuation in temperature near the walls and at the middle of the channel which may be attributed to the discontinuous change in wall temperature. For fluids having low Prandtl number such as air, the temperature assumes negative values.

S. S. Das, M. Mohanty, R. K. Padhy, M. Sahu

2012-01-01

283

Finite Difference Analysis of Radiative Free Convection Flow Past an Impulsively Started Vertical Plate with Variable Heat and Mass Flux  

Directory of Open Access Journals (Sweden)

Full Text Available A numerical solution of the unsteady radiative free convection flow of an incompressible viscous fluid past an impulsively started vertical plate with variable heat and mass flux is presented here. This type of problem finds application in many technological and engineering fields such as rocket propulsion systems, spacecraft re-entry aerothermodynamics, cosmical flight aerodynamics, plasma physics, glass production and furnace engineering. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing non-linear, coupled equations are solved using an implicit finite difference scheme. Numerical results for the velocity, temperature, concentration, the local and average skinfriction, the Nusselt and Sherwood number are shown graphically, for different values of Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number, radiation parameter, heat flux exponent and the mass flux exponent. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer. The local and average skin-friction increases with the increase in radiation parameter. For increasing values of radiation parameter the local as well as average Nusselt number increases.

V. Ramachandra Prasad; N. Bhaskar Reddy; R. Muthucumaraswamy; B. Vasu

2011-01-01

284

Prestack reverse-time migration with a time-space domain adaptive high-order staggered-grid finite-difference method  

Science.gov (United States)

With advanced computational power, prestack reverse-time migration (RTM) is being used increasingly in seismic imaging. The accuracy and efficiency of RTM strongly depends on the algorithms used for numerical solutions of wave equations. Hence, how to solve the wave equation accurately and rapidly is very important in the process of RTM. In this paper, in order to improve the accuracy of the numerical solution, we use a time-space domain staggered-grid finite-difference (SFD) method to solve the acoustic wave equation, and develop a new acoustic prestack RTM scheme based on this time-space domain high-order SFD. Synthetic and real data tests demonstrate that the RTM scheme improves the imaging quality significantly compared with the conventional SFD RTM. Meanwhile, in the process of wavefield extrapolation, we apply adaptive variable-length spatial operators to compute spatial derivatives to decrease computational costs effectively with little reduction of the accuracy of the numerical solutions.

Yan, Hongyong; Liu, Yang; Zhang, Hao

2013-03-01

285

High precision finite-differences time-domain direct modelling of wave equation for seismic oceanography experiments  

Science.gov (United States)

Holbrook et al. (2003) demonstrated recently the possibility of visualizing fine structures in the water column, like thermohaline intrusion or internal waves, through seismic exploration experiments. Seismic exploration is becoming a popular technique for providing high-lateral resolution images of the explored area, in contrast with the classical oceanography probes, like XBT or XCDT. In this work we present a wave propagation model based upon a high order finite-differences time-domain (FDTD) scheme which includes special absorbing conditions in the boundaries. FDTD algorithms are known for presenting problems with reflections on the computational edges. Classical boundary conditions, like those of Engquist, provide reflection coefficients or the order of 10-2. However, reflection coefficients of fine structures in the water we are trying to model are about 10-4. Thus, the key point of the algorithm we present is in the implementation of Perfectly Matched Layer (PML) boundary conditions. These consist in zones with high absorption (therefore, very low reflection coefficient). The PML implemented in this scheme consists in a second order algorithm in the time domain, to take advantage of its stability and convergence properties. In this work we specify the propagation algorithm, and compare it results with the with Engquist and PML absorbing boundaries conditions. The PML condition affords reflection coefficients in the numerical edges lower than 10-4. Holbrook, W.S., Paramo, P., Pearse, S. and Schmitt, R.W., 2003. Thermohaline fine structure in an oceanographic front from seismic reflection profiling. Science, 301, 821-824.

Sallares, V.; Kormann, J.; Cobo, P.; Biescas, B.; Carbonell, R.

2007-05-01

286

High Accuracy Arithmetic Average Discretization for Non-Linear Two Point Boundary Value Problems with a Source Function in Integral Form  

Directory of Open Access Journals (Sweden)

Full Text Available In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u´)+?K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.

Ranjan K. Mohanty; Deepika Dhall

2011-01-01

287

A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model  

Science.gov (United States)

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

McDonald, Michael G.; Harbaugh, Arlen W.;Translated by: Guo, Weixing; Lu, Guoping

1988-01-01

288

Calculating modes of quantum wire systems using a finite difference technique  

Directory of Open Access Journals (Sweden)

Full Text Available  In this paper, the Schrodinger equation for a quantum wire is solved using a finite difference approach. A new aspect in this work is plotting wave function on cross section of rectangular cross-sectional wire in two dimensions, periodically. It is found that the correct eigen energies occur when wave functions have a complete symmetry. If the value of eigen energy has a small increase or decrease in neighborhood of the correct energy the symmetry will be destroyed and aperturbation value at the first of wave function will be observed. In addition, the demand on computer memory varies linearly with the size of the system under investigation.

T Mardani

2013-01-01

289

WONDY V: a one-dimensional finite-difference wave-propagation code  

Energy Technology Data Exchange (ETDEWEB)

WONDY V solves the finite difference analogs to the Lagrangian equations of motion in one spatial dimension (planar, cylindrical, or spherical). Simulations of explosive detonation, energy deposition, plate impact, and dynamic fracture are possible, using a variety of existing material models. In addition, WONDY has proven to be a powerful tool in the evaluation of new constitutive models. A preprocessor is available to allocate storage arrays commensurate with problem size, and automatic rezoning may be employed to improve resolution. This document provides a description of the equations solved, available material models, operating instructions, and sample problems.

Kipp, M.E.; Lawrence, R.J.

1982-06-01

290

On Consistency of Finite Difference Approximations to the Navier-Stokes Equations  

CERN Multimedia

In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted method proposed based on the finite volume method, numerical integration, and difference elimination. The third approximation was derived by the standard replacement of the temporal derivatives with the forward differences and the spatial derivatives with the central differences. We prove that only one of these approximations is strongly consistent with the Navier--Stokes equations and present our numerical tests which show that this approximation has a better behavior than the other two.

Amodio, P; Gerdt, V; La Scala, R

2013-01-01

291

Improvement of accuracy and efficiency on the finite difference method for flows in ducts  

Science.gov (United States)

A higher-order method is examined for the purpose of applying the finite difference method to the Direct Numerical Simulation (DNS) of wall-bounded turbulent flows. The spatial derivatives in the basic equations are approximated by means of the Modified Differential Quadrature (MDQ) method. The fourth order Low-Storage Runge-Kutta (LSRK) method is adopted for the time marching. The Poisson equation is solved by Biconjugate Gradient (BCG) method. In the present report, numerical results for the flow in a square driven cavity are compared with some available results.

Kajishima, Takeo

1993-09-01

292

The Theory and Application of Upwind Finite Difference Fractional Steps Procedure for Seawater Intrusion  

Directory of Open Access Journals (Sweden)

Full Text Available Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.

Yirang Yuan; Hongxing Rui; Dong Liang; Changfeng Li

2012-01-01

293

A finite difference treatment of differential equation systems with widely differing time constants  

Energy Technology Data Exchange (ETDEWEB)

A consistent method of solving systems of coupled time-dependent differential equations with vastly divergent time constants has been developed. This method is directly applicable to finite difference techniques of solutions using matrix algebra. Application to systems of isotope burnup and buildup equations with time constants ranging from minutes to millions of years demonstrates the utility of the method. Similarity to the prompt jump method of reactor kinetics indicates applicability to a wider range of positive as well as negative time constant systems.

Dalton, G.R.; Gamble, M.T.

1983-08-01

294

Evolving black hole-neutron star binaries in general relativity using pseudospectral and finite difference methods  

CERN Multimedia

We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation.

Duez, Matthew D; Kidder, Lawrence E; Pfeiffer, Harald P; Scheel, Mark A; Teukolsky, Saul A

2008-01-01

295

Evolving black hole-neutron star binaries in general relativity using pseudospectral and finite difference methods  

International Nuclear Information System (INIS)

We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation.

2008-11-15

296

Simulation model of a gel shallow solar pond using finite difference method  

International Nuclear Information System (INIS)

[en] A solar pond consists of carboxy methyl cellulose as a gel layer and it floats on the convective zone. A simulation model for the gel shallow solar pond is developed by using energy balance equation. The energy balance equation for the convection zone (salt water) is written in the form of partial differential equation. The parameters involved in the energy balance equation are heat loss, heat capacity and solar energy gain though the surface insolation and is solved by finite difference method. The thermal performance of the GSSP model is analyzed by making use of monthly mean hourly radiation for Coimbatore, India (11 degree N latitude). (Author)

2000-01-01

297

Analysis of oscillational instabilities in acoustic levitation using the finite-difference time-domain method  

DEFF Research Database (Denmark)

The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic levitation devices and to describe their evolution in time to further understand the physical mechanism involved. The study shows that the method gives accurate results for steady state conditions, and that it is a promising tool for simulations with a moving object.

Santillan, Arturo Orozco

2011-01-01

298

Finite Difference Time Domain (FDTD) Simulations of Electromagnetic Wave Propagation Using a Spreadsheet  

CERN Multimedia

We describe a simple and intuitive implementation of the method of finite difference time domain simulations for propagating electromagnetic waves using the simplest possible tools available in Microsoft Excel. The method overcomes the usual obstacles of familiarity with programming languages as it relies on little more than the cut and paste features that are standard in Excel. Avenues of exploration by students are proposed and sample graphs are included. The pedagogical effectiveness of the implementation was tested during an Independent Activities Period class, composed of 80% freshmen, at MIT, and yielded positive results.

Ward, D W; Cantarella, Jason; Fu, Joseph H.G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C.; Cantarella, Jason; Fu, Joseph H.G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C.; Cantarella, Jason; Fu, Joseph H.G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C.; Cantarella, Jason; Fu, Joseph H.G.; Kusner, Rob; Sullivan, John M.; Wrinkle, Nancy C.; Gelaki, Shlomo; Ward, David W.; Nelson, Keith A.

2004-01-01

299

Plasma heating with Alfven waves in tokamak with finite difference method  

International Nuclear Information System (INIS)

[en] Alfven wave is a branched of magneto hydrodynamic waves which its frequency is below Ion cyclotron frequency (MHz scale). Using of these waves for Tokamaks additional heating is under research because of Ohmic heating doesn't have enough capability in reaching fusion conditions. In this way we used finite difference method in solving Maxwell equations then we used it to illustrate power absorption rate delivered from Alfven waves for a Tokamak with specific parameters. For achieving this goal Gradshafranov equation was solved and then fluxes surfaces and dispersion relations for some different models of Tokamak plasma was illustrated and discussed.

2006-01-01

300

HEMP 3D -- a finite difference program for calculating elastic-plastic flow  

Energy Technology Data Exchange (ETDEWEB)

The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time. Presented here is an update of the 1975 report on the HEMP 3D numerical technique. The present report includes the sliding surface routines programmed by Robert Gulliford.

Wilkins, M.L.

1993-05-26

 
 
 
 
301

Finite-difference time domain solution of light scattering by arbitrarily shaped particles and surfaces  

DEFF Research Database (Denmark)

This chapter reviews the fundamental methods and some of the applications of the three-dimensional (3D) finite-difference time-domain (FDTD) technique for the modeling of light scattering by arbitrarily shaped dielectric particles and surfaces. The emphasis is on the details of the FDTD algorithms for particle and surface scattering calculations and the uniaxial perfectly matched layer (UPML) absorbing boundary conditions for truncation of the FDTD grid. We show that the FDTD approach has a significant potential for studying the light scattering by cloud, dust, and biological particles. The applications of the FDTD approach for beam scattering by arbitrarily shaped surfaces are also discussed.

Tanev, Stoyan; Sun, Wenbo

2012-01-01

302

Analysis of a metallic nano-rod polarizer using finite-difference-time-domain method.  

Science.gov (United States)

The polarization behavior of metallic nano-rods has been analyzed by means of the finite-difference-time-domain method. When the average spacing between the nano-rods is less than a half wavelength, the layer reflects the light polarized parallel to the nano-rods, as in a nano-slit. However, when the spacing is larger than a half wavelength, the metallic surface absorbs the light, polarized perpendicular to the rods, leading to a polarization switching. Multiple layers of nano-rods can make a polarizer with a high extinction ratio and good transmittance. PMID:20358945

Lee, Baek-Woon; Ju, Young-Gu

2010-05-01

303

Analysis of a metallic nano-rod polarizer using finite-difference-time-domain method.  

UK PubMed Central (United Kingdom)

The polarization behavior of metallic nano-rods has been analyzed by means of the finite-difference-time-domain method. When the average spacing between the nano-rods is less than a half wavelength, the layer reflects the light polarized parallel to the nano-rods, as in a nano-slit. However, when the spacing is larger than a half wavelength, the metallic surface absorbs the light, polarized perpendicular to the rods, leading to a polarization switching. Multiple layers of nano-rods can make a polarizer with a high extinction ratio and good transmittance.

Lee BW; Ju YG

2010-05-01

304

Finite-difference calculations of unsteady premixed flame-flow interactions  

Energy Technology Data Exchange (ETDEWEB)

A conservative, explicit, hybrid, finite-difference method based on the techniques of flux splitting and flux correction is presented for the calculation of one-dimensional, premixed, flame-flow interactions. The intent has been to eliminate flame structure resolution, which is computationally expensive, and focus on the pressures and temperatures resulting from the interactions. Accordinly, the flame is treated as a discontinuity propagating in an Eulerian grid and obeying a specified, empirical burning law. Comparisons with closed-form solution of flame-flow interaction problems involving shock, expansion wave, and contact discontinuity show that the method correctly predicts the outcome of the interactions.

Mulpuru, S.R.; Wilkin, G.B.

1983-01-01

305

Optimal error estimates and energy conservation identities of the ADI-FDTD scheme on staggered grids for 3D Maxwell's equations  

CERN Document Server

This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell equations. Precisely, for the case with a perfectly electric conducting (PEC) boundary condition we establish the optimal second-order error estimates in both space and time in the discrete $H^1$-norm for the ADI-FDTD scheme and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero then the discrete $L^2$-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. A key ingredient is two new discrete energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell equations introduced in this paper. Furthermore, we prove that, in addition to two known discrete energy identities which are seco...

Gao, Liping

2011-01-01

306

Finite difference method calculations of X-ray absorption fine structure for copper  

International Nuclear Information System (INIS)

[en] The finite difference method is extended to calculate X-ray absorption fine structure (XAFS) for solid state copper. These extensions include the incorporation of a Monte Carlo frozen phonon technique to simulate the effect of thermal vibrations under a correlated Debye-Waller model, and the inclusion of broadening effects from inelastic processes. Spectra are obtained over an energy range in excess of 300 eV above the K absorption edge-more than twice the greatest energy range previously reported for a solid state calculation using this method. We find this method is highly sensitive to values of the photoelectron inelastic mean free path, allowing us to probe the accuracy of current models of this parameter, particularly at low energies. We therefore find that experimental data for the photoelectron inelastic mean free path can be obtained by this method. Our results compare favourably with high precision measurements of the X-ray mass attenuation coefficient for copper, reaching agreement to within 3%, and improving previous results using the finite difference method by an order of magnitude

2007-01-15

307

A fast referenceless PRFS-based MR thermometry by phase finite difference  

International Nuclear Information System (INIS)

Proton resonance frequency shift-based MR thermometry is a promising temperature monitoring approach for thermotherapy but its accuracy is vulnerable to inter-scan motion. Model-based referenceless thermometry has been proposed to address this problem but phase unwrapping is usually needed before the model fitting process. In this paper, a referenceless MR thermometry method using phase finite difference that avoids the time consuming phase unwrapping procedure is proposed. Unlike the previously proposed phase gradient technique, the use of finite difference in the new method reduces the fitting error resulting from the ringing artifacts associated with phase discontinuity in the calculation of the phase gradient image. The new method takes into account the values at the perimeter of the region of interest because of their direct relevance to the extrapolated baseline phase of the region of interest (where temperature increase takes place). In simulation study, in vivo and ex vivo experiments, the new method has a root-mean-square temperature error of 0.35 °C, 1.02 °C and 1.73 °C compared to 0.83 °C, 2.81 °C, and 3.76 °C from the phase gradient method, respectively. The method also demonstrated a slightly higher, albeit small, temperature accuracy than the original referenceless MR thermometry method. The proposed method is computationally efficient (?0.1 s per image), making it very suitable for the real time temperature monitoring. (paper)

2013-08-21

308

A fast referenceless PRFS-based MR thermometry by phase finite difference  

Science.gov (United States)

Proton resonance frequency shift-based MR thermometry is a promising temperature monitoring approach for thermotherapy but its accuracy is vulnerable to inter-scan motion. Model-based referenceless thermometry has been proposed to address this problem but phase unwrapping is usually needed before the model fitting process. In this paper, a referenceless MR thermometry method using phase finite difference that avoids the time consuming phase unwrapping procedure is proposed. Unlike the previously proposed phase gradient technique, the use of finite difference in the new method reduces the fitting error resulting from the ringing artifacts associated with phase discontinuity in the calculation of the phase gradient image. The new method takes into account the values at the perimeter of the region of interest because of their direct relevance to the extrapolated baseline phase of the region of interest (where temperature increase takes place). In simulation study, in vivo and ex vivo experiments, the new method has a root-mean-square temperature error of 0.35 °C, 1.02 °C and 1.73 °C compared to 0.83 °C, 2.81 °C, and 3.76 °C from the phase gradient method, respectively. The method also demonstrated a slightly higher, albeit small, temperature accuracy than the original referenceless MR thermometry method. The proposed method is computationally efficient (?0.1 s per image), making it very suitable for the real time temperature monitoring.

Zou, Chao; Shen, Huan; He, Mengyue; Tie, Changjun; Chung, Yiu-Cho; Liu, Xin

2013-08-01

309

Finite difference based vibration simulation analysis of a segmented distributed piezoelectric structronic plate system  

Science.gov (United States)

Electrical modeling of piezoelectric structronic systems by analog circuits has the disadvantages of huge circuit structure and low precision. However, studies of electrical simulation of segmented distributed piezoelectric structronic plate systems (PSPSs) by using output voltage signals of high-speed digital circuits to evaluate the real-time dynamic displacements are scarce in the literature. Therefore, an equivalent dynamic model based on the finite difference method (FDM) is presented to simulate the actual physical model of the segmented distributed PSPS with simply supported boundary conditions. By means of the FDM, the four-ordered dynamic partial differential equations (PDEs) of the main structure/segmented distributed sensor signals/control moments of the segmented distributed actuator of the PSPS are transformed to finite difference equations. A dynamics matrix model based on the Newmark-? integration method is established. The output voltage signal characteristics of the lower modes (m digital simulation for vibration analysis of segmented distributed PSPSs presented in this paper can provide a reference for further research into the electrical simulation of PSPSs.

Ren, B. Y.; Wang, L.; Tzou, H. S.; Yue, H. H.

2010-08-01

310

Modeling of tension-modulated strings using finite difference and digital waveguide techniques  

Science.gov (United States)

Tension modulation is a nonlinear phenomenon where large-amplitude string vibrations cause the tension of the string to vary. This results in an initial pitch glide and energy coupling between modes, causing for example the generation of missing harmonics. The presentation discusses two methods for numerical simulation of the tension modulation nonlinearity from the sound synthesis point of view. The tension modulation is assumed to propagate instantaneously along the string. In the digital waveguide approach, spatially distributed fractional delay filters are used in modulating the string length during run time. Energy-preserving techniques can be used in implementing the fractional delays. In the finite difference approach, time-domain interpolation is used to artificially modulate the wave propagation velocity. The generation of missing harmonics is implemented in the finite difference model by creating an additional excitation point at the string termination. In the waveguide model, the same effect can be obtained by using suitable approximations in the string elongation calculation. Synthesis results for both techniques are presented. Also, a brief comparison of the models with a discussion on stability issues is provided. [This research has been funded by the Academy of Finland (Project No. 104934), S3TK graduate school, and Tekniikan edistamissaatio.

Pakarinen, Jyri

2005-09-01

311

Comparison of finite difference based methods to obtain sensitivities of stochastic chemical kinetic models.  

UK PubMed Central (United Kingdom)

Sensitivity analysis is a powerful tool in determining parameters to which the system output is most responsive, in assessing robustness of the system to extreme circumstances or unusual environmental conditions, in identifying rate limiting pathways as a candidate for drug delivery, and in parameter estimation for calculating the Hessian of the objective function. Anderson [SIAM J. Numer. Anal. 50, 2237 (2012)] shows the advantages of the newly developed coupled finite difference (CFD) estimator over the common reaction path (CRP) [M. Rathinam, P. W. Sheppard, and M. Khammash, J. Chem. Phys. 132, 034103 (2010)] estimator. In this paper, we demonstrate the superiority of the CFD estimator over the common random number (CRN) estimator in a number of scenarios not considered previously in the literature, including the sensitivity of a negative log likelihood function for parameter estimation, the sensitivity of being in a rare state, and a sensitivity with fast fluctuating species. In all examples considered, the superiority of CFD over CRN is demonstrated. We also provide an example in which the CRN method is superior to the CRP method, something not previously observed in the literature. These examples, along with Anderson's results, lead to the conclusion that CFD is currently the best estimator in the class of finite difference estimators of stochastic chemical kinetic models.

Srivastava R; Anderson DF; Rawlings JB

2013-02-01

312

Fast quasi-explicit finite difference simulation of electrochemical responses initiated by a discontinuous perturbation  

Energy Technology Data Exchange (ETDEWEB)

Commencing in the early 60s the application of explicit finite difference (EFD) methods to the analysis of electrochemical problems paralleled the development and availability of fast, main-frame, digital computers. The appeal of the EFD method has been its simplicity of principle and of application. EFD algorithms, however, are notoriously inefficient for solving certain types of stiff problems (e.g., problems involving a wide dynamic range of time constants). In this presentation the author discusses the principles and some applications of a fast quasi-explicit finite difference (FQEFD) method in which the computational speed is enhanced, by many orders of magnitude in some cases, without compromising the user friendliness which has popularized the EFD method. The method is designed to treat electrochemical responses to a discontinuous (e.g, chronoamperometric) perturbation and utilizes the DuFort-Frankel algorithm (1) with exponentially expanding space (2) and exponentially expanding time grids. (A previously published version of the FQEFD method (3,4) was designed to treat electrochemical responses to a continuous (e.g., cyclic voltammetric) perturbation and utilizes the DuFort-Frankel (3) algorithm in conjunction with an exponentially expanding space grid and a uniform time grid. The development of the basic FQEFD equations was presented there). The protocol for introducing the expanding time grid is straightforward and is discussed. 7 refs., 1 fig. 1 tab.

Feldberg, S.W.

1991-01-01

313

Mimetic discretizations for Maxwell`s equations  

Energy Technology Data Exchange (ETDEWEB)

The authors have constructed reliable finite difference methods for approximating the solution to Maxwell`s equations using accurate discrete analogs of differential operators that satisfy the identifies and theorems of vector and tensor calculus in discrete form. The numerical approximation does not have spurious modes and mimics many fundamental properties of the underlying physical problem including conservation laws, symmetries in the solution, and the nondivergence of particular vector fields. Numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous and for nonorthogonal, nonsmooth computational grids.

Hyman, J.M.; Shashkov, M. [Los Alamos National Lab., NM (United States)

1999-05-20

314

Construction of Superconvergent Discretizations with Differential-Difference Invariants  

Energy Technology Data Exchange (ETDEWEB)

To incorporate symmetry properties of second-order differential equations into finite difference equations, the concept of differential-difference invariants is introduced. This concept is applied to discretizing homogeneous eigenvalue problems and inhomogeneous two-point boundary value problems with various combinations of Dirichlet, Neumann, and Robin boundary conditions. It is demonstrated that discretizations constructed with differential-difference invariants yield exact results for eigenvalue spectra and superconvergent results for numerical solutions of differential equations.

R.A. Axford

2005-08-12

315

Accurate measurement of sample conductivity in a diamond anvil cell with axis symmetrical electrodes and finite difference calculation  

Directory of Open Access Journals (Sweden)

Full Text Available We report a relatively precise method of conductivity measurement in a diamond anvil cell with axis symmetrical electrodes and finite difference calculation. The axis symmetrical electrodes are composed of two parts: one is a round thin-film electrode deposited on diamond facet and the other is the inside wall of metal gasket. Due to the asymmetrical configuration of the two electrodes, finite difference method can be applied to calculate the conductivity of sample, which can reduce the measurement error.

Jie Yang; Gang Peng; Yonghao Han; Chunxiao Gao

2011-01-01

316

Discrete surfaces of constant mean curvature via dressing  

CERN Multimedia

We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the dressing action on discrete CMC surfaces to arrive at a classification for periodic discrete CMC surfaces.

Haak, G

1997-01-01

317

New approach for Finite Difference Method for Thermal Analysis of Passive Solar Systems  

CERN Document Server

Mathematical treatment of massive wall systems is a useful tool for investigation of these solar applications. The objectives of this work are to develop (and validate) a numerical solution model for predication the thermal behaviour of passive solar systems with massive wall, to improve knowledge of using indirect passive solar systems and assess its energy efficiency according to climatic conditions in Bulgaria. The problem of passive solar systems with massive walls is modelled by thermal and mass transfer equations. As a boundary conditions for the mathematical problem are used equations, which describe influence of weather data and constructive parameters of building on the thermal performance of the passive system. The mathematical model is solved by means of finite differences method and improved solution procedure. In article are presented results of theoretical and experimental study for developing and validating a numerical solution model for predication the thermal behaviour of passive solar system...

Shtrakov, S; Shtrakov, Stanko; Stoilov, Anton

2005-01-01

318

Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Chemistry  

UK PubMed Central (United Kingdom)

We present an expanded mixed finite element method for solving second orderelliptic partial differential equations on geometrically general domains. For the lowest-order RaviartThomasapproximating spaces, we use quadrature rules to reduce the method to cell-centered finitedifferences, possibly enhanced with some face-centered pressures. This substantially reduces the computationalcomplexity of the problem to a symmetric, positive definite system for essentially only asmany unknowns as elements. Our new method handles general shape elements (triangles, quadrilaterals,and hexahedra) and full tensor coefficients, while the standard mixed formulation reducesto finite differences only in special cases with rectangular elements. As in other mixed methods,we maintain the local approximation of the divergence (i.e., local mass conservation). In contrast,Galerkin finite element methods facilitate general element shapes at the cost of achieving only globalmass conservation. Our metho...

T. Arbogast; C. N. Dawson; P. T. Keenan; M. F. Wheeler; I. Yotov; Todd Arbogast; Clint N. Dawson; Philip T. Keenan; Mary F. Wheeler

319

Finite-difference modeling of the cryostability of helium II cooled conductor packs  

International Nuclear Information System (INIS)

[en] In this chapter, constant heat step inputs are simulated so that the model heat transfer results can be compared with experimental results to understand the accuracy of the analytical simulation for future work. The Convair thermal analyzer finite-difference computer program is used to simulate a typical helium II conductor pack geometry. A transient disturbance in a coil is examined using numeric methods. The conductors, insulation, and helium II are modeled as mass nodes with temperature-dependent densities, heat capacities, and thermal conductivities. The three major heat transfer regimes (Kapitza conductance, constant heat flux, and film boiling) are modeled by defining an effective heat transfer coefficient that simulates the appropriate heat transfer mechanism between the conductor surface and adjacent helium

1984-01-01

320

A Slowness Matching Finite Difference Method for Traveltimes Beyond Transmission Caustics  

UK PubMed Central (United Kingdom)

Conventional finite difference eikonal solvers produce only the first arrival time.However suitable solvers (of sufficiently high order of accuracy) may be extended viaFermat's principle to yield a simple algorithm which computes all traveltimes to eachsubsurface point, with cost on the same order as that of a first arrival solver.IntroductionFormally, traveltime is the solution solution ø of the eikonal equationjrø (x)j = s(x)where s(x) is the slowness field of a material supporting linear wave propagation. Asidefrom its wave applications (seismology, electromagnetics,...), this equation and ones likeare useful in the calculus of variations, image processing (shape-from-shading, mathematicalmorphology, segmentation), differential games, and so on.Certain solutions ø (x s ; x) of the eikonal equation represent the time taken by a wavemoving at slowness s(x) to travel from source point x s to x. For x near x s , these areordinary differentiable functions satisfying the e...

William W. Symes

 
 
 
 
321

Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments  

DEFF Research Database (Denmark)

In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the THz probe pulse and can be determined solely by the pump pulse duration. Our method is found to reproduce complicated two-dimensional transient conductivity maps exceedingly well, demonstrating the power of the time-domain numerical method for extracting ultrafast and dynamic transport parameters from time-resolved THz spectroscopy experiments. The numerical implementation is available online. (C) 2011 Optical Society of America

Larsen, Casper; Cooke, David G.

2011-01-01

322

Finite-Difference and Pseudospectral Time-Domain Methods Applied to Backwards-Wave Metamaterials  

CERN Document Server

Backwards-wave (BW) materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions. These materials were predicted to have many unusual electromagnetic properties, among them amplification of the near-field of a point source, which could lead to the perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev. Lett. 85, 3966 (2000)]. Often systems containing BW materials are simulated using the finite-difference time-domain (FDTD) technique. We show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving BW materials problematic. The pseudospectral time-domain (PSTD) technique, on the other hand, uses a collocated grid and is free of this artifact. It is also shown that when modeling the dispersive BW material, the linear frequency approximation method introduces error that affects the frequency of ...

Feise, M W; Bevelacqua, P J; Feise, Michael W.; Schneider, John B.; Bevelacqua, Peter J.

2004-01-01

323

Finite-Difference Time-Domain Study of Guided Modes in Nano-plasmonic Waveguides  

CERN Multimedia

The finite-difference time-domain (FDTD) method is applied for studying plasmonic waveguide formed by silver nanorods at optical frequencies. The dispersion diagram of periodic structures formed by an infinite number of nanorods is calculated by applying Bloch's periodic boundary condition therefore only one unit-cell is modelled in simulations. The frequency dispersion of silver nanorods is characterised by Drude material model and taken into account in FDTD simulations by a simple differential equation method. The dispersion diagram calculated using the FDTD method is verified by comparing the frequency domain embedding method. The change of dispersion diagram caused by the elliptical inclusion and different number of rows of nanorods is analysed. Wave propagation in the waveguides formed by a finite number (nine) of nanorods is studied and the transmission for different waveguides is calculated and compared with the corresponding dispersion diagrams. The simulation results show that row(s) of nanorods can ...

Zhao, Y; Zhao, Yan; Hao, Yang

2006-01-01

324

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains  

CERN Document Server

We present an efficient finite difference method for the computation of parameter sensitivities for a wide class of continuous time Markov chains. The motivating class of models, and the source of our examples, are the stochastic chemical kinetic models commonly used in the biosciences, though other natural application areas include population processes and queuing networks. The method is essentially derived by making effective use of the random time change representation of Kurtz, and is no harder to implement than any standard continuous time Markov chain algorithm, such as "Gillespie's algorithm" or the next reaction method. Further, the method is analytically tractable, and, for a given number of realizations of the stochastic process, produces an estimator with substantially lower variance than that obtained using other common methods. Therefore, the computational complexity required to solve a given problem is lowered greatly. In this work, we present the method together with the theoretical analysis de...

Anderson, David F

2011-01-01

325

Analysis of polarization dependence of a nano-slit using finite-difference-time-domain method.  

Science.gov (United States)

We analyzed the polarization dependent behavior of a nano-slit using a quasi-periodic finite-difference-time-domain (FDTD). In the simulation, the transmission decreases nearly to zero when the polarization is parallel to a slit, and the slit is narrower than a half wavelength. On the other hand, transmission of polarization perpendicular to the slit produces monotonic decrease with a decrease of the slit width. The polarization discrimination can be attributed to the different boundary conditions for two polarizations. According to a derived simple formula, the parallel polarization decays exponentially with the thickness of the slit when the width is smaller than a half wavelength. The exponential decay is verified by the simulation. In addition, the calculated transmission of aluminum nano-slit has a similar polarization behavior to that of a dielectric nano-slit. PMID:19198376

Lee, Baek-Woon; Ju, Young-Gu

2008-10-01

326

Analysis of polarization dependence of a nano-slit using finite-difference-time-domain method.  

UK PubMed Central (United Kingdom)

We analyzed the polarization dependent behavior of a nano-slit using a quasi-periodic finite-difference-time-domain (FDTD). In the simulation, the transmission decreases nearly to zero when the polarization is parallel to a slit, and the slit is narrower than a half wavelength. On the other hand, transmission of polarization perpendicular to the slit produces monotonic decrease with a decrease of the slit width. The polarization discrimination can be attributed to the different boundary conditions for two polarizations. According to a derived simple formula, the parallel polarization decays exponentially with the thickness of the slit when the width is smaller than a half wavelength. The exponential decay is verified by the simulation. In addition, the calculated transmission of aluminum nano-slit has a similar polarization behavior to that of a dielectric nano-slit.

Lee BW; Ju YG

2008-10-01

327

FDiff3: a finite-difference solver for facilitating understanding of heat conduction and numerical analysis  

Energy Technology Data Exchange (ETDEWEB)

The growing requirement for energy thrift and hence the increasing emphasis on 'low-purchased-energy' designs are stimulating the need for more accurate insights into the thermal behaviours of buildings and their components. This better understanding is preferably achieved, rather than by using 'closed software' or teaching the relevant mathematics outside heat-transfer lessons, but from embedding the pertinent tutoring while dealing with heat-transfer problems using an open-source code approach. Hence a finite-difference software program (FDiff3) has been composed to show the principles of numerical analysis as well as improve the undergraduates' perception of transient conduction. The pedagogic approach behind the development, its present capabilities and applications to sample test-cases are discussed. (author)

Russell, M.B. [University of Hertfordshire, Hatfield (United Kingdom). Department of Aerospace, Automotive and Design Engineering; Probert, S.D. [Cranfield University, Bedfordshire (United Kingdom). School of Engineering

2004-12-01

328

Finite-difference solution to the Schrodinger equation for the helium isoelectronic sequence  

International Nuclear Information System (INIS)

[en] The method described previously for the solution of the Schrodinger equation for S-type states of helium has been applied to the helium isoelectronic sequence. The Schrodinger equation, which is an elliptic partial-differential equation, is converted to a set of finite-difference equations which are solved by a relaxed iterative technique. The method is applied to the 11S two-electron systems for Z=1 through 8 and 23S state for Z=3. The results include expectation values of the total energy, kinetic and potential terms, and rsup(n), n = -2, -1, 1, 2, and are compared with the work of Pekeris. The total energy for the hydrogen ion, which has only one bound state, is -0.52746 and differs from Pekeris' value by 0.055%. Other total energy values differ by 0.004% or less. (Auth.)

1979-01-01

329

Attenuation of wave in a thin plasma layer by finite-difference time-domain analysis  

International Nuclear Information System (INIS)

The attenuation of the electromagnetic wave in a thin plasma layer at high pressure is investigated with finite-difference time-domain method. The effects of the plasma thickness, plasma density distribution function, collision frequency between electron and neutrals, and the frequency of incident wave on the attenuation of the electromagnetic wave are discussed. Numerical results indicate that the phase shift is sensitive to plasma distributions, and the attenuation of wave depends on its frequency, the plasma thickness, plasma density distribution, and collision frequency. In the case of a thin plasma layer, the attenuation of wave is strong only at the low band of frequency for the different distribution functions with a certain collision frequency. Plasmas with a certain thickness for high collision frequency are capable of absorbing microwave radiation over a wider frequency range for the different plasma distributions.

2007-03-01

330

A Novel Gray Image Watermarking Scheme  

Digital Repository Infrastructure Vision for European Research (DRIVER)

An effective and integrated image watermarking scheme mainly includes watermark generation, watermark embedding, watermark identification, and watermark attack. In this paper, a novel discrete wavelet transform domain image watermark scheme is proposed to meet the watermarking properties: security, ...

Yongqiang Chen; Yanqing Zhang; Hanping Hu; Hefei Ling

331

FPGA compression of ECG signals by using modified convolution scheme of the Discrete Wavelet Transform/ Compresión de señales ECG sobre FPGA utilizando un esquema modificado de convolución de la Transformada Wavelet Discreta  

Scientific Electronic Library Online (English)

Full Text Available Abstract in spanish Este documento presenta el diseño basado en FPGA para la compresión de señales ECG utilizando la Transformada Wavelet Discreta y un método de codificación sin pérdida de información. A diferencia de los trabajos clásicos para modo off-line, el trabajo actual permite la compresión en tiempo real de la señal ECG por medio de la reducción de la información redundante. Se propone un modelo para el esquema de convolución en formato punto fijo, el cual tiene buen d (more) esempeño en relación a la tasa de salida, la latencia del sistema, la máxima frecuencia de operación y la calidad de la señal comprimida. La arquitectura propuesta, la cuantización utilizada y el método de codificación proporcionan un PRD que es apto para el análisis clínico. Abstract in english This paper presents FPGA design of ECG compression by using the Discrete Wavelet Transform (DWT) and one lossless encoding method. Unlike the classical works based on off-line mode, the current work allows the real-time processing of the ECG signal to reduce the redundant information. A model is developed for a fixed-point convolution scheme which has a good performance in relation to the throughput, the latency, the maximum frequency of operation and the quality of the c (more) ompressed signal. The quantization of the coefficients of the filters and the selected fixed-threshold give a low error in relation to clinical applications.

Ballesteros, Dora M; Moreno, Diana Marcela; Gaona, Andrés E

2012-04-01

332

GPU-accelerated 3D neutron diffusion code based on finite difference method  

Energy Technology Data Exchange (ETDEWEB)

Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)

Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)

2012-07-01

333

Composite centered schemes for multidimensional conservation laws  

Energy Technology Data Exchange (ETDEWEB)

The oscillations of a centered second order finite difference scheme and the excessive diffusion of a first order centered scheme can be overcome by global composition of the two, that is by performing cycles consisting of several time steps of the second order method followed by one step of the diffusive method. The authors show the effectiveness of this approach on some test problems in two and three dimensions.

Liska, R. [Czech Technical Univ., Prague (Czech Republic). Faculty of Nuclear Sciences and Physical Engineering; Wendroff, B. [Los Alamos National Lab., NM (United States)

1998-05-08

334

Solution of the scalar wave equation over very long distances using nonlinear solitary waves: Relation to finite difference methods  

Science.gov (United States)

The linear wave equation represents the basis of many linear electromagnetic and acoustic propagation problems. Features that a computational model must have, to capture large scale realistic effects (for over the horizon or "OTH" radar communication, for example), include propagation of short waves with scattering and partial absorption by complex topography. For these reasons, it is not feasible to use Green's Function or any simple integral method, which neglects these intermediate effects and requires a known propagation function between source and observer. In this paper, we describe a new method for propagating such short waves over long distances, including intersecting scattered waves. The new method appears to be much simpler than conventional high frequency schemes: Lagrangian "particle" based approaches, such as "ray tracing" become very complex in 3-D, especially for waves that may be expanding, or even intersecting. The other high frequency scheme in common use, the Eikonal, also has difficulty with intersecting waves.Our approach, based on nonlinear solitary waves concentrated about centroid surfaces of physical wave features, is related to that of Whitham [1], which involves solving wave fronts propagating on characteristics. Then, the evolving electromagnetic (or acoustic) field can be approximated as a collection of propagating co-dimension one surfaces (for example, 2-D surfaces in three dimensions). This approach involves solving propagation equations discretely on an Eulerian grid to approximate the linear wave equation. However, to propagate short waves over long distances, conventional Eulerian numerical methods, which attempt to resolve the structure of each wave, require far too many grid cells and are not feasible on current or foreseeable computers. Instead, we employ an "extended" wave equation that captures the important features of the propagating waves. This method is first formulated at the partial differential equation (PDE) level, as a wave equation with an added "confining" term that involves both a positive and a negative dissipation. Once we have the stable PDE, the discrete formulation is simply a multidimensional PDE with (stable) perturbations caused by the discretization. The resulting discrete solution can then be low order and very simple and yet remain stable over arbitrarily long times. When discretized and solved on an Eulerian grid, this new method allows far coarser grids than required by conventional resolution considerations, while still accounting for the effects of varying atmospheric and topographic features. An important point is that the new method is in the same form as conventional discrete wave equation methods. However, the conventional solution eventually decays, and only the "intermediate asymptotic" solution can be used. Simply by adding an extra term, we show that a nontrivial true asymptotic solution can be obtained. A similar solitary wave based approach has been used successfully in a different problem (involving "Vorticity Confinement"), for a number of years.

Steinhoff, John; Chitta, Subhashini

2012-08-01

335

A finite difference thermal model of a cylindrical microwave heating applicator using locally conformal overlapping grids: part II--numerical results and experimental evaluation.  

Science.gov (United States)

In this paper, we present numerical results obtained from a robust, locally conformal 3-D Orthogonal Grid Finite Difference (OGFD) thermal algorithm introduced in Part I of our current investigation [Al-Rizzo et al., 2006] integrated with an Orthogonal Grid Finite-Difference Time Domain (OGFDTD) scheme [Al-Rizzo et al., 2000], which accurately models the volumetric electromagnetic (EM) power deposition pattern. A unified meshing scheme, which utilizes identical overlapping grids in Cartesian and cylindrical coordinates, is employed within the load zone in the OGFDTD and OGFD models. Local temperature profiles excited by the absorbed microwave energy were measured at seven locations within the sample as a function of heating time. In order to benchmark, or validate our model, an alternative analysis of the coupled EM and thermal simulations was performed using state-of-the-art, Finite Element Method-based Ansoft's High Frequency Structure Simulator (HFSS) and the coupled thermal/stress analysis tool ePHYSICS (http://www.ansoft.com). Additionally, we compare our numerical simulations against measured dynamic temperature profiles induced within a mineral ore sample maintained for exposure period of 28.5 minutes inside a cylindrical multimode heating furnace energized at 915 MHz with a microwave source power of 12.5 kW and accompanied with significant temperature elevation. A combination of convective and radiation thermal boundary conditions are considered at the interfaces between the cavity walls, air, and sample. There is a general agreement between simulated and measured spatial and temporal temperature profiles, which validates the proposed model. Results indicate that inevitable fluctuations in the frequency spectrum and output power of the magnetron, non-uniformity of sample packing, and heat released by uncontrolled exothermic chemical reactions have a significant effect on the comparisons between measured and computed temperature patterns. PMID:17278792

Al-Rizzo, Hussain M; Adada, Rami; Tranquilla, Jim M; Ma, Feng; Ionescu, Bogdan C

2006-01-01

336

A finite difference thermal model of a cylindrical microwave heating applicator using locally conformal overlapping grids: part II--numerical results and experimental evaluation.  

UK PubMed Central (United Kingdom)

In this paper, we present numerical results obtained from a robust, locally conformal 3-D Orthogonal Grid Finite Difference (OGFD) thermal algorithm introduced in Part I of our current investigation [Al-Rizzo et al., 2006] integrated with an Orthogonal Grid Finite-Difference Time Domain (OGFDTD) scheme [Al-Rizzo et al., 2000], which accurately models the volumetric electromagnetic (EM) power deposition pattern. A unified meshing scheme, which utilizes identical overlapping grids in Cartesian and cylindrical coordinates, is employed within the load zone in the OGFDTD and OGFD models. Local temperature profiles excited by the absorbed microwave energy were measured at seven locations within the sample as a function of heating time. In order to benchmark, or validate our model, an alternative analysis of the coupled EM and thermal simulations was performed using state-of-the-art, Finite Element Method-based Ansoft's High Frequency Structure Simulator (HFSS) and the coupled thermal/stress analysis tool ePHYSICS (http://www.ansoft.com). Additionally, we compare our numerical simulations against measured dynamic temperature profiles induced within a mineral ore sample maintained for exposure period of 28.5 minutes inside a cylindrical multimode heating furnace energized at 915 MHz with a microwave source power of 12.5 kW and accompanied with significant temperature elevation. A combination of convective and radiation thermal boundary conditions are considered at the interfaces between the cavity walls, air, and sample. There is a general agreement between simulated and measured spatial and temporal temperature profiles, which validates the proposed model. Results indicate that inevitable fluctuations in the frequency spectrum and output power of the magnetron, non-uniformity of sample packing, and heat released by uncontrolled exothermic chemical reactions have a significant effect on the comparisons between measured and computed temperature patterns.

Al-Rizzo HM; Adada R; Tranquilla JM; Ma F; Ionescu BC

2006-01-01

337

Discrete Stein characterizations and discrete information distances  

CERN Document Server

We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.

Ley, Christophe

2012-01-01

338

Implementation of a Courant violating scheme for mixture drift-flux equations  

Energy Technology Data Exchange (ETDEWEB)

Mixture models are commonly used in the simulation of transient two-phase flows as simplifications of six-equation models, with the drift-flux models as a common way to describe relative phase motion. This is particularly true in simulator and control system modeling where solutions that are faster than real time are necessary, and as a means for incorporating thermal-hydraulic feedback into steady-state and transient neutronics calculations. Variations on semi-implicit finite difference schemes are some of the more commonly used temporal discretization schemes. The maximum time step size associated with these schemes is normally assumed to be limited by stability considerations to the material transport time across any computational cell (Courant limit). In applications requiring solutions that are faster than real time or the calculation of thermal-hydraulic feedback in reactor kinetics codes, time-step sizes that are restricted by the material Courant limit may result in prohibitive run times. A Courant violating scheme is examined for the mixture drift-flux equations, which for rapid transients is at least as fast as classic semi-implicit methods and for slow transients allows time step sizes many times greater than the material Courant limit.

Kim, K. [Korea Atomic Energy Research Inst., Taejeon (Korea, Republic of); Doster, J.M. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Nuclear Engineering

1995-01-01

339

Discrete random walk models for space-time fractional diffusion  

International Nuclear Information System (INIS)

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order ? is part of (0,2] and skewness ? (module??{?,2-?}), and the first-order time derivative with a Caputo derivative of order ? is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation

2002-11-01

340

An iterative finite difference method for solving the quantum hydrodynamic equations of motion  

Energy Technology Data Exchange (ETDEWEB)

The quantum hydrodynamic equations of motion associated with the de Broglie-Bohm description of quantum mechanics describe a time evolving probability density whose 'fluid' elements evolve as a correlated ensemble of particle trajectories. These equations are intuitively appealing due to their similarities with classical fluid dynamics and the appearance of a generalized Newton's equation of motion in which the total force contains both a classical and quantum contribution. However, the direct numerical solution of the quantum hydrodynamic equations (QHE) is fraught with challenges: the probability 'fluid' is highly-compressible, it has zero viscosity, the quantum potential ('pressure') is non-linear, and if that weren't enough the quantum potential can also become singular during the course of the calculations. Collectively these properties are responsible for the notorious numerical instabilities associated with a direct numerical solution of the QHE. The most successful and stable numerical approach that has been used to date is based on the Moving Least Squares (MLS) algorithm. The improved stability of this approach is due to the repeated local least squares fitting which effectively filters or reduces the numerical noise which tends to accumulate with time. However, this method is also subject to instabilities if it is pushed too hard. In addition, the stability of the MLS approach often comes at the expense of reduced resolution or fidelity of the calculation (i.e., the MLS filtering eliminates the higher-frequency components of the solution which may be of interest). Recently, a promising new solution method has been developed which is based on an iterative solution of the QHE using finite differences. This method (referred to as the Iterative Finite Difference Method or IFDM) is straightforward to implement, computationally efficient, stable, and its accuracy and convergence properties are well understood. A brief overview of the IFDM will be presented followed by a couple of benchmark applications on one- and two-dimensional Eckart barrier scattering problems.

Kendrick, Brian K [Los Alamos National Laboratory

2010-01-01

 
 
 
 
341

Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere.  

Science.gov (United States)

Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms. PMID:19045635

de Groot-Hedlin, C

2008-09-01

342

Numerical simulation of viscoelastic flows using integral constitutive equations: A finite difference approach  

Science.gov (United States)

This work presents a numerical technique for simulating incompressible, isothermal, viscoelastic flows of fluids governed by the upper-convected Maxwell (UCM) and K BKZ (Kaye Bernstein, Kearsley and Zapas) integral models. The numerical technique described herein is an extension of the GENSMAC method to the solution of the momentum and mass conservation equations to include integral constitutive equations. The governing equations are solved by the finite difference method on a staggered grid using a Marker-and-Cell approach. The Finger tensor B(t) is computed in an Eulerian framework using the ideas of the deformation fields method. However, improvements to the deformation fields method are introduced: the Finger tensor B(x,t) is obtained by a second-order accurate method and the stress tensor ?(x,t) is computed by a second-order quadrature formula. The numerical method presented in this work is validated by comparing the predictions of velocity and stress fields in two-dimensional fully-developed channel flow of a Maxwell fluid with the corresponding analytic solutions. Furthermore, the flow through a planar 4:1 contraction is investigated and the numerical results were compared with the corresponding experimental data. Finally, the UCM and the K BKZ models were used to simulate the planar 4:1 contraction flow over a wide range of Reynolds and Weissenberg numbers and the numerical results obtained are in agreement with published data.

Tomé, M. F.; de Araujo, M. S. B.; Alves, M. A.; Pinho, F. T.

2008-04-01

343

A Coupled Finite Difference and Moving Least Squares Simulation of Violent Breaking Wave Impact  

DEFF Research Database (Denmark)

Two model for simulation of free surface flow is presented. The first model is a finite difference based potential flow model with non-linear kinematic and dynamic free surface boundary conditions. The second model is a weighted least squares based incompressible and inviscid flow model. A special feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep and overturning wave impacts on a vertical breakwater. Wave groups with five different wave heights are propagated from offshore to the vicinity of the breakwater, where the waves are steep, but still smooth and non-overturning. These waves are used as initial condition for the weighted least squares based incompressible and inviscid model and the wave impacts on the vertical breakwater are simulated in this model. The resulting maximum pressures and forces on the breakwater are relatively high when compared with other studies and this is due to the incompressible nature of the present model.

Lindberg, Ole; Bingham, Harry B.

2012-01-01

344

Finite difference prediction of superconductor multidimensional quench propagation and conductor pack temperature rise  

International Nuclear Information System (INIS)

[en] Typical superconducting magnet quench programs such as the General Dynamics SUPERQ computer code predict adiabatic conductor pack temperature rise during quench, with all the joule heat dissipated in a single conductor node and in the helium surrounding that node. If two and three-dimensional transport of energy by conduction and convection away from the node is considered, the peak temperature will be realistically reduced, and if drying is assumed, the normal zone will propagate transversely as well as longitudinally. Convair THERMAL ANALYZER (finite difference) models examine 2-D and 3-D propagation velocities of normal zones and temperature rises of the pool-boiling conductor pack during quench and different modes of current dump, in response to realistically computed joule heating, conductor pack heat transfer, helium hydrodynamics, energy transport, and storage. Temperature rise of different conductor packs with minimal boiling and no vapor flow energy transport show a general temperature rise 25K less than predicted by SUPERQ. More realistic assumptions of peripheral wetting or rewetting in better ventilated zones of the conductor pack, partial or attenuated decaying boiling in the conductor pack, and associated decaying vapor flow accompanying current dump predicts temperature rises 62% of those with SUPERQ. This model result agrees with experience obtained in the General Dynamics Large Coil Program (LCP)2,3 and in the Japanese Large Coil Test (LCt) magnet

1983-01-01

345

Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods.  

Science.gov (United States)

A new hybrid finite-difference (FD) and pseudospectral (PS) method adapted to the modeling of piezoelectric transducers (PZTs) is presented. The time-dependent equations of propagation are solved using the PS method while the electric field induced in the piezoelectric material is determined through a FD representation. The purpose of this combination is to keep the advantages of both methods in one model: the adaptability of FD representation to model piezoelectric elements with various geometries and materials, and the low number of nodes per wavelength required by the PS method. This approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances, directly coupled to the calculation of the electric field created inside the piezoelectric material, which is difficult with classical algorithms. These operations are computed using variables located on spatially and temporally staggered grids, which attenuate Gibbs phenomenon and increase the algorithm's accuracy. The two-dimensional modeling of a PZT plate excited by a 50 MHz sinusoidal electrical signal is performed. The results are successfully compared to those obtained using the finite-element (FE) algorithm of ATILA software with configurations spatially and temporally adapted to the FE requirements. The cost efficiency of the FD-PS time-domain method is quantified and verified. PMID:18537368

Filoux, E; Callé, S; Certon, D; Lethiecq, M; Levassort, F

2008-06-01

346

Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods.  

UK PubMed Central (United Kingdom)

A new hybrid finite-difference (FD) and pseudospectral (PS) method adapted to the modeling of piezoelectric transducers (PZTs) is presented. The time-dependent equations of propagation are solved using the PS method while the electric field induced in the piezoelectric material is determined through a FD representation. The purpose of this combination is to keep the advantages of both methods in one model: the adaptability of FD representation to model piezoelectric elements with various geometries and materials, and the low number of nodes per wavelength required by the PS method. This approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances, directly coupled to the calculation of the electric field created inside the piezoelectric material, which is difficult with classical algorithms. These operations are computed using variables located on spatially and temporally staggered grids, which attenuate Gibbs phenomenon and increase the algorithm's accuracy. The two-dimensional modeling of a PZT plate excited by a 50 MHz sinusoidal electrical signal is performed. The results are successfully compared to those obtained using the finite-element (FE) algorithm of ATILA software with configurations spatially and temporally adapted to the FE requirements. The cost efficiency of the FD-PS time-domain method is quantified and verified.

Filoux E; Callé S; Certon D; Lethiecq M; Levassort F

2008-06-01

347

Solving the time-dependent Schrödinger equation using finite difference methods  

Scientific Electronic Library Online (English)

Full Text Available Abstract in spanish Resolvemos la ecuación de Schrödinger dependiente del tiempo en una y dos dimensiones usando diferencias finitas. La evolución se lleva a cabo usando el método de líneas. Los casos ilustrativos incluyen: la partícula en una caja y en un potencial de oscilador armónico en una y dos dimensiones. Como ejemplos poco comunes presentamos la evolución de dos solitones y mostramos la dependencia temporal del comportamiento solitónico en una dimensión y la estabilizació (more) n de un modelo de gas atómico en dos dimensiones. Los códigos usados para generar los resultados en este manuscrito se encuentran disponibles a la menor petición, y esperamos que este hecho ayude a los estudiantes a adquirir un mejor entendimiento de la solución de ecuaciones diferenciales parciales relacionadas con sistemas dinámicos Abstract in english We solve the time-dependent Schrödinger equation in one and two dimensions using the finite difference approximation. The evolution is carried out using the method of lines. The illustrative cases include: the particle in a box and the harmonic oscillator in one and two dimensions. As non-standard examples we evolve two solitons and show the time-dependent solitonic behavior in one dimension and the stabilization of an atomic gas model in two dimensions. The codes used t (more) o generate the results in this manuscript are freely available under request, and we expect this material could help students to have a better grasp of the solution of partial differential equations related to dynamical systems

Becerril, R; Guzmán, F.S; Rendón-Romero, A; Valdez-Alvarado, S

2008-12-01

348

Vapor cooled lead and stacks thermal performance and design analysis by finite difference techniques  

International Nuclear Information System (INIS)

Investigation of the combined thermal performance of the stacks and vapor-cooled leads for the Mirror Fusion Test Facility-B (MFTF-B) demonstrates considerable interdependency. For instance, the heat transfer to the vapor-cooled lead (VCL) from warm bus heaters, environmental enclosure, and stack is a significant additional heat load to the joule heating in the leads, proportionately higher for the lower current leads that have fewer current-carrying, counter flow coolant copper tubes. Consequently, the specific coolant flow (G/sec-kA-lead pair) increases as the lead current decreases. The definition of this interdependency and the definition of necessary thermal management has required an integrated thermal model for the entire stack/VCL assemblies. Computer simulations based on finite difference thermal analyses computed all the heat interchanges of the six different stack/VCL configurations. These computer simulations verified that the heat load of the stacks beneficially alters the lead temperature profile to provide added stability against thermal runaway. Significant energy is transferred through low density foam filler in the stack from warm ambient sources to the vapor-cooled leads

1984-01-01

349

Vapor cooled lead and stacks thermal performance and design analysis by finite difference techniques  

Energy Technology Data Exchange (ETDEWEB)

Investigation of the combined thermal performance of the stacks and vapor-cooled leads for the Mirror Fusion Test Facility-B (MFTF-B) demonstrates considerable interdependency. For instance, the heat transfer to the vapor-cooled lead (VCL) from warm bus heaters, environmental enclosure, and stack is a significant additional heat load to the joule heating in the leads, proportionately higher for the lower current leads that have fewer current-carrying, counter flow coolant copper tubes. Consequently, the specific coolant flow (G/sec-kA-lead pair) increases as the lead current decreases. The definition of this interdependency and the definition of necessary thermal management has required an integrated thermal model for the entire stack/VCL assemblies. Computer simulations based on finite difference thermal analyses computed all the heat interchanges of the six different stack/VCL configurations. These computer simulations verified that the heat load of the stacks beneficially alters the lead temperature profile to provide added stability against thermal runaway. Significant energy is transferred through low density foam filler in the stack from warm ambient sources to the vapor-cooled leads.

Peck, S.D.; O' Loughlin, J.M.; Christensen, E.H.

1984-09-01

350

Finite difference solution of the time dependent neutron group diffusion equations  

International Nuclear Information System (INIS)

[en] In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods

1975-01-01

351

GEOTHERM: A finite difference code for testing metamorphic P–T–t paths and tectonic models  

Science.gov (United States)

Here, time-dependent solutions for the heat conduction equation are numerically evaluated in 1D space using a fully implicit algorithm based on the finite difference method, assuming temperature-dependence of thermal conductivity. The method is implemented using the package 'GEOTHERM', comprising 13 MATLAB-derived scripts and 3 Excel spreadsheets. In the package, the initial state of the modeled crust, including its thickness, average density, and average heat production rate, can be configured by the user. The exhumation/burial history and metamorphic evolution of the crust are simulated by changing these initial values to fit the vertical displacement rates of the crust imposed by the user. Once the inputs have been made, the variations with depth of temperature, proportion of melt, and shear stress, as well as average values of heat flow at the surface and across the Moho, are calculated and displayed in five separate plots. The code is demonstrated with respect to the Carboniferous evolution of the South Variscan Belt. The best fit to independent petrologic constraints derived from thermobarometry is obtained with an early Carboniferous (342 Ma) slab break-off and a shear strain rate of 10?13 s?1 between 318 and 305 Ma.

Casini, Leonardo; Puccini, Antonio; Cuccuru, Stefano; Maino, Matteo; Oggiano, Giacomo

2013-09-01

352

DETERMINATION OF MOISTURE DIFFUSION COEFFICIENT OF LARCH BOARD WITH FINITE DIFFERENCE METHOD  

Directory of Open Access Journals (Sweden)

Full Text Available This paper deals with the moisture diffusion coefficient of Dahurian Larch (Larix gmelinii Rupr.) by use of the Finite Difference Method (FDM). To obtain moisture distributions the dimensional boards of Dahurian Larch were dried, from which test samples were cut and sliced evenly into 9 pieces in different drying periods, so that moisture distributions at different locations and times across the thickness of Dahurian Larch were obtained with a weighing method. With these experimental data, FDM was used to solve Fick’s one-dimensional unsteady-state diffusion equation, and the moisture diffusion coefficient across the thickness at specified time was obtained. Results indicated that the moisture diffusion coefficient decreased from the surface to the center of the Dahurian Larch wood, and it decreased with decreasing moisture content at constant wood temperature; as the wood temperature increased, the moisture diffusion coefficient increased, and the effect of the wood temperature on the moisture diffusion coefficient was more significant than that of moisture content. Moisture diffusion coefficients were different for the two experiments due to differing diffusivity of the specimens.

Qiaofang Zhou; Yingchun Cai; Yan Xu; Xiangling Zhang

2011-01-01

353

Evaluation of explicit finite-difference techniques for LMFBR safety analysis  

International Nuclear Information System (INIS)

[en] In the past few years, the use of explicit finite-difference (EFD) and finite-element computer programs for reactor safety calculations has steadily increased. One of the major areas of application has been for the analysis of hypothetical core disruptive accidents in liquid metal fast breeder reactors. Most of these EFD codes were derived to varying degrees from the same roots, but the codes are large and have progressed rapidly, so there may be substantial differences among them in spite of a common ancestry. When this fact is coupled with the complexity of HCDA calculations, it is not possible to assure that independent calculations of an HCDA will produce substantially the same results. Given the extreme importance of nuclear safety, it is essential to be sure that HCDA analyses are correct, and additional code validation is therefore desirable. A comparative evaluation of HCDA computational techniques is being performed under an ERDA-sponsored program called APRICOT (Analysis of PRImary COntainment Transients). The philosophy, calculations, and preliminary results from this program are described in this paper

1976-10-08

354

Acceleration of 3D Finite Difference AWP-ODC for seismic simulation on GPU Fermi Architecture  

Science.gov (United States)

AWP-ODC, a highly scalable parallel finite-difference application, enables petascale 3D earthquake calculations. This application generates realistic dynamic earthquake source description and detailed physics-based anelastic ground motions at frequencies pertinent to safe building design. In 2010, the code achieved M8, a full dynamical simulation of a magnitude-8 earthquake on the southern San Andreas fault up to 2-Hz, the largest-ever earthquake simulation. Building on the success of the previous work, we have implemented CUDA on AWP-ODC to accelerate wave propagation on GPU platform. Our CUDA development aims on aggressive parallel efficiency, optimized global and shared memory access to make the best use of GPU memory hierarchy. The benchmark on NVIDIA Tesla C2050 graphics cards demonstrated many tens of speedup in single precision compared to serial implementation at a testing problem size, while an MPI-CUDA implementation is in the progress to extend our solver to multi-GPU clusters. Our CUDA implementation has been carefully verified for accuracy.

Zhou, J.; Cui, Y.; Choi, D.

2011-12-01

355

New schemes for a two-dimensional inverse problem with temperature overspecification  

Directory of Open Access Journals (Sweden)

Full Text Available Two different finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the (3,3) alternating direction implicit (ADI) finite difference scheme and the (3,9) alternating direction implicit formula. These schemes are unconditionally stable. The basis of analysis of the finite difference equation considered here is the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyett [17]. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. These schemes use less central processor times than the fully implicit schemes for two-dimensional diffusion with temperature overspecification. The alternating direction implicit schemes developed in this report use more CPU times than the fully explicit finite difference schemes, but their unconditional stability is significant. The results of numerical experiments are presented, and accuracy and the Central Processor (CPU) times needed for each of the methods are discussed. We also give error estimates in the maximum norm for each of these methods.

Dehghan Mehdi

2001-01-01

356

PKC Scheme Based on DDLP  

Directory of Open Access Journals (Sweden)

Full Text Available This paper introduces the concept of public key cryptosystem, whose security is based on double discrete logarithm problem (DDLP) with distinct discrete exponents in the multiplicative group of finite fields. The adversary has to solve distinct discrete logarithm problems simultaneously in order to recover a corresponding plaintext from the received cipertext. Therefore, this scheme is expected to gain a higher level of security. We next show that, the newly developed scheme is efficient with respect to encryption and decryption and the validity of this algorithm is proven by applying to message that are text and returning the original message in various numerical examples.

Chandrashekhar Meshram; Suchitra A. Meshram

2012-01-01

357

Calculation method of reflectance distributions for computer-generated holograms using the finite-difference time-domain method.  

UK PubMed Central (United Kingdom)

The research on reflectance distributions in computer-generated holograms (CGHs) is particularly sparse, and the textures of materials are not expressed. Thus, we propose a method for calculating reflectance distributions in CGHs that uses the finite-difference time-domain method. In this method, reflected light from an uneven surface made on a computer is analyzed by finite-difference time-domain simulation, and the reflected light distribution is applied to the CGH as an object light. We report the relations between the surface roughness of the objects and the reflectance distributions, and show that the reflectance distributions are given to CGHs by imaging simulation.

Ichikawa T; Sakamoto Y; Subagyo A; Sueoka K

2011-12-01

358

Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135  

Science.gov (United States)

We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.

Toyokuni, G.; Takenaka, H.

2007-12-01

359

An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension  

Energy Technology Data Exchange (ETDEWEB)

Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.

Bolstad, John H.

1982-06-01

360

Three-dimensional finite-difference modeling of non-linear ground notion  

Energy Technology Data Exchange (ETDEWEB)

We present a hybrid finite-difference technique capable of modeling non-linear soil amplification from the 3-D finite-fault radiation pattern for earthquakes in arbitrary earth models. The method is applied to model non-linear effects in the soils of the San Fernando Valley (SFV) from the 17 January 1994 M 6.7 Northridge earthquake. 0-7 Hz particle velocities are computed for an area of 17 km by 19 km immediately above the causative fault and 5 km below the surface where peak strike-parallel, strike-perpendicular, vertical, and total velocities reach values of 71 cm/s, 145 cm/s, 152 cm/s, and 180 cm/s, respectively. Selected Green`s functions and a soil model for the SFV are used to compute the approximate stress level during the earthquake, and comparison to the values for near-surface alluvium at the U.S. Nevada Test Site suggests that the non-linear regime may have been entered. We use selected values from the simulated particle velocity distribution at 5 km depth to compute the non-linear response in a soil column below a site within the Van Norman Complex in SFV, where the strongest ground motion was recorded. Since site-specific non- linear material parameters from the SFV are currently unavailable, values are taken from analyses of observed Test Site ground motions. Preliminary results show significant reduction of spectral velocities at the surface normalized to the peak source velocity due to non-linear effects when the peak velocity increases from 32 cm/s (approximately linear case) to 64 cm/s (30-92%), 93 cm/s (7-83%), and 124 cm/s (2-70%). The largest reduction occurs for frequencies above 1 Hz.

Jones, E.M. [Los Alamos National Lab., NM (United States); Olsen, K.B. [California Univ., Santa Barbara, CA (United States). Inst. for Crustal Studies

1997-08-01

 
 
 
 
361

Development and comparison of practical discretization methods for the neutron diffusion equation over general quadrilateral partitions  

International Nuclear Information System (INIS)

[en] Several low-order finite element and finite difference discretizations for the multigroup diffusion equation over a quadrilateral mesh in the plane have been developed. Included are hybrid methods which reduce to higher-order discretizations for model problems with uniform mesh subdivisions. Each of these methods can be easily extended to three dimensions using a pseudo variational approach. Extensive numerical experimentations and comparisons are summarized and indicate that the low order methods for suitable triangulations are in general better than the low order finite difference and isoparametric bilinear finite element methods for quadrilaterals. (19 references) (U.S.)

1975-04-15

362

A PRACTICAL PROXY SIGNATURE SCHEME  

Directory of Open Access Journals (Sweden)

Full Text Available A proxy signature scheme is a variation of the ordinary digital signature scheme which enables a proxy signer to generate signatures on behalf of an original signer. In this paper, we present two efficient types of proxy signature scheme. The first one is the proxy signature for warrant partial delegation combines an advantage of two well known warrant partial delegation schemes. This proposed proxy signature scheme is based on the difficulty of solving the discrete logarithm problem. The second proposed scheme is based on threshold delegation the proxy signer power to sign the message is share. We claim that the proposed proxy signature schemes meet the security requirements and more practical than the existing proxy signature schemes.

Sattar Aboud; Sufian Yousef

2012-01-01

363

Multi-component seismic-resolution analysis using finite-difference acquisition modelling  

Science.gov (United States)

Various rules-of-thumb (e.g. Fresnel radius, Rayleigh limit) are commonly used to predict seismic resolution, based on the dominant frequency on the image. However, seismic resolution ultimately depends on more fundamental parameters including survey design, source bandwidth, geology, and data processing. A more instructive analysis is possible via numerical modelling of the acquisition process. Here we demonstrate the improved insight available with this approach, using examples taken from the petroleum and coal sectors. We use viscoelastic finite-difference modelling to simulate 2D multi-component acquisition sequences. The ability to allow for anelastic attenuation is important as it permits a more realistic comparison of the resolution achievable on P-wave and converted-wave (PS) imagery. An examination of vertical resolution for a wedge model on a petroleum scale indicates that processed P-wave sections have poorer resolution (62m) than predicted by the Widess (20m) and Rayleigh (40m) resolution limits. For this model the vertical resolution for the PS data is comparable to that of the P-wave data. This is in agreement with the theoretical relative-resolution relationship. A second example examines detection of lens-like features at petroleum depth. The resolving ability on the P-wave imagery is broadly consistent with analytical predictions appropriate to migrated data (100m laterally and 40m vertically). Again PS resolution is comparable to P resolution. Analysis of a typical coal target suggests that barren-zones of width 5-10m can be resolved. The interplay of wavelength and attenuation is such that the PS image is likely to exhibit comparable, or slightly reduced, lateral resolution, provided statics are not a problem. Resolution can be downgraded significantly if statics are more severe, and in practice this is likely to have greater impact on the PS image. Realistic numerical modelling, simulating the full acquisition and processing sequence, leads to a more pragmatic understanding of seismic resolution issues. It is a valuable tool for survey planning and image interpretation.

Strong, Shaun; Hearn, Steve

2008-12-01

364

A finite-difference frequency-domain code for electromagnetic induction tomography  

Energy Technology Data Exchange (ETDEWEB)

We are developing a new 3D code for application to electromagnetic induction tomography and applications to environmental imaging problems. We have used the finite-difference frequency- domain formulation of Beilenhoff et al. (1992) and the anisotropic PML (perfectly matched layer) approach (Berenger, 1994) to specify boundary conditions following Wu et al. (1997). PML deals with the fact that the computations must be done in a finite domain even though the real problem is effectively of infinite extent. The resulting formulas for the forward solver reduce to a problem of the form Ax = y, where A is a non-Hermitian matrix with real values off the diagonal and complex values along its diagonal. The matrix A may be either symmetric or nonsymmetric depending on details of the boundary conditions chosen (i.e., the particular PML used in the application). The basic equation must be solved for the vector x (which represents field quantities such as electric and magnetic fields) with the vector y determined by the boundary conditions and transmitter location. Of the many forward solvers that could be used for this system, relatively few have been thoroughly tested for the type of matrix encountered in our problem. Our studies of the stability characteristics of the Bi-CG algorithm raised questions about its reliability and uniform accuracy for this application. We have found the stability characteristics of Bi-CGSTAB [an alternative developed by van der Vorst (1992) for such problems] to be entirely adequate for our application, whereas the standard Bi-CG was quite inadequate. We have also done extensive validation of our code using semianalytical results as well as other codes. The new code is written in Fortran and is designed to be easily parallelized, but we have not yet tested this feature of the code. An adjoint method is being developed for solving the inverse problem for conductivity imaging (for mapping underground plumes), and this approach, when ready, will make repeated use of the current forward modeling code.

Sharpe, R M; Berryman, J G; Buettner, H M; Champagne, N J.,II; Grant, J B

1998-12-17

365

A finite-difference frequency-domain code for electromagnetic induction tomography  

International Nuclear Information System (INIS)

We are developing a new 3D code for application to electromagnetic induction tomography and applications to environmental imaging problems. We have used the finite-difference frequency- domain formulation of Beilenhoff et al. (1992) and the anisotropic PML (perfectly matched layer) approach (Berenger, 1994) to specify boundary conditions following Wu et al. (1997). PML deals with the fact that the computations must be done in a finite domain even though the real problem is effectively of infinite extent. The resulting formulas for the forward solver reduce to a problem of the form Ax = y, where A is a non-Hermitian matrix with real values off the diagonal and complex values along its diagonal. The matrix A may be either symmetric or nonsymmetric depending on details of the boundary conditions chosen (i.e., the particular PML used in the application). The basic equation must be solved for the vector x (which represents field quantities such as electric and magnetic fields) with the vector y determined by the boundary conditions and transmitter location. Of the many forward solvers that could be used for this system, relatively few have been thoroughly tested for the type of matrix encountered in our problem. Our studies of the stability characteristics of the Bi-CG algorithm raised questions about its reliability and uniform accuracy for this application. We have found the stability characteristics of Bi-CGSTAB [an alternative developed by van der Vorst (1992) for such problems] to be entirely adequate for our application, whereas the standard Bi-CG was quite inadequate. We have also done extensive validation of our code using semi-analytical results as well as other codes. The new code is written in Fortran and is designed to be easily parallelized, but we have not yet tested this feature of the code. An adjoint method is being developed for solving the inverse problem for conductivity imaging (for mapping underground plumes), and this approach, when ready, will make repeated use of the current forward modeling code

1998-01-01

366

Acoustic VTI modeling and pre-stack reverse-time migration based on the time-space domain staggered-grid finite-difference method  

Science.gov (United States)

Reverse-time migration (RTM) is based on seismic numerical modeling algorithms, and the accuracy and efficiency of RTM strongly depend on the algorithm used for numerical solution of wave equations. Finite-difference (FD) methods have been widely used to solve the wave equation in seismic numerical modeling and RTM. In this paper, we derive a series of time-space domain staggered-grid FD coefficients for acoustic vertical transversely isotropic (VTI) equations, and adopt these difference coefficients to solve the equations, then analyze the numerical dispersion and stability, and compare the time-space domain staggered-grid FD method with the conventional method. The numerical analysis results demonstrate that the time-space domain staggered-grid FD method has greater accuracy and better stability than the conventional method under the same discretizations. Moreover, we implement the pre-stack acoustic VTI RTM by the conventional and time-space domain high-order staggered-grid FD methods, respectively. The migration results reveal that the time-space domain staggered-grid FD method can provide clearer and more accurate image with little influence on computational efficiency, and the new FD method can adopt a larger time step to reduce the computation time and preserve the imaging accuracy as well in RTM. Meanwhile, when considering the anisotropy in RTM for the VTI model, the imaging quality of the acoustic VTI RTM is better than that of the acoustic isotropic RTM.

Yan, Hongyong; Liu, Yang

2013-03-01

367

Discrete Folding  

CERN Multimedia

Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a face-centered-cubic lattice are treated. The 3d-folding problem corresponds to a 96-vertex model and exhibits a first-order folding transition from a crumpled phase to a completely flat phase as the bending rigidity increases.

Bowick, M J; Golinelli, O; Guitter, E; Bowick, Mark; Francesco, Philippe Di; Golinelli, Olivier; Guitter, Emmanuel

1996-01-01

368

Seismic Risk Analysis of Discrete Systems.  

Science.gov (United States)

Two efficient schemes have been developed for the analysis of systems of discrete sites. Both schemes have the same objective of finding the probability of simultaneous failure of any number of sites belonging to a given system of sites subject to threats...

G. Taleb-Agha R. V. Whitman

1975-01-01

369

Computational evaluation of convection schemes in fluid dynamics problems  

CERN Document Server

This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are analyzed and implemented in the context of normalized variables of Leonard. In order to access the performance of the schemes, Riemann problems for 1D Burgers, Euler and shallow water equations are considered. From the numerical results, the schemes are ranked according to their performance in solving these non-linear equations. The best scheme is then applied in the numerical simulation of tridimensional incompressible moving free surface flows.

Ferreira, Valdemir Garcia; Corrêa, Laís; Candezano, Miguel Antonio Caro; Cirilo, Eliandro Rodrigues; Natti, Paulo Laerte; Romeiro, Neyva Maria Lopes; 10.5433/1679-0375.2012v33n2p107

2013-01-01

370

Numerical calculation of fully-developed laminar flows in arbitrary cross-sections using finite difference method  

Directory of Open Access Journals (Sweden)

Full Text Available The finite difference method has adequate accuracy to calculate fully-developed laminar flows in regular cross-sectional domains, but in irregular domains such flows are solved using the finite element method or structured grids. However, it has become apparent that we can use the finite difference method freely even if domains are complex. The non-slip condition on the wall must be imposed. Even in irregular domains, this boundary condition can be introduced indirectly by adding a single procedure to set the boundary condition. The calculations have similar accuracy as in regular domains. The proposed method has a wide range of applications; as a first step, fully-developed laminar flows are investigated in the paper.

Tsugio Fukuchi

2011-01-01

371

Thermal analysis of plasma facing components of SST-1 Tokamak by finite difference and finite element methods  

International Nuclear Information System (INIS)

[en] Thermal analysis is a prime consideration in the design of plasma facing components (PFC) cooling during plasma operation in a Tokamak device. The task is greatly simplified by using computer-based numerical techniques. Finite difference method (FDM) and finite element method (FEM) are the two methods generally being used for thermal analysis. FEM is gaining wide acceptance for such problems because it performs all the necessary computations in the computer. FDM, in contrast, requires significant amounts of data to be calculated for input into the computer program. This can provide accurate thermal analysis in less time and less computer memory than FEM. An efficient finite difference (FD) code has been developed to derive the two-dimensional temperature profile in different PFC modules subjected to steady-state condition. The details of the code and comparison of its results with finite element (FE) analysis are presented in this paper

2004-01-01

372

Finite difference method for inner-layer equations in the resistive MagnetoHydroDynamic stability analysis  

International Nuclear Information System (INIS)

[en] The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)

1996-01-01

373

The calculation of critical discharge rates with a one-dimensional finite difference model with consideration of discharge geometry  

International Nuclear Information System (INIS)

[en] To determine critical discharge rates a one-dimensional finite difference model describing the one- and two-phase flow is used to simulate the fluid flow in the flow path closest to the discharge orifice where local pressure drop is strongest. The critical mass flow rate is limited to sonic flow at the discharge orifice. Thermodynamic nonequilibrium phenomena are taken into account. In the case of a discharge nozzle with a complicated geometry, the calculation of the critical discharge rate depends on how well the streamlines along the nozzle are simulated. A good approximation of the discharge geometry is possible with the 1-D finite difference model. The model was verified by the results of serval experiments. The influence of the discharge geometry has been extensively investigated using the results of the LOBI-nozzle calibration tests

1983-01-01

374

Finite difference method for inner-layer equations in the resistive MagnetoHydroDynamic stability analysis  

Energy Technology Data Exchange (ETDEWEB)

The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)

Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko

1996-08-01

375

Analysis by finite differences of unsteady state heat transfer in a wall. Error evaluation and grid selection  

Energy Technology Data Exchange (ETDEWEB)

Unsteady state heat transfer in a three-layer wall using a model with finite differences of the Crank-Nicholson type is analyzed. A special analysis of calculation errors at the input face and at the interface separating two media leads to suggest a space/time grid that produces minimal errors. Finally, the results are compared to those given by an explicit method for the determination of response factors of a building wall.

Abgrall, M.; Padet, J. (I.U.T. de Reims, (France))

1982-12-01

376

Study of two-dimensional transient cavity fields using the finite-difference time-domain technique  

International Nuclear Information System (INIS)

[en] This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs

1988-01-01

377

Discrete-Time Approximations of the  

UK PubMed Central (United Kingdom)

This paper studies the relation between discrete-time and continuoustimeprincipal-agent models. We derive the continuous-time model as a limit of discretetimemodels with ever shorter periods and show that optimal incentive schemes in thediscrete-time models approximate the optimal incentive scheme in the continuous model,which is linear in accounts. Under the additional assumption that the principal observesonly cumulative total profits at the end and the agent can destroy profits unnoticed, anincentive scheme that is linear in total profits is shown to be approximately optimal inthe discrete-time model when the length of the period is small.

Martin F. Hellwig; Klaus M. Schmidt

378

Extensions of Noether's Second Theorem: from continuous to discrete systems  

CERN Document Server

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational problem whose symmetries depend upon a set of free or partly-constrained functions. Our approach extends further to deal with finite difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.

Hydon, Peter E

2011-01-01

379

Discrete wave mechanics: The hydrogen atom with angular momentum.  

UK PubMed Central (United Kingdom)

A discrete wave mechanical treatment of the hydrogen atom is extended to deal with states involving nonzero angular momentum. Only the radial portions of the wave vectors are covered. It is predicted that there is a nonzero minimum distance between the electron and the nucleus; this threshold distance increases with increasing angular momentum. Appropriate finite difference equations are formulated. The states with angular momentum exhibit the same degeneracy as do corresponding energy levels obtained from solutions of Schrödinger's equation.

Wall FT

1987-03-01

380

D++, a C++ class library for finite difference solution of PDEs on quadrilaterals  

UK PubMed Central (United Kingdom)

We have extended a tool, D++, for solving partial differential equations.It is a class library derived from a matrix package called Newmatand is implemented in C++. With D++ it is possible to approximatefirst and second order derivatives in space and to implement the boundaryconditions Neumann, Dirichlet, Periodic and Robin. It uses a secondorder central difference scheme on the inner points of the domain and askew method on the boundary points. The package can be used for solvingequations on a rectangular domain or a domain given by a set of gridpoints.Contents1 Introduction 32 Implementation 63 Technical Description 83.1 The Original System : : : : : : : : : : : : : : : : : : : : : : : : : 83.1.1 Class ScalarGridFunction : : : : : : : : : : : : : : : : : : 83.1.2 Class BaseGrid : : : : : : : : : : : : : : : : : : : : : : : : 83.1.3 Class Timer : : : : : : : : : : : : : : : : : : : : : : : : : : 123.2 The Extensions : : : : : : : : : : : : : : : : : : : : : : : : ...

Katarina Gustavsson; Carin Lundin

 
 
 
 
381

Compatible Spatial Discretizations for Partial Differential Equations  

Energy Technology Data Exchange (ETDEWEB)

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations. + Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations. + Relationships between different compatible spatial discretization methods and concepts which have been developed; + Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings. + How solvers address the demands placed upon them by compatible spatial discretizations. This report provides information about the program and abstracts of all the presentations.

Arnold, Douglas, N, ed.

2004-11-25

382

MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation  

Science.gov (United States)

A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton-Raphson formulation, respectively.

Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.

2013-01-01

383

Gridsize induced error in the discretization of exchange processes at the tropopause  

Scientific Electronic Library Online (English)

Full Text Available Abstract in spanish Estudiamos el error introducido por el método de las diferencias finitas en la discretización de un modelo global simplificado 2-D de transporte de gases traza, para casos en que los coeficientes de difusión, que relacionan el flujo con el gradiente de la razón de mezcla, tienen discontinuidades de salto en la tropopausa. Analizamos el método convencional de celdas tanto para el caso de un flujo ascendente típico, como también para el caso de un flujo descendente t (more) ípico con reacciones químicas, comparando las aproximaciones de las soluciones correspondientes para diferentes tamaños de paso de discretización. Para el flujo descendente típico resulta que si la rejilla no es suficientemente fina se pueden generar grandes errores; estos se propagan fundamentalmente en la troposfera. En cambio, el flujo típicamente ascendente resulta ser relativamente insensible al tamaño de paso de la discretización. Abstract in english We study the accuracy of the finite differences discretization scheme for a 2-D simplified model of global tracer transport, in the case that the diffusion coefficients relating flux to the gradient of the mixing ratio have discontinuity jumps at the tropopause. We analyze the conventional box method for a typical downward flow with chemical reaction and for a typical upward flow, comparing the approximations of the solutions, for different discretization gridsizes. It tu (more) rns out that the jumps may introduce remarkable errors in the discrete solutions, in the case of a typical downward flow; these errors propagate mainly into the troposphere. A noticeable improvement is achieved by reducing the gridsize. However, a typical upward flow is rather insensitive to the chosen gridsizes.

FIEBIG-WITTMAACK, M.

2005-07-01

384

A hybrid absorbing boundary condition for frequency-domain finite-difference modelling  

Science.gov (United States)

Liu and Sen (2010 Geophysics 75 A1-6 2012 Geophys. Prospect. 60 1114-32) proposed an efficient hybrid scheme to significantly absorb boundary reflections for acoustic and elastic wave modelling in the time domain. In this paper, we extend the hybrid absorbing boundary condition (ABC) into the frequency domain and develop specific strategies for regular-grid and staggered-grid modelling, respectively. Numerical modelling tests of acoustic, visco-acoustic, elastic and vertically transversely isotropic (VTI) equations show significant absorptions for frequency-domain modelling. The modelling results of the Marmousi model and the salt model also demonstrate the effectiveness of the hybrid ABC. For elastic modelling, the hybrid Higdon ABC and the hybrid Clayton and Engquist (CE) ABC are implemented, respectively. Numerical simulations show that the hybrid Higdon ABC gets better absorption than the hybrid CE ABC, especially for S-waves. We further compare the hybrid ABC with the classical perfectly matched layer (PML). Results show that the two ABCs cost the same computation time and memory space for the same absorption width. However, the hybrid ABC is more effective than the PML for the same small absorption width and the absorption effects of the two ABCs gradually become similar when the absorption width is increased.

Ren, Zhiming; Liu, Yang

2013-10-01

385

Space-time FLAVORS: finite difference, multisymlectic, and pseudospectral integrators for multiscale PDEs  

CERN Multimedia

We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i) Multiscale: they are based on flow averaging and have a computational cost determined by mesoscopic steps in space and time instead of microscopic steps in space and time; (ii) Versatile: the method is based on averaging the flows of the given PDEs (which may have hidden slow and fast processes). This bypasses the need for identifying explicitly (or numerically) the slow variables or reduced effective PDEs; (iii) Nonintrusive: A pre-existing numerical scheme resolving the microscopic time scale can be used as a black box and easily turned into one of the integrators in this paper by turning the large coefficients on over a microscopic timescale and off during a mesoscopic timescale; (iv) Convergent over two scales: strongly over slow processes and in the sense of measures over ...

Tao, Molei; Marsden, Jerrold E

2011-01-01

386

Metadata Schemes  

Indian Academy of Sciences (India)

metadata schemes metadata schemes set of metadata elements, with associated semantics and syntax for describing a particular type of resources metadata elements and their meaning/ definition content: values given to metadata elements ...

387

An investigation of discretization errors for mesh centered finite difference approximations to the transport equation using a spherical harmonic expansion of the flux  

Energy Technology Data Exchange (ETDEWEB)

The multigroup Transport Equation for the flux column vector {Psi}(r,{Omega}) at location r in the direction of unit vector {Omega}, {Omega}.{nabla}{Psi}(r,{Omega}) + {sigma}{sub t}(r){Psi}(r,{Omega})

Fletcher, J.K. [Power Reactor and Nuclear Fuel Development Corp., Oarai, Ibaraki (Japan). Oarai Engineering Center

1997-07-01

388

Analysis of a discretization method for the Richards' equation  

UK PubMed Central (United Kingdom)

We analyse a discretization method for a class of degenerate parabolic problems that includesthe Richards' equation. This analysis applies to the pressure-based formulation andconsiders both variably and fully saturated regimes. A regularization approach is combinedwith the Euler implicit scheme to achieve the time discretization. Equivalence between thetwo kinds of formulation is demonstrated for the semi-discrete case. Mixed finite elementsare employed for the discretization in space. Error estimates are obtained, showing that thescheme is convergent.

F. Radu; I. S. Pop; P. Knabner

389

On Compatibility of Discrete Relations  

CERN Multimedia

An approach to compatibility analysis of systems of discrete relations is proposed. Unlike the Groebner basis technique, the proposed scheme is not based on the polynomial ring structure. It uses more primitive set-theoretic and topological concepts and constructions. We illustrate the approach by application to some two-state cellular automata. In the two-state case the Groebner basis method is also applicable, and we compare both approaches.

Kornyak, V V

2005-01-01

390

High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI.  

Science.gov (United States)

A spectrum of higher-order schemes is developed to solve the Navier- Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated b...

D. V. Gaitonde M. R. Visbal

1998-01-01

391

Discrete Pearson distributions  

Energy Technology Data Exchange (ETDEWEB)

These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.

Bowman, K.O. [Oak Ridge National Lab., TN (United States); Shenton, L.R. [Georgia Univ., Athens, GA (United States); Kastenbaum, M.A. [Kastenbaum (M.A.), Basye, VA (United States)

1991-11-01

392

Jet schemes for advection problems  

CERN Document Server

We present a systematic methodology to develop high order accurate numerical approaches for linear advection problems. These methods are based on evolving parts of the jet of the solution in time, and are thus called jet schemes. Through the tracking of characteristics and the use of suitable Hermite interpolations, high order is achieved in an optimally local fashion, i.e. the update for the data at any grid point uses information from a single grid cell only. We show that jet schemes can be interpreted as advect-and-project processes in function spaces, where the projection step minimizes a stability functional. Furthermore, this function space framework makes it possible to systematically inherit update rules for the higher derivatives from the ODE solver for the characteristics. Jet schemes of orders up to five are applied in numerical benchmark tests, and systematically compared with classical WENO finite difference schemes. It is observed that jet schemes tend to possess a higher accuracy than WENO sche...

Seibold, Benjamin; Rosales, Rodolfo Ruben

2011-01-01

393

Pre-stack reverse-time migration based on the time-space domain adaptive high-order finite-difference method in acoustic VTI medium  

Science.gov (United States)

With the increment of seismic exploration precision requirement, it is significant to develop the anisotropic migration methods. Pre-stack reverse-time migration (RTM) is performed based on acoustic vertical transversely isotropic (VTI) wave equations, and the accuracy and efficiency of RTM strongly depend on the algorithms used for wave equation numerical solution. Finite-difference (FD) methods have been widely used in numerical solution of wave equations. The conventional FD method derives spatial FD coefficients from the space domain dispersion relation, and it is difficult to satisfy the time-space domain dispersion relation of the wave equation exactly. In this paper, we adopt a time-space domain FD method to solve acoustic VTI wave equations. Dispersion analysis and numerical modelling results demonstrate that the time-space domain FD method has greater accuracy than the conventional FD method under the same discretizations. The time-space domain high-order FD method is also applied in the wavefield extrapolation of acoustic VTI pre-stack RTM. The model tests demonstrate that the acoustic VTI pre-stack RTM based on the time-space domain FD method can obtain better images than that based on the conventional FD method, and the processing results show that the imaging quality of the acoustic VTI RTM is clearer and more correct than that of acoustic isotropic RTM. Meanwhile, in the process of wavefield forward and backward extrapolation, we employ adaptive variable-length spatial operators to compute spatial derivatives to improve the computational efficiency effectively almost without reducing the imaging accuracy.

Yan, Hongyong; Liu, Yang

2013-02-01

394

Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach  

Science.gov (United States)

Using first principles calculations based on density functional theory and a coupled finite-fields/finite-differences approach, we study the dielectric properties, phonon dispersions and Raman spectra of ZnO, a material whose internal polarization fields require special treatment to correctly reproduce the ground state electronic structure and the coupling with external fields. Our results are in excellent agreement with existing experimental measurements and provide an essential reference for the characterization of crystallinity, composition, piezo- and thermo-electricity of the plethora of ZnO-derived nanostructured materials used in optoelectronics and sensor devices.

Calzolari, Arrigo; Nardelli, Marco Buongiorno

2013-01-01

395

Three-dimensional analysis of subwavelength diffractive optical elements with the finite-difference time-domain method.  

Science.gov (United States)

We present a three-dimensional (3D) analysis of subwavelength diffractive optical elements (DOE's), using the finite-difference time-domain (FDTD) method. To this end we develop and apply efficient 3D FDTD methods that exploit DOE properties, such as symmetry. An axisymmetric method is validated experimentally and is used to validate the more general 3D method. Analyses of subwavelength gratings and lenses, both with and without rotational symmetry, are presented in addition to a 2 x 2 subwavelength focusing array generator. PMID:18345211

Mirotznik, M S; Prather, D W; Mait, J N; Beck, W A; Shi, S; Gao, X

2000-06-10

396

Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach  

Science.gov (United States)

Using first principles calculations based on density functional theory and a coupled finite-fields/finite-differences approach, we study the dielectric properties, phonon dispersions and Raman spectra of ZnO, a material whose internal polarization fields require special treatment to correctly reproduce the ground state electronic structure and the coupling with external fields. Our results are in excellent agreement with existing experimental measurements and provide an essential reference for the characterization of crystallinity, composition, piezo- and thermo-electricity of the plethora of ZnO-derived nanostructured materials used in optoelectronics and sensor devices.

Calzolari, Arrigo; Nardelli, Marco Buongiorno

2013-10-01

397

Wave propagation in laminates using the nonhomogenized dynamic method of cells: An alternative to standard finite-difference hydrodynamic approaches  

Energy Technology Data Exchange (ETDEWEB)

The nonhomogenized dynamic method of cells (NHDMOC) uses a truncated expansion for the particle displacement field; the expansion parameter is the local cell position vector. In the NHDMOC, specifying the cell structure is similar to specifying the spatial grid used in a finite-difference hydrodynamic calculation. The expansion coefficients for the particle displacement field are determined by the equation of motion, any relevant constitutive relations, plus continuity of traction and displacement at all cell boundaries. The authors derive and numerically solve the NHDMOC equations for the first, second, and third-order expansions, appropriate for modeling a plate-impact experiment. The performance of the NHDMOC is tested, at each order, for its ability to resolve a shock-wave front as it propagates through homogeneous and laminated targets. They find for both cases that the displacement field expansion converges rapidly: given the same cell widths, the first-order theory gives only a qualitative description of the propagating stress wave; the second-order theory performs much better; and the third-order theory gives small refinements over the second-order theory. The performance of the third-order NHDMOC is then compared to that of a standard finite-difference hydrodynamic calculation. The two methods differ in that the former uses a finite-difference solution to update the time dependence of the equations, whereas the hydrodynamic calculation uses finite-difference solutions for both the temporal and spatial variables. Both theories are used to model shock-wave propagation in stainless steel arising from high-velocity planar impact. To achieve the same high-quality resolution of the stress and particle velocity profiles, the NHDMOC consistently requires less fine spatial and temporal grids, and substantially less artificial viscosity to control unphysical high-frequency oscillations in the numerical solutions. Finally, the third-order NHDMOC theory is used to calculate the particle velocity for a shock-wave experiment involving an epoxy-graphite laminate. Constitutive relations suitable for the various materials are used. This includes linear and nonlinear elasticity, and when appropriate, viscoelasticity. The results agree well with the corresponding plate-impact experiment, and are compared to the second-order theory of Clements, Johnson, and Hixson.

Clements, B.E.; Johnson, J.N.

1997-09-01

398

Achieving Energy Conservation in Poisson-Boltzmann Molecular Dynamics: Accuracy and Precision with Finite-Difference Algorithms.  

UK PubMed Central (United Kingdom)

Violation of energy conservation in Poisson-Boltzmann molecular dynamics, due to the limited accuracy and precision of numerical methods, is a major bottleneck preventing its wide adoption in biomolecular simulations. We explored the ideas of enforcing interface conditions by the immerse interface method and of removing charge singularity to improve the finite-difference methods. Our analysis of these ideas on an analytical test system shows significant improvement in both energies and forces. Our analysis further indicates the need for more accurate force calculation, especially the boundary force calculation.

Wang J; Cai Q; Li ZL; Zhao HK; Luo R

2009-01-01

399

Finite-Difference Time-Domain Method Solution of Fundamental Space-Filling Mode in Photonic Crystal Fibers  

Directory of Open Access Journals (Sweden)

Full Text Available In this study, a Finite-Difference Time-Domain (FDTD) method for the full-vectorial analysis of Fundamental Space-filling Mode (FSM) of photonic crystal fibers is introduced. In order to increase the accuracy of results obtained by this method, an initial field distribution is proposed and Padé approximation technique is applied. By comparing the effective index and chromatic dispersion results obtained by FDTD method and FDTD Effective Index Method (FDTD-EIM), the influence of the accuracy of the solution on the Effective Index Method (EIM) which is based on FDTD is also investigated.

M. Mansourabadi; A. Poorkazemi; M. Shamloufard; Y. Riazi

2009-01-01

400

Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method.  

UK PubMed Central (United Kingdom)

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results.

Çapo?lu ?R; White CA; Rogers JD; Subramanian H; Taflove A; Backman V

2011-05-01

 
 
 
 
401

Perfectly matched layer method in the finite-difference time-domain and frequency-domain calculations  

DEFF Research Database (Denmark)

A complex-coordinate method known under the guise of the perfectly matched layer (PML) method for treating unbounded domains in computational electrodynamics is related to similar techniques in fluid dynamics and classical quantum theory. It may also find use in electronic-structure finite-difference simulations. Straightforward transfer of the PML formulation to other fields does not seem feasible, however, since it is a unique feature of electrodynamics - the natural invariance - that allows analytic trick of complex coordinate scaling to be represented as pure modification of local material parameters within thin layers of space adjacent to the computational domain boundaries, i.e., the PMLs.

Shyroki, Dzmitry; Lavrinenko, Andrei

2007-01-01

402

A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks  

International Nuclear Information System (INIS)

[en] A high-order particle-source-in-cell (PSIC) algorithm is presented for the computation of the interaction between shocks, small scale structures, and liquid and/or solid particles in high-speed engineering applications. The improved high-order finite difference weighted essentially non-oscillatory (WENO-Z) method for solution of the hyperbolic conservation laws that govern the shocked carrier gas flow, lies at the heart of the algorithm. Finite sized particles are modeled as points and are traced in the Lagrangian frame. The physical coupling of particles in the Lagrangian frame and the gas in the Eulerian frame through momentum and energy exchange, is numerically treated through high-order interpolation and weighing. The centered high-order interpolation of the fluid properties to the particle location is shown to lead to numerical instability in shocked flow. An essentially non-oscillatory interpolation (ENO) scheme is devised for the coupling that improves stability. The ENO based algorithm is shown to be numerically stable and to accurately capture shocks, small flow features and particle dispersion. Both the carrier gas and the particles are updated in time without splitting with a third-order Runge-Kutta TVD method. One and two-dimensional computations of a shock moving into a particle cloud demonstrates the characteristics of the WENO-Z based PSIC method (PSIC/WENO-Z). The PSIC/WENO-Z computations are not only in excellent agreement with the numerical simulations with a third-order Rusanov based PSIC and physical experiments in [V. Boiko, V.P. Kiselev, S.P. Kiselev, A. Papyrin, S. Poplavsky, V. Fomin, Shock wave interaction with a cloud of particles, Shock Waves, 7 (1997) 275-285], but also show a significant improvement in the resolution of small scale structures. In two-dimensional simulations of the Mach 3 shock moving into forty thousand bronze particles arranged in the shape of a rectangle, the long time accuracy of the high-order method is demonstrated. The fifth-order PSIC/WENO-Z method with the fifth-order ENO interpolation scheme improves the small scale structure resolution over the third-order PSIC/WENO-Z method with a second-order central interpolation scheme. Preliminary analysis of the particle interaction with the flow structures shows that sharp particle material arms form on the side of the rectangular shape. The arms initially shield the particles from the accelerated flow behind the shock. A reflected compression wave, however, reshocks the particle arm from the shielded area and mixes the particles

2009-03-20

403

Numerical simulation of temperature distribution using finite difference equations and estimation of the grain size during friction stir processing  

International Nuclear Information System (INIS)

[en] Highlights: ? Magnesium alloy AE42 was friction stir processed under different cooling conditions. ? Heat flow model was developed using finite difference heat equations. ? Generalized MATLAB code was developed for solving heat flow model. ? Regression equation for estimation of grain size was developed. - Abstract: The present investigation is aimed at developing a heat flow model to simulate temperature history during friction stir processing (FSP). A new approach of developing implicit form of finite difference heat equations solved using MATLAB code was used. A magnesium based alloy AE42 was friction stir processed (FSPed) at different FSP parameters and cooling conditions. Temperature history was continuously recorded in the nugget zone during FSP using data acquisition system and k type thermocouples. The developed code was validated at different FSP parameters and cooling conditions during FSP experimentation. The temperature history at different locations in the nugget zone at different instants of time was further utilized for the estimation of grain growth rate and final average grain size of the FSPed specimen. A regression equation relating the final grain size, maximum temperature during FSP and the cooling rate was developed. The metallurgical characterization was done using optical microscopy, SEM, and FIB-SIM analysis. The simulated temperature profiles and final average grain size were found to be in good agreement with the experimental results. The presence of fine precipitate particles generated in situ in the investigated magnesium alloy also contributed in the evolution of fine grain structure through Zener pining effect at the grain boundaries.

2012-05-01

404

Contact transformations for difference schemes  

CERN Document Server

We define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the continuous limit. We use a simple example to show that the class is not empty and that such "contact transformations for discrete systems" genuinely exist.

Levi, Decio; Winternitz, Pavel

2011-01-01

405

A Greedy Omnidirectional Relay Scheme  

CERN Multimedia

A greedy omnidirectional relay scheme is developed, and the corresponding achievable rate region is obtained for the all-source all-cast problem. The discussions are first based on the general discrete memoryless channel model, and then applied to the additive white Gaussian noise (AWGN) models, both with full-duplex and with half-duplex modes.

Xie, Liang-Liang

2009-01-01

406

Discrete Hamiltonian Variational Integrators  

CERN Multimedia

We consider the continuous and discrete-time Hamilton's variational principle on phase space, and characterize the exact discrete Hamiltonian which provides an exact correspondence between discrete and continuous Hamiltonian mechanics. The variational characterization of the exact discrete Hamiltonian naturally leads to a class of generalized Galerkin Hamiltonian variational integrators, which include the symplectic partitioned Runge-Kutta methods. We also characterize the group invariance properties of discrete Hamiltonians which lead to a discrete Noether's theorem.

Leok, Melvin

2010-01-01

407

Efficient Discretization of Stochastic Integrals  

CERN Multimedia

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.

Fukasawa, Masaaki

2012-01-01

408

Solutions of multigravity theories and discretized braneworlds  

International Nuclear Information System (INIS)

[en] We determine solutions to 5D Einstein gravity with a discrete fifth dimension. The properties of the solutions depend on the discretization scheme we use and some of them have no continuum counterpart. In particular, we find that the negligence of the lapse field (along the discretized direction) gives rise to a Randall-Sundrum-type metric with a negative tension brane. However, no brane source is required. We show that this result is robust under changes in the discretization scheme. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We find, however, one particular scheme which leads to an undetermined lapse reflecting the reparametrization invariance of the continuum theory. We also find other solutions, with no continuum counterpart with changes in the metric signature or avoidance of singularity. We show that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales. We also discuss some cosmological solutions

2004-04-07

409

Conservative numerical schemes for Euler-Lagrange equations  

International Nuclear Information System (INIS)

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

1999-01-01

410

Conservative numerical schemes for Euler-Lagrange equations  

Energy Technology Data Exchange (ETDEWEB)

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada

1999-05-01

411

Multicomponent mass transport model: theory and numerical implementation (discrete-parcel-random-walk version)  

International Nuclear Information System (INIS)

The Multicomponent Mass Transfer (MMT) Model is a generic computer code, currently in its third generation, that was developed to predict the movement of radiocontaminants in the saturated and unsaturated sediments of the Hanford Site. This model was designed to use the water movement patterns produced by the unsaturated and saturated flow models coupled with dispersion and soil-waste reaction submodels to predict contaminant transport. This report documents the theorical foundation and the numerical solution procedure of the current (third) generation of the MMT Model. The present model simulates mass transport processes using an analog referred to as the Discrete-Parcel-Random-Walk (DPRW) algorithm. The basic concepts of this solution technique are described and the advantages and disadvantages of the DPRW scheme are discussed in relation to more conventional numerical techniques such as the finite-difference and finite-element methods. Verification of the numerical algorithm is demonstrated by comparing model results with known closed-form solutions. A brief error and sensitivity analysis of the algorithm with respect to numerical parameters is also presented. A simulation of the tritium plume beneath the Hanford Site is included to illustrate the use of the model in a typical application. 32 figs

1977-01-01

412

A New Algorithm that Developed Finite Difference Method for Solving Laplace Equation for a Plate with Four Different Constant Temperature Boundary Conditions  

Directory of Open Access Journals (Sweden)

Full Text Available Solving Laplace equation ?2T = 0 using analytical methods is difficult, so numerical methods are used. One of the numerical methods for solving Laplace equation is finite difference method. We know that knotting and writing finite difference method for a specific body, eventually will give rise to linear algebraic equations. In this study, a new algorithm use for develop finite difference method for solving Laplace equation. In this algorithm, the temperature