A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE PAGES

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

2017-02-05

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme.

PubMed

Li, Shaohong L; Truhlar, Donald G

2015-07-14

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations and atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Shaohong L.; Truhlar, Donald G.

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations andmore » atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.« less

Improving Rydberg Excitations within Time-Dependent Density Functional Theory with Generalized Gradient Approximations: The Exchange-Enhancement-for-Large-Gradient Scheme

DOE PAGES

Li, Shaohong L.; Truhlar, Donald G.

2015-05-22

Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations andmore » atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.« less

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

PubMed

Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E

2018-03-14

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions

NASA Astrophysics Data System (ADS)

Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.

2018-03-01

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

The Evolution and Discharge of Electric Fields within a Thunderstorm

NASA Astrophysics Data System (ADS)

Hager, William W.; Nisbet, John S.; Kasha, John R.

1989-05-01

A 3-dimensional electrical model for a thunderstorm is developed and finite difference approximations to the model are analyzed. If the spatial derivatives are approximated by a method akin to the ☐ scheme and if the temporal derivative is approximated by either a backward difference or the Crank-Nicholson scheme, we show that the resulting discretization is unconditionally stable. The forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity. Max-norm error estimates for the discrete approximations are established. To handle the propagation of lightning, special numerical techniques are devised based on the Inverse Matrix Modification Formula and Cholesky updates. Numerical comparisons between the model and theoretical results of Wilson and Holzer-Saxon are presented. We also apply our model to a storm observed at the Kennedy Space Center on July 11, 1978.

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

Approximate optimal guidance for the advanced launch system

NASA Technical Reports Server (NTRS)

Feeley, T. S.; Speyer, J. L.

1993-01-01

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

High-Order Space-Time Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2013-01-01

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

Fully polynomial-time approximation scheme for a special case of a quadratic Euclidean 2-clustering problem

NASA Astrophysics Data System (ADS)

Kel'manov, A. V.; Khandeev, V. I.

2016-02-01

The strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters of given sizes (cardinalities) minimizing the sum (over both clusters) of the intracluster sums of squared distances from the elements of the clusters to their centers is considered. It is assumed that the center of one of the sought clusters is specified at the desired (arbitrary) point of space (without loss of generality, at the origin), while the center of the other one is unknown and determined as the mean value over all elements of this cluster. It is shown that unless P = NP, there is no fully polynomial-time approximation scheme for this problem, and such a scheme is substantiated in the case of a fixed space dimension.

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

An explicit mixed numerical method for mesoscale model

NASA Technical Reports Server (NTRS)

Hsu, H.-M.

1981-01-01

A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.

A Novel Iterative Scheme for the Very Fast and Accurate Solution of Non-LTE Radiative Transfer Problems

NASA Astrophysics Data System (ADS)

Trujillo Bueno, J.; Fabiani Bendicho, P.

1995-12-01

Iterative schemes based on Gauss-Seidel (G-S) and optimal successive over-relaxation (SOR) iteration are shown to provide a dramatic increase in the speed with which non-LTE radiation transfer (RT) problems can be solved. The convergence rates of these new RT methods are identical to those of upper triangular nonlocal approximate operator splitting techniques, but the computing time per iteration and the memory requirements are similar to those of a local operator splitting method. In addition to these properties, both methods are particularly suitable for multidimensional geometry, since they neither require the actual construction of nonlocal approximate operators nor the application of any matrix inversion procedure. Compared with the currently used Jacobi technique, which is based on the optimal local approximate operator (see Olson, Auer, & Buchler 1986), the G-S method presented here is faster by a factor 2. It gives excellent smoothing of the high-frequency error components, which makes it the iterative scheme of choice for multigrid radiative transfer. This G-S method can also be suitably combined with standard acceleration techniques to achieve even higher performance. Although the convergence rate of the optimal SOR scheme developed here for solving non-LTE RT problems is much higher than G-S, the computing time per iteration is also minimal, i.e., virtually identical to that of a local operator splitting method. While the conventional optimal local operator scheme provides the converged solution after a total CPU time (measured in arbitrary units) approximately equal to the number n of points per decade of optical depth, the time needed by this new method based on the optimal SOR iterations is only √n/2√2. This method is competitive with those that result from combining the above-mentioned Jacobi and G-S schemes with the best acceleration techniques. Contrary to what happens with the local operator splitting strategy currently in use, these novel methods remain effective even under extreme non-LTE conditions in very fine grids.

COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp

Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme,more » we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.« less

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

A numerical scheme to solve unstable boundary value problems

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.

1977-01-01

The considered scheme makes it possible to determine an unstable steady state solution in cases in which, because of lack of symmetry, such a solution cannot be obtained analytically, and other time integration or relaxation schemes, because of instability, fail to converge. The iterative solution of a single complex equation is discussed and a nonlinear system of equations is considered. Described applications of the scheme are related to a steady state solution with shear instability, an unstable nonlinear Ekman boundary layer, and the steady state solution of a baroclinic atmosphere with asymmetric forcing. The scheme makes use of forward and backward time integrations of the original spatial differential operators and of an approximation of the adjoint operators. Only two computations of the time derivative per iteration are required.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Incorporation of Three-dimensional Radiative Transfer into a Very High Resolution Simulation of Horizontally Inhomogeneous Clouds

NASA Astrophysics Data System (ADS)

Ishida, H.; Ota, Y.; Sekiguchi, M.; Sato, Y.

2016-12-01

A three-dimensional (3D) radiative transfer calculation scheme is developed to estimate horizontal transport of radiation energy in a very high resolution (with the order of 10 m in spatial grid) simulation of cloud evolution, especially for horizontally inhomogeneous clouds such as shallow cumulus and stratocumulus. Horizontal radiative transfer due to inhomogeneous clouds seems to cause local heating/cooling in an atmosphere with a fine spatial scale. It is, however, usually difficult to estimate the 3D effects, because the 3D radiative transfer often needs a large resource for computation compared to a plane-parallel approximation. This study attempts to incorporate a solution scheme that explicitly solves the 3D radiative transfer equation into a numerical simulation, because this scheme has an advantage in calculation for a sequence of time evolution (i.e., the scene at a time is little different from that at the previous time step). This scheme is also appropriate to calculation of radiation with strong absorption, such as the infrared regions. For efficient computation, this scheme utilizes several techniques, e.g., the multigrid method for iteration solution, and a correlated-k distribution method refined for efficient approximation of the wavelength integration. For a case study, the scheme is applied to an infrared broadband radiation calculation in a broken cloud field generated with a large eddy simulation model. The horizontal transport of infrared radiation, which cannot be estimated by the plane-parallel approximation, and its variation in time can be retrieved. The calculation result elucidates that the horizontal divergences and convergences of infrared radiation flux are not negligible, especially at the boundaries of clouds and within optically thin clouds, and the radiative cooling at lateral boundaries of clouds may reduce infrared radiative heating in clouds. In a future work, the 3D effects on radiative heating/cooling will be able to be included into atmospheric numerical models.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Time dependent density functional calculation of plasmon response in clusters

NASA Astrophysics Data System (ADS)

Wang, Feng; Zhang, Feng-Shou; Eric, Suraud

2003-02-01

We have introduced a theoretical scheme for the efficient description of the optical response of a cluster based on the time-dependent density functional theory. The practical implementation is done by means of the fully fledged time-dependent local density approximation scheme, which is solved directly in the time domain without any linearization. As an example we consider the simple Na2 cluster and compute its surface plasmon photoabsorption cross section, which is in good agreement with the experiments.

Sythesis of MCMC and Belief Propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahn, Sungsoo; Chertkov, Michael; Shin, Jinwoo

Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus (LC) approach whichmore » allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops. Furthermore, we also design an efficient rejection-free MCMC scheme for approximating the full series. The main novelty underlying our design is in utilizing the concept of cycle basis, which provides an efficient decomposition of the generalized loops. In essence, the proposed MCMC schemes run on transformed GM built upon the non-trivial BP solution, and our experiments show that this synthesis of BP and MCMC outperforms both direct MCMC and bare BP schemes.« less

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

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

NASA Astrophysics Data System (ADS)

Muhiddin, F. A.; Sulaiman, J.

2017-09-01

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

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

NASA Astrophysics Data System (ADS)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

FDTD simulation of EM wave propagation in 3-D media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, T.; Tripp, A.C.

1996-01-01

A finite-difference, time-domain solution to Maxwell`s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second-order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth-order scheme, the optimized scheme imposes stricter limitations on the time stepmore » sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth-order scheme. The temporal derivatives are approximated by second-order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite-difference solution is compared to closed-form solutions for conducting and nonconducting whole spaces and to an integral-equation solution for a 3-D body in a homogeneous half-space. In all cases, the finite-difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow-depth and small-scale investigations.« less

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Galilean invariant resummation schemes of cosmological perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peloso, Marco; Pietroni, Massimo, E-mail: peloso@physics.umn.edu, E-mail: massimo.pietroni@unipr.it

2017-01-01

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them inmore » the so called Time-Flow, or TRG, equations.« less

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

High-speed cylindrical collapse of two perfect fluids

NASA Astrophysics Data System (ADS)

Sharif, M.; Ahmad, Zahid

2007-09-01

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by c s , d s . It is shown that the high-speed approximation scheme breaks down by non-zero pressures p 1, p 2 when c s , d s are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainty on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa (Prog Theor Phys 113:73, 2005) for the perfect fluid.

Watching excitons move: the time-dependent transition density matrix

NASA Astrophysics Data System (ADS)

Ullrich, Carsten

2012-02-01

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.

A spectral radius scaling semi-implicit iterative time stepping method for reactive flow simulations with detailed chemistry

NASA Astrophysics Data System (ADS)

Xie, Qing; Xiao, Zhixiang; Ren, Zhuyin

2018-09-01

A spectral radius scaling semi-implicit time stepping scheme has been developed for simulating unsteady compressible reactive flows with detailed chemistry, in which the spectral radius in the LUSGS scheme has been augmented to account for viscous/diffusive and reactive terms and a scalar matrix is proposed to approximate the chemical Jacobian using the minimum species destruction timescale. The performance of the semi-implicit scheme, together with a third-order explicit Runge-Kutta scheme and a Strang splitting scheme, have been investigated in auto-ignition and laminar premixed and nonpremixed flames of three representative fuels, e.g., hydrogen, methane, and n-heptane. Results show that the minimum species destruction time scale can well represent the smallest chemical time scale in reactive flows and the proposed scheme can significantly increase the allowable time steps in simulations. The scheme is stable when the time step is as large as 10 μs, which is about three to five orders of magnitude larger than the smallest time scales in various tests considered. For the test flames considered, the semi-implicit scheme achieves second order of accuracy in time. Moreover, the errors in quantities of interest are smaller than those from the Strang splitting scheme indicating the accuracy gain when the reaction and transport terms are solved coupled. Results also show that the relative efficiency of different schemes depends on fuel mechanisms and test flames. When the minimum time scale in reactive flows is governed by transport processes instead of chemical reactions, the proposed semi-implicit scheme is more efficient than the splitting scheme. Otherwise, the relative efficiency depends on the cost in sub-iterations for convergence within each time step and in the integration for chemistry substep. Then, the capability of the compressible reacting flow solver and the proposed semi-implicit scheme is demonstrated for capturing the hydrogen detonation waves. Finally, the performance of the proposed method is demonstrated in a two-dimensional hydrogen/air diffusion flame.

A Discrete Approximation Framework for Hereditary Systems.

DTIC Science & Technology

1980-05-01

schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical...an appropriately chosen Hilbert space. We then proceed to develop general approximation schemes for the solutions to the homogeneous AEE which in turn...rich classes of these schemes . In addition, two particular families of approximation schemes included in the general framework are developed and

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1985-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

NASA Astrophysics Data System (ADS)

Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled

2017-02-01

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr; Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr; Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound aremore » also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.« less

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

NASA Astrophysics Data System (ADS)

Cheng, Qing; Yang, Xiaofeng; Shen, Jie

2017-07-01

In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows.

PubMed

Sanjeevi, Sathish K P; Zarghami, Ahad; Padding, Johan T

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Choice of no-slip curved boundary condition for lattice Boltzmann simulations of high-Reynolds-number flows

NASA Astrophysics Data System (ADS)

Sanjeevi, Sathish K. P.; Zarghami, Ahad; Padding, Johan T.

2018-04-01

Various curved no-slip boundary conditions available in literature improve the accuracy of lattice Boltzmann simulations compared to the traditional staircase approximation of curved geometries. Usually, the required unknown distribution functions emerging from the solid nodes are computed based on the known distribution functions using interpolation or extrapolation schemes. On using such curved boundary schemes, there will be mass loss or gain at each time step during the simulations, especially apparent at high Reynolds numbers, which is called mass leakage. Such an issue becomes severe in periodic flows, where the mass leakage accumulation would affect the computed flow fields over time. In this paper, we examine mass leakage of the most well-known curved boundary treatments for high-Reynolds-number flows. Apart from the existing schemes, we also test different forced mass conservation schemes and a constant density scheme. The capability of each scheme is investigated and, finally, recommendations for choosing a proper boundary condition scheme are given for stable and accurate simulations.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Damageable contact between an elastic body and a rigid foundation

NASA Astrophysics Data System (ADS)

Campo, M.; Fernández, J. R.; Silva, A.

2009-02-01

In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme.

Weak Galerkin method for the Biot’s consolidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

Comparison of Several Dissipation Algorithms for Central Difference Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.; Turkel, E.

1997-01-01

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme

NASA Technical Reports Server (NTRS)

Tadmor, E.

1983-01-01

The Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u sub t + f sub x (u) = 0 where f(u) is, say, strictly convex double dot f dot a sub asterisk 0 is studied. The divided differences of the numerical solution at time t do not exceed 2 (t dot a sub asterisk) to the -1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude in sharp contrast to liner problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitive insight into the large-time behavior of the numerical computation.

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Jorgenson, Philip C. E.

2007-01-01

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Global collocation methods for approximation and the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Solomonoff, A.; Turkel, E.

1986-01-01

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

NASA Astrophysics Data System (ADS)

Wang, Enjiang; Liu, Yang

2018-01-01

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

Convergence of generalized MUSCL schemes

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

Semi-discrete generalizations of the second order extension of Godunov's scheme, known as the MUSCL scheme, are constructed, starting with any three point E scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Approximate Synchrony: An Abstraction for Distributed Almost Synchronous Systems

DTIC Science & Technology

2015-05-29

finding bugs. Verification of the TSCH Protocol. Time Synchronized Channel Hopping (TSCH) is a Medium Access Control scheme that enables low power...allotted by the schedule and remain in sleep mode otherwise. In the ab- sence of precise time-synchronization, the time-slots across nodes would not be

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaodong; Xia, Yidong; Luo, Hong

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE PAGES

Liu, Xiaodong; Xia, Yidong; Luo, Hong; ...

2016-10-05

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Computation of turbulent pipe and duct flow using third order upwind scheme

NASA Technical Reports Server (NTRS)

Kawamura, T.

1986-01-01

The fully developed turbulence in a circular pipe and in a square duct is simulated directly without using turbulence models in the Navier-Stokes equations. The utilized method employs a third-order upwind scheme for the approximation to the nonlinear term and the second-order Adams-Bashforth method for the time derivative in the Navier-Stokes equation. The computational results appear to capture the large-scale turbulent structures at least qualitatively. The significance of the artificial viscosity inherent in the present scheme is discussed.

The construction of high-accuracy schemes for acoustic equations

NASA Technical Reports Server (NTRS)

Tang, Lei; Baeder, James D.

1995-01-01

An accuracy analysis of various high order schemes is performed from an interpolation point of view. The analysis indicates that classical high order finite difference schemes, which use polynomial interpolation, hold high accuracy only at nodes and are therefore not suitable for time-dependent problems. Thus, some schemes improve their numerical accuracy within grid cells by the near-minimax approximation method, but their practical significance is degraded by maintaining the same stencil as classical schemes. One-step methods in space discretization, which use piecewise polynomial interpolation and involve data at only two points, can generate a uniform accuracy over the whole grid cell and avoid spurious roots. As a result, they are more accurate and efficient than multistep methods. In particular, the Cubic-Interpolated Psuedoparticle (CIP) scheme is recommended for computational acoustics.

Neural-network-based state feedback control of a nonlinear discrete-time system in nonstrict feedback form.

PubMed

Jagannathan, Sarangapani; He, Pingan

2008-12-01

In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability.

Dynamics of moment neuronal networks.

PubMed

Feng, Jianfeng; Deng, Yingchun; Rossoni, Enrico

2006-04-01

A theoretical framework is developed for moment neuronal networks (MNNs). Within this framework, the behavior of the system of spiking neurons is specified in terms of the first- and second-order statistics of their interspike intervals, i.e., the mean, the variance, and the cross correlations of spike activity. Since neurons emit and receive spike trains which can be described by renewal--but generally non-Poisson--processes, we first derive a suitable diffusion-type approximation of such processes. Two approximation schemes are introduced: the usual approximation scheme (UAS) and the Ornstein-Uhlenbeck scheme. It is found that both schemes approximate well the input-output characteristics of spiking models such as the IF and the Hodgkin-Huxley models. The MNN framework is then developed according to the UAS scheme, and its predictions are tested on a few examples.

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE PAGES

Svyatsky, Daniil; Lipnikov, Konstantin

2017-03-18

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Svyatsky, Daniil; Lipnikov, Konstantin

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

DOE PAGES

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2017-09-28

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.« less

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

NASA Astrophysics Data System (ADS)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2018-01-01

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

An O([Formula: see text]) algorithm for sorting signed genomes by reversals, transpositions, transreversals and block-interchanges.

PubMed

Yu, Shuzhi; Hao, Fanchang; Leong, Hon Wai

2016-02-01

We consider the problem of sorting signed permutations by reversals, transpositions, transreversals, and block-interchanges. The problem arises in the study of species evolution via large-scale genome rearrangement operations. Recently, Hao et al. gave a 2-approximation scheme called genome sorting by bridges (GSB) for solving this problem. Their result extended and unified the results of (i) He and Chen - a 2-approximation algorithm allowing reversals, transpositions, and block-interchanges (by also allowing transversals) and (ii) Hartman and Sharan - a 1.5-approximation algorithm allowing reversals, transpositions, and transversals (by also allowing block-interchanges). The GSB result is based on introduction of three bridge structures in the breakpoint graph, the L-bridge, T-bridge, and X-bridge that models goodreversal, transposition/transreversal, and block-interchange, respectively. However, the paper by Hao et al. focused on proving the 2-approximation GSB scheme and only mention a straightforward [Formula: see text] algorithm. In this paper, we give an [Formula: see text] algorithm for implementing the GSB scheme. The key idea behind our faster GSB algorithm is to represent cycles in the breakpoint graph by their canonical sequences, which greatly simplifies the search for these bridge structures. We also give some comparison results (running time and computed distances) against the original GSB implementation.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

2017-04-01

Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

The Method of Space-time Conservation Element and Solution Element: Development of a New Implicit Solver

NASA Technical Reports Server (NTRS)

Chang, S. C.; Wang, X. Y.; Chow, C. Y.; Himansu, A.

1995-01-01

The method of space-time conservation element and solution element is a nontraditional numerical method designed from a physicist's perspective, i.e., its development is based more on physics than numerics. It uses only the simplest approximation techniques and yet is capable of generating nearly perfect solutions for a 2-D shock reflection problem used by Helen Yee and others. In addition to providing an overall view of the new method, we introduce a new concept in the design of implicit schemes, and use it to construct a highly accurate solver for a convection-diffusion equation. It is shown that, in the inviscid case, this new scheme becomes explicit and its amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, its principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Triangle based TVD schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

1990-01-01

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

Development and Application of a Numerical Framework for Improving Building Foundation Heat Transfer Calculations

NASA Astrophysics Data System (ADS)

Kruis, Nathanael J. F.

Heat transfer from building foundations varies significantly in all three spatial dimensions and has important dynamic effects at all timescales, from one hour to several years. With the additional consideration of moisture transport, ground freezing, evapotranspiration, and other physical phenomena, the estimation of foundation heat transfer becomes increasingly sophisticated and computationally intensive to the point where accuracy must be compromised for reasonable computation time. The tools currently available to calculate foundation heat transfer are often either too limited in their capabilities to draw meaningful conclusions or too sophisticated to use in common practices. This work presents Kiva, a new foundation heat transfer computational framework. Kiva provides a flexible environment for testing different numerical schemes, initialization methods, spatial and temporal discretizations, and geometric approximations. Comparisons within this framework provide insight into the balance of computation speed and accuracy relative to highly detailed reference solutions. The accuracy and computational performance of six finite difference numerical schemes are verified against established IEA BESTEST test cases for slab-on-grade heat conduction. Of the schemes tested, the Alternating Direction Implicit (ADI) scheme demonstrates the best balance between accuracy, performance, and numerical stability. Kiva features four approaches of initializing soil temperatures for an annual simulation. A new accelerated initialization approach is shown to significantly reduce the required years of presimulation. Methods of approximating three-dimensional heat transfer within a representative two-dimensional context further improve computational performance. A new approximation called the boundary layer adjustment method is shown to improve accuracy over other established methods with a negligible increase in computation time. This method accounts for the reduced heat transfer from concave foundation shapes, which has not been adequately addressed to date. Within the Kiva framework, three-dimensional heat transfer that can require several days to simulate is approximated in two-dimensions in a matter of seconds while maintaining a mean absolute deviation within 3%.

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

NASA Astrophysics Data System (ADS)

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

2013-02-01

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.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Application of Krylov exponential propagation to fluid dynamics equations

NASA Technical Reports Server (NTRS)

Saad, Youcef; Semeraro, David

1991-01-01

An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.

Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

NASA Technical Reports Server (NTRS)

Weinberg, B. C.; Mcdonald, H.

1980-01-01

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Wu, Xinyuan

2017-07-01

In this paper we explore arbitrarily high-order Lagrange collocation-type time-stepping schemes for effectively solving high-dimensional nonlinear Klein-Gordon equations with different boundary conditions. We begin with one-dimensional periodic boundary problems and first formulate an abstract ordinary differential equation (ODE) on a suitable infinity-dimensional function space based on the operator spectrum theory. We then introduce an operator-variation-of-constants formula which is essential for the derivation of our arbitrarily high-order Lagrange collocation-type time-stepping schemes for the nonlinear abstract ODE. The nonlinear stability and convergence are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix under some suitable smoothness assumptions. With regard to the two dimensional Dirichlet or Neumann boundary problems, our new time-stepping schemes coupled with discrete Fast Sine / Cosine Transformation can be applied to simulate the two-dimensional nonlinear Klein-Gordon equations effectively. All essential features of the methodology are present in one-dimensional and two-dimensional cases, although the schemes to be analysed lend themselves with equal to higher-dimensional case. The numerical simulation is implemented and the numerical results clearly demonstrate the advantage and effectiveness of our new schemes in comparison with the existing numerical methods for solving nonlinear Klein-Gordon equations in the literature.

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Ford, Neville J.; Connolly, Joseph A.

2009-07-01

We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.

Convergence Rates of Finite Difference Stochastic Approximation Algorithms

DTIC Science & Technology

2016-06-01

dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It

Proxy-SU(3) symmetry in heavy deformed nuclei

NASA Astrophysics Data System (ADS)

Bonatsos, Dennis; Assimakis, I. E.; Minkov, N.; Martinou, Andriana; Cakirli, R. B.; Casten, R. F.; Blaum, K.

2017-06-01

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

2002-01-01

We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Dumbser, Michael; Siviglia, Annunziato; Toro, Eleuterio F.

2010-03-01

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space-time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.

Implicit time accurate simulation of unsteady flow

NASA Astrophysics Data System (ADS)

van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

2001-03-01

Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

Approximation-Based Discrete-Time Adaptive Position Tracking Control for Interior Permanent Magnet Synchronous Motors.

PubMed

Yu, Jinpeng; Shi, Peng; Yu, Haisheng; Chen, Bing; Lin, Chong

2015-07-01

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

Radiative Transfer and Satellite Remote Sensing of Cirrus Clouds Using FIRE-2-IFO Data

NASA Technical Reports Server (NTRS)

2000-01-01

Under the support of the NASA grant, we have developed a new geometric-optics model (GOM2) for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. From comparisons with the results computed by the finite difference time domain (FDTD) method, we show that the novel geometric-optics can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as approximately 6. We demonstrate that the present model converges to the conventional ray tracing method for large size parameters and produces single-scattering results close to those computed by the FDTD method for size parameters along the minimum dimension smaller than approximately 20. We demonstrate that neither the conventional geometric optics method nor the Lorenz-Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20. On the satellite remote sensing algorithm development and validation, we have developed a numerical scheme to identify multilayer cirrus cloud systems using AVHRR data. We have applied this scheme to the satellite data collected over the FIRE-2-IFO area during nine overpasses within seven observation dates. Determination of the threshold values used in the detection scheme are based on statistical analyses of these satellite data.

Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio

2017-10-01

We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method, sharing most of it interesting features and being applicable to general hyperbolic systems. To test the properties of our schemes a number of numerical experiments involving the RMHD equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction. It is worth emphasizing that, although this work focuses on RMHD, the proposed schemes are suitable to be applied to general hyperbolic systems.

Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems

NASA Astrophysics Data System (ADS)

Arrarás, A.; Portero, L.; Yotov, I.

2014-01-01

We study space and time discretizations for mixed formulations of parabolic problems. The spatial approximation is based on the multipoint flux mixed finite element method, which reduces to an efficient cell-centered pressure system on general grids, including triangles, quadrilaterals, tetrahedra, and hexahedra. The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit Runge-Kutta methods. The resulting scheme is unconditionally stable and computationally efficient, as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for Schwarz-type iteration. Convergence analysis for both the semidiscrete and fully discrete schemes is presented.

Parallel algorithm for computation of second-order sequential best rotations

NASA Astrophysics Data System (ADS)

Redif, Soydan; Kasap, Server

2013-12-01

Algorithms for computing an approximate polynomial matrix eigenvalue decomposition of para-Hermitian systems have emerged as a powerful, generic signal processing tool. A technique that has shown much success in this regard is the sequential best rotation (SBR2) algorithm. Proposed is a scheme for parallelising SBR2 with a view to exploiting the modern architectural features and inherent parallelism of field-programmable gate array (FPGA) technology. Experiments show that the proposed scheme can achieve low execution times while requiring minimal FPGA resources.

On High-Order Upwind Methods for Advection

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2017-01-01

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2??-1, which is higher than the expected order of ??.

Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

NASA Astrophysics Data System (ADS)

Clark, Martyn P.; Kavetski, Dmitri

2010-10-01

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng Shibiao

2004-06-01

We propose a scheme for approximately and conditionally teleporting an unknown atomic state in cavity QED. Our scheme does not involve the Bell-state measurement and thus an additional atom is unnecessary. Only two atoms and one single-mode cavity are required. The scheme may be used to teleport the state of a cavity mode to another mode using a single atom. The idea may also be used to teleport the state of a trapped ion.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

An atomistic simulation scheme for modeling crystal formation from solution.

PubMed

Kawska, Agnieszka; Brickmann, Jürgen; Kniep, Rüdiger; Hochrein, Oliver; Zahn, Dirk

2006-01-14

We present an atomistic simulation scheme for investigating crystal growth from solution. Molecular-dynamics simulation studies of such processes typically suffer from considerable limitations concerning both system size and simulation times. In our method this time-length scale problem is circumvented by an iterative scheme which combines a Monte Carlo-type approach for the identification of ion adsorption sites and, after each growth step, structural optimization of the ion cluster and the solvent by means of molecular-dynamics simulation runs. An important approximation of our method is based on assuming full structural relaxation of the aggregates between each of the growth steps. This concept only holds for compounds of low solubility. To illustrate our method we studied CaF2 aggregate growth from aqueous solution, which may be taken as prototypes for compounds of very low solubility. The limitations of our simulation scheme are illustrated by the example of NaCl aggregation from aqueous solution, which corresponds to a solute/solvent combination of very high salt solubility.

Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Yu, Ping; Scott, J. R.

1989-01-01

A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.

Advances in numerical and applied mathematics

NASA Technical Reports Server (NTRS)

South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)

1986-01-01

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

PubMed Central

Orio, Patricio; Soudry, Daniel

2012-01-01

Background The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled gating particles, while the DA was modeled using uncoupled gating particles. Implementations of DA with coupled particles, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. Main Contributions We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable – allowing an easy, transparent and efficient DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when short time steps or low channel numbers were used. PMID:22629320

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems.

PubMed

Narayanan, Vignesh; Jagannathan, Sarangapani

2017-06-08

This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

NASA Astrophysics Data System (ADS)

Robertson, Christopher; Habershon, Scott

2018-03-01

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Central Upwind Scheme for a Compressible Two-Phase Flow Model

PubMed Central

Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

Central upwind scheme for a compressible two-phase flow model.

PubMed

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm. [considering transonic flow

NASA Technical Reports Server (NTRS)

Desideri, J. A.; Steger, J. L.; Tannehill, J. C.

1978-01-01

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

PubMed Central

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN). In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging. PMID:23227108

Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging.

PubMed

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Use of corrected centrifugal sudden approximations for the calculation of effective cross sections. II. The N sub 2 --He system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thachuk, M.; McCourt, F.R.W.

1991-09-15

A series of centrifugal sudden (CS) and infinite-order sudden (IOS) approximations together with their corrected versions, respectively, the corrected centrifugal sudden (CCS) and corrected infinite-order sudden (CIOS) approximations, originally introduced by McLenithan and Secrest (J. Chem. Phys. {bold 80}, 2480 (1987)), have been compared with the close-coupled (CC) method for the N{sub 2}--He interaction. This extends previous work using the H{sub 2}--He system (J. Chem. Phys. {bold 93}, 3931 (1990)) to an interaction which is more anisotropic and more classical in nature. A set of eleven energy dependent cross sections, including both relaxation and production types, has been calculated usingmore » the {ital LF}- and {ital LA}-labeling schemes for the CS approximation, as well as the {ital KI}-, {ital KF}-, {ital KA}-, and {ital KM}-labeling schemes for the IOS approximation. The latter scheme is defined as {ital KM}={ital K}=max({ital k}{sub {ital j}},{ital k}{sub {ital j}{sub {ital I}}}). Further, a number of temperature dependent cross sections formed from thermal averages of the above set have also been compared at 100 and 200 K. These comparisons have shown that the CS approximation produced accurate results for relaxation type cross sections regardless of the {ital L}-labeling scheme chosen, but inaccurate results for production type cross sections. Further, except for one particular cross section, the CCS approximation did not generally improve the accuracy of the CS results using either the {ital LF}- or {ital LA}-labeling schemes. The accuracy of the IOS results vary greatly between the cross sections with the most accurate values given by the {ital KM}-labeling scheme. The CIOS approximation generally increases the accuracy of the corresponding IOS results but does not completely eliminate the errors associated with them.« less

On some Approximation Schemes for Steady Compressible Viscous Flow

NASA Astrophysics Data System (ADS)

Bause, M.; Heywood, J. G.; Novotny, A.; Padula, M.

This paper continues our development of approximation schemes for steady compressible viscous flow based on an iteration between a Stokes like problem for the velocity and a transport equation for the density, with the aim of improving their suitability for computations. Such schemes seem attractive for computations because they offer a reduction to standard problems for which there is already highly refined software, and because of the guidance that can be drawn from an existence theory based on them. Our objective here is to modify a recent scheme of Heywood and Padula [12], to improve its convergence properties. This scheme improved upon an earlier scheme of Padula [21], [23] through the use of a special ``effective pressure'' in linking the Stokes and transport problems. However, its convergence is limited for several reasons. Firstly, the steady transport equation itself is only solvable for general velocity fields if they satisfy certain smallness conditions. These conditions are met here by using a rescaled variant of the steady transport equation based on a pseudo time step for the equation of continuity. Another matter limiting the convergence of the scheme in [12] is that the Stokes linearization, which is a linearization about zero, has an inevitably small range of convergence. We replace it here with an Oseen or Newton linearization, either of which has a wider range of convergence, and converges more rapidly. The simplicity of the scheme offered in [12] was conducive to a relatively simple and clearly organized proof of its convergence. The proofs of convergence for the more complicated schemes proposed here are structured along the same lines. They strengthen the theorems of existence and uniqueness in [12] by weakening the smallness conditions that are needed. The expected improvement in the computational performance of the modified schemes has been confirmed by Bause [2], in an ongoing investigation.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle

NASA Astrophysics Data System (ADS)

Yen, Guan-Wei

1989-08-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle. M.S. Thesis

NASA Technical Reports Server (NTRS)

Yen, Guan-Wei

1989-01-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Efficient full decay inversion of MRS data with a stretched-exponential approximation of the ? distribution

NASA Astrophysics Data System (ADS)

Behroozmand, Ahmad A.; Auken, Esben; Fiandaca, Gianluca; Christiansen, Anders Vest; Christensen, Niels B.

2012-08-01

We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining significant differences between the three approaches. All together, a full MRS forward response is calculated in about 20 s and scales so that on 10 processors the calculation time is reduced to about 3-4 s. The proposed approach is examined through synthetic data and through a field example, which demonstrate the capability of the scheme. The results of the field example agree well the information from an in-site borehole.

Modeling Phosphorous Losses from Seasonal Manure Application Schemes

NASA Astrophysics Data System (ADS)

Menzies, E.; Walter, M. T.

2015-12-01

Excess nutrient loading, especially nitrogen and phosphorus, to surface waters is a common and significant problem throughout the United States. While pollution remediation efforts are continuously improving, the most effective treatment remains to limit the source. Appropriate timing of fertilizer application to reduce nutrient losses is currently a hotly debated topic in the Northeastern United States; winter spreading of manure is under special scrutiny. We plan to evaluate the loss of phosphorous to surface waters from agricultural systems under varying seasonal fertilization schemes in an effort to determine the impacts of fertilizers applied throughout the year. The Cayuga Lake basin, located in the Finger Lakes region of New York State, is a watershed dominated by agriculture where a wide array of land management strategies can be found. The evaluation will be conducted on the Fall Creek Watershed, a large sub basin in the Cayuga Lake Watershed. The Fall Creek Watershed covers approximately 33,000 ha in central New York State with approximately 50% of this land being used for agriculture. We plan to use the Soil and Water Assessment Tool (SWAT) to model a number of seasonal fertilization regimes such as summer only spreading and year round spreading (including winter applications), as well as others. We will use the model to quantify the phosphorous load to surface waters from these different fertilization schemes and determine the impacts of manure applied at different times throughout the year. More detailed knowledge about how seasonal fertilization schemes impact phosphorous losses will provide more information to stakeholders concerning the impacts of agriculture on surface water quality. Our results will help farmers and extensionists make more informed decisions about appropriate timing of manure application for reduced phosphorous losses and surface water degradation as well as aid law makers in improving policy surrounding manure application.

Variationally consistent approximation scheme for charge transfer

NASA Technical Reports Server (NTRS)

Halpern, A. M.

1978-01-01

The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Sethian, James A.

1997-01-01

Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

An Efficient Quantum Somewhat Homomorphic Symmetric Searchable Encryption

NASA Astrophysics Data System (ADS)

Sun, Xiaoqiang; Wang, Ting; Sun, Zhiwei; Wang, Ping; Yu, Jianping; Xie, Weixin

2017-04-01

In 2009, Gentry first introduced an ideal lattices fully homomorphic encryption (FHE) scheme. Later, based on the approximate greatest common divisor problem, learning with errors problem or learning with errors over rings problem, FHE has developed rapidly, along with the low efficiency and computational security. Combined with quantum mechanics, Liang proposed a symmetric quantum somewhat homomorphic encryption (QSHE) scheme based on quantum one-time pad, which is unconditional security. And it was converted to a quantum fully homomorphic encryption scheme, whose evaluation algorithm is based on the secret key. Compared with Liang's QSHE scheme, we propose a more efficient QSHE scheme for classical input states with perfect security, which is used to encrypt the classical message, and the secret key is not required in the evaluation algorithm. Furthermore, an efficient symmetric searchable encryption (SSE) scheme is constructed based on our QSHE scheme. SSE is important in the cloud storage, which allows users to offload search queries to the untrusted cloud. Then the cloud is responsible for returning encrypted files that match search queries (also encrypted), which protects users' privacy.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.

1983-01-01

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

Optimal rotated staggered-grid finite-difference schemes for elastic wave modeling in TTI media

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2015-11-01

The rotated staggered-grid finite-difference (RSFD) is an effective approach for numerical modeling to study the wavefield characteristics in tilted transversely isotropic (TTI) media. But it surfaces from serious numerical dispersion, which directly affects the modeling accuracy. In this paper, we propose two different optimal RSFD schemes based on the sampling approximation (SA) method and the least-squares (LS) method respectively to overcome this problem. We first briefly introduce the RSFD theory, based on which we respectively derive the SA-based RSFD scheme and the LS-based RSFD scheme. Then different forms of analysis are used to compare the SA-based RSFD scheme and the LS-based RSFD scheme with the conventional RSFD scheme, which is based on the Taylor-series expansion (TE) method. The contrast in numerical accuracy analysis verifies the greater accuracy of the two proposed optimal schemes, and indicates that these schemes can effectively widen the wavenumber range with great accuracy compared with the TE-based RSFD scheme. Further comparisons between these two optimal schemes show that at small wavenumbers, the SA-based RSFD scheme performs better, while at large wavenumbers, the LS-based RSFD scheme leads to a smaller error. Finally, the modeling results demonstrate that for the same operator length, the SA-based RSFD scheme and the LS-based RSFD scheme can achieve greater accuracy than the TE-based RSFD scheme, while for the same accuracy, the optimal schemes can adopt shorter difference operators to save computing time.

Optimizing phonon space in the phonon-coupling model

NASA Astrophysics Data System (ADS)

Tselyaev, V.; Lyutorovich, N.; Speth, J.; Reinhard, P.-G.

2017-08-01

We present a new scheme to select the most relevant phonons in the phonon-coupling model, named here the time-blocking approximation (TBA). The new criterion, based on the phonon-nucleon coupling strengths rather than on B (E L ) values, is more selective and thus produces much smaller phonon spaces in the TBA. This is beneficial in two respects: first, it curbs the computational cost, and second, it reduces the danger of double counting in the expansion basis of the TBA. We use here the TBA in a form where the coupling strength is regularized to keep the given Hartree-Fock ground state stable. The scheme is implemented in a random-phase approximation and TBA code based on the Skyrme energy functional. We first explore carefully the cutoff dependence with the new criterion and can work out a natural (optimal) cutoff parameter. Then we use the freshly developed and tested scheme for a survey of giant resonances and low-lying collective states in six doubly magic nuclei looking also at the dependence of the results when varying the Skyrme parametrization.

A symmetrical image encryption scheme in wavelet and time domain

NASA Astrophysics Data System (ADS)

Luo, Yuling; Du, Minghui; Liu, Junxiu

2015-02-01

There has been an increasing concern for effective storages and secure transactions of multimedia information over the Internet. Then a great variety of encryption schemes have been proposed to ensure the information security while transmitting, but most of current approaches are designed to diffuse the data only in spatial domain which result in reducing storage efficiency. A lightweight image encryption strategy based on chaos is proposed in this paper. The encryption process is designed in transform domain. The original image is decomposed into approximation and detail components using integer wavelet transform (IWT); then as the more important component of the image, the approximation coefficients are diffused by secret keys generated from a spatiotemporal chaotic system followed by inverse IWT to construct the diffused image; finally a plain permutation is performed for diffusion image by the Logistic mapping in order to reduce the correlation between adjacent pixels further. Experimental results and performance analysis demonstrate the proposed scheme is an efficient, secure and robust encryption mechanism and it realizes effective coding compression to satisfy desirable storage.

Reentrant behaviors in the phase diagram of spin-1 planar ferromagnet with single-ion anisotropy

NASA Astrophysics Data System (ADS)

Rabuffo, I.; De Cesare, L.; Caramico D'Auria, A.; Mercaldo, M. T.

2018-05-01

We used the two-time Green function framework to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of (d > 2)-dimensional spin-1planar ferromagnets, which exhibit a magnetic field induced quantum phase transition. We tackled the problem using two different kind of approximations: the Anderson-Callen decoupling scheme and the Devlin approach. In the latter scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point, for certain values of the single-ion anisotropy parameter. We compare the results obtained within the two approximation schemes. In particular, we recover the same qualitative behavior. We show the phase diagram, close to the field-induced quantum critical point and the behavior of the susceptibility for different values of the single-ion anisotropy parameter, enhancing the differences between the two different scenarios (i.e. with and without reentrant behavior).

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

System and method for implementing periodic early discard in on-chip buffer memories of network elements

DOEpatents

Francini, Andrea

2013-05-14

An advance is made over the prior art in accordance with the principles of the present invention that is directed to a new approach for a system and method for a buffer management scheme called Periodic Early Discard (PED). The invention builds on the observation that, in presence of TCP traffic, the length of a queue can be stabilized by selection of an appropriate frequency for packet dropping. For any combination of number of TCP connections and distribution of the respective RTT values, there exists an ideal packet drop frequency that prevents the queue from over-flowing or under-flowing. While the value of the ideal packet drop frequency may quickly change over time and is sensitive to the series of TCP connections affected by past packet losses, and most of all is impossible to compute inline, it is possible to approximate it with a margin of error that allows keeping the queue occupancy within a pre-defined range for extended periods of time. The PED scheme aims at tracking the (unknown) ideal packet drop frequency, adjusting the approximated value based on the evolution of the queue occupancy, with corrections of the approximated packet drop frequency that occur at a timescale that is comparable to the aggregate time constant of the set of TCP connections that traverse the queue.

Energy management of three-dimensional minimum-time intercept. [for aircraft flight optimization

NASA Technical Reports Server (NTRS)

Kelley, H. J.; Cliff, E. M.; Visser, H. G.

1985-01-01

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

Kernel-density estimation and approximate Bayesian computation for flexible epidemiological model fitting in Python.

PubMed

Irvine, Michael A; Hollingsworth, T Déirdre

2018-05-26

Fitting complex models to epidemiological data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, the complex models may take a long time to run, and it can be difficult to fully capture the heterogeneity in the data. We develop an adaptive approximate Bayesian computation scheme to fit a variety of epidemiologically relevant data with minimal hyper-parameter tuning by using an adaptive tolerance scheme. We implement a novel kernel density estimation scheme to capture both dispersed and multi-dimensional data, and directly compare this technique to standard Bayesian approaches. We then apply the procedure to a complex individual-based simulation of lymphatic filariasis, a human parasitic disease. The procedure and examples are released alongside this article as an open access library, with examples to aid researchers to rapidly fit models to data. This demonstrates that an adaptive ABC scheme with a general summary and distance metric is capable of performing model fitting for a variety of epidemiological data. It also does not require significant theoretical background to use and can be made accessible to the diverse epidemiological research community. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Real-time and high accuracy frequency measurements for intermediate frequency narrowband signals

NASA Astrophysics Data System (ADS)

Tian, Jing; Meng, Xiaofeng; Nie, Jing; Lin, Liwei

2018-01-01

Real-time and accurate measurements of intermediate frequency signals based on microprocessors are difficult due to the computational complexity and limited time constraints. In this paper, a fast and precise methodology based on the sigma-delta modulator is designed and implemented by first generating the twiddle factors using the designed recursive scheme. This scheme requires zero times of multiplications and only half amounts of addition operations by using the discrete Fourier transform (DFT) and the combination of the Rife algorithm and Fourier coefficient interpolation as compared with conventional methods such as DFT and Fast Fourier Transform. Experimentally, when the sampling frequency is 10 MHz, the real-time frequency measurements with intermediate frequency and narrowband signals have a measurement mean squared error of ±2.4 Hz. Furthermore, a single measurement of the whole system only requires approximately 0.3 s to achieve fast iteration, high precision, and less calculation time.

A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

NASA Astrophysics Data System (ADS)

Cheng, Jun-Bo; Huang, Weizhang; Jiang, Song; Tian, Baolin

2017-11-01

A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.

A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-08-01

In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Verrière, M.; Dubray, N.; Schunck, N.

2016-03-01

We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr; CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex; Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity ofmore » the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less

The effectiveness of Hong Kong's Construction Waste Disposal Charging Scheme.

PubMed

Hao, Jane L; Hills, Martin J; Tam, Vivian W Y

2008-12-01

The Hong Kong Government introduced the Construction Waste Disposal Charging Scheme in December 2005 to ensure that disposal of construction and demolition (C&D) waste is properly priced to reduce such waste. The charging scheme is not only intended to provide an economic incentive for contractors and developers to reduce waste but also to encourage reuse and recycling of waste material thereby slowing down the depletion of limited landfill and public filling capacities. This paper examines the effectiveness of the charging scheme 1 year after implementation. A survey was conducted at Tseung Kwan O Area 137 and Tuen Mun Area 38, and daily C&D waste records were collected from landfills and public filling facilities between January 2006 and December 2006. The results of the survey show that waste has been reduced by approximately 60% in landfills, by approximately 23% in public fills, and by approximately 65% in total waste between 2005 and 2006. Suggestions for improving the scheme are provided.

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

Adaptive mesh fluid simulations on GPU

NASA Astrophysics Data System (ADS)

Wang, Peng; Abel, Tom; Kaehler, Ralf

2010-10-01

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.

Numerical viscosity and the entropy condition for conservative difference schemes

NASA Technical Reports Server (NTRS)

Tadmor, E.

1983-01-01

Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis

2009-10-01

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hunt, H.B. III; Rosenkrantz, D.J.; Stearns, R.E.

We study both the complexity and approximability of various graph and combinatorial problems specified using two dimensional narrow periodic specifications (see [CM93, HW92, KMW67, KO91, Or84b, Wa93]). The following two general kinds of results are presented. (1) We prove that a number of natural graph and combinatorial problems are NEXPTIME- or EXPSPACE-complete when instances are so specified; (2) In contrast, we prove that the optimization versions of several of these NEXPTIME-, EXPSPACE-complete problems have polynomial time approximation algorithms with constant performance guarantees. Moreover, some of these problems even have polynomial time approximation schemes. We also sketch how our NEXPTIME-hardness resultsmore » can be used to prove analogous NEXPTIME-hardness results for problems specified using other kinds of succinct specification languages. Our results provide the first natural problems for which there is a proven exponential (and possibly doubly exponential) gap between the complexities of finding exact and approximate solutions.« less

Microfluidic proportional flow controller

PubMed Central

Prentice-Mott, Harrison; Toner, Mehmet; Irimia, Daniel

2011-01-01

Precise flow control in microfluidic chips is important for many biochemical assays and experiments at microscale. While several technologies for controlling fluid flow have been implemented either on- or off-chip, these can provide either high-speed or high-precision control, but seldom could accomplish both at the same time. Here we describe a new on-chip, pneumatically activated flow controller that allows for fast and precise control of the flow rate through a microfluidic channel. Experimental results show that the new proportional flow controllers exhibited a response time of approximately 250 ms, while our numerical simulations suggest that faster actuation down to approximately 50 ms could be achieved with alternative actuation schemes. PMID:21874096

Interpretation of ES, CS, and IOS approximations within a translational--internal coupling scheme. I. Atom--diatom collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coombe, D.A.; Snider, R.F.

1979-12-01

Rotational invariance is applied to the description of atom--diatom collisions in a translational--internal coupling scheme, to obtain energy sudden (ES), centrifugal sudden (CS), and infinite order sudden (IOS) approximations to the reduced scattering S matrix S (j-barlambda-bar;L;jlambda). The method of presentation emphasizes that the translational--internal coupling scheme is actually the more natural description of collision processes in which one or more directions are assumed to be conserved.

Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity

NASA Astrophysics Data System (ADS)

Kiefer, Claus; Wichmann, David

2018-06-01

We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this scheme and show that unitarity can be restored by an appropriate modification which requires back reaction from matter onto the gravitational sector. In our analysis, we heavily rely on the gauge aspects of the standard Born-Oppenheimer scheme in molecular physics.

Approximation methods for inverse problems involving the vibration of beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.

Interpretation of ES, CS, and IOS approximations within a translational-internal coupling scheme. II. Application to atom--diatom kinetic cross sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coombe, D.A.; Snider, R.F.

1980-02-15

ES, CS, and IOS approximations to atom--diatom kinetic cross sections are derived. In doing so, reduced S-matrices in a translational-internal coupling scheme are stressed. This entails the insertion of recently obtained approximate reduced S-matrices in the translational-internal coupling scheme into previously derived general expressions for the kinetic cross sections. Of special interest is the structure (rotational j quantum number dependence) of the kinetic cross sections associated with the Senftleben Beenakker effects and of pure internal state relaxation phenomena. The viscomagnetic effect is used as an illustrative example. It is found in particular that there is a great similarity of structuremore » between the energy sudden (and IOS) approximation and the previously derived distorted wave Born results.« less

Fast viscosity solutions for shape from shading under a more realistic imaging model

NASA Astrophysics Data System (ADS)

Wang, Guohui; Han, Jiuqiang; Jia, Honghai; Zhang, Xinman

2009-11-01

Shape from shading (SFS) has been a classical and important problem in the domain of computer vision. The goal of SFS is to reconstruct the 3-D shape of an object from its 2-D intensity image. To this end, an image irradiance equation describing the relation between the shape of a surface and its corresponding brightness variations is used. Then it is derived as an explicit partial differential equation (PDE). Using the nonlinear programming principle, we propose a detailed solution to Prados and Faugeras's implicit scheme for approximating the viscosity solution of the resulting PDE. Furthermore, by combining implicit and semi-implicit schemes, a new approximation scheme is presented. In order to accelerate the convergence speed, we adopt the Gauss-Seidel idea and alternating sweeping strategy to the approximation schemes. Experimental results on both synthetic and real images are performed to demonstrate that the proposed methods are fast and accurate.

An efficient method for quantum transport simulations in the time domain

NASA Astrophysics Data System (ADS)

Wang, Y.; Yam, C.-Y.; Frauenheim, Th.; Chen, G. H.; Niehaus, T. A.

2011-11-01

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. The density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier ab initio implementations of this formalism, the Hamiltonian is here approximated in the spirit of the density functional based tight-binding (DFTB) method. Results are presented for two prototypical molecular devices and compared to full TDDFT calculations. The temporal profile of the current traces is qualitatively well captured by the DFTB scheme. Steady state currents show considerable variations, both in comparison of approximate and full TDDFT, but also among TDDFT calculations with different basis sets.

XML Reconstruction View Selection in XML Databases: Complexity Analysis and Approximation Scheme

NASA Astrophysics Data System (ADS)

Chebotko, Artem; Fu, Bin

Query evaluation in an XML database requires reconstructing XML subtrees rooted at nodes found by an XML query. Since XML subtree reconstruction can be expensive, one approach to improve query response time is to use reconstruction views - materialized XML subtrees of an XML document, whose nodes are frequently accessed by XML queries. For this approach to be efficient, the principal requirement is a framework for view selection. In this work, we are the first to formalize and study the problem of XML reconstruction view selection. The input is a tree T, in which every node i has a size c i and profit p i , and the size limitation C. The target is to find a subset of subtrees rooted at nodes i 1, ⋯ , i k respectively such that c_{i_1}+\\cdots +c_{i_k}le C, and p_{i_1}+\\cdots +p_{i_k} is maximal. Furthermore, there is no overlap between any two subtrees selected in the solution. We prove that this problem is NP-hard and present a fully polynomial-time approximation scheme (FPTAS) as a solution.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

NASA Astrophysics Data System (ADS)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes

NASA Technical Reports Server (NTRS)

Adeniji-Fashola, A.; Chen, C. P.

1990-01-01

Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the Eulerian and Lagrangian modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.

A Closely Coupled Experimental and Numerical Approach for Hypersonic and High Enthalpy Flow Investigations Utilising the HEG Shock Tunnel and the DLR TAU Code

DTIC Science & Technology

2010-04-01

factorization scheme (Lower-Upper Symmetric Gauss- Seidel ) can be used for time integration. Additional convergence acceleration is achieved by the...of the full Stefan -Maxwell equations. The diffusive mass flux of species S is computed according to: for 1 for jS S S Sm j jm S j eS jd S S S j j j...approximate factorization scheme (Lower-Upper Symmetric Gauss- Seidel ). For steady state problems, equation (69) reduces to R=0 because ddU t

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Statistical inferences with jointly type-II censored samples from two Pareto distributions

NASA Astrophysics Data System (ADS)

Abu-Zinadah, Hanaa H.

2017-08-01

In the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

Robust LS-SVM-based adaptive constrained control for a class of uncertain nonlinear systems with time-varying predefined performance

NASA Astrophysics Data System (ADS)

Luo, Jianjun; Wei, Caisheng; Dai, Honghua; Yuan, Jianping

2018-03-01

This paper focuses on robust adaptive control for a class of uncertain nonlinear systems subject to input saturation and external disturbance with guaranteed predefined tracking performance. To reduce the limitations of classical predefined performance control method in the presence of unknown initial tracking errors, a novel predefined performance function with time-varying design parameters is first proposed. Then, aiming at reducing the complexity of nonlinear approximations, only two least-square-support-vector-machine-based (LS-SVM-based) approximators with two design parameters are required through norm form transformation of the original system. Further, a novel LS-SVM-based adaptive constrained control scheme is developed under the time-vary predefined performance using backstepping technique. Wherein, to avoid the tedious analysis and repeated differentiations of virtual control laws in the backstepping technique, a simple and robust finite-time-convergent differentiator is devised to only extract its first-order derivative at each step in the presence of external disturbance. In this sense, the inherent demerit of backstepping technique-;explosion of terms; brought by the recursive virtual controller design is conquered. Moreover, an auxiliary system is designed to compensate the control saturation. Finally, three groups of numerical simulations are employed to validate the effectiveness of the newly developed differentiator and the proposed adaptive constrained control scheme.

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Giorgos, E-mail: garab@math.uoc.gr; Katsoulakis, Markos A., E-mail: markos@math.umass.edu; Plechac, Petr, E-mail: plechac@math.udel.edu

2012-10-01

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decompositionmore » corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.« less

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

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

A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

NASA Astrophysics Data System (ADS)

Stolk, Christiaan C.

2016-06-01

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

NASA Technical Reports Server (NTRS)

Janus, J. Mark; Whitfield, David L.

1990-01-01

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Experiences on p-Version Time-Discontinuous Galerkin's Method for Nonlinear Heat Transfer Analysis and Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Hou, Gene

2004-01-01

The focus of this research is on the development of analysis and sensitivity analysis equations for nonlinear, transient heat transfer problems modeled by p-version, time discontinuous finite element approximation. The resulting matrix equation of the state equation is simply in the form ofA(x)x = c, representing a single step, time marching scheme. The Newton-Raphson's method is used to solve the nonlinear equation. Examples are first provided to demonstrate the accuracy characteristics of the resultant finite element approximation. A direct differentiation approach is then used to compute the thermal sensitivities of a nonlinear heat transfer problem. The report shows that only minimal coding effort is required to enhance the analysis code with the sensitivity analysis capability.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Verriere, M.; Dubray, N.; ...

2015-11-30

In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle amore » realistic calculation of fission dynamics.« less

Performance analysis of cross-seeding WDM-PON system using transfer matrix method

NASA Astrophysics Data System (ADS)

Simatupang, Joni Welman; Pukhrambam, Puspa Devi; Huang, Yen-Ru

2016-12-01

In this paper, a model based on the transfer matrix method is adopted to analyze the effects of Rayleigh backscattering and Fresnel multiple reflections on a cross-seeding WDM-PON system. As part of analytical approximation methods, this time-independent model is quite simple but very efficient when it is applied to various WDM-PON transmission systems, including the cross-seeding scheme. The cross seeding scheme is most beneficial for systems with low loop-back ONU gain or low reflection loss at the drop fiber for upstream data in bidirectional transmission. However for downstream data transmission, multiple reflections power could destroy the usefulness of the cross-seeding scheme when the reflectivity is high enough and the RN is positioned near OLT or close to ONU.

An Efficient Semi-fragile Watermarking Scheme for Tamper Localization and Recovery

NASA Astrophysics Data System (ADS)

Hou, Xiang; Yang, Hui; Min, Lianquan

2018-03-01

To solve the problem that remote sensing images are vulnerable to be tampered, a semi-fragile watermarking scheme was proposed. Binary random matrix was used as the authentication watermark, which was embedded by quantizing the maximum absolute value of directional sub-bands coefficients. The average gray level of every non-overlapping 4×4 block was adopted as the recovery watermark, which was embedded in the least significant bit. Watermarking detection could be done directly without resorting to the original images. Experimental results showed our method was robust against rational distortions to a certain extent. At the same time, it was fragile to malicious manipulation, and realized accurate localization and approximate recovery of the tampered regions. Therefore, this scheme can protect the security of remote sensing image effectively.

Dynamical emergence of Markovianity in local time scheme.

PubMed

Jeknić-Dugić, J; Arsenijević, M; Dugić, M

2016-06-01

Recently we pointed out the so-called local time scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper, we introduce and analyse in depth a rather non-standard dynamical map that is imposed by the scheme. On the one hand, the map does not allow for introducing a properly defined generator of the evolution nor does it represent a quantum channel. On the other hand, the map is linear, positive, trace preserving and unital as well as completely positive, but is not divisible and therefore non-Markovian. Nevertheless, we provide quantitative criteria for dynamical emergence of time-coarse-grained Markovianity, for exact dynamics of an open system, as well as for operationally defined approximation of a closed or open many-particle system. A closed system never reaches a steady state, whereas an open system may reach a unique steady state given by the Lüders-von Neumann formula; where the smaller the open system, the faster a steady state is attained. These generic findings extend the standard open quantum systems theory and substantially tackle certain cosmological issues.

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

An efficient indexing scheme for binary feature based biometric database

NASA Astrophysics Data System (ADS)

Gupta, P.; Sana, A.; Mehrotra, H.; Hwang, C. Jinshong

2007-04-01

The paper proposes an efficient indexing scheme for binary feature template using B+ tree. In this scheme the input image is decomposed into approximation, vertical, horizontal and diagonal coefficients using the discrete wavelet transform. The binarized approximation coefficient at second level is divided into four quadrants of equal size and Hamming distance (HD) for each quadrant with respect to sample template of all ones is measured. This HD value of each quadrant is used to generate upper and lower range values which are inserted into B+ tree. The nodes of tree at first level contain the lower and upper range values generated from HD of first quadrant. Similarly, lower and upper range values for the three quadrants are stored in the second, third and fourth level respectively. Finally leaf node contains the set of identifiers. At the time of identification, the test image is used to generate HD for four quadrants. Then the B+ tree is traversed based on the value of HD at every node and terminates to leaf nodes with set of identifiers. The feature vector for each identifier is retrieved from the particular bin of secondary memory and matched with test feature template to get top matches. The proposed scheme is implemented on ear biometric database collected at IIT Kanpur. The system is giving an overall accuracy of 95.8% at penetration rate of 34%.

Fault diagnosis for analog circuits utilizing time-frequency features and improved VVRKFA

NASA Astrophysics Data System (ADS)

He, Wei; He, Yigang; Luo, Qiwu; Zhang, Chaolong

2018-04-01

This paper proposes a novel scheme for analog circuit fault diagnosis utilizing features extracted from the time-frequency representations of signals and an improved vector-valued regularized kernel function approximation (VVRKFA). First, the cross-wavelet transform is employed to yield the energy-phase distribution of the fault signals over the time and frequency domain. Since the distribution is high-dimensional, a supervised dimensionality reduction technique—the bilateral 2D linear discriminant analysis—is applied to build a concise feature set from the distributions. Finally, VVRKFA is utilized to locate the fault. In order to improve the classification performance, the quantum-behaved particle swarm optimization technique is employed to gradually tune the learning parameter of the VVRKFA classifier. The experimental results for the analog circuit faults classification have demonstrated that the proposed diagnosis scheme has an advantage over other approaches.

A Novel Energy Efficient Topology Control Scheme Based on a Coverage-Preserving and Sleep Scheduling Model for Sensor Networks

PubMed Central

Shi, Binbin; Wei, Wei; Wang, Yihuai; Shu, Wanneng

2016-01-01

In high-density sensor networks, scheduling some sensor nodes to be in the sleep mode while other sensor nodes remain active for monitoring or forwarding packets is an effective control scheme to conserve energy. In this paper, a Coverage-Preserving Control Scheduling Scheme (CPCSS) based on a cloud model and redundancy degree in sensor networks is proposed. Firstly, the normal cloud model is adopted for calculating the similarity degree between the sensor nodes in terms of their historical data, and then all nodes in each grid of the target area can be classified into several categories. Secondly, the redundancy degree of a node is calculated according to its sensing area being covered by the neighboring sensors. Finally, a centralized approximation algorithm based on the partition of the target area is designed to obtain the approximate minimum set of nodes, which can retain the sufficient coverage of the target region and ensure the connectivity of the network at the same time. The simulation results show that the proposed CPCSS can balance the energy consumption and optimize the coverage performance of the sensor network. PMID:27754405

A Novel Energy Efficient Topology Control Scheme Based on a Coverage-Preserving and Sleep Scheduling Model for Sensor Networks.

PubMed

Shi, Binbin; Wei, Wei; Wang, Yihuai; Shu, Wanneng

2016-10-14

In high-density sensor networks, scheduling some sensor nodes to be in the sleep mode while other sensor nodes remain active for monitoring or forwarding packets is an effective control scheme to conserve energy. In this paper, a Coverage-Preserving Control Scheduling Scheme (CPCSS) based on a cloud model and redundancy degree in sensor networks is proposed. Firstly, the normal cloud model is adopted for calculating the similarity degree between the sensor nodes in terms of their historical data, and then all nodes in each grid of the target area can be classified into several categories. Secondly, the redundancy degree of a node is calculated according to its sensing area being covered by the neighboring sensors. Finally, a centralized approximation algorithm based on the partition of the target area is designed to obtain the approximate minimum set of nodes, which can retain the sufficient coverage of the target region and ensure the connectivity of the network at the same time. The simulation results show that the proposed CPCSS can balance the energy consumption and optimize the coverage performance of the sensor network.

Efficient compression of molecular dynamics trajectory files.

PubMed

Marais, Patrick; Kenwood, Julian; Smith, Keegan Carruthers; Kuttel, Michelle M; Gain, James

2012-10-15

We investigate whether specific properties of molecular dynamics trajectory files can be exploited to achieve effective file compression. We explore two classes of lossy, quantized compression scheme: "interframe" predictors, which exploit temporal coherence between successive frames in a simulation, and more complex "intraframe" schemes, which compress each frame independently. Our interframe predictors are fast, memory-efficient and well suited to on-the-fly compression of massive simulation data sets, and significantly outperform the benchmark BZip2 application. Our schemes are configurable: atomic positional accuracy can be sacrificed to achieve greater compression. For high fidelity compression, our linear interframe predictor gives the best results at very little computational cost: at moderate levels of approximation (12-bit quantization, maximum error ≈ 10(-2) Å), we can compress a 1-2 fs trajectory file to 5-8% of its original size. For 200 fs time steps-typically used in fine grained water diffusion experiments-we can compress files to ~25% of their input size, still substantially better than BZip2. While compression performance degrades with high levels of quantization, the simulation error is typically much greater than the associated approximation error in such cases. Copyright © 2012 Wiley Periodicals, Inc.

A spectral nudging method for the ACCESS1.3 atmospheric model

NASA Astrophysics Data System (ADS)

Uhe, P.; Thatcher, M.

2015-06-01

A convolution-based method of spectral nudging of atmospheric fields is developed in the Australian Community Climate and Earth Systems Simulator (ACCESS) version 1.3 which uses the UK Met Office Unified Model version 7.3 as its atmospheric component. The use of convolutions allow for flexibility in application to different atmospheric grids. An approximation using one-dimensional convolutions is applied, improving the time taken by the nudging scheme by 10-30 times compared with a version using a two-dimensional convolution, without measurably degrading its performance. Care needs to be taken in the order of the convolutions and the frequency of nudging to obtain the best outcome. The spectral nudging scheme is benchmarked against a Newtonian relaxation method, nudging winds and air temperature towards ERA-Interim reanalyses. We find that the convolution approach can produce results that are competitive with Newtonian relaxation in both the effectiveness and efficiency of the scheme, while giving the added flexibility of choosing which length scales to nudge.

A spectral nudging method for the ACCESS1.3 atmospheric model

NASA Astrophysics Data System (ADS)

Uhe, P.; Thatcher, M.

2014-10-01

A convolution based method of spectral nudging of atmospheric fields is developed in the Australian Community Climate and Earth Systems Simulator (ACCESS) version 1.3 which uses the UK Met Office Unified Model version 7.3 as its atmospheric component. The use of convolutions allow flexibility in application to different atmospheric grids. An approximation using one-dimensional convolutions is applied, improving the time taken by the nudging scheme by 10 to 30 times compared with a version using a two-dimensional convolution, without measurably degrading its performance. Care needs to be taken in the order of the convolutions and the frequency of nudging to obtain the best outcome. The spectral nudging scheme is benchmarked against a Newtonian relaxation method, nudging winds and air temperature towards ERA-Interim reanalyses. We find that the convolution approach can produce results that are competitive with Newtonian relaxation in both the effectiveness and efficiency of the scheme, while giving the added flexibility of choosing which length scales to nudge.

Dual adaptive dynamic control of mobile robots using neural networks.

PubMed

Bugeja, Marvin K; Fabri, Simon G; Camilleri, Liberato

2009-02-01

This paper proposes two novel dual adaptive neural control schemes for the dynamic control of nonholonomic mobile robots. The two schemes are developed in discrete time, and the robot's nonlinear dynamic functions are assumed to be unknown. Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are used for function approximation. In each scheme, the unknown network parameters are estimated stochastically in real time, and no preliminary offline neural network training is used. In contrast to other adaptive techniques hitherto proposed in the literature on mobile robots, the dual control laws presented in this paper do not rely on the heuristic certainty equivalence property but account for the uncertainty in the estimates. This results in a major improvement in tracking performance, despite the plant uncertainty and unmodeled dynamics. Monte Carlo simulation and statistical hypothesis testing are used to illustrate the effectiveness of the two proposed stochastic controllers as applied to the trajectory-tracking problem of a differentially driven wheeled mobile robot.

High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields

DTIC Science & Technology

2011-11-12

there exists the hydrostatic balance where the flux produced by the pressure is canceled by the gravitational source term. Many astro - physical...approximation to W (x) to obtain an approximation to W ′(xi) = fx (U(xi, yj)). See again [7, 15] for more details of finite difference WENO schemes in

Relaxation approximations to second-order traffic flow models by high-resolution schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

2015-03-10

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reportedmore » demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.« less

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less

Applying the Explicit Time Central Difference Method for Numerical Simulation of the Dynamic Behavior of Elastoplastic Flexible Reinforced Plates

NASA Astrophysics Data System (ADS)

Yankovskii, A. P.

2017-12-01

Based on a stepwise algorithm involving central finite differences for the approximation in time, a mathematical model is developed for elastoplastic deformation of cross-reinforced plates with isotropically hardening materials of components of the composition. The model allows obtaining the solution of elastoplastic problems at discrete points in time by an explicit scheme. The initial boundary value problem of the dynamic behavior of flexible plates reinforced in their own plane is formulated in the von Kármán approximation with allowance for their weakened resistance to the transverse shear. With a common approach, the resolving equations corresponding to two variants of the Timoshenko theory are obtained. An explicit "cross" scheme for numerical integration of the posed initial boundary value problem has been constructed. The scheme is consistent with the incremental algorithm used for simulating the elastoplastic behavior of a reinforced medium. Calculations of the dynamic behavior have been performed for elastoplastic cylindrical bending of differently reinforced fiberglass rectangular elongated plates. It is shown that the reinforcement structure significantly affects their elastoplastic dynamic behavior. It has been found that the classical theory of plates is as a rule unacceptable for carrying out the required calculations (except for very thin plates), and the first version of the Timoshenko theory yields reasonable results only in cases of relatively thin constructions reinforced by lowmodulus fibers. Proceeding from the results of the work, it is recommended to use the second variant of the Timoshenko theory (as a more accurate one) for calculations of the elastoplastic behavior of reinforced plates.

Kondo necklace model in approximants of Fibonacci chains

NASA Astrophysics Data System (ADS)

Reyes, Daniel; Tarazona, H.; Cuba-Supanta, G.; Landauro, C. V.; Espinoza, R.; Quispe-Marcatoma, J.

2017-11-01

The low energy behavior of the one dimensional Kondo necklace model with structural aperiodicity is studied using a representation for the localized and conduction electron spins, in terms of local Kondo singlet and triplet operators at zero temperature. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. We determine the dependence between the structural aperiodicity modulation and the spin gap in a Fibonacci approximant chain at zero temperature and in the paramagnetic side of the phase diagram.

Comparison of dynamical approximation schemes for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.

A computer software system for the generation of global ocean tides including self-gravitation and crustal loading effects

NASA Technical Reports Server (NTRS)

Estes, R. H.

1977-01-01

A computer software system is described which computes global numerical solutions of the integro-differential Laplace tidal equations, including dissipation terms and ocean loading and self-gravitation effects, for arbitrary diurnal and semidiurnal tidal constituents. The integration algorithm features a successive approximation scheme for the integro-differential system, with time stepping forward differences in the time variable and central differences in spatial variables.

A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations

NASA Technical Reports Server (NTRS)

Dydson, Roger W.; Goodrich, John W.

2000-01-01

Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan

1989-01-01

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

A well-balanced finite volume scheme for the Euler equations with gravitation. The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification

NASA Astrophysics Data System (ADS)

Käppeli, R.; Mishra, S.

2016-03-01

Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

On simulating flow with multiple time scales using a method of averages

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L.G.

1997-12-31

The author presents a new computational method based on averaging to efficiently simulate certain systems with multiple time scales. He first develops the method in a simple one-dimensional setting and employs linear stability analysis to demonstrate numerical stability. He then extends the method to multidimensional fluid flow. His method of averages does not depend on explicit splitting of the equations nor on modal decomposition. Rather he combines low order and high order algorithms in a generalized predictor-corrector framework. He illustrates the methodology in the context of a shallow fluid approximation to an ocean basin circulation. He finds that his newmore » method reproduces the accuracy of a fully explicit second-order accurate scheme, while costing less than a first-order accurate scheme.« less

Terminal Sliding Mode-Based Consensus Tracking Control for Networked Uncertain Mechanical Systems on Digraphs.

PubMed

Chen, Gang; Song, Yongduan; Guan, Yanfeng

2018-03-01

This brief investigates the finite-time consensus tracking control problem for networked uncertain mechanical systems on digraphs. A new terminal sliding-mode-based cooperative control scheme is developed to guarantee that the tracking errors converge to an arbitrarily small bound around zero in finite time. All the networked systems can have different dynamics and all the dynamics are unknown. A neural network is used at each node to approximate the local unknown dynamics. The control schemes are implemented in a fully distributed manner. The proposed control method eliminates some limitations in the existing terminal sliding-mode-based consensus control methods and extends the existing analysis methods to the case of directed graphs. Simulation results on networked robot manipulators are provided to show the effectiveness of the proposed control algorithms.

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

Cluster analysis based on dimensional information with applications to feature selection and classification

NASA Technical Reports Server (NTRS)

Eigen, D. J.; Fromm, F. R.; Northouse, R. A.

1974-01-01

A new clustering algorithm is presented that is based on dimensional information. The algorithm includes an inherent feature selection criterion, which is discussed. Further, a heuristic method for choosing the proper number of intervals for a frequency distribution histogram, a feature necessary for the algorithm, is presented. The algorithm, although usable as a stand-alone clustering technique, is then utilized as a global approximator. Local clustering techniques and configuration of a global-local scheme are discussed, and finally the complete global-local and feature selector configuration is shown in application to a real-time adaptive classification scheme for the analysis of remote sensed multispectral scanner data.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)

2002-01-01

In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.

A new third order finite volume weighted essentially non-oscillatory scheme on tetrahedral meshes

NASA Astrophysics Data System (ADS)

Zhu, Jun; Qiu, Jianxian

2017-11-01

In this paper a third order finite volume weighted essentially non-oscillatory scheme is designed for solving hyperbolic conservation laws on tetrahedral meshes. Comparing with other finite volume WENO schemes designed on tetrahedral meshes, the crucial advantages of such new WENO scheme are its simplicity and compactness with the application of only six unequal size spatial stencils for reconstructing unequal degree polynomials in the WENO type spatial procedures, and easy choice of the positive linear weights without considering the topology of the meshes. The original innovation of such scheme is to use a quadratic polynomial defined on a big central spatial stencil for obtaining third order numerical approximation at any points inside the target tetrahedral cell in smooth region and switch to at least one of five linear polynomials defined on small biased/central spatial stencils for sustaining sharp shock transitions and keeping essentially non-oscillatory property simultaneously. By performing such new procedures in spatial reconstructions and adopting a third order TVD Runge-Kutta time discretization method for solving the ordinary differential equation (ODE), the new scheme's memory occupancy is decreased and the computing efficiency is increased. So it is suitable for large scale engineering requirements on tetrahedral meshes. Some numerical results are provided to illustrate the good performance of such scheme.

Neural adaptive control for vibration suppression in composite fin-tip of aircraft.

PubMed

Suresh, S; Kannan, N; Sundararajan, N; Saratchandran, P

2008-06-01

In this paper, we present a neural adaptive control scheme for active vibration suppression of a composite aircraft fin tip. The mathematical model of a composite aircraft fin tip is derived using the finite element approach. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes very accurately. Piezo-electric actuators and sensors are placed at optimal locations such that the vibration suppression is a maximum. Model-reference direct adaptive neural network control scheme is proposed to force the vibration level within the minimum acceptable limit. In this scheme, Gaussian neural network with linear filters is used to approximate the inverse dynamics of the system and the parameters of the neural controller are estimated using Lyapunov based update law. In order to reduce the computational burden, which is critical for real-time applications, the number of hidden neurons is also estimated in the proposed scheme. The global asymptotic stability of the overall system is ensured using the principles of Lyapunov approach. Simulation studies are carried-out using sinusoidal force functions of varying frequency. Experimental results show that the proposed neural adaptive control scheme is capable of providing significant vibration suppression in the multiple bending modes of interest. The performance of the proposed scheme is better than the H(infinity) control scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

PubMed

Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PubMed Central

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

An adaptive critic-based scheme for consensus control of nonlinear multi-agent systems

NASA Astrophysics Data System (ADS)

Heydari, Ali; Balakrishnan, S. N.

2014-12-01

The problem of decentralised consensus control of a network of heterogeneous nonlinear systems is formulated as an optimal tracking problem and a solution is proposed using an approximate dynamic programming based neurocontroller. The neurocontroller training comprises an initial offline training phase and an online re-optimisation phase to account for the fact that the reference signal subject to tracking is not fully known and available ahead of time, i.e., during the offline training phase. As long as the dynamics of the agents are controllable, and the communication graph has a directed spanning tree, this scheme guarantees the synchronisation/consensus even under switching communication topology and directed communication graph. Finally, an aerospace application is selected for the evaluation of the performance of the method. Simulation results demonstrate the potential of the scheme.

Improving the accuracy and efficiency of time-resolved electronic spectra calculations: cellular dephasing representation with a prefactor.

PubMed

Zambrano, Eduardo; Šulc, Miroslav; Vaníček, Jiří

2013-08-07

Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing representation. Here we improve both the accuracy of this approximation-with an amplitude correction derived from the phase-space propagator-and its efficiency-with an improved cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. We demonstrate the advantages of the new methodology by computing dispersed time-resolved stimulated emission spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast, we show that in strongly chaotic systems such as the quartic oscillator the original dephasing representation is more appropriate than either the cellular or prefactor-corrected methods.

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

NASA Astrophysics Data System (ADS)

Rose, F.; Dupuis, N.

2018-05-01

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

Low-complexity and modulation-format-independent carrier phase estimation scheme using linear approximation for elastic optical networks

NASA Astrophysics Data System (ADS)

Yang, Tao; Chen, Xue; Shi, Sheping; Sun, Erkun; Shi, Chen

2018-03-01

We propose a low-complexity and modulation-format-independent carrier phase estimation (CPE) scheme based on two-stage modified blind phase search (MBPS) with linear approximation to compensate the phase noise of arbitrary m-ary quadrature amplitude modulation (m-QAM) signals in elastic optical networks (EONs). Comprehensive numerical simulations are carried out in the case that the highest possible modulation format in EONs is 256-QAM. The simulation results not only verify its advantages of higher estimation accuracy and modulation-format independence, i.e., universality, but also demonstrate that the implementation complexity is significantly reduced by at least one-fourth in comparison with the traditional BPS scheme. In addition, the proposed scheme shows similar laser linewidth tolerance with the traditional BPS scheme. The slightly better OSNR performance of the scheme is also experimentally validated for PM-QPSK and PM-16QAM systems, respectively. The coexistent advantages of low-complexity and modulation-format-independence could make the proposed scheme an attractive candidate for flexible receiver-side DSP unit in EONs.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Structural and parameteric uncertainty quantification in cloud microphysics parameterization schemes

NASA Astrophysics Data System (ADS)

van Lier-Walqui, M.; Morrison, H.; Kumjian, M. R.; Prat, O. P.; Martinkus, C.

2017-12-01

Atmospheric model parameterization schemes employ approximations to represent the effects of unresolved processes. These approximations are a source of error in forecasts, caused in part by considerable uncertainty about the optimal value of parameters within each scheme -- parameteric uncertainty. Furthermore, there is uncertainty regarding the best choice of the overarching structure of the parameterization scheme -- structrual uncertainty. Parameter estimation can constrain the first, but may struggle with the second because structural choices are typically discrete. We address this problem in the context of cloud microphysics parameterization schemes by creating a flexible framework wherein structural and parametric uncertainties can be simultaneously constrained. Our scheme makes no assuptions about drop size distribution shape or the functional form of parametrized process rate terms. Instead, these uncertainties are constrained by observations using a Markov Chain Monte Carlo sampler within a Bayesian inference framework. Our scheme, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS), has flexibility to predict various sets of prognostic drop size distribution moments as well as varying complexity of process rate formulations. We compare idealized probabilistic forecasts from versions of BOSS with varying levels of structural complexity. This work has applications in ensemble forecasts with model physics uncertainty, data assimilation, and cloud microphysics process studies.

Computerized Liver Volumetry on MRI by Using 3D Geodesic Active Contour Segmentation

PubMed Central

Huynh, Hieu Trung; Karademir, Ibrahim; Oto, Aytekin; Suzuki, Kenji

2014-01-01

OBJECTIVE Our purpose was to develop an accurate automated 3D liver segmentation scheme for measuring liver volumes on MRI. SUBJECTS AND METHODS Our scheme for MRI liver volumetry consisted of three main stages. First, the preprocessing stage was applied to T1-weighted MRI of the liver in the portal venous phase to reduce noise and produce the boundary-enhanced image. This boundary-enhanced image was used as a speed function for a 3D fast-marching algorithm to generate an initial surface that roughly approximated the shape of the liver. A 3D geodesic-active-contour segmentation algorithm refined the initial surface to precisely determine the liver boundaries. The liver volumes determined by our scheme were compared with those manually traced by a radiologist, used as the reference standard. RESULTS The two volumetric methods reached excellent agreement (intraclass correlation coefficient, 0.98) without statistical significance (p = 0.42). The average (± SD) accuracy was 99.4% ± 0.14%, and the average Dice overlap coefficient was 93.6% ± 1.7%. The mean processing time for our automated scheme was 1.03 ± 0.13 minutes, whereas that for manual volumetry was 24.0 ± 4.4 minutes (p < 0.001). CONCLUSION The MRI liver volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time. PMID:24370139

Computerized liver volumetry on MRI by using 3D geodesic active contour segmentation.

PubMed

Huynh, Hieu Trung; Karademir, Ibrahim; Oto, Aytekin; Suzuki, Kenji

2014-01-01

Our purpose was to develop an accurate automated 3D liver segmentation scheme for measuring liver volumes on MRI. Our scheme for MRI liver volumetry consisted of three main stages. First, the preprocessing stage was applied to T1-weighted MRI of the liver in the portal venous phase to reduce noise and produce the boundary-enhanced image. This boundary-enhanced image was used as a speed function for a 3D fast-marching algorithm to generate an initial surface that roughly approximated the shape of the liver. A 3D geodesic-active-contour segmentation algorithm refined the initial surface to precisely determine the liver boundaries. The liver volumes determined by our scheme were compared with those manually traced by a radiologist, used as the reference standard. The two volumetric methods reached excellent agreement (intraclass correlation coefficient, 0.98) without statistical significance (p = 0.42). The average (± SD) accuracy was 99.4% ± 0.14%, and the average Dice overlap coefficient was 93.6% ± 1.7%. The mean processing time for our automated scheme was 1.03 ± 0.13 minutes, whereas that for manual volumetry was 24.0 ± 4.4 minutes (p < 0.001). The MRI liver volumetry based on our automated scheme agreed excellently with reference-standard volumetry, and it required substantially less completion time.

Channel coding/decoding alternatives for compressed TV data on advanced planetary missions.

NASA Technical Reports Server (NTRS)

Rice, R. F.

1972-01-01

The compatibility of channel coding/decoding schemes with a specific TV compressor developed for advanced planetary missions is considered. Under certain conditions, it is shown that compressed data can be transmitted at approximately the same rate as uncompressed data without any loss in quality. Thus, the full gains of data compression can be achieved in real-time transmission.

Neural-Network-Based Robust Optimal Tracking Control for MIMO Discrete-Time Systems With Unknown Uncertainty Using Adaptive Critic Design.

PubMed

Liu, Lei; Wang, Zhanshan; Zhang, Huaguang

2018-04-01

This paper is concerned with the robust optimal tracking control strategy for a class of nonlinear multi-input multi-output discrete-time systems with unknown uncertainty via adaptive critic design (ACD) scheme. The main purpose is to establish an adaptive actor-critic control method, so that the cost function in the procedure of dealing with uncertainty is minimum and the closed-loop system is stable. Based on the neural network approximator, an action network is applied to generate the optimal control signal and a critic network is used to approximate the cost function, respectively. In contrast to the previous methods, the main features of this paper are: 1) the ACD scheme is integrated into the controllers to cope with the uncertainty and 2) a novel cost function, which is not in quadric form, is proposed so that the total cost in the design procedure is reduced. It is proved that the optimal control signals and the tracking errors are uniformly ultimately bounded even when the uncertainty exists. Finally, a numerical simulation is developed to show the effectiveness of the present approach.

Parallel Computing of Upwelling in a Rotating Stratified Flow

NASA Astrophysics Data System (ADS)

Cui, A.; Street, R. L.

1997-11-01

A code for the three-dimensional, unsteady, incompressible, and turbulent flow has been implemented on the IBM SP2, using message passing. The effects of rotation and variable density are included. A finite volume method is used to discretize the Navier-Stokes equations in general curvilinear coordinates on a non-staggered grid. All the spatial derivatives are approximated using second-order central differences with the exception of the convection terms, which are handled with special upwind-difference schemes. The semi-implicit, second-order accurate, time-advancement scheme employs the Adams-Bashforth method for the explicit terms and Crank-Nicolson for the implicit terms. A multigrid method, with the four-color ZEBRA as smoother, is used to solve the Poisson equation for pressure, while the momentum equations are solved with an approximate factorization technique. The code was successfully validated for a variety test cases. Simulations of a laboratory model of coastal upwelling in a rotating annulus are in progress and will be presented.

Renormalization scheme dependence of high-order perturbative QCD predictions

NASA Astrophysics Data System (ADS)

Ma, Yang; Wu, Xing-Gang

2018-02-01

Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the sensitivity of pQCD prediction on the scheme parameters by using the scheme-dependent {βm ≥2}-terms. We adopt two four-loop examples, e+e-→hadrons and τ decays into hadrons, for detailed analysis. Our results show that under the conventional scale setting, by including more-and-more loop terms, the scheme dependence of the pQCD prediction cannot be reduced as efficiently as that of the scale dependence. Thus a proper scale-setting approach should be important to reduce the scheme dependence. We observe that the principle of minimum sensitivity could be such a scale-setting approach, which provides a practical way to achieve optimal scheme and scale by requiring the pQCD approximate be independent to the "unphysical" theoretical conventions.

Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

NASA Astrophysics Data System (ADS)

Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

2017-06-01

A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

An experiment-based comparative study of fuzzy logic control

NASA Technical Reports Server (NTRS)

Berenji, Hamid R.; Chen, Yung-Yaw; Lee, Chuen-Chein; Murugesan, S.; Jang, Jyh-Shing

1989-01-01

An approach is presented to the control of a dynamic physical system through the use of approximate reasoning. The approach has been implemented in a program named POLE, and the authors have successfully built a prototype hardware system to solve the cartpole balancing problem in real-time. The approach provides a complementary alternative to the conventional analytical control methodology and is of substantial use when a precise mathematical model of the process being controlled is not available. A set of criteria for comparing controllers based on approximate reasoning and those based on conventional control schemes is furnished.

Evaluating radiative transfer schemes treatment of vegetation canopy architecture in land surface models

NASA Astrophysics Data System (ADS)

Braghiere, Renato; Quaife, Tristan; Black, Emily

2016-04-01

Incoming shortwave radiation is the primary source of energy driving the majority of the Earth's climate system. The partitioning of shortwave radiation by vegetation into absorbed, reflected, and transmitted terms is important for most of biogeophysical processes, including leaf temperature changes and photosynthesis, and it is currently calculated by most of land surface schemes (LSS) of climate and/or numerical weather prediction models. The most commonly used radiative transfer scheme in LSS is the two-stream approximation, however it does not explicitly account for vegetation architectural effects on shortwave radiation partitioning. Detailed three-dimensional (3D) canopy radiative transfer schemes have been developed, but they are too computationally expensive to address large-scale related studies over long time periods. Using a straightforward one-dimensional (1D) parameterisation proposed by Pinty et al. (2006), we modified a two-stream radiative transfer scheme by including a simple function of Sun zenith angle, so-called "structure factor", which does not require an explicit description and understanding of the complex phenomena arising from the presence of vegetation heterogeneous architecture, and it guarantees accurate simulations of the radiative balance consistently with 3D representations. In order to evaluate the ability of the proposed parameterisation in accurately represent the radiative balance of more complex 3D schemes, a comparison between the modified two-stream approximation with the "structure factor" parameterisation and state-of-art 3D radiative transfer schemes was conducted, following a set of virtual scenarios described in the RAMI4PILPS experiment. These experiments have been evaluating the radiative balance of several models under perfectly controlled conditions in order to eliminate uncertainties arising from an incomplete or erroneous knowledge of the structural, spectral and illumination related canopy characteristics typical of model comparisons with in-situ observations. The structure factor parameters were obtained for each canopy structure through the inversion against direct and diffuse fraction of absorbed photosynthetically active radiation (fAPAR), and albedo PAR. Overall, the modified two-stream approximation consistently showed a good agreement with the RAMI4PILPS reference values under direct and diffuse illumination conditions. It is an efficient and accurate tool to derive PAR absorptance and reflectance for scenarios with different canopy densities, leaf densities and soil background albedos, with especial attention to brighter backgrounds, i.e., snowy. The major difficulty of its applicability in the real world is to acquire the parameterisation parameters from in-situ observations. The derivation of parameters from Digital Hemispherical Photographs (DHP) is highly promising at forest stands scales. DHP provide a permanent record and are a valuable information source for position, size, density, and distribution of canopy gaps. The modified two-stream approximation parameters were derived from gap probability data extracted from DHP obtained in a woody savannah in California, USA. Values of fAPAR and albedo PAR were evaluated against a tree-based vegetation canopy model, MAESPA, which used airborne LiDAR data to define the individual-tree locations, and extract structural information such as tree height and crown diameter. The parameterisation improved the performance of a two-stream approximation by making it achieves comparable results to complex 3D model calculations under observed conditions.

Conjunctively optimizing flash flood control and water quality in urban water reservoirs by model predictive control and dynamic emulation

NASA Astrophysics Data System (ADS)

Galelli, Stefano; Goedbloed, Albert; Schmitter, Petra; Castelletti, Andrea

2014-05-01

Urban water reservoirs are a viable adaptation option to account for increasing drinking water demand of urbanized areas as they allow storage and re-use of water that is normally lost. In addition, the direct availability of freshwater reduces pumping costs and diversifies the portfolios of drinking water supply. Yet, these benefits have an associated twofold cost. Firstly, the presence of large, impervious areas increases the hydraulic efficiency of urban catchments, with short time of concentration, increased runoff rates, losses of infiltration and baseflow, and higher risk of flash floods. Secondly, the high concentration of nutrients and sediments characterizing urban discharges is likely to cause water quality problems. In this study we propose a new control scheme combining Model Predictive Control (MPC), hydro-meteorological forecasts and dynamic model emulation to design real-time operating policies that conjunctively optimize water quantity and quality targets. The main advantage of this scheme stands in its capability of exploiting real-time hydro-meteorological forecasts, which are crucial in such fast-varying systems. In addition, the reduced computational requests of the MPC scheme allows coupling it with dynamic emulators of water quality processes. The approach is demonstrated on Marina Reservoir, a multi-purpose reservoir located in the heart of Singapore and characterized by a large, highly urbanized catchment with a short (i.e. approximately one hour) time of concentration. Results show that the MPC scheme, coupled with a water quality emulator, provides a good compromise between different operating objectives, namely flood risk reduction, drinking water supply and salinity control. Finally, the scheme is used to assess the effect of source control measures (e.g. green roofs) aimed at restoring the natural hydrological regime of Marina Reservoir catchment.

Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows

NASA Astrophysics Data System (ADS)

Nigro, A.; De Bartolo, C.; Crivellini, A.; Bassi, F.

2017-12-01

In this paper we investigate the possibility of using the high-order accurate A (α) -stable Second Derivative (SD) schemes proposed by Enright for the implicit time integration of the Discontinuous Galerkin (DG) space-discretized Navier-Stokes equations. These multistep schemes are A-stable up to fourth-order, but their use results in a system matrix difficult to compute. Furthermore, the evaluation of the nonlinear function is computationally very demanding. We propose here a Matrix-Free (MF) implementation of Enright schemes that allows to obtain a method without the costs of forming, storing and factorizing the system matrix, which is much less computationally expensive than its matrix-explicit counterpart, and which performs competitively with other implicit schemes, such as the Modified Extended Backward Differentiation Formulae (MEBDF). The algorithm makes use of the preconditioned GMRES algorithm for solving the linear system of equations. The preconditioner is based on the ILU(0) factorization of an approximated but computationally cheaper form of the system matrix, and it has been reused for several time steps to improve the efficiency of the MF Newton-Krylov solver. We additionally employ a polynomial extrapolation technique to compute an accurate initial guess to the implicit nonlinear system. The stability properties of SD schemes have been analyzed by solving a linear model problem. For the analysis on the Navier-Stokes equations, two-dimensional inviscid and viscous test cases, both with a known analytical solution, are solved to assess the accuracy properties of the proposed time integration method for nonlinear autonomous and non-autonomous systems, respectively. The performance of the SD algorithm is compared with the ones obtained by using an MF-MEBDF solver, in order to evaluate its effectiveness, identifying its limitations and suggesting possible further improvements.

40 CFR 761.316 - Interpreting PCB concentration measurements resulting from this sampling scheme.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 40 Protection of Environment 32 2013-07-01 2013-07-01 false Interpreting PCB concentration measurements resulting from this sampling scheme. 761.316 Section 761.316 Protection of Environment... scheme. (a) For an individual sample taken from an approximately 1 meter square portion of the entire...

Density functional theory for d- and f-electron materials and compounds

DOE PAGES

Mattson, Ann E.; Wills, John M.

2016-02-12

Here, the fundamental requirements for a computationally tractable Density Functional Theory-based method for relativistic f- and (nonrelativistic) d-electron materials and compounds are presented. The need for basing the Kohn–Sham equations on the Dirac equation is discussed. The full Dirac scheme needs exchange-correlation functionals in terms of four-currents, but ordinary functionals, using charge density and spin-magnetization, can be used in an approximate Dirac treatment. The construction of a functional that includes the additional confinement physics needed for these materials is illustrated using the subsystem-functional scheme. If future studies show that a full Dirac, four-current based, exchange-correlation functional is needed, the subsystemmore » functional scheme is one of the few schemes that can still be used for constructing functional approximations.« less

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

2002-01-01

We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

Approximate minimum-time trajectories for 2-link flexible manipulators

NASA Technical Reports Server (NTRS)

Eisler, G. R.; Segalman, D. J.; Robinett, R. D.

1989-01-01

Powell's nonlinear programming code, VF02AD, was used to generate approximate minimum-time tip trajectories for 2-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with horizontal-plane bending only. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness, EI, to transition from the semi-rigid to flexible case. Results show the level of compliance necessary to excite significant modal behavior. Quiescence of the final configuration is examined with the finite-element model.

Simplification of the time-dependent generalized self-interaction correction method using two sets of orbitals: Application of the optimized effective potential formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Messud, J.; Dinh, P. M.; Suraud, Eric

2009-10-15

We propose a simplification of the time-dependent self-interaction correction (TD-SIC) method using two sets of orbitals, applying the optimized effective potential (OEP) method. The resulting scheme is called time-dependent 'generalized SIC-OEP'. A straightforward approximation, using the spatial localization of one set of orbitals, leads to the 'generalized SIC-Slater' formalism. We show that it represents a great improvement compared to the traditional SIC-Slater and Krieger-Li-Iafrate formalisms.

Simplification of the time-dependent generalized self-interaction correction method using two sets of orbitals: Application of the optimized effective potential formalism

NASA Astrophysics Data System (ADS)

Messud, J.; Dinh, P. M.; Reinhard, P.-G.; Suraud, Eric

2009-10-01

We propose a simplification of the time-dependent self-interaction correction (TD-SIC) method using two sets of orbitals, applying the optimized effective potential (OEP) method. The resulting scheme is called time-dependent “generalized SIC-OEP.” A straightforward approximation, using the spatial localization of one set of orbitals, leads to the “generalized SIC-Slater” formalism. We show that it represents a great improvement compared to the traditional SIC-Slater and Krieger-Li-Iafrate formalisms.

Application of the θ-method to a telegraphic model of fluid flow in a dual-porosity medium

NASA Astrophysics Data System (ADS)

González-Calderón, Alfredo; Vivas-Cruz, Luis X.; Herrera-Hernández, Erik César

2018-01-01

This work focuses mainly on the study of numerical solutions, which are obtained using the θ-method, of a generalized Warren and Root model that includes a second-order wave-like equation in its formulation. The solutions approximately describe the single-phase hydraulic head in fractures by considering the finite velocity of propagation by means of a Cattaneo-like equation. The corresponding discretized model is obtained by utilizing a non-uniform grid and a non-uniform time step. A simple relationship is proposed to give the time-step distribution. Convergence is analyzed by comparing results from explicit, fully implicit, and Crank-Nicolson schemes with exact solutions: a telegraphic model of fluid flow in a single-porosity reservoir with relaxation dynamics, the Warren and Root model, and our studied model, which is solved with the inverse Laplace transform. We find that the flux and the hydraulic head have spurious oscillations that most often appear in small-time solutions but are attenuated as the solution time progresses. Furthermore, we show that the finite difference method is unable to reproduce the exact flux at time zero. Obtaining results for oilfield production times, which are in the order of months in real units, is only feasible using parallel implicit schemes. In addition, we propose simple parallel algorithms for the memory flux and for the explicit scheme.

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated onmore » three benchmarking systems, with special focus on approximation accuracy and efficiency.« less

Robust Algorithms for on Minor-Free Graphs Based on the Sherali-Adams Hierarchy

NASA Astrophysics Data System (ADS)

Magen, Avner; Moharrami, Mohammad

This work provides a Linear Programming-based Polynomial Time Approximation Scheme (PTAS) for two classical NP-hard problems on graphs when the input graph is guaranteed to be planar, or more generally Minor Free. The algorithm applies a sufficiently large number (some function of when approximation is required) of rounds of the so-called Sherali-Adams Lift-and-Project system. needed to obtain a -approximation, where f is some function that depends only on the graph that should be avoided as a minor. The problem we discuss are the well-studied problems, the and problems. An curious fact we expose is that in the world of minor-free graph, the is harder in some sense than the.

Well-balanced compressible cut-cell simulation of atmospheric flow.

PubMed

Klein, R; Bates, K R; Nikiforakis, N

2009-11-28

Cut-cell meshes present an attractive alternative to terrain-following coordinates for the representation of topography within atmospheric flow simulations, particularly in regions of steep topographic gradients. In this paper, we present an explicit two-dimensional method for the numerical solution on such meshes of atmospheric flow equations including gravitational sources. This method is fully conservative and allows for time steps determined by the regular grid spacing, avoiding potential stability issues due to arbitrarily small boundary cells. We believe that the scheme is unique in that it is developed within a dimensionally split framework, in which each coordinate direction in the flow is solved independently at each time step. Other notable features of the scheme are: (i) its conceptual and practical simplicity, (ii) its flexibility with regard to the one-dimensional flux approximation scheme employed, and (iii) the well-balancing of the gravitational sources allowing for stable simulation of near-hydrostatic flows. The presented method is applied to a selection of test problems including buoyant bubble rise interacting with geometry and lee-wave generation due to topography.

Optically pumped quantum magnetometer with combined advantages of M X and M Z devices

NASA Astrophysics Data System (ADS)

Vershovskii, A. K.; Dmitriev, S. P.; Pazgalev, A. S.

2013-10-01

A scheme of the magnetometer that simultaneously employs M X and M R magnetic resonance signals with the latter signal related to the radial component of the rotating atomic magnetic moment is proposed and tested. With respect to the shape, dynamic characteristics, and metrological parameters, the M R signal is similar to the M X signal that is widely used in magnetometry but the former signal can be detected simultaneously with the M X signal using a common radio optical scheme. The proposed device represents a fast M X magnetometer with the phase in the feedback loop that is controlled by a slow precise M R magnetometer implemented using the same atoms. The device that can be based on a conventional M X sensor simultaneously exhibits a relatively short response time (τ ≤ 0.1 s) and the accuracy that is approximately equal to the resolution of the quantum M X discriminator at times of 10-100 s. The scheme is experimentally tested, and the statistic estimate of reproducibility is (1.2 ± 1.1) pT.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Bingyu; Zheng, Liancun, E-mail: liancunzheng@ustb.edu.cn; Chen, Shengting

This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.

Characteristic-based algorithms for flows in thermo-chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Cinnella, Pasquale; Slack, David C.; Halt, David

1990-01-01

A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.

Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion

NASA Astrophysics Data System (ADS)

Sánchez-Vizuet, Tonatiuh; Cerfon, Antoine J.

2018-02-01

We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo-spectral collocation on a grid defined by the zeros of a non-standard family of orthogonal polynomials called Maxwell polynomials. Taking a one-dimensional equation describing energy diffusion due to Fokker-Planck collisions with a Maxwell-Boltzmann background distribution as the test bench for the performance of the scheme, we find that Maxwell based discretizations outperform other commonly used schemes in most situations, often by orders of magnitude. This provides a strong motivation for their use in high-dimensional gyrokinetic simulations. However, we also show that Maxwell based schemes are subject to a non-modal time stepping instability in their most straightforward implementation, so that special care must be given to the discrete representation of the linear operators in order to benefit from the advantages provided by Maxwell polynomials.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

A pattern jitter free AFC scheme for mobile satellite systems

NASA Technical Reports Server (NTRS)

Yoshida, Shousei

1993-01-01

This paper describes a scheme for pattern jitter free automatic frequency control (AFC) with a wide frequency acquisition range. In this scheme, equalizing signals fed to the frequency discriminator allow pattern jitter free performance to be achieved for all roll-off factors. In order to define the acquisition range, frequency discrimination characateristics are analyzed on a newly derived frequency domain model. As a result, it is shown that a sufficiently wide acquisition range over a given system symbol rate can be achieved independent of symbol timing errors. Additionally, computer simulation demonstrates that frequency jitter performance improves in proportion to E(sub b)/N(sub 0) because pattern-dependent jitter is suppressed in the discriminator output. These results show significant promise for applciation to mobile satellite systems, which feature relatively low symbol rate transmission with an approximately 0.4-0.7 roll-off factor.

Describing the dynamics of processes consisting simultaneously of Poissonian and non-Poissonian kinetics

NASA Astrophysics Data System (ADS)

Eule, S.; Friedrich, R.

2013-03-01

Dynamical processes exhibiting non-Poissonian kinetics with nonexponential waiting times are frequently encountered in nature. Examples are biochemical processes like gene transcription which are known to involve multiple intermediate steps. However, often a second process, obeying Poissonian statistics, affects the first one simultaneously, such as the degradation of mRNA in the above example. The aim of the present article is to provide a concise treatment of such random systems which are affected by regular and non-Poissonian kinetics at the same time. We derive the governing master equation and provide a controlled approximation scheme for this equation. The simplest approximation leads to generalized reaction rate equations. For a simple model of gene transcription we solve the resulting equation and show how the time evolution is influenced significantly by the type of waiting time distribution assumed for the non-Poissonian process.

Kalman Filters for Time Delay of Arrival-Based Source Localization

NASA Astrophysics Data System (ADS)

Klee, Ulrich; Gehrig, Tobias; McDonough, John

2006-12-01

In this work, we propose an algorithm for acoustic source localization based on time delay of arrival (TDOA) estimation. In earlier work by other authors, an initial closed-form approximation was first used to estimate the true position of the speaker followed by a Kalman filtering stage to smooth the time series of estimates. In the proposed algorithm, this closed-form approximation is eliminated by employing a Kalman filter to directly update the speaker's position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker's position. We tested our algorithm on a data set consisting of seminars held by actual speakers. Our experiments revealed that the proposed algorithm provides source localization accuracy superior to the standard spherical and linear intersection techniques. Moreover, the proposed algorithm, although relying on an iterative optimization scheme, proved efficient enough for real-time operation.

Implementation of an approximate self-energy correction scheme in the orthogonalized linear combination of atomic orbitals method of band-structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gu, Z.; Ching, W.Y.

Based on the Sterne-Inkson model for the self-energy correction to the single-particle energy in the local-density approximation (LDA), we have implemented an approximate energy-dependent and [bold k]-dependent [ital GW] correction scheme to the orthogonalized linear combination of atomic orbital-based local-density calculation for insulators. In contrast to the approach of Jenkins, Srivastava, and Inkson, we evaluate the on-site exchange integrals using the LDA Bloch functions throughout the Brillouin zone. By using a [bold k]-weighted band gap [ital E][sub [ital g

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

1989-01-01

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Optimal feedback control of turbulent channel flow

NASA Technical Reports Server (NTRS)

Bewley, Thomas; Choi, Haecheon; Temam, Roger; Moin, Parviz

1993-01-01

Feedback control equations were developed and tested for computing wall normal control velocities to control turbulent flow in a channel with the objective of reducing drag. The technique used is the minimization of a 'cost functional' which is constructed to represent some balance of the drag integrated over the wall and the net control effort. A distribution of wall velocities is found which minimizes this cost functional some time shortly in the future based on current observations of the flow near the wall. Preliminary direct numerical simulations of the scheme applied to turbulent channel flow indicates it provides approximately 17 percent drag reduction. The mechanism apparent when the scheme is applied to a simplified flow situation is also discussed.

Effective scheme of photolysis of GFP in live cell as revealed with confocal fluorescence microscopy

NASA Astrophysics Data System (ADS)

Glazachev, Yu I.; Orlova, D. Y.; Řezníčková, P.; Bártová, E.

2018-05-01

We proposed an effective kinetics scheme of photolysis of green fluorescent protein (GFP) observed in live cells with a commercial confocal fluorescence microscope. We investigated the photolysis of GFP-tagged heterochromatin protein, HP1β-GFP, in live nucleus with the pulse position modulation approach, which has several advantages over the classical pump-and-probe method. At the basis of the proposed scheme lies a process of photoswitching from the native fluorescence state to the intermediate fluorescence state, which has a lower fluorescence yield and recovers back to native state in the dark. This kinetics scheme includes four effective parameters (photoswitching, reverse switching, photodegradation rate constants, and relative brightness of the intermediate state) and covers the time scale from dozens of milliseconds to minutes of the experimental fluorescence kinetics. Additionally, the applicability of the scheme was demonstrated in the cases of continuous irradiation and the classical pump-and-probe approach using numerical calculations and analytical solutions. An interesting finding of experimental data analysis was that the overall photodegradation of GFP proceeds dominantly from the intermediate state, and demonstrated approximately the second-order reaction versus irradiation power. As a practical example, the proposed scheme elucidates the artifacts of fluorescence recovery after the photobleaching method, and allows us to propose some suggestions on how to diminish them.

Effective scheme of photolysis of GFP in live cell as revealed with confocal fluorescence microscopy.

PubMed

Glazachev, Yu I; Orlova, D Y; Řezníčková, P; Bártová, E

2018-03-23

We proposed an effective kinetics scheme of photolysis of green fluorescent protein (GFP) observed in live cells with a commercial confocal fluorescence microscope. We investigated the photolysis of GFP-tagged heterochromatin protein, HP1β-GFP, in live nucleus with the pulse position modulation approach, which has several advantages over the classical pump-and-probe method. At the basis of the proposed scheme lies a process of photoswitching from the native fluorescence state to the intermediate fluorescence state, which has a lower fluorescence yield and recovers back to native state in the dark. This kinetics scheme includes four effective parameters (photoswitching, reverse switching, photodegradation rate constants, and relative brightness of the intermediate state) and covers the time scale from dozens of milliseconds to minutes of the experimental fluorescence kinetics. Additionally, the applicability of the scheme was demonstrated in the cases of continuous irradiation and the classical pump-and-probe approach using numerical calculations and analytical solutions. An interesting finding of experimental data analysis was that the overall photodegradation of GFP proceeds dominantly from the intermediate state, and demonstrated approximately the second-order reaction versus irradiation power. As a practical example, the proposed scheme elucidates the artifacts of fluorescence recovery after the photobleaching method, and allows us to propose some suggestions on how to diminish them.

Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion

NASA Technical Reports Server (NTRS)

Erickson, W. D.; Prabhu, R. K.

1986-01-01

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning

NASA Astrophysics Data System (ADS)

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-08-01

{{\\ell }2,1} -minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the {{\\ell }2,1} -based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the {{\\ell }2,1} -minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the {{\\ell }2,1} -minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the {{\\ell }2,1} -minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning.

PubMed

Liu, Hongcheng; Dong, Peng; Xing, Lei

2017-07-20

[Formula: see text]-minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the [Formula: see text]-based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the [Formula: see text]-minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the [Formula: see text]-minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the [Formula: see text]-minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

Numerical methods for incompressible viscous flows with engineering applications

NASA Technical Reports Server (NTRS)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

EXPERIMENTAL AND MODEL-COMPUTED AREA AVERAGED VERTICAL PROFILES OF WIND SPEED FOR EVALUATION OF MESOSCALE URBAN CANOPY SCHEMES

EPA Science Inventory

Numerous urban canopy schemes have recently been developed for mesoscale models in order to approximate the drag and turbulent production effects of a city on the air flow. However, little data exists by which to evaluate the efficacy of the schemes since "area-averaged&quo...

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.

1985-01-01

The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.

Adaptive Approximation-Based Regulation Control for a Class of Uncertain Nonlinear Systems Without Feedback Linearizability.

PubMed

Wang, Ning; Sun, Jing-Chao; Han, Min; Zheng, Zhongjiu; Er, Meng Joo

2017-09-06

In this paper, for a general class of uncertain nonlinear (cascade) systems, including unknown dynamics, which are not feedback linearizable and cannot be solved by existing approaches, an innovative adaptive approximation-based regulation control (AARC) scheme is developed. Within the framework of adding a power integrator (API), by deriving adaptive laws for output weights and prediction error compensation pertaining to single-hidden-layer feedforward network (SLFN) from the Lyapunov synthesis, a series of SLFN-based approximators are explicitly constructed to exactly dominate completely unknown dynamics. By the virtue of significant advancements on the API technique, an adaptive API methodology is eventually established in combination with SLFN-based adaptive approximators, and it contributes to a recursive mechanism for the AARC scheme. As a consequence, the output regulation error can asymptotically converge to the origin, and all other signals of the closed-loop system are uniformly ultimately bounded. Simulation studies and comprehensive comparisons with backstepping- and API-based approaches demonstrate that the proposed AARC scheme achieves remarkable performance and superiority in dealing with unknown dynamics.

A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

NASA Astrophysics Data System (ADS)

Terrana, S.; Vilotte, J. P.; Guillot, L.

2018-04-01

We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm, when element polynomials of order k are used, and to exhibit the classical spectral convergence of SEM. Additional inexpensive local post-processing in both the elastic and the acoustic case allow to achieve higher convergence orders. The HDG scheme provides a natural framework for coupling classical, continuous Galerkin SEM with HDG-SEM in the same simulation, and it is shown numerically in this paper. As such, the proposed HDG-SEM can combine the efficiency of the continuous SEM with the flexibility of the HDG approaches. Finally, more complex numerical results, inspired from real geophysical applications, are presented to illustrate the capabilities of the method for wave propagation in heterogeneous elastic-acoustic media with complex geometries.

Characterization of Impulse Radio Intrabody Communication System for Wireless Body Area Networks.

PubMed

Cai, Zibo; Seyedi, MirHojjat; Zhang, Weiwei; Rivet, Francois; Lai, Daniel T H

2017-01-01

Intrabody communication (IBC) is a promising data communication technique for body area networks. This short-distance communication approach uses human body tissue as the medium of signal propagation. IBC is defined as one of the physical layers for the new IEEE 802.15.6 or wireless body area network (WBAN) standard, which can provide a suitable data rate for real-time physiological data communication while consuming lower power compared to that of radio-frequency protocols such as Bluetooth. In this paper, impulse radio (IR) IBC (IR-IBC) is examined using a field-programmable gate array (FPGA) implementation of an IBC system. A carrier-free pulse position modulation (PPM) scheme is implemented using an IBC transmitter in an FPGA board. PPM is a modulation technique that uses time-based pulse characteristics to encode data based on IR concepts. The transmission performance of the scheme was evaluated through signal propagation measurements of the human arm using 4- and 8-PPM transmitters, respectively. 4 or 8 is the number of symbols during modulations. It was found that the received signal-to-noise ratio (SNR) decreases approximately 8.0 dB for a range of arm distances (5-50 cm) between the transmitter and receiver electrodes with constant noise power and various signal amplitudes. The SNR for the 4-PPM scheme is approximately 2 dB higher than that for the 8-PPM one. In addition, the bit error rate (BER) is theoretically analyzed for the human body channel with additive white Gaussian noise. The 4- and 8-PPM IBC systems have average BER values of 10 -5 and 10 -10 , respectively. The results indicate the superiority of the 8-PPM scheme compared to the 4-PPM one when implementing the IBC system. The performance evaluation of the proposed IBC system will improve further IBC transceiver design.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Development and Implementation of a Transport Method for the Transport and Reaction Simulation Engine (TaRSE) based on the Godunov-Mixed Finite Element Method

USGS Publications Warehouse

James, Andrew I.; Jawitz, James W.; Munoz-Carpena, Rafael

2009-01-01

A model to simulate transport of materials in surface water and ground water has been developed to numerically approximate solutions to the advection-dispersion equation. This model, known as the Transport and Reaction Simulation Engine (TaRSE), uses an algorithm that incorporates a time-splitting technique where the advective part of the equation is solved separately from the dispersive part. An explicit finite-volume Godunov method is used to approximate the advective part, while a mixed-finite element technique is used to approximate the dispersive part. The dispersive part uses an implicit discretization, which allows it to run stably with a larger time step than the explicit advective step. The potential exists to develop algorithms that run several advective steps, and then one dispersive step that encompasses the time interval of the advective steps. Because the dispersive step is computationally most expensive, schemes can be implemented that are more computationally efficient than non-time-split algorithms. This technique enables scientists to solve problems with high grid Peclet numbers, such as transport problems with sharp solute fronts, without spurious oscillations in the numerical approximation to the solution and with virtually no artificial diffusion.

Adaptive Neural Network-Based Event-Triggered Control of Single-Input Single-Output Nonlinear Discrete-Time Systems.

PubMed

Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani

2016-01-01

This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

Optimal symmetric flight studies

NASA Technical Reports Server (NTRS)

Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.

1985-01-01

Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Rumsey, Christopher Lockwood

1991-01-01

A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haut, T. S.; Babb, T.; Martinsson, P. G.

2015-06-16

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

Online Distributed Learning Over Networks in RKH Spaces Using Random Fourier Features

NASA Astrophysics Data System (ADS)

Bouboulis, Pantelis; Chouvardas, Symeon; Theodoridis, Sergios

2018-04-01

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources, in a distributed setting. In contrast, the proposed method approximates the solution as a fixed-size vector (of larger dimension than the input space) using Random Fourier Features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme.

FASTPM: a new scheme for fast simulations of dark matter and haloes

NASA Astrophysics Data System (ADS)

Feng, Yu; Chu, Man-Yat; Seljak, Uroš; McDonald, Patrick

2016-12-01

We introduce FASTPM, a highly scalable approximated particle mesh (PM) N-body solver, which implements the PM scheme enforcing correct linear displacement (1LPT) evolution via modified kick and drift factors. Employing a two-dimensional domain decomposing scheme, FASTPM scales extremely well with a very large number of CPUs. In contrast to Comoving-Lagrangian (COLA) approach, we do not require to split the force or track separately the 2LPT solution, reducing the code complexity and memory requirements. We compare FASTPM with different number of steps (Ns) and force resolution factor (B) against three benchmarks: halo mass function from friends-of-friends halo finder; halo and dark matter power spectrum; and cross-correlation coefficient (or stochasticity), relative to a high-resolution TREEPM simulation. We show that the modified time stepping scheme reduces the halo stochasticity when compared to COLA with the same number of steps and force resolution. While increasing Ns and B improves the transfer function and cross-correlation coefficient, for many applications FASTPM achieves sufficient accuracy at low Ns and B. For example, Ns = 10 and B = 2 simulation provides a substantial saving (a factor of 10) of computing time relative to Ns = 40, B = 3 simulation, yet the halo benchmarks are very similar at z = 0. We find that for abundance matched haloes the stochasticity remains low even for Ns = 5. FASTPM compares well against less expensive schemes, being only 7 (4) times more expensive than 2LPT initial condition generator for Ns = 10 (Ns = 5). Some of the applications where FASTPM can be useful are generating a large number of mocks, producing non-linear statistics where one varies a large number of nuisance or cosmological parameters, or serving as part of an initial conditions solver.

Visualization Techniques Applied to 155-mm Projectile Analysis

DTIC Science & Technology

2014-11-01

semi-infinite Riemann problems are used in CFD++ to provide upwind flux information to the underlying transport scheme. Approximate Riemann solvers ...characteristics-based inflow/outflow boundary condition, which is based on solving a Riemann problem at the boundary. 2.3 Numerics Rolling/spinning is the...the solution files generated by the computational fluid dynamics (CFD) solver for the time-accurate rolling simulations at each timestep for the Mach

Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

NASA Technical Reports Server (NTRS)

Weinberg, B. C.; Mcdonald, H.

1982-01-01

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

PubMed

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

NASA Technical Reports Server (NTRS)

Boretti, A. A.

1990-01-01

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Exponential Methods for the Time Integration of Schroedinger Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

On the impact of topography and building mask on time varying gravity due to local hydrology

NASA Astrophysics Data System (ADS)

Deville, S.; Jacob, T.; Chéry, J.; Champollion, C.

2013-01-01

We use 3 yr of surface absolute gravity measurements at three sites on the Larzac plateau (France) to quantify the changes induced by topography and the building on gravity time-series, with respect to an idealized infinite slab approximation. Indeed, local topography and buildings housing ground-based gravity measurement have an effect on the distribution of water storage changes, therefore affecting the associated gravity signal. We first calculate the effects of surrounding topography and building dimensions on the gravity attraction for a uniform layer of water. We show that a gravimetric interpretation of water storage change using an infinite slab, the so-called Bouguer approximation, is generally not suitable. We propose to split the time varying gravity signal in two parts (1) a surface component including topographic and building effects (2) a deep component associated to underground water transfer. A reservoir modelling scheme is herein presented to remove the local site effects and to invert for the effective hydrological properties of the unsaturated zone. We show that effective time constants associated to water transfer vary greatly from site to site. We propose that our modelling scheme can be used to correct for the local site effects on gravity at any site presenting a departure from a flat topography. Depending on sites, the corrected signal can exceed measured values by 5-15 μGal, corresponding to 120-380 mm of water using the Bouguer slab formula. Our approach only requires the knowledge of daily precipitation corrected for evapotranspiration. Therefore, it can be a useful tool to correct any kind of gravimetric time-series data.

Optimal Control-Based Adaptive NN Design for a Class of Nonlinear Discrete-Time Block-Triangular Systems.

PubMed

Liu, Yan-Jun; Tong, Shaocheng

2016-11-01

In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.

Strategy for reflector pattern calculation - Let the computer do the work

NASA Technical Reports Server (NTRS)

Lam, P. T.; Lee, S.-W.; Hung, C. C.; Acosta, R.

1986-01-01

Using high frequency approximations, the secondary pattern of a reflector antenna can be calculated by numerically evaluating a radiation integral I(u,v). In recent years, tremendous effort has been expended to reducing I(u,v) to Fourier integrals. These reduction schemes are invariably reflector geometry dependent. Hence, different analyses/computer software development must be carried out for different reflector shapes/boundaries. It is pointed out, that, as the computer power improves, these reduction schemes are no longer necessary. Comparable accuracy and computation time can be achieved by evaluating I(u,v) by a brute force FFT described in this note. Furthermore, there is virtually no restriction on the reflector geometry by using the brute force FFT.

Event-Triggered Fault Detection of Nonlinear Networked Systems.

PubMed

Li, Hongyi; Chen, Ziran; Wu, Ligang; Lam, Hak-Keung; Du, Haiping

2017-04-01

This paper investigates the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme. A polynomial fuzzy fault detection filter is designed to generate a residual signal and detect faults in the system. A novel polynomial event-triggered scheme is proposed to determine the transmission of the signal. A fault detection filter is designed to guarantee that the residual system is asymptotically stable and satisfies the desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions are represented in terms of sum of squares (SOSs) and can be solved by SOS tools in MATLAB environment. A numerical example is provided to demonstrate the effectiveness of the proposed results.

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

Strategy for reflector pattern calculation: Let the computer do the work

NASA Technical Reports Server (NTRS)

Lam, P. T.; Lee, S. W.; Hung, C. C.; Acousta, R.

1985-01-01

Using high frequency approximations, the secondary pattern of a reflector antenna can be calculated by numerically evaluating a radiation integral I(u,v). In recent years, tremendous effort has been expended to reducing I(u,v) to Fourier integrals. These reduction schemes are invariably reflector geometry dependent. Hence, different analyses/computer software development must be carried out for different reflector shapes/boundaries. it is pointed out, that, as the computer power improves, these reduction schemes are no longer necessary. Comparable accuracy and computation time can be achieved by evaluating I(u,v) by a brute force FFT described in this note. Furthermore, there is virtually no restriction on the reflector geometry by using the brute force FFT.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

Private genome analysis through homomorphic encryption

PubMed Central

2015-01-01

Background The rapid development of genome sequencing technology allows researchers to access large genome datasets. However, outsourcing the data processing o the cloud poses high risks for personal privacy. The aim of this paper is to give a practical solution for this problem using homomorphic encryption. In our approach, all the computations can be performed in an untrusted cloud without requiring the decryption key or any interaction with the data owner, which preserves the privacy of genome data. Methods We present evaluation algorithms for secure computation of the minor allele frequencies and χ2 statistic in a genome-wide association studies setting. We also describe how to privately compute the Hamming distance and approximate Edit distance between encrypted DNA sequences. Finally, we compare performance details of using two practical homomorphic encryption schemes - the BGV scheme by Gentry, Halevi and Smart and the YASHE scheme by Bos, Lauter, Loftus and Naehrig. Results The approach with the YASHE scheme analyzes data from 400 people within about 2 seconds and picks a variant associated with disease from 311 spots. For another task, using the BGV scheme, it took about 65 seconds to securely compute the approximate Edit distance for DNA sequences of size 5K and figure out the differences between them. Conclusions The performance numbers for BGV are better than YASHE when homomorphically evaluating deep circuits (like the Hamming distance algorithm or approximate Edit distance algorithm). On the other hand, it is more efficient to use the YASHE scheme for a low-degree computation, such as minor allele frequencies or χ2 test statistic in a case-control study. PMID:26733152

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations

NASA Technical Reports Server (NTRS)

Shiuhong, Lui; Xu, Jun

1999-01-01

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.

Approximability of the d-dimensional Euclidean capacitated vehicle routing problem

NASA Astrophysics Data System (ADS)

Khachay, Michael; Dubinin, Roman

2016-10-01

Capacitated Vehicle Routing Problem (CVRP) is the well known intractable combinatorial optimization problem, which remains NP-hard even in the Euclidean plane. Since the introduction of this problem in the middle of the 20th century, many researchers were involved into the study of its approximability. Most of the results obtained in this field are based on the well known Iterated Tour Partition heuristic proposed by M. Haimovich and A. Rinnoy Kan in their celebrated paper, where they construct the first Polynomial Time Approximation Scheme (PTAS) for the single depot CVRP in ℝ2. For decades, this result was extended by many authors to numerous useful modifications of the problem taking into account multiple depots, pick up and delivery options, time window restrictions, etc. But, to the best of our knowledge, almost none of these results go beyond the Euclidean plane. In this paper, we try to bridge this gap and propose a EPTAS for the Euclidean CVRP for any fixed dimension.

Sensitivity of High-Resolution Simulations of Hurricane Bob (1991) to Planetary Boundary Layer Parameterizations

NASA Technical Reports Server (NTRS)

Braun, Scott A.; Tao, Wei-Kuo

1999-01-01

The MM5 mesoscale model is used to simulate Hurricane Bob (1991) using grids nested to high resolution (4 km). Tests are conducted to determine the sensitivity of the simulation to the available planetary boundary layer parameterizations, including the bulk-aerodynamic, Blackadar, Medium-RanGe Forecast (MRF) model, and Burk-Thompson boundary-layer schemes. Significant sensitivity is seen, with minimum central pressures varying by up to 17 mb. The Burk-Thompson and bulk-aerodynamic boundary-layer schemes produced the strongest storms while the MRF scheme produced the weakest storm. Precipitation structure of the simulated hurricanes also varied substantially with the boundary layer parameterizations. Diagnostics of boundary-layer variables indicated that the intensity of the simulated hurricanes generally increased as the ratio of the surface exchange coefficients for heat and momentum, C(sub h)/C(sub M), although the manner in which the vertical mixing takes place was also important. Findings specific to the boundary-layer schemes include: 1) the MRF scheme produces mixing that is too deep and causes drying of the lower boundary layer in the inner-core region of the hurricane; 2) the bulk-aerodynamic scheme produces mixing that is probably too shallow, but results in a strong hurricane because of a large value of C(sub h)/C(sub M) (approximately 1.3); 3) the MRF and Blackadar schemes are weak partly because of smaller surface moisture fluxes that result in a reduced value of C(sub h)/C(sub M) (approximately 0.7); 4) the Burk-Thompson scheme produces a strong storm with C(sub h)/C(sub M) approximately 1; and 5) the formulation of the wind-speed dependence of the surface roughness parameter, z(sub 0), is important for getting appropriate values of the surface exchange coefficients in hurricanes based upon current estimates of these parameters.

Optimal mapping of neural-network learning on message-passing multicomputers

NASA Technical Reports Server (NTRS)

Chu, Lon-Chan; Wah, Benjamin W.

1992-01-01

A minimization of learning-algorithm completion time is sought in the present optimal-mapping study of the learning process in multilayer feed-forward artificial neural networks (ANNs) for message-passing multicomputers. A novel approximation algorithm for mappings of this kind is derived from observations of the dominance of a parallel ANN algorithm over its communication time. Attention is given to both static and dynamic mapping schemes for systems with static and dynamic background workloads, as well as to experimental results obtained for simulated mappings on multicomputers with dynamic background workloads.

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Baumeister, Kenneth J.

1996-01-01

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Real-time and encryption efficiency improvements of simultaneous fusion, compression and encryption method based on chaotic generators

NASA Astrophysics Data System (ADS)

Jridi, Maher; Alfalou, Ayman

2018-03-01

In this paper, enhancement of an existing optical simultaneous fusion, compression and encryption (SFCE) scheme in terms of real-time requirements, bandwidth occupation and encryption robustness is proposed. We have used and approximate form of the DCT to decrease the computational resources. Then, a novel chaos-based encryption algorithm is introduced in order to achieve the confusion and diffusion effects. In the confusion phase, Henon map is used for row and column permutations, where the initial condition is related to the original image. Furthermore, the Skew Tent map is employed to generate another random matrix in order to carry out pixel scrambling. Finally, an adaptation of a classical diffusion process scheme is employed to strengthen security of the cryptosystem against statistical, differential, and chosen plaintext attacks. Analyses of key space, histogram, adjacent pixel correlation, sensitivity, and encryption speed of the encryption scheme are provided, and favorably compared to those of the existing crypto-compression system. The proposed method has been found to be digital/optical implementation-friendly which facilitates the integration of the crypto-compression system on a very broad range of scenarios.

Calculations of Hubbard U from first-principles

NASA Astrophysics Data System (ADS)

Aryasetiawan, F.; Karlsson, K.; Jepsen, O.; Schönberger, U.

2006-09-01

The Hubbard U of the 3d transition metal series as well as SrVO3 , YTiO3 , Ce, and Gd has been estimated using a recently proposed scheme based on the random-phase approximation. The values obtained are generally in good accord with the values often used in model calculations but for some cases the estimated values are somewhat smaller than those used in the literature. We have also calculated the frequency-dependent U for some of the materials. The strong frequency dependence of U in some of the cases considered in this paper suggests that the static value of U may not be the most appropriate one to use in model calculations. We have also made comparison with the constrained local density approximation (LDA) method and found some discrepancies in a number of cases. We emphasize that our scheme and the constrained local density approximation LDA method theoretically ought to give similar results and the discrepancies may be attributed to technical difficulties in performing calculations based on currently implemented constrained LDA schemes.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Early prediction of extreme stratospheric polar vortex states based on causal precursors

NASA Astrophysics Data System (ADS)

Kretschmer, Marlene; Runge, Jakob; Coumou, Dim

2017-08-01

Variability in the stratospheric polar vortex (SPV) can influence the tropospheric circulation and thereby winter weather. Early predictions of extreme SPV states are thus important to improve forecasts of winter weather including cold spells. However, dynamical models are usually restricted in lead time because they poorly capture low-frequency processes. Empirical models often suffer from overfitting problems as the relevant physical processes and time lags are often not well understood. Here we introduce a novel empirical prediction method by uniting a response-guided community detection scheme with a causal discovery algorithm. This way, we objectively identify causal precursors of the SPV at subseasonal lead times and find them to be in good agreement with known physical drivers. A linear regression prediction model based on the causal precursors can explain most SPV variability (r2 = 0.58), and our scheme correctly predicts 58% (46%) of extremely weak SPV states for lead times of 1-15 (16-30) days with false-alarm rates of only approximately 5%. Our method can be applied to any variable relevant for (sub)seasonal weather forecasts and could thus help improving long-lead predictions.

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response.

PubMed

Caricato, Marco

2018-04-07

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response

NASA Astrophysics Data System (ADS)

Caricato, Marco

2018-04-01

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Distributed Sleep Scheduling in Wireless Sensor Networks via Fractional Domatic Partitioning

NASA Astrophysics Data System (ADS)

Schumacher, André; Haanpää, Harri

We consider setting up sleep scheduling in sensor networks. We formulate the problem as an instance of the fractional domatic partition problem and obtain a distributed approximation algorithm by applying linear programming approximation techniques. Our algorithm is an application of the Garg-Könemann (GK) scheme that requires solving an instance of the minimum weight dominating set (MWDS) problem as a subroutine. Our two main contributions are a distributed implementation of the GK scheme for the sleep-scheduling problem and a novel asynchronous distributed algorithm for approximating MWDS based on a primal-dual analysis of Chvátal's set-cover algorithm. We evaluate our algorithm with ns2 simulations.

Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

NASA Astrophysics Data System (ADS)

Haegeman, Jutho; Swingle, Brian; Walter, Michael; Cotler, Jordan; Evenbly, Glen; Scholz, Volkher B.

2018-01-01

We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

Nonequilibrium flow computations. 1: An analysis of numerical formulations of conservation laws

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1988-01-01

Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed.

Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations

NASA Astrophysics Data System (ADS)

Penna, Vittorio; Richaud, Andrea

2017-11-01

We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians Ĥk, each one associated to momentum modes ±k . Each Ĥk is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but nontrivial closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly populated vortices, is investigated considering different choices of the initial conditions and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.

Phase Resolved Angular Velocity Control of Cross Flow Turbines

NASA Astrophysics Data System (ADS)

Strom, Benjamin; Brunton, Steven; Polagye, Brian

2015-11-01

Cross flow turbines have a number of operational advantages for the conversion of kinetic energy in marine or fluvial currents, but they are often less efficient than axial flow devices. Here a control scheme is presented in which the angular velocity of a cross flow turbine with two straight blades is prescribed as a function of azimuthal blade position, altering the time-varying effective angle of attack. Flume experiments conducted with a scale model turbine show approximately an 80% increase in turbine efficiency versus optimal constant angular velocity and constant resistive torque control schemes. Torque, drag, and lateral forces on one- and two-bladed turbines are analyzed and interpreted with bubble flow visualization to develop a simple model that describes the hydrodynamics responsible for the observed increase in mean efficiency. Challenges associated with implementing this control scheme on commercial-scale devices are discussed. If solutions are found, the performance increase presented here may impact the future development of cross flow turbines.

Separation of left and right lungs using 3D information of sequential CT images and a guided dynamic programming algorithm

PubMed Central

Park, Sang Cheol; Leader, Joseph Ken; Tan, Jun; Lee, Guee Sang; Kim, Soo Hyung; Na, In Seop; Zheng, Bin

2011-01-01

Objective this article presents a new computerized scheme that aims to accurately and robustly separate left and right lungs on CT examinations. Methods we developed and tested a method to separate the left and right lungs using sequential CT information and a guided dynamic programming algorithm using adaptively and automatically selected start point and end point with especially severe and multiple connections. Results the scheme successfully identified and separated all 827 connections on the total 4034 CT images in an independent testing dataset of CT examinations. The proposed scheme separated multiple connections regardless of their locations, and the guided dynamic programming algorithm reduced the computation time to approximately 4.6% in comparison with the traditional dynamic programming and avoided the permeation of the separation boundary into normal lung tissue. Conclusions The proposed method is able to robustly and accurately disconnect all connections between left and right lungs and the guided dynamic programming algorithm is able to remove redundant processing. PMID:21412104

Viscous compressible flow direct and inverse computation and illustrations

NASA Technical Reports Server (NTRS)

Yang, T. T.; Ntone, F.

1986-01-01

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Separation of left and right lungs using 3-dimensional information of sequential computed tomography images and a guided dynamic programming algorithm.

PubMed

Park, Sang Cheol; Leader, Joseph Ken; Tan, Jun; Lee, Guee Sang; Kim, Soo Hyung; Na, In Seop; Zheng, Bin

2011-01-01

This article presents a new computerized scheme that aims to accurately and robustly separate left and right lungs on computed tomography (CT) examinations. We developed and tested a method to separate the left and right lungs using sequential CT information and a guided dynamic programming algorithm using adaptively and automatically selected start point and end point with especially severe and multiple connections. The scheme successfully identified and separated all 827 connections on the total 4034 CT images in an independent testing data set of CT examinations. The proposed scheme separated multiple connections regardless of their locations, and the guided dynamic programming algorithm reduced the computation time to approximately 4.6% in comparison with the traditional dynamic programming and avoided the permeation of the separation boundary into normal lung tissue. The proposed method is able to robustly and accurately disconnect all connections between left and right lungs, and the guided dynamic programming algorithm is able to remove redundant processing.

[Part-time Work and Men's Health : Results based on Routine Data of a Statutory Health Insurance Scheme].

PubMed

Grobe, Thomas G

2016-08-01

With the introduction of a new occupational classification at the end of 2011, employment characteristics are reported by employees to social insurance agencies in Germany in more detail than in previous years. In addition to other changes, the new classification allows a distinction between full- and part-time work to be made. This provided a reason to consider the health-related aspects of part-time work on the basis of data from a statutory health insurance scheme. Our analysis is based on the data of 3.8 million employees insured with the Techniker Krankenkasse (TK), a statutory health insurance scheme, in 2012. In addition to daily information on employment situations, details of periods and diagnoses of sick leave and the drugs prescribed were available. Although approximately 50 % of women of middle to higher working age worked part-time in 2012, the corresponding percentage of men employed in part-time work was less than 10 %. Overall, part-time employees were on sick leave for fewer days than full-time employees, but among men, sick leave due to mental disorders was longer for part-time employees than for full-time employees, whereas women working part time were affected to a lesser extent by corresponding periods of absence than those working full time. The results provide indications for the assertion that men in gender-specifically atypical employment situations are more frequently affected by mental disorders. Further evidence supports this assertion. With the long-term availability of these new employment characteristics, longitudinal analyses could help to clarify this cause-effect relationship.

Self-Organizing Map Neural Network-Based Nearest Neighbor Position Estimation Scheme for Continuous Crystal PET Detectors

NASA Astrophysics Data System (ADS)

Wang, Yonggang; Li, Deng; Lu, Xiaoming; Cheng, Xinyi; Wang, Liwei

2014-10-01

Continuous crystal-based positron emission tomography (PET) detectors could be an ideal alternative for current high-resolution pixelated PET detectors if the issues of high performance γ interaction position estimation and its real-time implementation are solved. Unfortunately, existing position estimators are not very feasible for implementation on field-programmable gate array (FPGA). In this paper, we propose a new self-organizing map neural network-based nearest neighbor (SOM-NN) positioning scheme aiming not only at providing high performance, but also at being realistic for FPGA implementation. Benefitting from the SOM feature mapping mechanism, the large set of input reference events at each calibration position is approximated by a small set of prototypes, and the computation of the nearest neighbor searching for unknown events is largely reduced. Using our experimental data, the scheme was evaluated, optimized and compared with the smoothed k-NN method. The spatial resolutions of full-width-at-half-maximum (FWHM) of both methods averaged over the center axis of the detector were obtained as 1.87 ±0.17 mm and 1.92 ±0.09 mm, respectively. The test results show that the SOM-NN scheme has an equivalent positioning performance with the smoothed k-NN method, but the amount of computation is only about one-tenth of the smoothed k-NN method. In addition, the algorithm structure of the SOM-NN scheme is more feasible for implementation on FPGA. It has the potential to realize real-time position estimation on an FPGA with a high-event processing throughput.

Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia

NASA Astrophysics Data System (ADS)

Mansor, Nur Jariah; Jaffar, Maheran Mohd

2014-07-01

Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.

Compensation of strong thermal lensing in high-optical-power cavities.

PubMed

Zhao, C; Degallaix, J; Ju, L; Fan, Y; Blair, D G; Slagmolen, B J J; Gray, M B; Lowry, C M Mow; McClelland, D E; Hosken, D J; Mudge, D; Brooks, A; Munch, J; Veitch, P J; Barton, M A; Billingsley, G

2006-06-16

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors, we show for the first time that the time evolution of strong thermal lenses follows the predicted infinite sum of exponentials (approximated by a double exponential), and that such lenses can be compensated using an intracavity compensation plate heated on its cylindrical surface. We show that high finesse approximately 1400 can be achieved in cavities with internal compensation plates, and that mode matching can be maintained. The experiment achieves a wave front distortion similar to that expected for the input test mass substrate in the Advanced Laser Interferometer Gravitational Wave Observatory, and shows that thermal compensation schemes are viable. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.

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

NASA Astrophysics Data System (ADS)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Total Variation Diminishing (TVD) schemes of uniform accuracy

NASA Technical Reports Server (NTRS)

Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

1988-01-01

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management

NASA Astrophysics Data System (ADS)

Marcozzi, Michael D.

2008-12-01

We consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a European call option. Within a continuous-time framework, the dynamic management of a portfolio of assets is effected through continuous or point control, activation costs, and phase delay. The performance index is derived from the unique weak variational solution to the ultraparabolic Hamilton-Jacobi equation; the value function is the optimal realization of the performance index relative to all feasible portfolios. An approximation procedure based upon a temporal box scheme/finite element method is analyzed; numerical examples are presented in order to demonstrate the viability of the approach.

Real-time modeling of primitive environments through wavelet sensors and Hebbian learning

NASA Astrophysics Data System (ADS)

Vaccaro, James M.; Yaworsky, Paul S.

1999-06-01

Modeling the world through sensory input necessarily provides a unique perspective for the observer. Given a limited perspective, objects and events cannot always be encoded precisely but must involve crude, quick approximations to deal with sensory information in a real- time manner. As an example, when avoiding an oncoming car, a pedestrian needs to identify the fact that a car is approaching before ascertaining the model or color of the vehicle. In our methodology, we use wavelet-based sensors with self-organized learning to encode basic sensory information in real-time. The wavelet-based sensors provide necessary transformations while a rank-based Hebbian learning scheme encodes a self-organized environment through translation, scale and orientation invariant sensors. Such a self-organized environment is made possible by combining wavelet sets which are orthonormal, log-scale with linear orientation and have automatically generated membership functions. In earlier work we used Gabor wavelet filters, rank-based Hebbian learning and an exponential modulation function to encode textural information from images. Many different types of modulation are possible, but based on biological findings the exponential modulation function provided a good approximation of first spike coding of `integrate and fire' neurons. These types of Hebbian encoding schemes (e.g., exponential modulation, etc.) are useful for quick response and learning, provide several advantages over contemporary neural network learning approaches, and have been found to quantize data nonlinearly. By combining wavelets with Hebbian learning we can provide a real-time front-end for modeling an intelligent process, such as the autonomous control of agents in a simulated environment.

On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2014-01-01

A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.

Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.

Coherent control of molecular alignment of homonuclear diatomic molecules by analytically designed laser pulses.

PubMed

Zou, Shiyang; Sanz, Cristina; Balint-Kurti, Gabriel G

2008-09-28

We present an analytic scheme for designing laser pulses to manipulate the field-free molecular alignment of a homonuclear diatomic molecule. The scheme is based on the use of a generalized pulse-area theorem and makes use of pulses constructed around two-photon resonant frequencies. In the proposed scheme, the populations and relative phases of the rovibrational states of the molecule are independently controlled utilizing changes in the laser intensity and in the carrier-envelope phase difference, respectively. This allows us to create the correct coherent superposition of rovibrational states needed to achieve optimal molecular alignment. The validity and efficiency of the scheme are demonstrated by explicit application to the H(2) molecule. The analytically designed laser pulses are tested by exact numerical solutions of the time-dependent Schrodinger equation including laser-molecule interactions to all orders of the field strength. The design of a sequence of pulses to further enhance molecular alignment is also discussed and tested. It is found that the rotating wave approximation used in the analytic design of the laser pulses leads to small errors in the prediction of the relative phase of the rotational states. It is further shown how these errors may be easily corrected.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory.

PubMed

Li, Zhendong; Liu, Wenjian

2010-08-14

The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

Trellis Tone Modulation Multiple-Access for Peer Discovery in D2D Networks

PubMed Central

Lim, Chiwoo; Kim, Sang-Hyo

2018-01-01

In this paper, a new non-orthogonal multiple-access scheme, trellis tone modulation multiple-access (TTMMA), is proposed for peer discovery of distributed device-to-device (D2D) communication. The range and capacity of discovery are important performance metrics in peer discovery. The proposed trellis tone modulation uses single-tone transmission and achieves a long discovery range due to its low Peak-to-Average Power Ratio (PAPR). The TTMMA also exploits non-orthogonal resource assignment to increase the discovery capacity. For the multi-user detection of superposed multiple-access signals, a message-passing algorithm with supplementary schemes are proposed. With TTMMA and its message-passing demodulation, approximately 1.5 times the number of devices are discovered compared to the conventional frequency division multiple-access (FDMA)-based discovery. PMID:29673167

Trellis Tone Modulation Multiple-Access for Peer Discovery in D2D Networks.

PubMed

Lim, Chiwoo; Jang, Min; Kim, Sang-Hyo

2018-04-17

In this paper, a new non-orthogonal multiple-access scheme, trellis tone modulation multiple-access (TTMMA), is proposed for peer discovery of distributed device-to-device (D2D) communication. The range and capacity of discovery are important performance metrics in peer discovery. The proposed trellis tone modulation uses single-tone transmission and achieves a long discovery range due to its low Peak-to-Average Power Ratio (PAPR). The TTMMA also exploits non-orthogonal resource assignment to increase the discovery capacity. For the multi-user detection of superposed multiple-access signals, a message-passing algorithm with supplementary schemes are proposed. With TTMMA and its message-passing demodulation, approximately 1.5 times the number of devices are discovered compared to the conventional frequency division multiple-access (FDMA)-based discovery.

A fast iterative scheme for the linearized Boltzmann equation

NASA Astrophysics Data System (ADS)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

The Adler D-function for N = 1 SQCD regularized by higher covariant derivatives in the three-loop approximation

NASA Astrophysics Data System (ADS)

Kataev, A. L.; Kazantsev, A. E.; Stepanyantz, K. V.

2018-01-01

We calculate the Adler D-function for N = 1 SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the D-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for N = 1 SQCD is found in this scheme to the order O (αs2). The problem of scheme-dependence of the D-function and the NSVZ-like equation is briefly discussed.

Modelling Detailed-Chemistry Effects on Turbulent Diffusion Flames using a Parallel Solution-Adaptive Scheme

NASA Astrophysics Data System (ADS)

Jha, Pradeep Kumar

Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow. Comparisons are made between the predicted results of the present FPI scheme and Steady Laminar Flamelet Model (SLFM) approach for diffusion flames. The effects of grid resolution on the predicted overall flame solutions are also assessed. Other non-reacting flows have also been considered to further validate other aspects of the numerical scheme. The present schemes predict results which are in good agreement with published experimental results and reduces the computational cost involved in modelling turbulent diffusion flames significantly, both in terms of storage and processing time.

Field by field hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1993-01-01

A new and general approach to upwind splitting is presented. The design principle combines the robustness of flux vector splitting schemes in the capture of nonlinear waves and the accuracy of some flux difference splitting schemes in the resolution of linear waves. The new schemes are derived following a general hybridization technique performed directly at the basic level of the field by field decomposition involved in FDS methods. The scheme does not use a spatial switch to be tuned up according to the local smoothness of the approximate solution.

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

A Relaxation Method for Nonlocal and Non-Hermitian Operators

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Papageorgiou, D. G.; Braun, M.; Sofianos, S. A.

1996-06-01

We present a grid method to solve the time dependent Schrödinger equation (TDSE). It uses the Crank-Nicholson scheme to propagate the wavefunction forward in time and finite differences to approximate the derivative operators. The resulting sparse linear system is solved by the symmetric successive overrelaxation iterative technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-Hermitian matrices with real eigenvalues. We test the method by solving the TDSE in the imaginary time domain, thus converting the time propagation to asymptotic relaxation. Benchmark problems solved are both in one and two dimensions, with local, nonlocal, Hermitian and non-Hermitian Hamiltonians.

Computational modeling of fully-ionized, magnetized plasmas using the fluid approximation

NASA Astrophysics Data System (ADS)

Schnack, Dalton

2005-10-01

Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. However, the high dimensionality renders this approach impractical for computations for long time scales in relevant geometry. Fluid models, derived by taking velocity moments of the kinetic equation [1] and truncating (closing) the hierarchy at some level, are an approximation to the kinetic model. The reduced dimensionality allows a wider range of spatial and/or temporal scales to be explored. Several approximations have been used [2-5]. Successful computational modeling requires understanding the ordering and closure approximations, the fundamental waves supported by the equations, and the numerical properties of the discretization scheme. We review and discuss several ordering schemes, their normal modes, and several algorithms that can be applied to obtain a numerical solution. The implementation of kinetic parallel closures is also discussed [6].[1] S. Chapman and T.G. Cowling, ``The Mathematical Theory of Non-Uniform Gases'', Cambridge University Press, Cambridge, UK (1939).[2] R.D. Hazeltine and J.D. Meiss, ``Plasma Confinement'', Addison-Wesley Publishing Company, Redwood City, CA (1992).[3] L.E. Sugiyama and W. Park, Physics of Plasmas 7, 4644 (2000).[4] J.J. Ramos, Physics of Plasmas, 10, 3601 (2003).[5] P.J. Catto and A.N. Simakov, Physics of Plasmas, 11, 90 (2004).[6] E.D. Held et al., Phys. Plasmas 11, 2419 (2004)

Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bobylev, A.V., E-mail: alexander.bobylev@kau.se; Potapenko, I.F., E-mail: firena@yandex.ru

2013-08-01

Highlights: •A general approach to Monte Carlo methods for multicomponent plasmas is proposed. •We show numerical tests for the two-component (electrons and ions) case. •An optimal choice of parameters for speeding up the computations is discussed. •A rigorous estimate of the error of approximation is proved. -- Abstract: A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau–Fokker–Planck equations by Boltzmann equations of quasi-Maxwellian kind. It means that the total collision frequency for the corresponding Boltzmann equation does not depend on the velocities. This allows to make the simulation processmore » very simple since the collision pairs can be chosen arbitrarily, without restriction. It is shown that this approach includes the well-known methods of Takizuka and Abe (1977) [12] and Nanbu (1997) as particular cases, and generalizes the approach of Bobylev and Nanbu (2000). The numerical scheme of this paper is simpler than the schemes by Takizuka and Abe [12] and by Nanbu. We derive it for the general case of multicomponent plasmas and show some numerical tests for the two-component (electrons and ions) case. An optimal choice of parameters for speeding up the computations is also discussed. It is also proved that the order of approximation is not worse than O(√(ε)), where ε is a parameter of approximation being equivalent to the time step Δt in earlier methods. A similar estimate is obtained for the methods of Takizuka and Abe and Nanbu.« less

A memory efficient implementation scheme of Gauss error function in a Laguerre-Volterra network for neuroprosthetic devices

NASA Astrophysics Data System (ADS)

Li, Will X. Y.; Cui, Ke; Zhang, Wei

2017-04-01

Cognitive neural prosthesis is a manmade device which can be used to restore or compensate for lost human cognitive modalities. The generalized Laguerre-Volterra (GLV) network serves as a robust mathematical underpinning for the development of such prosthetic instrument. In this paper, a hardware implementation scheme of Gauss error function for the GLV network targeting reconfigurable platforms is reported. Numerical approximations are formulated which transform the computation of nonelementary function into combinational operations of elementary functions, and memory-intensive look-up table (LUT) based approaches can therefore be circumvented. The computational precision can be made adjustable with the utilization of an error compensation scheme, which is proposed based on the experimental observation of the mathematical characteristics of the error trajectory. The precision can be further customizable by exploiting the run-time characteristics of the reconfigurable system. Compared to the polynomial expansion based implementation scheme, the utilization of slice LUTs, occupied slices, and DSP48E1s on a Xilinx XC6VLX240T field-programmable gate array has decreased by 94.2%, 94.1%, and 90.0%, respectively. While compared to the look-up table based scheme, 1.0 ×1017 bits of storage can be spared under the maximum allowable error of 1.0 ×10-3 . The proposed implementation scheme can be employed in the study of large-scale neural ensemble activity and in the design and development of neural prosthetic device.

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

Controlling the high frequency response of H2 by ultra-short tailored laser pulses: A time-dependent configuration interaction study

NASA Astrophysics Data System (ADS)

Schönborn, Jan Boyke; Saalfrank, Peter; Klamroth, Tillmann

2016-01-01

We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H2 treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a "non-harmonic" response of H2 to a laser pulse. Specifically, we will show how adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.

Controlling the high frequency response of H{sub 2} by ultra-short tailored laser pulses: A time-dependent configuration interaction study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schönborn, Jan Boyke; Saalfrank, Peter; Klamroth, Tillmann, E-mail: klamroth@uni-potsdam.de

2016-01-28

We combine the stochastic pulse optimization (SPO) scheme with the time-dependent configuration interaction singles method in order to control the high frequency response of a simple molecular model system to a tailored femtosecond laser pulse. For this purpose, we use H{sub 2} treated in the fixed nuclei approximation. The SPO scheme, as similar genetic algorithms, is especially suited to control highly non-linear processes, which we consider here in the context of high harmonic generation. Here, we will demonstrate that SPO can be used to realize a “non-harmonic” response of H{sub 2} to a laser pulse. Specifically, we will show howmore » adding low intensity side frequencies to the dominant carrier frequency of the laser pulse and stochastically optimizing their contribution can create a high-frequency spectral signal of significant intensity, not harmonic to the carrier frequency. At the same time, it is possible to suppress the harmonic signals in the same spectral region, although the carrier frequency is kept dominant during the optimization.« less

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction.

PubMed

Wei, Jianming; Zhang, Youan; Sun, Meimei; Geng, Baoliang

2017-09-01

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Identification of multiple leaks in pipeline: Linearized model, maximum likelihood, and super-resolution localization

NASA Astrophysics Data System (ADS)

Wang, Xun; Ghidaoui, Mohamed S.

2018-07-01

This paper considers the problem of identifying multiple leaks in a water-filled pipeline based on inverse transient wave theory. The analytical solution to this problem involves nonlinear interaction terms between the various leaks. This paper shows analytically and numerically that these nonlinear terms are of the order of the leak sizes to the power two and; thus, negligible. As a result of this simplification, a maximum likelihood (ML) scheme that identifies leak locations and leak sizes separately is formulated and tested. It is found that the ML estimation scheme is highly efficient and robust with respect to noise. In addition, the ML method is a super-resolution leak localization scheme because its resolvable leak distance (approximately 0.15λmin , where λmin is the minimum wavelength) is below the Nyquist-Shannon sampling theorem limit (0.5λmin). Moreover, the Cramér-Rao lower bound (CRLB) is derived and used to show the efficiency of the ML scheme estimates. The variance of the ML estimator approximates the CRLB proving that the ML scheme belongs to class of best unbiased estimator of leak localization methods.

Quantum preservation of the measurements precision using ultra-short strong pulses in exact analytical solution

NASA Astrophysics Data System (ADS)

Berrada, K.; Eleuch, H.

2017-09-01

Various schemes have been proposed to improve the parameter-estimation precision. In the present work, we suggest an alternative method to preserve the estimation precision by considering a model that closely describes a realistic experimental scenario. We explore this active way to control and enhance the measurements precision for a two-level quantum system interacting with classical electromagnetic field using ultra-short strong pulses with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we investigate the variation of the precision with a few cycles pulse and a smooth phase jump over a finite time interval. We show that by acting on the shape of the phase transient and other parameters of the considered system, the amount of information may be increased and has smaller decay rate in the long time. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.

Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats

NASA Astrophysics Data System (ADS)

Stalter, S.; Yelash, L.; Emamy, N.; Statt, A.; Hanke, M.; Lukáčová-Medvid'ová, M.; Virnau, P.

2018-03-01

Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation boxes. We also argue that if colloidal systems are considered as opposed to atomistic systems, the gap between microscopic and macroscopic simulations regarding time and length scales is significantly smaller. We propose a novel reduced-order technique for the coupling to the macroscopic solver, which allows us to approximate a non-linear stress-strain relation efficiently and thus further reduce computational effort of microscopic simulations.

Overview of the relevant CFD work at Thiokol Corporation

NASA Technical Reports Server (NTRS)

Chwalowski, Pawel; Loh, Hai-Tien

1992-01-01

An in-house developed proprietary advanced computational fluid dynamics code called SHARP (Trademark) is a primary tool for many flow simulations and design analyses. The SHARP code is a time dependent, two dimensional (2-D) axisymmetric numerical solution technique for the compressible Navier-Stokes equations. The solution technique in SHARP uses a vectorizable implicit, second order accurate in time and space, finite volume scheme based on an upwind flux-difference splitting of a Roe-type approximated Riemann solver, Van Leer's flux vector splitting, and a fourth order artificial dissipation scheme with a preconditioning to accelerate the flow solution. Turbulence is simulated by an algebraic model, and ultimately the kappa-epsilon model. Some other capabilities of the code are 2-D two-phase Lagrangian particle tracking and cell blockages. Extensive development and testing has been conducted on the 3-D version of the code with flow, combustion, and turbulence interactions. The emphasis here is on the specific applications of SHARP in Solid Rocket Motor design. Information is given in viewgraph form.

Reducing power usage on demand

NASA Astrophysics Data System (ADS)

Corbett, G.; Dewhurst, A.

2016-10-01

The Science and Technology Facilities Council (STFC) datacentre provides large- scale High Performance Computing facilities for the scientific community. It currently consumes approximately 1.5MW and this has risen by 25% in the past two years. STFC has been investigating leveraging preemption in the Tier 1 batch farm to save power. HEP experiments are increasing using jobs that can be killed to take advantage of opportunistic CPU resources or novel cost models such as Amazon's spot pricing. Additionally, schemes from energy providers are available that offer financial incentives to reduce power consumption at peak times. Under normal operating conditions, 3% of the batch farm capacity is wasted due to draining machines. By using preempt-able jobs, nodes can be rapidly made available to run multicore jobs without this wasted resource. The use of preempt-able jobs has been extended so that at peak times machines can be hibernated quickly to save energy. This paper describes the implementation of the above and demonstrates that STFC could in future take advantage of such energy saving schemes.

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

NASA Astrophysics Data System (ADS)

Chen, Zhixiang; Fu, Bin

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.

A structure-preserving split finite element discretization of the split 1D linear shallow-water equations

NASA Astrophysics Data System (ADS)

Bauer, Werner; Behrens, Jörn

2017-04-01

We present a locally conservative, low-order finite element (FE) discretization of the covariant 1D linear shallow-water equations written in split form (cf. tet{[1]}). The introduction of additional differential forms (DF) that build pairs with the original ones permits a splitting of these equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star. Our novel discretization framework conserves this geometrical structure, in particular it provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. The discrete topological equations simply follow by trivial projections onto piecewise constant FE spaces without need to partially integrate. The discrete Hodge-stars operators, representing the discretized metric equations, are realized by nontrivial Galerkin projections (GP). Here they follow by projections onto either a piecewise constant (GP0) or a piecewise linear (GP1) space. Our framework thus provides essentially three different schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the same discrete dispersion relation and similar second-order convergence rates as the conventional P1-P1 FE scheme that approximates both velocity and height variables by piecewise linear spaces. The split scheme that applies both GP1 and GP0 is stable and shares the dispersion relation of the conventional P1-P0 FE scheme that approximates the velocity by a piecewise linear and the height by a piecewise constant space with corresponding second- and first-order convergence rates. Exhibiting for both velocity and height fields second-order convergence rates, we might consider the split GP1-GP0 scheme though as stable versions of the conventional P1-P1 FE scheme. For the split scheme applying twice GP0, we are not aware of a corresponding conventional formulation to compare with. Though exhibiting larger absolute error values, it shows similar convergence rates as the other split schemes, but does not provide a satisfactory approximation of the dispersion relation as short waves are propagated much to fast. Despite this, the finding of this new scheme illustrates the potential of our discretization framework as a toolbox to find and to study new FE schemes based on new combinations of FE spaces. [1] Bauer, W. [2016], A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics, GEM - International Journal on Geomathematics, 7(1), 31-101.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

A Runge-Kutta discontinuous finite element method for high speed flows

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. T.

1991-01-01

A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Dynamic Structure Factor: An Introduction

NASA Astrophysics Data System (ADS)

Sturm, K.

1993-02-01

The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the many-body system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the density-density response function defined in linear-response theory is shown using the fluctuation-dissipation theorem. This is important for calculations, since the response function can be calculated approximately from the independent-particle response function in self-consistent field approximations, such as the random-phase approximation or the local-density approximation of the density functional theory. Since the density-density response function also determines the dielectric function, the dynamic structure can be expressed by the dielectric function.

Radiation pressure driving of a dusty atmosphere

NASA Astrophysics Data System (ADS)

Tsang, Benny T.-H.; Milosavljević, Miloš

2015-10-01

Radiation pressure can be dynamically important in star-forming environments such as ultra-luminous infrared and submillimetre galaxies. Whether and how radiation drives turbulence and bulk outflows in star formation sites is still unclear. The uncertainty in part reflects the limitations of direct numerical schemes that are currently used to simulate radiation transfer and radiation-gas coupling. An idealized setup in which radiation is introduced at the base of a dusty atmosphere in a gravitational field has recently become the standard test for radiation-hydrodynamics methods in the context of star formation. To a series of treatments featuring the flux-limited diffusion approximation as well as a short-characteristics tracing and M1 closure for the variable Eddington tensor approximation, we here add another treatment that is based on the implicit Monte Carlo radiation transfer scheme. Consistent with all previous treatments, the atmosphere undergoes Rayleigh-Taylor instability and readjusts to a near-Eddington-limited state. We detect late-time net acceleration in which the turbulent velocity dispersion matches that reported previously with the short-characteristics-based radiation transport closure, the most accurate of the three preceding treatments. Our technical result demonstrates the importance of accurate radiation transfer in simulations of radiative feedback.

On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method

NASA Astrophysics Data System (ADS)

Londrillo, P.; del Zanna, L.

2004-03-01

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the constrained transport (CT) discretization technique for the magnetic field components, originally developed for the linear induction equation, which assures [∇.B]num=0 and its preservation in time to within machine accuracy in a finite-volume setting. We show that the CT formalism, when fully exploited, can be used as a general guideline to design the reconstruction procedures of the B vector field, to adapt standard upwind procedures for the momentum and energy equations, avoiding the onset of numerical monopoles of O(1) size, and to formulate approximate Riemann solvers for the induction equation. This general framework will be named here upwind constrained transport (UCT). To demonstrate the versatility of our method, we apply it to a variety of schemes, which are finally validated numerically and compared: a novel implementation for the MHD case of the second-order Roe-type positive scheme by Liu and Lax [J. Comput. Fluid Dyn. 5 (1996) 133], and both the second- and third-order versions of a central-type MHD scheme presented by Londrillo and Del Zanna [Astrophys. J. 530 (2000) 508], where the basic UCT strategies have been first outlined.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

Formation and structure of stable aggregates in binary diffusion-limited cluster-cluster aggregation processes

NASA Astrophysics Data System (ADS)

López-López, J. M.; Moncho-Jordá, A.; Schmitt, A.; Hidalgo-Álvarez, R.

2005-09-01

Binary diffusion-limited cluster-cluster aggregation processes are studied as a function of the relative concentration of the two species. Both, short and long time behaviors are investigated by means of three-dimensional off-lattice Brownian Dynamics simulations. At short aggregation times, the validity of the Hogg-Healy-Fuerstenau approximation is shown. At long times, a single large cluster containing all initial particles is found to be formed when the relative concentration of the minority particles lies above a critical value. Below that value, stable aggregates remain in the system. These stable aggregates are composed by a few minority particles that are highly covered by majority ones. Our off-lattice simulations reveal a value of approximately 0.15 for the critical relative concentration. A qualitative explanation scheme for the formation and growth of the stable aggregates is developed. The simulations also explain the phenomenon of monomer discrimination that was observed recently in single cluster light scattering experiments.

Impulse propagation in the nocturnal boundary layer: analysis of the geometric component.

PubMed

Blom, Philip; Waxler, Roger

2012-05-01

On clear dry nights over flat land, a temperature inversion and stable nocturnal wind jet lead to an acoustic duct in the lowest few hundred meters of the atmosphere. An impulsive signal propagating in such a duct is received at long ranges from the source as an extended wave train consisting of a series of weakly dispersed distinct arrivals followed by a strongly dispersed low-frequency tail. The leading distinct arrivals have been previously shown to be well modeled by geometric acoustics. In this paper, the geometric acoustics approximation for the leading arrivals is investigated. Using the solutions of the eikonal and transport equations, travel times, amplitudes, and caustic structures of the distinct arrivals have been determined. The time delay between and relative amplitudes of the direct-refracted and single ground reflection arrivals have been investigated as parameters for an inversion scheme. A two parameter quadratic approximation to the effective sound speed profile has been fit and found to be in strong agreement with meteorological measurements from the time of propagation.

Composite Intelligent Learning Control of Strict-Feedback Systems With Disturbance.

PubMed

Xu, Bin; Sun, Fuchun

2018-02-01

This paper addresses the dynamic surface control of uncertain nonlinear systems on the basis of composite intelligent learning and disturbance observer in presence of unknown system nonlinearity and time-varying disturbance. The serial-parallel estimation model with intelligent approximation and disturbance estimation is built to obtain the prediction error and in this way the composite law for weights updating is constructed. The nonlinear disturbance observer is developed using intelligent approximation information while the disturbance estimation is guaranteed to converge to a bounded compact set. The highlight is that different from previous work directly toward asymptotic stability, the transparency of the intelligent approximation and disturbance estimation is included in the control scheme. The uniformly ultimate boundedness stability is analyzed via Lyapunov method. Through simulation verification, the composite intelligent learning with disturbance observer can efficiently estimate the effect caused by system nonlinearity and disturbance while the proposed approach obtains better performance with higher accuracy.

Local Laplacian Coding From Theoretical Analysis of Local Coding Schemes for Locally Linear Classification.

PubMed

Pang, Junbiao; Qin, Lei; Zhang, Chunjie; Zhang, Weigang; Huang, Qingming; Yin, Baocai

2015-12-01

Local coordinate coding (LCC) is a framework to approximate a Lipschitz smooth function by combining linear functions into a nonlinear one. For locally linear classification, LCC requires a coding scheme that heavily determines the nonlinear approximation ability, posing two main challenges: 1) the locality making faraway anchors have smaller influences on current data and 2) the flexibility balancing well between the reconstruction of current data and the locality. In this paper, we address the problem from the theoretical analysis of the simplest local coding schemes, i.e., local Gaussian coding and local student coding, and propose local Laplacian coding (LPC) to achieve the locality and the flexibility. We apply LPC into locally linear classifiers to solve diverse classification tasks. The comparable or exceeded performances of state-of-the-art methods demonstrate the effectiveness of the proposed method.

Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series

NASA Astrophysics Data System (ADS)

Sultana, Tahmina; Takagi, Hiroaki; Morimatsu, Miki; Teramoto, Hiroshi; Li, Chun-Biu; Sako, Yasushi; Komatsuzaki, Tamiki

2013-12-01

We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ˜3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.

Airfoil Shape Optimization based on Surrogate Model

NASA Astrophysics Data System (ADS)

Mukesh, R.; Lingadurai, K.; Selvakumar, U.

2018-02-01

Engineering design problems always require enormous amount of real-time experiments and computational simulations in order to assess and ensure the design objectives of the problems subject to various constraints. In most of the cases, the computational resources and time required per simulation are large. In certain cases like sensitivity analysis, design optimisation etc where thousands and millions of simulations have to be carried out, it leads to have a life time of difficulty for designers. Nowadays approximation models, otherwise called as surrogate models (SM), are more widely employed in order to reduce the requirement of computational resources and time in analysing various engineering systems. Various approaches such as Kriging, neural networks, polynomials, Gaussian processes etc are used to construct the approximation models. The primary intention of this work is to employ the k-fold cross validation approach to study and evaluate the influence of various theoretical variogram models on the accuracy of the surrogate model construction. Ordinary Kriging and design of experiments (DOE) approaches are used to construct the SMs by approximating panel and viscous solution algorithms which are primarily used to solve the flow around airfoils and aircraft wings. The method of coupling the SMs with a suitable optimisation scheme to carryout an aerodynamic design optimisation process for airfoil shapes is also discussed.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1994-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1993-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

NASA Astrophysics Data System (ADS)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

An adaptive grid algorithm for one-dimensional nonlinear equations

NASA Technical Reports Server (NTRS)

Gutierrez, William E.; Hills, Richard G.

1990-01-01

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Second derivatives for approximate spin projection methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thompson, Lee M.; Hratchian, Hrant P., E-mail: hhratchian@ucmerced.edu

2015-02-07

The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical secondmore » derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.« less

Spline approximations for nonlinear hereditary control systems

NASA Technical Reports Server (NTRS)

Daniel, P. L.

1982-01-01

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

2002-01-01

We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Warming, R. F.; Harten, A.

1983-01-01

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Viscous flow computations using a second-order upwind differencing scheme

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1988-01-01

In the present computations of a wide range of fluid flow problems by means of the primitive variables-incorporating Navier-Stokes equations, a mixed second-order upwinding scheme approximates the convective terms of the transport equations and the scheme's accuracy is verified for convection-dominated high Re number flow problems. An adaptive dissipation scheme is used as a monotonic supersonic shock flow capture mechanism. Many benchmark fluid flow problems, including the compressible and incompressible, laminar and turbulent, over a wide range of M and Re numbers, are presently studied to verify the accuracy and robustness of this numerical method.

Factorizable Schemes for the Equations of Fluid Flow

NASA Technical Reports Server (NTRS)

Sidilkover, David

1999-01-01

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

NASA Technical Reports Server (NTRS)

Fukumori, Ichiro; Malanotte-Rizzoli, Paola

1995-01-01

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

NASA Astrophysics Data System (ADS)

Fukumori, Ichiro; Malanotte-Rizzoli, Paola

1995-04-01

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kaiman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Speeding up the learning of robot kinematics through function decomposition.

PubMed

Ruiz de Angulo, Vicente; Torras, Carme

2005-11-01

The main drawback of using neural networks or other example-based learning procedures to approximate the inverse kinematics (IK) of robot arms is the high number of training samples (i.e., robot movements) required to attain an acceptable precision. We propose here a trick, valid for most industrial robots, that greatly reduces the number of movements needed to learn or relearn the IK to a given accuracy. This trick consists in expressing the IK as a composition of learnable functions, each having half the dimensionality of the original mapping. Off-line and on-line training schemes to learn these component functions are also proposed. Experimental results obtained by using nearest neighbors and parameterized self-organizing map, with and without the decomposition, show that the time savings granted by the proposed scheme grow polynomially with the precision required.

Landmark-Based 3D Elastic Registration of Pre- and Postoperative Liver CT Data

NASA Astrophysics Data System (ADS)

Lange, Thomas; Wörz, Stefan; Rohr, Karl; Schlag, Peter M.

The qualitative and quantitative comparison of pre- and postoperative image data is an important possibility to validate computer assisted surgical procedures. Due to deformations after surgery a non-rigid registration scheme is a prerequisite for a precise comparison. Interactive landmark-based schemes are a suitable approach. Incorporation of a priori knowledge about the anatomical structures to be registered may help to reduce interaction time and improve accuracy. Concerning pre- and postoperative CT data of oncological liver resections the intrahepatic vessels are suitable anatomical structures. In addition to using landmarks at vessel branchings, we here introduce quasi landmarks at vessel segments with anisotropic localization precision. An experimental comparison of interpolating thin-plate splines (TPS) and Gaussian elastic body splines (GEBS) as well as approximating GEBS on both types of landmarks is performed.

Time-dependent diffusive acceleration of test particles at shocks

NASA Astrophysics Data System (ADS)

Drury, L. O'C.

1991-07-01

A theoretical description is developed for the acceleration of test particles at a steady plane nonrelativistic shock. The mean and the variance of the acceleration-time distribution are expressed analytically for the condition under which the diffusion coefficient is arbitrarily dependent on position and momentum. The formula for an acceleration rate with arbitrary spatial variation in the diffusion coefficient developed by Drury (1987) is supplemented by a general theory of time dependence. An approximation scheme is developed by means of the analysis which permits the description of the spectral cutoff resulting from the finite shock age. The formulas developed in the analysis are also of interest for analyzing the observations of heliospheric shocks made from spacecraft.

Global Journal of Computer Science and Technology. Volume 9, Issue 5 (Ver. 2.0)

ERIC Educational Resources Information Center

Dixit, R. K.

2010-01-01

This is a special issue published in version 1.0 of "Global Journal of Computer Science and Technology." Articles in this issue include: (1) [Theta] Scheme (Orthogonal Milstein Scheme), a Better Numerical Approximation for Multi-dimensional SDEs (Klaus Schmitz Abe); (2) Input Data Processing Techniques in Intrusion Detection…

Robust inertia-free attitude takeover control of postcapture combined spacecraft with guaranteed prescribed performance.

PubMed

Luo, Jianjun; Wei, Caisheng; Dai, Honghua; Yin, Zeyang; Wei, Xing; Yuan, Jianping

2018-03-01

In this paper, a robust inertia-free attitude takeover control scheme with guaranteed prescribed performance is investigated for postcapture combined spacecraft with consideration of unmeasurable states, unknown inertial property and external disturbance torque. Firstly, to estimate the unavailable angular velocity of combination accurately, a novel finite-time-convergent tracking differentiator is developed with a quite computationally achievable structure free from the unknown nonlinear dynamics of combined spacecraft. Then, a robust inertia-free prescribed performance control scheme is proposed, wherein, the transient and steady-state performance of combined spacecraft is first quantitatively studied by stabilizing the filtered attitude tracking errors. Compared with the existing works, the prominent advantage is that no parameter identifications and no neural or fuzzy nonlinear approximations are needed, which decreases the complexity of robust controller design dramatically. Moreover, the prescribed performance of combined spacecraft is guaranteed a priori without resorting to repeated regulations of the controller parameters. Finally, four illustrative examples are employed to validate the effectiveness of the proposed control scheme and tracking differentiator. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

Comparative study of nonideal beam effects in high gain harmonic generation and self-seeded free electron lasers

NASA Astrophysics Data System (ADS)

Marinelli, Agostino; Pellegrini, Claudio; Giannessi, Luca; Reiche, Sven

2010-07-01

In this paper we investigate and compare the properties of two narrow-bandwidth free-electron laser (FEL) schemes, one using self-seeding and the other high gain harmonic generation (HGHG). The two systems have been thoroughly studied analytically and numerically in the past. The aim of this work is to compare their performances when the FEL is driven by an electron beam with nonideal properties, thus including effects such as shot-to-shot energy fluctuations and nonlinear energy chirp. In both cases nonlinearities produce a bandwidth larger than the Fourier transform limited value. However, our analysis indicates that, for approximately the same output power levels, the self-seeding scheme is less affected than the HGHG scheme by quadratic energy chirps in the electron beam longitudinal phase space. This is confirmed by a specific numerical example corresponding to SPARX parameters where the electron beam was optimized to minimize the FEL gain length. The work has been carried out with the aid of the time dependent FEL codes GENESIS 1.3 (3D) and PERSEO (1D).

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

Galerkin v. discrete-optimal projection in nonlinear model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin Thomas; Barone, Matthew Franklin; Antil, Harbir

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes.more » We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.« less

GMX approximation for the linear E ⊗ ɛ Jahn-Teller effect

NASA Astrophysics Data System (ADS)

Mancini, Jay D.; Fessatidis, Vassilios; Bowen, Samuel P.

2006-02-01

A newly developed generalized moments expansion (GMX) based on the t-expansion of Horn and Weinstein is applied to a linear E ⊗ ɛ Jahn-Teller system. Comparisons are made with other moments schemes as well a coupled cluster approximation.

Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity

NASA Astrophysics Data System (ADS)

Hamon, F. P.; Mallison, B.; Tchelepi, H.

2016-12-01

In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem to compute the numerical flux. Heterogeneous numerical tests demonstrate that this extended IHU scheme is non-oscillatory and convergent upon refinement. They also illustrate the superior accuracy and nonlinear convergence rate of the IHU scheme compared with the standard phase-based upstream weighting approach.

Approximate treatment of semicore states in GW calculations with application to Au clusters.

PubMed

Xian, Jiawei; Baroni, Stefano; Umari, P

2014-03-28

We address the treatment of transition metal atoms in GW electronic-structure calculations within the plane-wave pseudo-potential formalism. The contributions of s and p semi-core electrons to the self-energy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G0W0 level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nano-clusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore states are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au20 and Au32, that would be otherwise very difficult to deal with.

Approximate treatment of semicore states in GW calculations with application to Au clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xian, Jiawei; Baroni, Stefano; CNR-IOM Democritos, Theory-Elettra group, Trieste

We address the treatment of transition metal atoms in GW electronic-structure calculations within the plane-wave pseudo-potential formalism. The contributions of s and p semi-core electrons to the self-energy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G{sub 0}W{sub 0} level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nano-clusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore statesmore » are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au{sub 20} and Au{sub 32}, that would be otherwise very difficult to deal with.« less

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

NASA Astrophysics Data System (ADS)

Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe

2018-02-01

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

Electronic excitation of molecules in solution calculated using the symmetry-adapted cluster–configuration interaction method in the polarizable continuum model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukuda, Ryoichi, E-mail: fukuda@ims.ac.jp; Ehara, Masahiro; Elements Strategy Initiative for Catalysts and Batteries

2015-12-31

The effects from solvent environment are specific to the electronic states; therefore, a computational scheme for solvent effects consistent with the electronic states is necessary to discuss electronic excitation of molecules in solution. The PCM (polarizable continuum model) SAC (symmetry-adapted cluster) and SAC-CI (configuration interaction) methods are developed for such purposes. The PCM SAC-CI adopts the state-specific (SS) solvation scheme where solvent effects are self-consistently considered for every ground and excited states. For efficient computations of many excited states, we develop a perturbative approximation for the PCM SAC-CI method, which is called corrected linear response (cLR) scheme. Our test calculationsmore » show that the cLR PCM SAC-CI is a very good approximation of the SS PCM SAC-CI method for polar and nonpolar solvents.« less

An improved fault detection classification and location scheme based on wavelet transform and artificial neural network for six phase transmission line using single end data only.

PubMed

Koley, Ebha; Verma, Khushaboo; Ghosh, Subhojit

2015-01-01

Restrictions on right of way and increasing power demand has boosted development of six phase transmission. It offers a viable alternative for transmitting more power, without major modification in existing structure of three phase double circuit transmission system. Inspite of the advantages, low acceptance of six phase system is attributed to the unavailability of a proper protection scheme. The complexity arising from large number of possible faults in six phase lines makes the protection quite challenging. The proposed work presents a hybrid wavelet transform and modular artificial neural network based fault detector, classifier and locator for six phase lines using single end data only. The standard deviation of the approximate coefficients of voltage and current signals obtained using discrete wavelet transform are applied as input to the modular artificial neural network for fault classification and location. The proposed scheme has been tested for all 120 types of shunt faults with variation in location, fault resistance, fault inception angles. The variation in power system parameters viz. short circuit capacity of the source and its X/R ratio, voltage, frequency and CT saturation has also been investigated. The result confirms the effectiveness and reliability of the proposed protection scheme which makes it ideal for real time implementation.

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

PubMed Central

Vitalis, Andreas; Pappu, Rohit V.

2014-01-01

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom. PMID:25053299

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

The morphology of faint galaxies in Medium Deep Survey images using WFPC2

NASA Technical Reports Server (NTRS)

Griffiths, R. E.; Casertano, S.; Ratnatunga, K. U.; Neuschaefer, L. W.; Ellis, R. S.; Gilmore, G. F.; Glazebrook, K.; Santiago, B.; Huchra, J. P.; Windhorst, R. A.

1994-01-01

First results from Hubble Space Telescope (HST) Medium Deep Survey images taken with Wide Field/Planetary Camera-2 (WFPC2) demonstrate that galaxy classifications can be reliably performed to magnitudes I814 approximately less than 22.0 in the F815W band. Published spectroscopic surveys to this depth indicate a mean redshift of bar-z approximately 0.5. We have classified over 200 galaxies in nine WFPC2 fields according to a basic morphological scheme. The majority of these faint galaxies appear to be similar to regular Hubble-sequence examples observed at low redshift. To the precision of our classification scheme, the relative proportion of spheroidal and disk systems of normal appearance is as expected from nearby samples, indicating that the bulk of the local galaxy population was in place at half the Hubble time. However, the most intriguing result is the relatively high proportion (approximately 40%) of objects which are in some way anomalous, and which may be of relevance in understanding the origin of the familiar excess population of faint galaxies established by others. These diverse objects include apparently interacting pairs whose multiple structure is only revealed with HST's angular resolution, galaxies with superluminous star-forming regions, diffuse low surface brightness galaxies of various forms, and compact galaxies. These anomalous galaxies contribute a substantial fraction of the excess counts at our limiting magnitude, and may provide insights into the 'faint blue galaxy' problem.

General relaxation schemes in multigrid algorithms for higher order singularity methods

NASA Technical Reports Server (NTRS)

Oskam, B.; Fray, J. M. J.

1981-01-01

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Robustness of controllers designed using Galerkin type approximations

NASA Technical Reports Server (NTRS)

Morris, K. A.

1990-01-01

One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Multiple grid problems on concurrent-processing computers

NASA Technical Reports Server (NTRS)

Eberhardt, D. S.; Baganoff, D.

1986-01-01

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Event-Triggered Distributed Control of Nonlinear Interconnected Systems Using Online Reinforcement Learning With Exploration.

PubMed

Narayanan, Vignesh; Jagannathan, Sarangapani

2017-09-07

In this paper, a distributed control scheme for an interconnected system composed of uncertain input affine nonlinear subsystems with event triggered state feedback is presented by using a novel hybrid learning scheme-based approximate dynamic programming with online exploration. First, an approximate solution to the Hamilton-Jacobi-Bellman equation is generated with event sampled neural network (NN) approximation and subsequently, a near optimal control policy for each subsystem is derived. Artificial NNs are utilized as function approximators to develop a suite of identifiers and learn the dynamics of each subsystem. The NN weight tuning rules for the identifier and event-triggering condition are derived using Lyapunov stability theory. Taking into account, the effects of NN approximation of system dynamics and boot-strapping, a novel NN weight update is presented to approximate the optimal value function. Finally, a novel strategy to incorporate exploration in online control framework, using identifiers, is introduced to reduce the overall cost at the expense of additional computations during the initial online learning phase. System states and the NN weight estimation errors are regulated and local uniformly ultimately bounded results are achieved. The analytical results are substantiated using simulation studies.

Weighted statistical parameters for irregularly sampled time series

NASA Astrophysics Data System (ADS)

Rimoldini, Lorenzo

2014-01-01

Unevenly spaced time series are common in astronomy because of the day-night cycle, weather conditions, dependence on the source position in the sky, allocated telescope time and corrupt measurements, for example, or inherent to the scanning law of satellites like Hipparcos and the forthcoming Gaia. Irregular sampling often causes clumps of measurements and gaps with no data which can severely disrupt the values of estimators. This paper aims at improving the accuracy of common statistical parameters when linear interpolation (in time or phase) can be considered an acceptable approximation of a deterministic signal. A pragmatic solution is formulated in terms of a simple weighting scheme, adapting to the sampling density and noise level, applicable to large data volumes at minimal computational cost. Tests on time series from the Hipparcos periodic catalogue led to significant improvements in the overall accuracy and precision of the estimators with respect to the unweighted counterparts and those weighted by inverse-squared uncertainties. Automated classification procedures employing statistical parameters weighted by the suggested scheme confirmed the benefits of the improved input attributes. The classification of eclipsing binaries, Mira, RR Lyrae, Delta Cephei and Alpha2 Canum Venaticorum stars employing exclusively weighted descriptive statistics achieved an overall accuracy of 92 per cent, about 6 per cent higher than with unweighted estimators.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Multitasking the code ARC3D. [for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Barton, John T.; Hsiung, Christopher C.

1986-01-01

The CRAY multitasking system was developed in order to utilize all four processors and sharply reduce the wall clock run time. This paper describes the techniques used to modify the computational fluid dynamics code ARC3D for this run and analyzes the achieved speedup. The ARC3D code solves either the Euler or thin-layer N-S equations using an implicit approximate factorization scheme. Results indicate that multitask processing can be used to achieve wall clock speedup factors of over three times, depending on the nature of the program code being used. Multitasking appears to be particularly advantageous for large-memory problems running on multiple CPU computers.

Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra

NASA Astrophysics Data System (ADS)

Rezakhah, Saeid; Maleki, Yasaman

2016-07-01

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.

Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

NASA Astrophysics Data System (ADS)

Liang, Junhao; Din, Anwarud; Zhou, Tianshou

2018-03-01

While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

Approximate inference on planar graphs using loop calculus and belief progagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chertkov, Michael; Gomez, Vicenc; Kappen, Hilbert

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyzemore » in detail both the loop series and the Pfaffian series for models with binary variables and pairwise interactions, and show that the first term of the Pfaffian series can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.« less

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows

NASA Astrophysics Data System (ADS)

Stelling, G. S.; Duinmeijer, S. P. A.

2003-12-01

This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations.

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

NASA Astrophysics Data System (ADS)

Huyakorn, P. S.; Panday, S.; Wu, Y. S.

1994-06-01

A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.

Adaptive critic designs for discrete-time zero-sum games with application to H(infinity) control.

PubMed

Al-Tamimi, Asma; Abu-Khalaf, Murad; Lewis, Frank L

2007-02-01

In this correspondence, adaptive critic approximate dynamic programming designs are derived to solve the discrete-time zero-sum game in which the state and action spaces are continuous. This results in a forward-in-time reinforcement learning algorithm that converges to the Nash equilibrium of the corresponding zero-sum game. The results in this correspondence can be thought of as a way to solve the Riccati equation of the well-known discrete-time H(infinity) optimal control problem forward in time. Two schemes are presented, namely: 1) a heuristic dynamic programming and 2) a dual-heuristic dynamic programming, to solve for the value function and the costate of the game, respectively. An H(infinity) autopilot design for an F-16 aircraft is presented to illustrate the results.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

The Determinants of School District Salary Incentives: An Empirical Analysis of, Where and Why

ERIC Educational Resources Information Center

Martin, Stephanie M.

2010-01-01

Most public school districts in the United States use a salary schedule to determine compensation for teachers within the district. However, some school districts have implemented incentive pay schemes that allow flexibility at the school or even individual teacher level. These compensation schemes in some ways may more closely approximate a…

Factorized Runge-Kutta-Chebyshev Methods

NASA Astrophysics Data System (ADS)

O'Sullivan, Stephen

2017-05-01

The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) explicit schemes for the integration of large systems of PDEs with diffusive terms are presented. The schemes are simple to implement through ordered sequences of forward Euler steps with complex stepsizes, and easily parallelised for large scale problems on distributed architectures. Preserving 7 digits for accuracy at 16 digit precision, the schemes are theoretically capable of maintaining internal stability for acceleration factors in excess of 6000 with respect to standard explicit Runge-Kutta methods. The extent of the stability domain is approximately the same as that of RKC schemes, and a third longer than in the case of RKL2 schemes. Extension of FRKC methods to fourth-order, by both complex splitting and Butcher composition techniques, is also discussed. A publicly available implementation of FRKC2 schemes may be obtained from maths.dit.ie/frkc

An Automatic Detection System of Lung Nodule Based on Multi-Group Patch-Based Deep Learning Network.

PubMed

Jiang, Hongyang; Ma, He; Qian, Wei; Gao, Mengdi; Li, Yan

2017-07-14

High-efficiency lung nodule detection dramatically contributes to the risk assessment of lung cancer. It is a significant and challenging task to quickly locate the exact positions of lung nodules. Extensive work has been done by researchers around this domain for approximately two decades. However, previous computer aided detection (CADe) schemes are mostly intricate and time-consuming since they may require more image processing modules, such as the computed tomography (CT) image transformation, the lung nodule segmentation and the feature extraction, to construct a whole CADe system. It is difficult for those schemes to process and analyze enormous data when the medical images continue to increase. Besides, some state of the art deep learning schemes may be strict in the standard of database. This study proposes an effective lung nodule detection scheme based on multi-group patches cut out from the lung images, which are enhanced by the Frangi filter. Through combining two groups of images, a four-channel convolution neural networks (CNN) model is designed to learn the knowledge of radiologists for detecting nodules of four levels. This CADe scheme can acquire the sensitivity of 80.06% with 4.7 false positives per scan and the sensitivity of 94% with 15.1 false positives per scan. The results demonstrate that the multi-group patch-based learning system is efficient to improve the performance of lung nodule detection and greatly reduce the false positives under a huge amount of image data.

2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization

NASA Astrophysics Data System (ADS)

Fernández-Nieto, E. D.; Garres-Díaz, J.; Mangeney, A.; Narbona-Reina, G.

2018-03-01

We present here numerical modelling of granular flows with the μ (I) rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier-Stokes equations with the μ (I) rheology through an asymptotic analysis; under the hypothesis of a one-dimensional flow, this model takes into account side walls friction; (ii) a multilayer discretization following Fernández-Nieto et al. (2016) [20]. In this new numerical scheme, we propose an appropriate treatment of the rheological terms through a hydrostatic reconstruction which allows this scheme to be well-balanced and therefore to deal with dry areas. Based on academic tests, we first evaluate the influence of the width of the channel on the normal profiles of the downslope velocity thanks to the multilayer approach that is intrinsically able to describe changes from Bagnold to S-shaped (and vice versa) velocity profiles. We also check the well-balanced property of the proposed numerical scheme. We show that approximating side walls friction using single-layer models may lead to strong errors. Secondly, we compare the numerical results with experimental data on granular collapses. We show that the proposed scheme allows us to qualitatively reproduce the deposit in the case of a rigid bed (i.e. dry area) and that the error made by replacing the dry area by a small layer of material may be large if this layer is not thin enough. The proposed model is also able to reproduce the time evolution of the free surface and of the flow/no-flow interface. In addition, it reproduces the effect of erosion for granular flows over initially static material lying on the bed. This is possible when using a variable friction coefficient μ (I) but not with a constant friction coefficient.

Relaxation and approximate factorization methods for the unsteady full potential equation

NASA Technical Reports Server (NTRS)

Shankar, V.; Ide, H.; Gorski, J.

1984-01-01

The unsteady form of the full potential equation is solved in conservation form, using implicit methods based on approximate factorization and relaxation schemes. A local time linearization for density is introduced to enable solution to the equation in terms of phi, the velocity potential. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity, to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi obtained from requirements of density continuity. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. Results are presented for flows over airfoils, cylinders, and spheres. Comparisons are made with available Euler and full potential results.

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis.

PubMed

Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg

2016-12-13

We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.

Frequency and time-domain inspiral templates for comparable mass compact binaries in eccentric orbits

NASA Astrophysics Data System (ADS)

Tanay, Sashwat; Haney, Maria; Gopakumar, Achamveedu

2016-03-01

Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the postcircular scheme of Yunes et al. [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian amplitude and 2PN-order Fourier phase while incorporating eccentricity effects up to sixth order at each PN order. The importance of incorporating eccentricity evolution contributions to the Fourier phase in a PN-consistent manner is also demonstrated. Second, we present an accurate and efficient prescription to incorporate orbital eccentricity into the quasicircular time-domain TaylorT4 approximant at 2PN order. New features include the use of rational functions in orbital eccentricity to implement the 1.5PN-order tail contributions to the far-zone fluxes. This leads to closed form PN-accurate differential equations for evolving eccentric orbits, and the resulting time-domain approximant is accurate and efficient to handle initial orbital eccentricities ≤0.9 . Preliminary GW data analysis implications are probed using match estimates.

Testing approximations for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

The Osher scheme for real gases

NASA Technical Reports Server (NTRS)

Suresh, Ambady; Liou, Meng-Sing

1990-01-01

An extension of Osher's approximate Riemann solver to include gases with an arbitrary equation of state is presented. By a judicious choice of thermodynamic variables, the Riemann invariats are reduced to quadratures which are then approximated numerically. The extension is rigorous and does not involve any further assumptions or approximations over the ideal gas case. Numerical results are presented to demonstrate the feasibility and accuracy of the proposed method.

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Anerson, W. Kyle; Bonhaus, Daryl L.

1994-01-01

An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over a RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3 element and 4 element airfoil configurations. For the calculations, two one equation turbulence models are utilized. For the NACA 0012 airfoil, a pressure distribution and force data are compared with other computational results as well as with experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3 element configuration. For the 4 element case, comparisons of surface pressure distributions with experiment are made. In general, the agreement between the computations and the experiment is good.

Efficient Conservative Reformulation Schemes for Lithium Intercalation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urisanga, PC; Rife, D; De, S

Porous electrode theory coupled with transport and reaction mechanisms is a widely used technique to model Li-ion batteries employing an appropriate discretization or approximation for solid phase diffusion with electrode particles. One of the major difficulties in simulating Li-ion battery models is the need to account for solid phase diffusion in a second radial dimension r, which increases the computation time/cost to a great extent. Various methods that reduce the computational cost have been introduced to treat this phenomenon, but most of them do not guarantee mass conservation. The aim of this paper is to introduce an inherently mass conservingmore » yet computationally efficient method for solid phase diffusion based on Lobatto III A quadrature. This paper also presents coupling of the new solid phase reformulation scheme with a macro-homogeneous porous electrode theory based pseudo 20 model for Li-ion battery. (C) The Author(s) 2015. Published by ECS. All rights reserved.« less

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Incorporation of perceptually adaptive QIM with singular value decomposition for blind audio watermarking

NASA Astrophysics Data System (ADS)

Hu, Hwai-Tsu; Chou, Hsien-Hsin; Yu, Chu; Hsu, Ling-Yuan

2014-12-01

This paper presents a novel approach for blind audio watermarking. The proposed scheme utilizes the flexibility of discrete wavelet packet transformation (DWPT) to approximate the critical bands and adaptively determines suitable embedding strengths for carrying out quantization index modulation (QIM). The singular value decomposition (SVD) is employed to analyze the matrix formed by the DWPT coefficients and embed watermark bits by manipulating singular values subject to perceptual criteria. To achieve even better performance, two auxiliary enhancement measures are attached to the developed scheme. Performance evaluation and comparison are demonstrated with the presence of common digital signal processing attacks. Experimental results confirm that the combination of the DWPT, SVD, and adaptive QIM achieves imperceptible data hiding with satisfying robustness and payload capacity. Moreover, the inclusion of self-synchronization capability allows the developed watermarking system to withstand time-shifting and cropping attacks.

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Ash, Robert L.

1992-01-01

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Multigrid methods for numerical simulation of laminar diffusion flames

NASA Technical Reports Server (NTRS)

Liu, C.; Liu, Z.; Mccormick, S.

1993-01-01

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

NASA Astrophysics Data System (ADS)

Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

2013-09-01

In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Tropical cyclone intensity change. A quantitative forecasting scheme

NASA Technical Reports Server (NTRS)

Dropco, K. M.; Gray, W. M.

1981-01-01

One to two day future tropical cyclone intensity change from both a composite and an individual case point-of-view are discussed. Tropical cyclones occurring in the Gulf of Mexico during the period 1957-1977 form the primary data source. Weather charts of the NW Atlantic were initially examined, but few differences were found between intensifying and non-intensifying cyclones. A rawinsonde composite analysis detected composite differences in the 200 mb height fields, the 850 mb temperature fields, the 200 mb zonal wind and the vertical shears of the zonal wind. The individual cyclones which make up the composite study were then separately examined using this composite case knowledge. Similar parameter differences were found in a majority of individual cases. A cyclone intensity change forecast scheme was tested against independent storm cases. Correct predictions of intensification or non-intensification could be made approximately 75% of the time.

Intelligent robust tracking control for a class of uncertain strict-feedback nonlinear systems.

PubMed

Chang, Yeong-Chan

2009-02-01

This paper addresses the problem of designing robust tracking controls for a large class of strict-feedback nonlinear systems involving plant uncertainties and external disturbances. The input and virtual input weighting matrices are perturbed by bounded time-varying uncertainties. An adaptive fuzzy-based (or neural-network-based) dynamic feedback tracking controller will be developed such that all the states and signals of the closed-loop system are bounded and the trajectory tracking error should be as small as possible. First, the adaptive approximators with linearly parameterized models are designed, and a partitioned procedure with respect to the developed adaptive approximators is proposed such that the implementation of the fuzzy (or neural network) basis functions depends only on the state variables but does not depend on the tuning approximation parameters. Furthermore, we extend to design the nonlinearly parameterized adaptive approximators. Consequently, the intelligent robust tracking control schemes developed in this paper possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.

Detecting Thermal Cloaks via Transient Effects

PubMed Central

Sklan, Sophia R.; Bai, Xue; Li, Baowen; Zhang, Xiang

2016-01-01

Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and an approximate, homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous κ and inhomogeneous ρcp is known to be exact (no signals scattering and only mean values penetrating to the cloak’s interior), the sensitivity of diffusive cloaks to defects and approximations has not been analyzed. We analytically demonstrate that these approximate cloaks are detectable. Although they work as perfect cloaks in the steady-state, their transient (time-dependent) response is imperfect and a small amount of heat is scattered. This is sufficient to determine the presence of a cloak and any heat source it contains, but the material composition hidden within the cloak is not detectable in practice. To demonstrate the feasibility of this technique, we constructed a cloak with similar approximation and directly detected its presence using these transient temperature deviations outside the cloak. Due to limitations in the range of experimentally accessible volumetric specific heats, our detection scheme should allow us to find any realizable cloak, assuming a sufficiently large temperature difference. PMID:27605153

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

NASA Technical Reports Server (NTRS)

Yee, H. C.

1995-01-01

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Unified theory of quantized electrons, phonons, and photons out of equilibrium: A simplified ab initio approach based on the generalized Baym-Kadanoff ansatz

NASA Astrophysics Data System (ADS)

de Melo, Pedro Miguel M. C.; Marini, Andrea

2016-04-01

We present a full ab initio description of the coupled out-of-equilibrium dynamics of photons, phonons, and electrons. In the present approach, the quantized nature of the electromagnetic field as well as of the nuclear oscillations is fully taken into account. The result is a set of integrodifferential equations, written on the Keldysh contour, for the Green's functions of electrons, phonons, and photons where the different kinds of interactions are merged together. We then concentrate on the electronic dynamics in order to reduce the problem to a computationally feasible approach. By using the generalized Baym-Kadanoff ansatz and the completed collision approximation, we introduce a series of efficient but controllable approximations. In this way, we reduce all equations to a set of decoupled equations for the density matrix that describe all kinds of static and dynamical correlations. The final result is a coherent, general, and inclusive scheme to calculate several physical quantities: carrier dynamics, transient photoabsorption, and light emission, all of which include, at the same time, electron-electron, electron-phonon, and electron-photon interactions. We further discuss how all these observables can be easily calculated within the present scheme using a fully atomistic ab initio approach.

Experimental comparison of landmark-based methods for 3D elastic registration of pre- and postoperative liver CT data

NASA Astrophysics Data System (ADS)

Lange, Thomas; Wörz, Stefan; Rohr, Karl; Schlag, Peter M.

2009-02-01

The qualitative and quantitative comparison of pre- and postoperative image data is an important possibility to validate surgical procedures, in particular, if computer assisted planning and/or navigation is performed. Due to deformations after surgery, partially caused by the removal of tissue, a non-rigid registration scheme is a prerequisite for a precise comparison. Interactive landmark-based schemes are a suitable approach, if high accuracy and reliability is difficult to achieve by automatic registration approaches. Incorporation of a priori knowledge about the anatomical structures to be registered may help to reduce interaction time and improve accuracy. Concerning pre- and postoperative CT data of oncological liver resections the intrahepatic vessels are suitable anatomical structures. In addition to using branching landmarks for registration, we here introduce quasi landmarks at vessel segments with high localization precision perpendicular to the vessels and low precision along the vessels. A comparison of interpolating thin-plate splines (TPS), interpolating Gaussian elastic body splines (GEBS) and approximating GEBS on landmarks at vessel branchings as well as approximating GEBS on the introduced vessel segment landmarks is performed. It turns out that the segment landmarks provide registration accuracies as good as branching landmarks and can improve accuracy if combined with branching landmarks. For a low number of landmarks segment landmarks are even superior.

Application of two direct runoff prediction methods in Puerto Rico

USGS Publications Warehouse

Sepulveda, N.

1997-01-01

Two methods for predicting direct runoff from rainfall data were applied to several basins and the resulting hydrographs compared to measured values. The first method uses a geomorphology-based unit hydrograph to predict direct runoff through its convolution with the excess rainfall hyetograph. The second method shows how the resulting hydraulic routing flow equation from a kinematic wave approximation is solved using a spectral method based on the matrix representation of the spatial derivative with Chebyshev collocation and a fourth-order Runge-Kutta time discretization scheme. The calibrated Green-Ampt (GA) infiltration parameters are obtained by minimizing the sum, over several rainfall events, of absolute differences between the total excess rainfall volume computed from the GA equations and the total direct runoff volume computed from a hydrograph separation technique. The improvement made in predicting direct runoff using a geomorphology-based unit hydrograph with the ephemeral and perennial stream network instead of the strictly perennial stream network is negligible. The hydraulic routing scheme presented here is highly accurate in predicting the magnitude and time of the hydrograph peak although the much faster unit hydrograph method also yields reasonable results.

Real-Time Control of an Exoskeleton Hand Robot with Myoelectric Pattern Recognition.

PubMed

Lu, Zhiyuan; Chen, Xiang; Zhang, Xu; Tong, Kay-Yu; Zhou, Ping

2017-08-01

Robot-assisted training provides an effective approach to neurological injury rehabilitation. To meet the challenge of hand rehabilitation after neurological injuries, this study presents an advanced myoelectric pattern recognition scheme for real-time intention-driven control of a hand exoskeleton. The developed scheme detects and recognizes user's intention of six different hand motions using four channels of surface electromyography (EMG) signals acquired from the forearm and hand muscles, and then drives the exoskeleton to assist the user accomplish the intended motion. The system was tested with eight neurologically intact subjects and two individuals with spinal cord injury (SCI). The overall control accuracy was [Formula: see text] for the neurologically intact subjects and [Formula: see text] for the SCI subjects. The total lag of the system was approximately 250[Formula: see text]ms including data acquisition, transmission and processing. One SCI subject also participated in training sessions in his second and third visits. Both the control accuracy and efficiency tended to improve. These results show great potential for applying the advanced myoelectric pattern recognition control of the wearable robotic hand system toward improving hand function after neurological injuries.

Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer.

PubMed

Müller, Dirk K; Pampel, André; Möller, Harald E

2013-05-01

Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data. Copyright © 2013 Elsevier Inc. All rights reserved.

Fast local-MP2 method with density-fitting for crystals. II. Test calculations and application to the carbon dioxide crystal

NASA Astrophysics Data System (ADS)

Usvyat, Denis; Maschio, Lorenzo; Manby, Frederick R.; Casassa, Silvia; Schütz, Martin; Pisani, Cesare

2007-08-01

A density fitting scheme for calculating electron repulsion integrals used in local second order Møller-Plesset perturbation theory for periodic systems (DFP) is presented. Reciprocal space techniques are systematically adopted, for which the use of Poisson fitting functions turned out to be instrumental. The role of the various parameters (truncation thresholds, density of the k net, Coulomb versus overlap metric, etc.) on computational times and accuracy is explored, using as test cases primitive-cell- and conventional-cell-diamond, proton-ordered ice, crystalline carbon dioxide, and a three-layer slab of magnesium oxide. Timings and results obtained when the electron repulsion integrals are calculated without invoking the DFP approximation, are taken as the reference. It is shown that our DFP scheme is both accurate and very efficient once properly calibrated. The lattice constant and cohesion energy of the CO2 crystal are computed to illustrate the capabilities of providing a physically correct description also for weakly bound crystals, in strong contrast to present density functional approaches.

Multicore runup simulation by under water avalanche using two-layer 1D shallow water equations

NASA Astrophysics Data System (ADS)

Bagustara, B. A. R. H.; Simanjuntak, C. A.; Gunawan, P. H.

2018-03-01

The increasing of layers in shallow water equations (SWE) produces more dynamic model than the one-layer SWE model. The two-layer 1D SWE model has different density for each layer. This model becomes more dynamic and natural, for instance in the ocean, the density of water will decreasing from the bottom to the surface. Here, the source-centered hydro-static reconstruction (SCHR) numerical scheme will be used to approximate the solution of two-layer 1D SWE model, since this scheme is proved to satisfy the mathematical properties for shallow water equation. Additionally in this paper, the algorithm of SCHR is adapted to the multicore architecture. The simulation of runup by under water avalanche is elaborated here. The results show that the runup is depend on the ratio of density of each layers. Moreover by using grid sizes Nx = 8000, the speedup and efficiency by 2 threads are obtained 1.74779 times and 87.3896 % respectively. Nevertheless, by 4 threads the speedup and efficiency are obtained 2.93132 times and 73.2830 % respectively by similar number of grid sizes Nx = 8000.

Gas Flows in Rocket Motors. Volume 3. Appendix D. Computer Code Listings

DTIC Science & Technology

1989-08-01

Information Service, where it will be available to the general public, including foreign nationals. Prepared for the Astronautics Laboratory (AFSC) Air Force...SYMIMETRIC TRANSONIC NOZZLE FLOW~ IN CENEPAL COORDINATE SYSTEM C+ USING TIME ITERATIVE CD/’CD SCHEME * c VIITH THIN-LAYER APPROXIMATED NAVIER-STOIKE’S...Q( 1,1, 2) ,RHOU( 1, 1)), DIMENSION ADD(4) DIMENSION PRE(4,4), PADD (4) C SAI-DIRECTION ENTRY ADDX COF:F=O.125D0*OMEGAX DO 70 J=I,,JL DO 70 I=1,IL IF

Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints.

PubMed

He, Pingan; Jagannathan, S

2007-04-01

A novel adaptive-critic-based neural network (NN) controller in discrete time is designed to deliver a desired tracking performance for a class of nonlinear systems in the presence of actuator constraints. The constraints of the actuator are treated in the controller design as the saturation nonlinearity. The adaptive critic NN controller architecture based on state feedback includes two NNs: the critic NN is used to approximate the "strategic" utility function, whereas the action NN is employed to minimize both the strategic utility function and the unknown nonlinear dynamic estimation errors. The critic and action NN weight updates are derived by minimizing certain quadratic performance indexes. Using the Lyapunov approach and with novel weight updates, the uniformly ultimate boundedness of the closed-loop tracking error and weight estimates is shown in the presence of NN approximation errors and bounded unknown disturbances. The proposed NN controller works in the presence of multiple nonlinearities, unlike other schemes that normally approximate one nonlinearity. Moreover, the adaptive critic NN controller does not require an explicit offline training phase, and the NN weights can be initialized at zero or random. Simulation results justify the theoretical analysis.

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

Edgeworth expansions of stochastic trading time

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann

2010-08-01

Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986) [8], we propose to apply the Duru-Kleinert process-cum-time transformation in path integral to formulate the transition density of the forward. The method leads to asymptotic expansions of the transition density around a Gaussian kernel corresponding to the average activity in the market conditional on the forward value. The approximation is numerically illustrated for pricing vanilla options under the CEV model and the popular normal SABR model. The asymptotics can also be used for Monte Carlo simulations or backward integration schemes.

Capturing planar shapes by approximating their outlines

NASA Astrophysics Data System (ADS)

Sarfraz, M.; Riyazuddin, M.; Baig, M. H.

2006-05-01

A non-deterministic evolutionary approach for approximating the outlines of planar shapes has been developed. Non-uniform Rational B-splines (NURBS) have been utilized as an underlying approximation curve scheme. Simulated Annealing heuristic is used as an evolutionary methodology. In addition to independent studies of the optimization of weight and knot parameters of the NURBS, a separate scheme has also been developed for the optimization of weights and knots simultaneously. The optimized NURBS models have been fitted over the contour data of the planar shapes for the ultimate and automatic output. The output results are visually pleasing with respect to the threshold provided by the user. A web-based system has also been developed for the effective and worldwide utilization. The objective of this system is to provide the facility to visualize the output to the whole world through internet by providing the freedom to the user for various desired input parameters setting in the algorithm designed.

An asymptotic preserving multidimensional ALE method for a system of two compressible flows coupled with friction

NASA Astrophysics Data System (ADS)

Del Pino, S.; Labourasse, E.; Morel, G.

2018-06-01

We present a multidimensional asymptotic preserving scheme for the approximation of a mixture of compressible flows. Fluids are modelled by two Euler systems of equations coupled with a friction term. The asymptotic preserving property is mandatory for this kind of model, to derive a scheme that behaves well in all regimes (i.e. whatever the friction parameter value is). The method we propose is defined in ALE coordinates, using a Lagrange plus remap approach. This imposes a multidimensional definition and analysis of the scheme.

Multi-level optimization of a beam-like space truss utilizing a continuum model

NASA Technical Reports Server (NTRS)

Yates, K.; Gurdal, Z.; Thangjitham, S.

1992-01-01

A continuous beam model is developed for approximate analysis of a large, slender, beam-like truss. The model is incorporated in a multi-level optimization scheme for the weight minimization of such trusses. This scheme is tested against traditional optimization procedures for savings in computational cost. Results from both optimization methods are presented for comparison.

Multiple environment single system quantum mechanical/molecular mechanical (MESS-QM/MM) calculations. 1. Estimation of polarization energies.

PubMed

Sodt, Alexander J; Mei, Ye; König, Gerhard; Tao, Peng; Steele, Ryan P; Brooks, Bernard R; Shao, Yihan

2015-03-05

In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Toward automatic time-series forecasting using neural networks.

PubMed

Yan, Weizhong

2012-07-01

Over the past few decades, application of artificial neural networks (ANN) to time-series forecasting (TSF) has been growing rapidly due to several unique features of ANN models. However, to date, a consistent ANN performance over different studies has not been achieved. Many factors contribute to the inconsistency in the performance of neural network models. One such factor is that ANN modeling involves determining a large number of design parameters, and the current design practice is essentially heuristic and ad hoc, this does not exploit the full potential of neural networks. Systematic ANN modeling processes and strategies for TSF are, therefore, greatly needed. Motivated by this need, this paper attempts to develop an automatic ANN modeling scheme. It is based on the generalized regression neural network (GRNN), a special type of neural network. By taking advantage of several GRNN properties (i.e., a single design parameter and fast learning) and by incorporating several design strategies (e.g., fusing multiple GRNNs), we have been able to make the proposed modeling scheme to be effective for modeling large-scale business time series. The initial model was entered into the NN3 time-series competition. It was awarded the best prediction on the reduced dataset among approximately 60 different models submitted by scholars worldwide.

Effects of pulmonary inhalation on hyperpolarized krypton-83 magnetic resonance T1 relaxation

NASA Astrophysics Data System (ADS)

Stupic, K. F.; Elkins, N. D.; Pavlovskaya, G. E.; Repine, J. E.; Meersmann, T.

2011-07-01

The 83Kr magnetic resonance (MR) relaxation time T1 of krypton gas in contact with model surfaces was previously found to be highly sensitive to surface composition, surface-to-volume ratio, and surface temperature. The work presented here explored aspects of pulmonary 83Kr T1 relaxation measurements in excised lungs from healthy rats using hyperpolarized (hp) 83Kr with approximately 4.4% spin polarization. MR spectroscopy without spatial resolution was applied to the ex vivo lungs that actively inhale hp 83Kr through a custom designed ventilation system. Various inhalation schemes were devised to study the influence of anatomical dead space upon the measured 83Kr T1 relaxation times. The longitudinal 83Kr relaxation times in the distal airways and the respiratory zones were independent of the lung inhalation volume, with T1 = 1.3 s and T1 = 1.0 s, depending only on the applied inhalation scheme. The obtained data were highly reproducible between different specimens. Further, the 83Kr T1 relaxation times in excised lungs were unaffected by the presence of up to 40% oxygen in the hp gas mixture. The results support the possible importance of 83Kr as a biomarker for evaluating lung function.

Interpretation of ES, CS, and IOS approximations within a translational--internal coupling scheme. IV. ES and IOS molecule--molecule cross sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snider, R.F.; Parvatiyar, M.G.

1981-05-15

Properties of energy sudden and infinite order sudden translational--internal reduced S matrices are given for general molecule--molecule collisions. Formal similarities with the distorted wave Born approximation are discussed. Structural simplifications of energy dependent and kinetic cross sections associated with making the ES approximation are described. Conceptual difficulties associated with applying the ES and IOS approximations to kinetic processes dominated by energetically inelastic collisions are pointed out.

Nonlinear Analysis of Auscultation Signals in TCM Using the Combination of Wavelet Packet Transform and Sample Entropy.

PubMed

Yan, Jian-Jun; Wang, Yi-Qin; Guo, Rui; Zhou, Jin-Zhuan; Yan, Hai-Xia; Xia, Chun-Ming; Shen, Yong

2012-01-01

Auscultation signals are nonstationary in nature. Wavelet packet transform (WPT) has currently become a very useful tool in analyzing nonstationary signals. Sample entropy (SampEn) has recently been proposed to act as a measurement for quantifying regularity and complexity of time series data. WPT and SampEn were combined in this paper to analyze auscultation signals in traditional Chinese medicine (TCM). SampEns for WPT coefficients were computed to quantify the signals from qi- and yin-deficient, as well as healthy, subjects. The complexity of the signal can be evaluated with this scheme in different time-frequency resolutions. First, the voice signals were decomposed into approximated and detailed WPT coefficients. Then, SampEn values for approximated and detailed coefficients were calculated. Finally, SampEn values with significant differences in the three kinds of samples were chosen as the feature parameters for the support vector machine to identify the three types of auscultation signals. The recognition accuracy rates were higher than 90%.

Nonlinear Analysis of Auscultation Signals in TCM Using the Combination of Wavelet Packet Transform and Sample Entropy

PubMed Central

Yan, Jian-Jun; Wang, Yi-Qin; Guo, Rui; Zhou, Jin-Zhuan; Yan, Hai-Xia; Xia, Chun-Ming; Shen, Yong

2012-01-01

Auscultation signals are nonstationary in nature. Wavelet packet transform (WPT) has currently become a very useful tool in analyzing nonstationary signals. Sample entropy (SampEn) has recently been proposed to act as a measurement for quantifying regularity and complexity of time series data. WPT and SampEn were combined in this paper to analyze auscultation signals in traditional Chinese medicine (TCM). SampEns for WPT coefficients were computed to quantify the signals from qi- and yin-deficient, as well as healthy, subjects. The complexity of the signal can be evaluated with this scheme in different time-frequency resolutions. First, the voice signals were decomposed into approximated and detailed WPT coefficients. Then, SampEn values for approximated and detailed coefficients were calculated. Finally, SampEn values with significant differences in the three kinds of samples were chosen as the feature parameters for the support vector machine to identify the three types of auscultation signals. The recognition accuracy rates were higher than 90%. PMID:22690242

Spectral Element Method for the Simulation of Unsteady Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.

A new flux splitting scheme

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Christopher J., Jr.

1993-01-01

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

A new flux splitting scheme

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Steffen, Christopher J., Jr.

1991-01-01

A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Introducing a new methodology for the calculation of local philicity and multiphilic descriptor: an alternative to the finite difference approximation

NASA Astrophysics Data System (ADS)

Sánchez-Márquez, Jesús; Zorrilla, David; García, Víctor; Fernández, Manuel

2018-07-01

This work presents a new development based on the condensation scheme proposed by Chamorro and Pérez, in which new terms to correct the frozen molecular orbital approximation have been introduced (improved frontier molecular orbital approximation). The changes performed on the original development allow taking into account the orbital relaxation effects, providing equivalent results to those achieved by the finite difference approximation and leading also to a methodology with great advantages. Local reactivity indices based on this new development have been obtained for a sample set of molecules and they have been compared with those indices based on the frontier molecular orbital and finite difference approximations. A new definition based on the improved frontier molecular orbital methodology for the dual descriptor index is also shown. In addition, taking advantage of the characteristics of the definitions obtained with the new condensation scheme, the descriptor local philicity is analysed by separating the components corresponding to the frontier molecular orbital approximation and orbital relaxation effects, analysing also the local parameter multiphilic descriptor in the same way. Finally, the effect of using the basis set is studied and calculations using DFT, CI and Möller-Plesset methodologies are performed to analyse the consequence of different electronic-correlation levels.

From Sub-basin to Grid Scale Soil Moisture Disaggregation in SMART, A Semi-distributed Hydrologic Modeling Framework

NASA Astrophysics Data System (ADS)

Ajami, H.; Sharma, A.

2016-12-01

A computationally efficient, semi-distributed hydrologic modeling framework is developed to simulate water balance at a catchment scale. The Soil Moisture and Runoff simulation Toolkit (SMART) is based upon the delineation of contiguous and topologically connected Hydrologic Response Units (HRUs). In SMART, HRUs are delineated using thresholds obtained from topographic and geomorphic analysis of a catchment, and simulation elements are distributed cross sections or equivalent cross sections (ECS) delineated in first order sub-basins. ECSs are formulated by aggregating topographic and physiographic properties of the part or entire first order sub-basins to further reduce computational time in SMART. Previous investigations using SMART have shown that temporal dynamics of soil moisture are well captured at a HRU level using the ECS delineation approach. However, spatial variability of soil moisture within a given HRU is ignored. Here, we examined a number of disaggregation schemes for soil moisture distribution in each HRU. The disaggregation schemes are either based on topographic based indices or a covariance matrix obtained from distributed soil moisture simulations. To assess the performance of the disaggregation schemes, soil moisture simulations from an integrated land surface-groundwater model, ParFlow.CLM in Baldry sub-catchment, Australia are used. ParFlow is a variably saturated sub-surface flow model that is coupled to the Common Land Model (CLM). Our results illustrate that the statistical disaggregation scheme performs better than the methods based on topographic data in approximating soil moisture distribution at a 60m scale. Moreover, the statistical disaggregation scheme maintains temporal correlation of simulated daily soil moisture while preserves the mean sub-basin soil moisture. Future work is focused on assessing the performance of this scheme in catchments with various topographic and climate settings.

An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.

1994-01-01

An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.

Fast and robust estimation of spectro-temporal receptive fields using stochastic approximations.

PubMed

Meyer, Arne F; Diepenbrock, Jan-Philipp; Ohl, Frank W; Anemüller, Jörn

2015-05-15

The receptive field (RF) represents the signal preferences of sensory neurons and is the primary analysis method for understanding sensory coding. While it is essential to estimate a neuron's RF, finding numerical solutions to increasingly complex RF models can become computationally intensive, in particular for high-dimensional stimuli or when many neurons are involved. Here we propose an optimization scheme based on stochastic approximations that facilitate this task. The basic idea is to derive solutions on a random subset rather than computing the full solution on the available data set. To test this, we applied different optimization schemes based on stochastic gradient descent (SGD) to both the generalized linear model (GLM) and a recently developed classification-based RF estimation approach. Using simulated and recorded responses, we demonstrate that RF parameter optimization based on state-of-the-art SGD algorithms produces robust estimates of the spectro-temporal receptive field (STRF). Results on recordings from the auditory midbrain demonstrate that stochastic approximations preserve both predictive power and tuning properties of STRFs. A correlation of 0.93 with the STRF derived from the full solution may be obtained in less than 10% of the full solution's estimation time. We also present an on-line algorithm that allows simultaneous monitoring of STRF properties of more than 30 neurons on a single computer. The proposed approach may not only prove helpful for large-scale recordings but also provides a more comprehensive characterization of neural tuning in experiments than standard tuning curves. Copyright © 2015 Elsevier B.V. All rights reserved.

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch; Pappu, Rohit V.

2014-07-21

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear inmore » the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.« less

A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

NASA Astrophysics Data System (ADS)

Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.

2015-02-01

Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations

NASA Astrophysics Data System (ADS)

Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur

2017-11-01

Two novel control-volume methods are presented for flow in fractured media, and involve coupling the control-volume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the results demonstrate the method is also robust for transient flow. Furthermore, we present FPS coupled with a lower-dimensional fracture model, where fractures are strictly lower-dimensional in the physical mesh as well as in the computational domain. We present a comparison of the hybrid-grid FPS method and the lower-dimensional fracture model for several cases of isotropic and anisotropic fractured media which illustrate the benefits of the respective methods.