#### Sample records for chebyshev spectral methods

1. Relaxation schemes for Chebyshev spectral multigrid methods

NASA Technical Reports Server (NTRS)

Kang, Yimin; Fulton, Scott R.

1993-01-01

Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.

2. Preconditioned minimal residual methods for Chebyshev spectral calculations

NASA Technical Reports Server (NTRS)

Canuto, C.; Quarteroni, A.

1985-01-01

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

3. Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

NASA Technical Reports Server (NTRS)

Johnson, Duane

1996-01-01

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

4. Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations

NASA Technical Reports Server (NTRS)

Canuto, C.; Quarteroni, A.

1983-01-01

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

5. Spectral methods for the Euler equations. II - Chebyshev methods and shock fitting

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

1985-01-01

The Chebyshev spectral collocation method for the Euler gasdynamic equations is described. It is used with shock fitting to compute several two-dimensional gasdynamic flows. Examples include a shock/acoustic wave interaction, a shock/vortex interaction, and the classical blunt-body problem. With shock fitting, the spectral method has a clear advantage over second-order finite differences in that equivalent accuracy can be obtained with far fewer grid points.

6. Spectral methods for the Euler equations: Chebyshev methods and shock-fitting

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

1984-01-01

The Chebyshev spectral collocation method for the Euler gas-dynamic equations is described. It is used with shock fitting to compute several two-dimensional, gas-dynamic flows. Examples include a shock-acoustic wave interaction, a shock/vortex interaction, and the classical blunt body problem. With shock fitting, the spectral method has a clear advantage over second order finite differences in that equivalent accuracy can be obtained with far fewer grid points.

7. Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods

Julien, Keith; Watson, Mike

2009-03-01

A robust methodology is presented for efficiently solving partial differential equations using Chebyshev spectral techniques. It is well known that differential equations in one dimension can be solved efficiently with Chebyshev discretizations, O( N) operations for N unknowns, however this efficiency is lost in higher dimensions due to the coupling between modes. This paper presents the "quasi-inverse" technique (QIT), which combines optimizations of one-dimensional spectral differentiation matrices with Kronecker matrix products to build efficient multi-dimensional operators. This strategy results in O( N2 D-1 ) operations for ND unknowns, independent of the form of the differential operators. QIT is compared to the matrix diagonalization technique (MDT) of Haidvogel and Zang [D.B. Haidvogel, T. Zang, The accurate solution of Poisson's equation by expansion in Chebyshev polynomials, J. Comput. Phys. 30 (1979) 167-180] and Shen [J. Shen, Efficient spectral-Galerkin method. II. Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comp. 16 (1) (1995) 74-87]. While the cost for MDT and QIT are the same in two dimensions, there are significant differences. MDT utilizes an eigenvalue/eigenvector decomposition and can only be used for relatively simple differential equations. QIT is based upon intrinsic properties of the Chebyshev polynomials and is adaptable to linear PDEs with constant coefficients in simple domains. We present results for a standard suite of test problems, and discuss of the adaptability of QIT to more complicated problems.

8. Efficient rational Chebyshev pseudo-spectral method with domain decomposition for optical waveguides modal analysis.

PubMed

Abdrabou, Amgad; Heikal, A M; Obayya, S S A

2016-05-16

We propose an accurate and computationally efficient rational Chebyshev multi-domain pseudo-spectral method (RC-MDPSM) for modal analysis of optical waveguides. For the first time, we introduce rational Chebyshev basis functions to efficiently handle semi-infinite computational subdomains. In addition, the efficiency of these basis functions is enhanced by employing an optimized algebraic map; thus, eliminating the use of PML-like absorbing boundary conditions. For leaky modes, we derived a leaky modes boundary condition at the guide-substrate interface providing an efficient technique to accurately model leaky modes with very small refractive index imaginary part. The efficiency and numerical precision of our technique are demonstrated through the analysis of high-index contrast dielectric and plasmonic waveguides, and the highly-leaky ARROW structure; where finding ARROW leaky modes using our technique clearly reflects its robustness.

9. A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

10. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

11. Dynamic analysis of beam-cable coupled systems using Chebyshev spectral element method

Huang, Yi-Xin; Tian, Hao; Zhao, Yang

2017-05-01

The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.

12. Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.

PubMed

Hejranfar, Kazem; Hajihassanpour, Mahya

2015-01-01

In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential

13. Non-oscillatory spectral element Chebyshev method for shock wave calculations

SciTech Connect

1993-07-01

A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example. 20 refs., 10 figs.

14. On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

15. Chebyshev collocation spectral method for one-dimensional radiative heat transfer in linearly anisotropic-scattering cylindrical medium

Zhou, Rui-Rui; Li, Ben-Wen

2017-03-01

In this study, the Chebyshev collocation spectral method (CCSM) is developed to solve the radiative integro-differential transfer equation (RIDTE) for one-dimensional absorbing, emitting and linearly anisotropic-scattering cylindrical medium. The general form of quadrature formulas for Chebyshev collocation points is deduced. These formulas are proved to have the same accuracy as the Gauss-Legendre quadrature formula (GLQF) for the F-function (geometric function) in the RIDTE. The explicit expressions of the Lagrange basis polynomials and the differentiation matrices for Chebyshev collocation points are also given. These expressions are necessary for solving an integro-differential equation by the CCSM. Since the integrand in the RIDTE is continuous but non-smooth, it is treated by the segments integration method (SIM). The derivative terms in the RIDTE are carried out to improve the accuracy near the origin. In this way, a fourth order accuracy is achieved by the CCSM for the RIDTE, whereas it's only a second order one by the finite difference method (FDM). Several benchmark problems (BPs) with various combinations of optical thickness, medium temperature distribution, degree of anisotropy, and scattering albedo are solved. The results show that present CCSM is efficient to obtain high accurate results, especially for the optically thin medium. The solutions rounded to seven significant digits are given in tabular form, and show excellent agreement with the published data. Finally, the solutions of RIDTE are used as benchmarks for the solution of radiative integral transfer equations (RITEs) presented by Sutton and Chen (JQSRT 84 (2004) 65-103). A non-uniform grid refined near the wall is advised to improve the accuracy of RITEs solutions.

16. Cell averaging Chebyshev methods for hyperbolic problems

NASA Technical Reports Server (NTRS)

Wei, Cai; Gottlieb, David; Harten, Ami

1990-01-01

A cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form is described. Formulas are presented for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in spectral methods. The cell averaging methods presented are proven stable for linear scalar hyperbolic equations and present numerical simulations of shock-density wave interaction using the new cell averaging Chebyshev methods.

17. Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel

NASA Technical Reports Server (NTRS)

Karageorghis, Andreas; Phillips, Timothy N.

1990-01-01

The numerical simulation of steady planar two-dimensional, laminar flow of an incompressible fluid through an abruptly contracting channel using spectral domain decomposition methods is described. The key features of the method are the decomposition of the flow region into a number of rectangular subregions and spectral approximations which are pointwise C(1) continuous across subregion interfaces. Spectral approximations to the solution are obtained for Reynolds numbers in the range 0 to 500. The size of the salient corner vortex decreases as the Reynolds number increases from 0 to around 45. As the Reynolds number is increased further the vortex grows slowly. A vortex is detected downstream of the contraction at a Reynolds number of around 175 that continues to grow as the Reynolds number is increased further.

18. Chebyshev recursion methods: Kernel polynomials and maximum entropy

SciTech Connect

Silver, R.N.; Roeder, H.; Voter, A.F.; Kress, J.D.

1995-10-01

The authors describe two Chebyshev recursion methods for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). They are especially applicable to physical properties involving large numbers of eigenstates, which include densities of states, spectral functions, thermodynamics, total energies, as well as forces for molecular dynamics and Monte Carlo simulations. The authors apply Chebyshev methods to the electronic structure of Si, the thermodynamics of Heisenberg antiferromagnets, and a polaron problem.

19. A variant of Chebyshev?s method with sixth-order convergence

Kou, Jisheng; Li, Yitian

2006-11-01

In this paper, we present a new variant of Chebyshev?s method for solving non-linear equations. Analysis of convergence shows that the new method has sixth-order convergence. Per iteration the new method requires two evaluations of the function, one of its first derivative and one of its second derivative. Thus the efficiency, in term of function evaluations, of the new method is better than that of Chebyshev?s method. Numerical examples verifying the theory are given.

20. Mapped Chebyshev pseudo-spectral method for simulating the shear wave propagation in the plane of symmetry of a transversely isotropic viscoelastic medium.

PubMed

Qiang, Bo; Brigham, John C; McGough, Robert J; Greenleaf, James F; Urban, Matthew W

2017-03-01

Shear wave elastography is a versatile technique that is being applied to many organs. However, in tissues that exhibit anisotropic material properties, special care must be taken to estimate shear wave propagation accurately and efficiently. A two-dimensional simulation method is implemented to simulate the shear wave propagation in the plane of symmetry in transversely isotropic viscoelastic media. The method uses a mapped Chebyshev pseudo-spectral method to calculate the spatial derivatives and an Adams-Bashforth-Moulton integrator with variable step sizes for time marching. The boundaries of the two-dimensional domain are surrounded by perfectly matched layers to approximate an infinite domain and minimize reflection errors. In an earlier work, we proposed a solution for estimating the apparent shear wave elasticity and viscosity of the spatial group velocity as a function of rotation angle through a low-frequency approximation by a Taylor expansion. With the solver implemented in MATLAB, the simulated results in this paper match well with the theory. Compared to the finite element method simulations we used before, the pseudo-spectral solver consumes less memory and is faster and achieves better accuracy.

1. Recurrence Relations for Chebyshev-Type Methods

SciTech Connect

Ezquerro, J. A.; Hernandez, M. A. mahernan@dmc.unirioja.es

2000-03-15

The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A , instead of the second Frechet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided.

2. Pseudo spectral Chebyshev representation of few-group cross sections on sparse grids

SciTech Connect

Bokov, P. M.; Botes, D.; Zimin, V. G.

2012-07-01

This paper presents a pseudo spectral method for representing few-group homogenised cross sections, based on hierarchical polynomial interpolation. The interpolation is performed on a multi-dimensional sparse grid built from Chebyshev nodes. The representation is assembled directly from the samples using basis functions that are constructed as tensor products of the classical one-dimensional Lagrangian interpolation functions. The advantage of this representation is that it combines the accuracy of Chebyshev interpolation with the efficiency of sparse grid methods. As an initial test, this interpolation method was used to construct a representation for the two-group macroscopic cross sections of a VVER pin cell. (authors)

3. Rational Chebyshev pseudospectral method for long-short wave equations

Liu, Zeting; Lv, Shujuan

2017-02-01

We consider the initial boundary value problem of the Long-Short wave equations on the whole line. Firstly, a three level linear fully discrete pseudospectral scheme are structured based on central difference in time and rational Chebyshev functions in space which are orthogonal in the L2 space with weight 1. Secondly, the first-order differential matrix about rational Chebyshev functions is derived by the first-order differential matrix of Chebyshev polynomials, the entries of the matrix are just Chebyshev polynomials and Chebyshev Gauss collocation points. Thirdly, the numerical implementations are described and numerical results for the rational Chebyshev pseudospectral scheme are verified that a second-order accuracy in time and spectral accuracy in space.

4. The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points

NASA Technical Reports Server (NTRS)

Don, Wai Sun; Gottlieb, David

1993-01-01

We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.

5. Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes

SciTech Connect

Javaloyes, J.

2015-10-01

This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of broad-area laser diodes and amplifiers. This spectral method can be used in combination with the delay algebraic equations approach developed in [1], which substantially reduces the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in [2] as a particular case. It is also extended to the consideration of index guiding with an arbitrary transverse profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allow handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model.

6. Solution of acoustic workshop problems by a spectral multidomain method

NASA Technical Reports Server (NTRS)

Kopriva, Davis A.; Kolias, John H.

1995-01-01

We use a new staggered grid Chebyshev spectral multidomain method to solve three of the Workshop benchmark problems. The method defines solution unknowns at the nodes of the Chebyshev Gauss quadrature, and the fluxes at the nodes of the Chebyshev Gauss-Lobatto quadrature. The Chebyshev spectral method gives exponentially convergent phase and dissipation errors. The multidomain approximation gives the method flexibility. Using the method, we solve problems in Categories 1 and 5 of the benchmark problems.

7. Numerical approximation of Lévy-Feller fractional diffusion equation via Chebyshev-Legendre collocation method

Sweilam, N. H.; Abou Hasan, M. M.

2016-08-01

This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.

8. Quadrature imposition of compatibility conditions in Chebyshev methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Streett, C. L.

1990-01-01

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

9. Modified Chebyshev-Picard Iteration Methods for Orbit Propagation

Bai, Xiaoli; Junkins, John L.

2011-10-01

Modified Chebyshev-Picard Iteration methods are presented for solving high precision, long-term orbit propagation problems. Fusing Chebyshev polynomials with the classical Picard iteration method, the proposed methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to traditional, step-wise, forward integration methods. Numerical results demonstrate that for orbit propagation problems, the presented methods are comparable to or superior to a state-of-the-art 12th order Runge-Kutta-Nystrom method in a serial processor as measured by both precision and efficiency. We have found revolutionary long solution arcs with more than eleven digit path approximations over one to three lower-case Earth orbit periods, multiple solution arcs can be patched continuously together to achieve very long-term propagation, leading to more than ten digit accuracy with built-in precise interpolation. Of revolutionary practical promise to much more efficiently solving high precision, long-term orbital trajectory propagation problems is the observation that the presented methods are well suited to massive parallelization because computation of force functions along each path iteration can be rigorously distributed over many parallel cores with negligible cross communication needed.

10. Short-time Chebyshev wave packet method for molecular photoionization

Sun, Zhaopeng; Zheng, Yujun

2016-08-01

In this letter we present the extended usage of short-time Chebyshev wave packet method in the laser induced molecular photoionization dynamics. In our extension, the polynomial expansion of the exponential in the time evolution operator, the Hamiltonian operator can act on the wave packet directly which neatly avoids the matrix diagonalization. This propagation scheme is of obvious advantages when the dynamical system has large Hamiltonian matrix. Computational simulations are performed for the calculation of photoelectronic distributions from intense short pulse ionization of K2 and NaI which represent the Born-Oppenheimer (BO) model and Non-BO one, respectively.

11. Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

12. A composite Chebyshev finite difference method for nonlinear optimal control problems

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

2013-06-01

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

13. A fast Chebyshev method for simulating flexible-wing propulsion

Moore, M. Nicholas J.

2017-09-01

We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with O (Nlog ⁡ N) operations, where N is the number of collocation points on the wing. This is in contrast to the minimum O (N2) cost of a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of near-optimal complexity, O (Nlog ⁡ N) , allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.

14. Spectral methods for time dependent problems

NASA Technical Reports Server (NTRS)

1990-01-01

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

15. Modified Chebyshev-Picard Iteration Methods for Solution of Boundary Value Problems

Bai, Xiaoli; Junkins, John L.

2011-10-01

Modified Chebyshev-Picard iteration methods are presented for solving boundary value problems. Chebyshev polynomials are used to approximate the state trajectory in Picard iterations, while the boundary conditions are maintained by constraining the coefficients of the Chebyshev polynomials. Using Picard iteration and Clenshaw-Curtis quadrature, the presented methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to step-wise, forward integration approaches, which render the methods well-suited for parallel computation because computation of force functions along each path iteration can be rigorously distributed over many parallel cores with negligible cross communication needed. The presented methods solve optimal control problems through Pontryagin's principle without requiring shooting methods or gradient information. The methods are demonstrated to be computationally efficient and strikingly accurate when compared with Battin's method for a classical Lambert's problem and with a Chebyshev pseudospectral method for an optimal trajectory design problem. The reported simulation results obtained on a serial machine suggest a strong basis for optimism of using the presented methods for solving more challenging boundary value problems, especially when highly parallel architectures are fully exploited.

16. A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

17. Hubbell rectangular source integral calculation using a fast Chebyshev wavelets method.

PubMed

2016-07-01

An integration method based on Chebyshev wavelets is presented and used to calculate the Hubbell rectangular source integral. A study of the convergence and the accuracy of the method was carried out by comparing it to previous studies. Copyright © 2016 Elsevier Ltd. All rights reserved.

18. A Chebyshev condition for accelerating convergence of iterative tomographic methods-solving large least squares problems

Olson, Allen H.

1987-08-01

The Simultaneous Iterative Reconstruction Technique (SIRT) is a variation of Richardson's method for solving linear systems with positive definitive matrices, and can be used for solving any least squares problem. Previous SIRT methods used in tomography have suggested a constant normalization factor for the step size. With this normalization, the convergence rate of the eigencomponents decreases as the eigenvalue decreases, making these methods impractical for obtaining large bandwidth solutions. By allowing the normalization factor to change with each iteration, the error after k iterations is shown to be a k th order polynomial. The factors are then chosen to yield a Chebyshev polynomial so that the maximum error in the iterative method is minimized over a prescribed range of eigenvalues. Compared with k iterations using a constant normalization, the Chebyshev method requires only √ and has the property that all eigencomponents converge at the same rate. Simple expressions are given which permit the number of iterations to be determined in advanced based upon the desired accuracy and bandwidth. A stable ordering of the Chebyshev factors is also given which minimizes the effects of numerical roundoff. Since a good upper bound for the maximum eigenvalue of the normal matrix is essential to the calculations, the well known 'power method with shift of origin' is combined with the Chebyshev method to estimate its value.

19. 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method

Zhou, D.; Lo, S. H.; Cheung, Y. K.

2009-02-01

The three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev-Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time.

20. Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

1. Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations

PubMed Central

Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long

2014-01-01

This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. PMID:24977177

2. A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations

Ramos, Higinio; Vigo-Aguiar, Jesus

2007-07-01

In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge-Kutta method having stage order four. The method thus obtained have good properties relatives to stability including an unbounded stability domain and large [alpha]-value concerning A([alpha])-stability. A strategy for changing the step size, based on a pair of methods in a similar way to the embedding pair in the Runge-Kutta schemes, is presented. The numerical examples reveals that this method is very promising when it is used for solving stiff initial-value problems.

3. A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

NASA Technical Reports Server (NTRS)

Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.

1994-01-01

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

4. Modified Chebyshev pseudospectral method with O(N exp -1) time step restriction

NASA Technical Reports Server (NTRS)

Kosloff, Dan; Tal-Ezer, Hillel

1989-01-01

The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N exp 2) where N is the number of grid points. As a result of this, the allowable time step in an explicit time marching algorithm is O(N exp -2) which, in many cases, is much below the time step dictated by the physics of the partial differential equation. A new set of interpolating points is introduced such that the eigenvalues of the differentiation operator are O(N) and the allowable time step is O(N exp -1). The properties of the new algorithm are similar to those of the Fourier method. The new algorithm also provides a highly accurate solution for non-periodic boundary value problems.

5. Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

SciTech Connect

Isotalo, Aarno; Pusa, Maria

2016-05-01

The Chebyshev Rational Approximation Method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant sub-steps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the LU decompositions for the linear solves required in CRAM only need to be formed on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. Lastly, with substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.

6. Preconditioners for the spectral multigrid method

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Hussaini, M. Y.; Zang, T. A.

1986-01-01

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

7. A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries.

PubMed

Nielsen, S A; Hesthaven, J S

2002-05-01

The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE.

8. Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

9. Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

10. The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

11. Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon

1986-01-01

An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

12. Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

DOE PAGES

Isotalo, Aarno; Pusa, Maria

2016-05-01

The Chebyshev Rational Approximation Method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant sub-steps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the LU decompositions for the linear solves required in CRAM only need to be formed on the first substep. Themore » improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. Lastly, with substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.« less

13. On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, Claudio; Quarteroni, Alfio

1987-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

14. On the boundary treatment in spectral methods for hyperbolic systems

NASA Technical Reports Server (NTRS)

Canuto, C.; Quarteroni, A.

1986-01-01

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

15. Discrete ordinates (SN) method for the first solution of the transport equation using Chebyshev polynomials

Öztürk, Hakan

2016-11-01

First estimates for the numerical solution of the one-dimensional neutron transport equation for one-speed neutrons in a finite homogeneous slab is studied. The neutrons are assumed to be scattered isotropically through the medium. Then the discrete ordinates form of the transport equation is solved for the eigenvalue spectrum using the Chebyshev polynomials of second kind in the neutron angular flux. Therefore, the calculated eigenvalues for various values of the c0, the mean number of secondary neutrons per collision, are given in the tables using the Gauss-Chebyshev quadrature set.

16. Hydromagnetic Hiemenz flow of micropolar fluid over a nonlinearly stretching/shrinking sheet: Dual solutions by using Chebyshev Spectral Newton Iterative Scheme

Mahmood, Asad; Chen, Bin; Ghaffari, Abuzar

2016-10-01

Hydromagnetic stagnation point flow and heat transfer over a nonlinearly stretching/shrinking surface of micropolar fluid is investigated. The numerical simulation is carried out through Chebyshev Spectral Newton Iterative Scheme, after transforming the governing equations into dimensionless boundary layer form. The dual solutions are reported for different values of magnetic and material parameters against the limited range of stretching/shrinking parameter. It is also noted that second solution only occurs for the negative values of stretching/shrinking parameter, whereas for the positive values unique solution exists. The effects of dimensionless parameters are described through graphs. It is seen that the flow and heat transfer rates can be controlled through the material parameter and magnetic force.

17. Removal of spurious modes encountered in solving stability problems by spectral methods

NASA Technical Reports Server (NTRS)

Zebib, Abdelfattah

1987-01-01

A technique based on the Galerkin approximation is developed to remove spurious roots arising when Chebyshev spectral methods are used to solve eigenvalue problems in hydrodynamic stability. The derivation of Galerkin-Chebyshev approximations is explained, and numerical results for the Orr-Sommerfeld equations of plane Poiseuille flow and a Blasius profile are presented in tables and compared with those obtained by the method of Zebib (1984). It is pointed out that the present method does not increase the size of the algebraic system to be solved.

18. Spectral methods for CFD

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Streett, Craig L.; Hussaini, M. Yousuff

1989-01-01

One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched.

19. An adaptive pseudo-spectral method for reaction diffusion problems

NASA Technical Reports Server (NTRS)

Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M.

1987-01-01

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

20. A conservative staggered-grid Chebyshev multidomain method for compressible flows

NASA Technical Reports Server (NTRS)

Kopriva, David A.; Kolias, John H.

1995-01-01

We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

1. Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

2. Multistage spectral relaxation method for solving the hyperchaotic complex systems.

PubMed

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

3. Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

PubMed Central

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. PMID:25386624

4. A conservative staggered-grid Chebyshev multidomain method for compressible flows

SciTech Connect

Kopriva, D.A.; Kolias, J.H.

1996-04-01

The authors present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute. 41 refs., 23 figs., 1 tab.

5. Preconditioning matrices for Chebyshev derivative operators

NASA Technical Reports Server (NTRS)

Rothman, Ernest E.

1986-01-01

The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.

6. General relativistic neutrino transport using spectral methods

Peres, Bruno; Penner, Andrew Jason; Novak, Jérôme; Bonazzola, Silvano

2014-02-01

We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, θ, ϕ, ɛ, Θ, Φ), and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (θ, ϕ, Θ, Φ), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.

7. Mapping implicit spectral methods to distributed memory architectures

NASA Technical Reports Server (NTRS)

Overman, Andrea L.; Vanrosendale, John

1991-01-01

Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

8. Spectral methods for the Euler equations - The blunt body problem revisited

NASA Technical Reports Server (NTRS)

Kopriva, David A.; Zang, Thomas A.; Hussaini, M. Y.

1991-01-01

The present use of the Chebyshev spectral collocation method, in conjunction with shock-fitting, to solve the blunt-body problem gives attention to the boundary and the shock-acceleration equations. The crux of these procedures is the use of the characteristic compatibility relations to compute the body pressure and shock velocity. It is shown that converged solutions are obtainable without artificial smoothing, and that spectral accuracy is achieved.

9. Milling Stability Analysis Based on Chebyshev Segmentation

HUANG, Jianwei; LI, He; HAN, Ping; Wen, Bangchun

2016-09-01

Chebyshev segmentation method was used to discretize the time period contained in delay differential equation, then the Newton second-order difference quotient method was used to calculate the cutter motion vector at each time endpoint, and the Floquet theory was used to determine the stability of the milling system after getting the transfer matrix of milling system. Using the above methods, a two degree of freedom milling system stability issues were investigated, and system stability lobe diagrams were got. The results showed that the proposed methods have the following advantages. Firstly, with the same calculation accuracy, the points needed to represent the time period are less by the Chebyshev Segmentation than those of the average segmentation, and the computational efficiency of the Chebyshev Segmentation is higher. Secondly, if the time period is divided into the same parts, the stability lobe diagrams got by Chebyshev segmentation method are more accurate than those of the average segmentation.

10. Time-domain simulation of acoustic wave propagation and interaction with flexible structures using Chebyshev collocation method

Wang, Chunqi; Huang, Lixi

2012-09-01

A time-domain Chebyshev collocation (ChC) method is used to simulate acoustic wave propagation and its interaction with flexible structures in ducts. The numerical formulation is described using a two-dimensional duct noise control system, which consists of an expansion chamber and a tensioned membrane covering the side-branch cavity. Full coupling between the acoustic wave and the structural vibration of the tensioned membrane is considered in the modelling. A systematic method of solution is developed for the discretized differential equations over multiple physical domains. The time-domain ChC model is tested against analytical solutions under two conditions: one with an initial state of wave motion; the other with a time-dependent acoustic source. Comparisons with the finite-difference time-domain (FDTD) method are also made. Results show that the time-domain ChC method is highly accurate and computationally efficient for the time-dependent solution of duct acoustic problems. For illustrative purposes, the time-domain ChC method is applied to investigate the acoustic performance of three typical duct noise control devices: the expansion chamber, the quarter wavelength resonator and the drum silencer. The time-dependent simulation of the sound-structure interaction in the drum silencer reveals the delicate role of the membrane mass and tension in its sound reflection capability.

11. A Chebyshev method for state-to-state reactive scattering using reactant-product decoupling: OH + H2 → H2O + H

Cvitaš, Marko T.; Althorpe, Stuart C.

2013-08-01

We extend a recently developed wave packet method for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions [M. T. Cvitaš and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)], 10.1021/jp8111974 to include the Chebyshev propagator. The method uses the further partitioned approach to reactant-product decoupling, which uses artificial decoupling potentials to partition the coordinate space of the reaction into separate reactant, product, and transition-state regions. Separate coordinates and basis sets can then be used that are best adapted to each region. We derive improved Chebyshev partitioning formulas which include Mandelshtam-and-Taylor-type decoupling potentials, and which are essential for the non-unitary discrete variable representations that must be used in 4-atom reactive scattering calculations. Numerical tests on the fully dimensional OH + H2 → H2O + H reaction for J = 0 show that the new version of the method is as efficient as the previously developed split-operator version. The advantages of the Chebyshev propagator (most notably the ease of parallelization for J > 0) can now be fully exploited in state-to-state reactive scattering calculations on 4-atom reactions.

12. Accuracy and speed in computing the Chebyshev collocation derivative

NASA Technical Reports Server (NTRS)

Don, Wai-Sun; Solomonoff, Alex

1991-01-01

We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

13. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations.

PubMed

Banerjee, Amartya S; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E

2016-10-21

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

14. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

Banerjee, Amartya S.; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E.

2016-10-01

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

15. Spectral method for solution of the fractional transport equation

Kadem, Abdelouahab; Luchko, Yury; Baleanu, Dumitru

2010-08-01

In this paper, the Chebyshev polynomials expansion method is applied to find both an analytical solution of the fractional transport equation in the one-dimensional plane geometry and its numerical approximations. The idea of the method is in reducing of the fractional transport equation to a system of the linear fractional differential equations for the unknown coefficients of the Chebyshev polynomials expansion. The obtained system of equations is then solved by using the operational method for the Caputo fractional derivative.

16. A review of spectral methods

NASA Technical Reports Server (NTRS)

Lustman, L.

1984-01-01

An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

17. Spectral methods for discontinuous problems

NASA Technical Reports Server (NTRS)

Abarbanel, S.; Gottlieb, D.; Tadmor, E.

1985-01-01

Spectral methods yield high-order accuracy even when applied to problems with discontinuities, though not in the sense of pointwise accuracy. Two different procedures are presented which recover pointwise accurate approximations from the spectral calculations.

18. Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

NASA Technical Reports Server (NTRS)

Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.

1998-01-01

We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

19. Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

NASA Technical Reports Server (NTRS)

Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.

1998-01-01

We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

20. Improved Parker's method for topographic models using Chebyshev series and low rank approximation

Wu, Leyuan; Lin, Qiang

2017-03-01

We present a new method to improve the convergence of the well-known Parker's formula for the modelling of gravity and magnetic fields caused by sources with complex topography. In the original Parker's formula, two approximations are made, which may cause considerable numerical errors and instabilities: 1) the approximation of the forward and inverse continuous Fourier transforms using their discrete counterparts, the forward and inverse Fast Fourier Transform (FFT) algorithms; 2) the approximation of the exponential function with its Taylor series expansion. In a previous paper of ours, we have made an effort addressing the first problem by applying the Gauss-FFT method instead of the standard FFT algorithm. The new Gauss-FFT based method shows improved numerical efficiency and agrees well with space-domain analytical or hybrid analytical-numerical algorithms. However, even under the simplifying assumption of a calculation surface being a level plane above all topographic sources, the method may still fail or become inaccurate under certain circumstances. When the peaks of the topography approach the observation surface too closely, the number of terms of the Taylor series expansion needed to reach a suitable precision becomes large and slows the calculation. We show in this paper that this problem is caused by the second approximation mentioned above, and it is due to the convergence property of the Taylor series expansion that the algorithm becomes inaccurate for certain topographic models with large amplitudes. Based on this observation, we present a modified Parker's method using low rank approximation (LRA) of the exponential function in virtue of the Chebfun software system. In this way, the optimal rate of convergence is achieved. Some pre-computation is needed but will not cause significant computational overheads. Synthetic and real model tests show that the method now works well for almost any practical topographic model, provided that the assumption

1. Improved Parker's method for topographic models using Chebyshev series and low rank approximation

Wu, Leyuan; Lin, Qiang

2017-05-01

We present a new method to improve the convergence of the well-known Parker's formula for the modelling of gravity and magnetic fields caused by sources with complex topography. In the original Parker's formula, two approximations are made, which may cause considerable numerical errors and instabilities: (1) the approximation of the forward and inverse continuous Fourier transforms using their discrete counterparts, the forward and inverse Fast Fourier Transform (FFT) algorithms; (2) the approximation of the exponential function with its Taylor series expansion. In a previous paper of ours, we have made an effort addressing the first problem by applying the Gauss-FFT method instead of the standard FFT algorithm. The new Gauss-FFT based method shows improved numerical efficiency and agrees well with space-domain analytical or hybrid analytical-numerical algorithms. However, even under the simplifying assumption of a calculation surface being a level plane above all topographic sources, the method may still fail or become inaccurate under certain circumstances. When the peaks of the topography approach the observation surface too closely, the number of terms of the Taylor series expansion needed to reach a suitable precision becomes large and slows the calculation. We show in this paper that this problem is caused by the second approximation mentioned above, and it is due to the convergence property of the Taylor series expansion that the algorithm becomes inaccurate for certain topographic models with large amplitudes. Based on this observation, we present a modified Parker's method using low rank approximation of the exponential function in virtue of the Chebfun software system. In this way, the optimal rate of convergence is achieved. Some pre-computation is needed but will not cause significant computational overheads. Synthetic and real model tests show that the method now works well for almost any practical topographic model, provided that the assumption, that

2. Multidimensional Chebyshev interpolation for warm and hot dense matter.

PubMed

Faussurier, Gérald; Blancard, Christophe

2017-05-01

We propose a scheme based on a multidimensional Chebyshev interpolation to approximate smooth functions that depend on more than one variable. The present method generalizes the one dimensional Chebyshev approximation. The multidimensional approach can be used for generating databases like equation of state in the warm and hot dense matter. It is well suited to the present advance of massively parallel supercomputers.

3. Multidimensional Chebyshev interpolation for warm and hot dense matter

Faussurier, Gérald; Blancard, Christophe

2017-05-01

We propose a scheme based on a multidimensional Chebyshev interpolation to approximate smooth functions that depend on more than one variable. The present method generalizes the one dimensional Chebyshev approximation. The multidimensional approach can be used for generating databases like equation of state in the warm and hot dense matter. It is well suited to the present advance of massively parallel supercomputers.

4. A computationally efficient spectral method for modeling core dynamics

Marti, P.; Calkins, M. A.; Julien, K.

2016-08-01

An efficient, spectral numerical method is presented for solving problems in a spherical shell geometry that employs spherical harmonics in the angular dimensions and Chebyshev polynomials in the radial direction. We exploit the three-term recurrence relation for Chebyshev polynomials that renders all matrices sparse in spectral space. This approach is significantly more efficient than the collocation approach and is generalizable to both the Galerkin and tau methodologies for enforcing boundary conditions. The sparsity of the matrices reduces the computational complexity of the linear solution of implicit-explicit time stepping schemes to O(N) operations, compared to O>(N2>) operations for a collocation method. The method is illustrated by considering several example problems of important dynamical processes in the Earth's liquid outer core. Results are presented from both fully nonlinear, time-dependent numerical simulations and eigenvalue problems arising from the investigation of the onset of convection and the inertial wave spectrum. We compare the explicit and implicit temporal discretization of the Coriolis force; the latter becomes computationally feasible given the sparsity of the differential operators. We find that implicit treatment of the Coriolis force allows for significantly larger time step sizes compared to explicit algorithms; for hydrodynamic and dynamo problems at an Ekman number of E=10-5, time step sizes can be increased by a factor of 3 to 16 times that of the explicit algorithm, depending on the order of the time stepping scheme. The implementation with explicit Coriolis force scales well to at least 2048 cores, while the implicit implementation scales to 512 cores.

5. Spectral methods on arbitrary grids

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David

1995-01-01

Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.

6. Method of multivariate spectral analysis

DOEpatents

Keenan, Michael R.; Kotula, Paul G.

2004-01-06

A method of determining the properties of a sample from measured spectral data collected from the sample by performing a multivariate spectral analysis. The method can include: generating a two-dimensional matrix A containing measured spectral data; providing a weighted spectral data matrix D by performing a weighting operation on matrix A; factoring D into the product of two matrices, C and S.sup.T, by performing a constrained alternating least-squares analysis of D=CS.sup.T, where C is a concentration intensity matrix and S is a spectral shapes matrix; unweighting C and S by applying the inverse of the weighting used previously; and determining the properties of the sample by inspecting C and S. This method can be used to analyze X-ray spectral data generated by operating a Scanning Electron Microscope (SEM) with an attached Energy Dispersive Spectrometer (EDS).

7. The Chebyshev Polynomials: Patterns and Derivation

ERIC Educational Resources Information Center

Sinwell, Benjamin

2004-01-01

The Chebyshev polynomials named after a Russian mathematician, Pafnuty Lvovich Chebyshev, have various mathematical applications. A process for obtaining Chebyshev polynomials, and a mathematical inquiry into the patterns they generate, is presented.

8. Chebyshev matrix product state approach for time evolution

Halimeh, Jad C.; Kolley, Fabian; McCulloch, Ian P.

2015-09-01

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011), 10.1103/PhysRevB.83.195115]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the nonprojective method and more efficient information storage, data compression, and less computational effort.

9. The application of the boundary element method in BEM++ to small extreme Chebyshev ice particles and the remote detection of the ice crystal number concentration of small atmospheric ice particles

Baran, Anthony J.; Groth, Samuel P.

2017-09-01

The measurement of the shape and size distributions of small atmospheric ice particles (i.e. less than about 100 μm in size) is still an unresolved problem in atmospheric physics. This paper is composed of two parts, each addressing one of these measurements. In the first part, we report on an application of a new open-source electromagnetic boundary element method (BEM) called ;BEM++; to characterise the shape of small ice particles through the simulation of the two-dimensional (2D) light scattering patterns of extreme Chebyshev ice particles. Previous electromagnetic studies of Chebyshev particles have concentrated upon high Chebyshev orders, but with low Chebyshev deformation parameters. Here, we extend such studies by concentrating on the 2D light scattering properties of Chebyshev particles with extreme deformation parameters, up to 0.5, and with Chebyshev orders up to 16, at a size parameter of 15, in a fixed orientation. The results demonstrate the applicability of BEM++ to the study of the electromagnetic scattering properties of extreme particles and the usefulness of measuring the light scattering patterns of particles in 2D to mimic the scattering behaviours of highly irregular particles, such as dendritic atmospheric ice or hazardous biological and/or aerosol particles. In the second part, we demonstrate the potential application of remotely sensed very-high-resolution brightness temperature measurements of optically thin cirrus between wavelengths of about 8.0 and 12.0 μm to resolve the current atmospheric physics issue of determining the number concentration of small ice particles with size less than about 100 μm.

10. Efficient modified Chebyshev differentiation matrices for fractional differential equations

Dabiri, Arman; Butcher, Eric A.

2017-09-01

This paper compares several fractional operational matrices for solving a system of linear fractional differential equations (FDEs) of commensurate or incommensurate order. For this purpose, three fractional collocation differentiation matrices (FCDMs) based on finite differences are first proposed and compared with Podlubny's matrix previously used in the literature, after which two new efficient FCDMs based on Chebyshev collocation are proposed. It is shown via an error analysis that the use of the well-known property of fractional differentiation of polynomial bases applied to these methods results in a limitation in the size of the obtained Chebyshev-based FCDMs. To compensate for this limitation, a new fast spectrally accurate FCDM for fractional differentiation which does not require the use of the gamma function is proposed. Then, the Schur-Pade and Schur decomposition methods are implemented to enhance and improve numerical stability. Therefore, this method overcomes the previous limitation regarding the size limitation. In several illustrative examples, the convergence and computation time of the proposed FCDMs are compared and their advantages and disadvantages are outlined.

11. Spectral methods in fluid dynamics

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1986-01-01

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

12. Spectral methods in time for a class of parabolic partial differential equations

SciTech Connect

Ierley, G. ); Spencer, B. ); Worthing, R. )

1992-09-01

In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time. 14 refs., 9 figs.

13. Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas

2013-03-01

Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

14. Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems.

DTIC Science & Technology

1982-12-01

1971. [41] H.E. Wrigley. Accelerating the Jacobi method for solving simultaneous equations by Chebyshev extrapolation when the eigenvalues of the Iteration Matrix are complex. Computer Journal 6:16-176, 1963. L. 4 kit~ 444 1-f

15. A spectral element method for fluid dynamics - Laminar flow in a channel expansion

NASA Technical Reports Server (NTRS)

Patera, A. T.

1984-01-01

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

16. Data compression using Chebyshev transform

NASA Technical Reports Server (NTRS)

Cheng, Andrew F. (Inventor); Hawkins, III, S. Edward (Inventor); Nguyen, Lillian (Inventor); Monaco, Christopher A. (Inventor); Seagrave, Gordon G. (Inventor)

2007-01-01

The present invention is a method, system, and computer program product for implementation of a capable, general purpose compression algorithm that can be engaged on the fly. This invention has particular practical application with time-series data, and more particularly, time-series data obtained form a spacecraft, or similar situations where cost, size and/or power limitations are prevalent, although it is not limited to such applications. It is also particularly applicable to the compression of serial data streams and works in one, two, or three dimensions. The original input data is approximated by Chebyshev polynomials, achieving very high compression ratios on serial data streams with minimal loss of scientific information.

17. Thermal analysis of a fully wet porous radial fin with natural convection and radiation using the spectral collocation method

Khani, F.; Darvishi, M. T.; Gorla, R. S.. R.; Gireesha, B. J.

2016-05-01

Heat transfer with natural convection and radiation effect on a fully wet porous radial fin is considered. The radial velocity of the buoyancy driven flow at any radial location is obtained by applying Darcy's law. The obtained non-dimensionalized ordinary differential equation involving three highly nonlinear terms is solved numerically with the spectral collocation method. In this approach, the dimensionless temperature is approximated by Chebyshev polynomials and discretized by Chebyshev-Gausse-Lobatto collocation points. A particular algorithm is used to reduce the nonlinearity of the conservation of energy equation. The present analysis characterizes the effect of ambient temperature in different ways and it provides a better picture regarding the effect of ambient temperature on the thermal performance of the fin. The profiles for temperature distributions and dimensionless base heat flow are obtained for different parameters which influence the heat transfer rate.

18. A linear-scaling spectral-element method for computing electrostatic potentials.

PubMed

Watson, Mark A; Hirao, Kimihiko

2008-11-14

A new linear-scaling method is presented for the fast numerical evaluation of the electronic Coulomb potential. Our approach uses a simple real-space partitioning of the system into cubic cells and a spectral-element representation of the density in a tensorial basis of high-order Chebyshev polynomials. Electrostatic interactions between non-neighboring cells are described using the fast multipole method. The remaining near-field interactions are computed in the tensorial basis as a sum of differential contributions by exploiting the numerical low-rank separability of the Coulomb operator. The method is applicable to arbitrary charge densities, avoids the Poisson equation, and does not involve the solution of any systems of linear equations. Above all, an adaptive resolution of the Chebyshev basis in each cell facilitates the accurate and efficient treatment of molecular systems. We demonstrate the performance of our implementation for quantum chemistry with benchmark calculations on the noble gas atoms, long-chain alkanes, and diamond fragments. We conclude that the spectral-element method can be a competitive tool for the accurate computation of electrostatic potentials in large-scale molecular systems.

19. Spectral Methods for Numerical Relativity.

PubMed

Grandclément, Philippe; Novak, Jérôme

2009-01-01

Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.

20. Stability analysis of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Lustman, L.; Tadmor, E.

1986-01-01

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

1. A spectral element-FCT method for the compressible Euler equations

SciTech Connect

1994-11-01

A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements.

2. The problem of convexity of Chebyshev sets

Balaganskii, V. S.; Vlasov, L. P.

1996-12-01

Contents Introduction §1. Definitions and notation §2. Reference theorems §3. Some results Chapter I. Characterization of Banach spaces by means of the relations between approximation properties of sets §1. Existence, uniqueness §2. Prom approximate compactness to 'sun'-property §3. From 'sun'-property to approximate compactness §4. Differentiability in the direction of the gradient is sufficient for Fréchet and Gâteaux differentiability §5. Sets with convex complement Chapter II. The structure of Chebyshev and related sets §1. The isolated point method §2. Restrictions of the type \\vert\\overline{W}\\vert < \\vert X\\vert §3. The case where M is locally compact §4. The case where W lies in a hyperplane §5. Other cases Chapter III. Selected results §1. Some applications of the theory of monotone operators §2. A non-convex Chebyshev set in pre-Hilbert space §3. The example of Klee (discrete Chebyshev set) §4. A survey of some other results Conclusion Bibliography

3. Numerical relativity and spectral methods

Grandclement, P.

2016-12-01

The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.

4. Shock capturing by the spectral viscosity method

NASA Technical Reports Server (NTRS)

1989-01-01

A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods than pollutes the unstable Gibbs oscillations overall the computational domain, and the lack of entropy dissipation prevents convergences in these cases. The Spectral Viscosity method, which is based on high frequency dependent vanishing viscosity regularization of the classical spectral methods is discussed. It is shown that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.

5. On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media.

PubMed

Magagula, Vusi M; Motsa, Sandile S; Sibanda, Precious; Dlamini, Phumlani G

2016-01-01

The paper presents a significant improvement to the implementation of the spectral relaxation method (SRM) for solving nonlinear partial differential equations that arise in the modelling of fluid flow problems. Previously the SRM utilized the spectral method to discretize derivatives in space and finite differences to discretize in time. In this work we seek to improve the performance of the SRM by applying the spectral method to discretize derivatives in both space and time variables. The new approach combines the relaxation scheme of the SRM, bivariate Lagrange interpolation as well as the Chebyshev spectral collocation method. The technique is tested on a system of four nonlinear partial differential equations that model unsteady three-dimensional magneto-hydrodynamic flow and mass transfer in a porous medium. Computed solutions are compared with previously published results obtained using the SRM, the spectral quasilinearization method and the Keller-box method. There is clear evidence that the new approach produces results that as good as, if not better than published results determined using the other methods. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The technique also leads to faster convergence to the required solution.

6. Spectral Methods for Magnetic Anomalies

Parker, R. L.; Gee, J. S.

2013-12-01

Spectral methods, that is, those based in the Fourier transform, have long been employed in the analysis of magnetic anomalies. For example, Schouten and MaCamy's Earth filter is used extensively to map patterns to the pole, and Parker's Fourier transform series facilitates forward modeling and provides an efficient algorithm for inversion of profiles and surveys. From a different, and perhaps less familiar perspective, magnetic anomalies can be represented as the realization of a stationary stochastic process and then statistical theory can be brought to bear. It is vital to incorporate the full 2-D power spectrum, even when discussing profile data. For example, early analysis of long profiles failed to discover the small-wavenumber peak in the power spectrum predicted by one-dimensional theory. The long-wavelength excess is the result of spatial aliasing, when energy leaks into the along-track spectrum from the cross-track components of the 2-D spectrum. Spectral techniques may be used to improve interpolation and downward continuation of survey data. They can also evaluate the reliability of sub-track magnetization models both across and and along strike. Along-strike profiles turn out to be surprisingly good indicators of the magnetization directly under them; there is high coherence between the magnetic anomaly and the magnetization over a wide band. In contrast, coherence is weak at long wavelengths on across-strike lines, which is naturally the favored orientation for most studies. When vector (or multiple level) measurements are available, cross-spectral analysis can reveal the wavenumber interval where the geophysical signal resides, and where noise dominates. One powerful diagnostic is that the phase spectrum between the vertical and along-path components of the field must be constant 90 degrees. To illustrate, it was found that on some very long Project Magnetic lines, only the lowest 10% of the wavenumber band contain useful geophysical signal. In this

7. Spectral Methods in General Relativistic MHD Simulations

Garrison, David

2012-03-01

In this talk I discuss the use of spectral methods in improving the accuracy of a General Relativistic Magnetohydrodynamic (GRMHD) computer code. I introduce SpecCosmo, a GRMHD code developed as a Cactus arrangement at UHCL, and show simulation results using both Fourier spectral methods and finite differencing. This work demonstrates the use of spectral methods with the FFTW 3.3 Fast Fourier Transform package integrated with the Cactus Framework to perform spectral differencing using MPI.

8. A Multi-domain Spectral Method for Supersonic Reactive Flows

NASA Technical Reports Server (NTRS)

Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This paper has a dual purpose: it presents a multidomain Chebyshev method for the solution of the two-dimensional reactive compressible Navier-Stokes equations, and it reports the results of the application of this code to the numerical simulations of high Mach number reactive flows in recessed cavity. The computational method utilizes newly derived interface boundary conditions as well as an adaptive filtering technique to stabilize the computations. The results of the simulations are relevant to recessed cavity flameholders.

9. Estrada index and Chebyshev polynomials

Ginosar, Yuval; Gutman, Ivan; Mansour, Toufik; Schork, Matthias

2008-03-01

Let G be a graph whose eigenvalues are λ1, λ2,…, λn. The Estrada index of G is equal to ∑i=1ne. We point out certain classes of graphs whose characteristic polynomials are closely connected to the Chebyshev polynomials of the second kind. Various relations, in particular approximations, for the Estrada index of these graphs are obtained.

10. A synthesis procedure for dual-band impedance transformer using Chebyshev polynomials

Castaldi, G.; Fiumara, Vincenzo; Pinto, I. M.

2004-04-01

In this paper, we propose a new synthesis method which allows the design of equi-ripple dual-band impedance transformers and is based on a straightforward generalization of the well-known Chebyshev synthesis of single band transformer. As compared to a single-band Chebyshev transformer encompassing both required passbands, the proposed design yields significantly better performance.

11. A Multidomain Spectral Method for Scalar and Vectorial Poisson Equations with Noncompact Sources

Grandclément, P.; Bonazzola, S.; Gourgoulhon, E.; Marck, J.-A.

2001-06-01

We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type ΔN/ +λ∇(nablaċ)=S, with λ≠-1. The source can extend in all the Euclidean space R3, provided it decays at least as r-3. A multidomain approach is used, along with spherical coordinates (r, θ, φ). In each domain, Chebyshev polynomials (in r or 1/r) and spherical harmonics (in θ and φ) expansions are used. If the source decays as r-k the error of the numerical solution is shown to decrease at least as N-2(k-2), where N is the number of Chebyshev coefficients. The error is even evanescents; i.e., it decreases as exp(-N), if the source does not contain any spherical harmonics of index l>=k-3 (scalar case) or l>=k-5 (vectorial case).

12. Method of photon spectral analysis

DOEpatents

Gehrke, R.J.; Putnam, M.H.; Killian, E.W.; Helmer, R.G.; Kynaston, R.L.; Goodwin, S.G.; Johnson, L.O.

1993-04-27

A spectroscopic method to rapidly measure the presence of plutonium in soils, filters, smears, and glass waste forms by measuring the uranium L-shell x-ray emissions associated with the decay of plutonium. In addition, the technique can simultaneously acquire spectra of samples and automatically analyze them for the amount of americium and [gamma]-ray emitting activation and fission products present. The samples are counted with a large area, thin-window, n-type germanium spectrometer which is equally efficient for the detection of low-energy x-rays (10-2,000 keV), as well as high-energy [gamma] rays (>1 MeV). A 8,192- or 16,384 channel analyzer is used to acquire the entire photon spectrum at one time. A dual-energy, time-tagged pulser, that is injected into the test input of the preamplifier to monitor the energy scale, and detector resolution. The L x-ray portion of each spectrum is analyzed by a linear-least-squares spectral fitting technique. The [gamma]-ray portion of each spectrum is analyzed by a standard Ge [gamma]-ray analysis program. This method can be applied to any analysis involving x- and [gamma]-ray analysis in one spectrum and is especially useful when interferences in the x-ray region can be identified from the [gamma]-ray analysis and accommodated during the x-ray analysis.

13. Method of photon spectral analysis

DOEpatents

Gehrke, Robert J.; Putnam, Marie H.; Killian, E. Wayne; Helmer, Richard G.; Kynaston, Ronnie L.; Goodwin, Scott G.; Johnson, Larry O.

1993-01-01

A spectroscopic method to rapidly measure the presence of plutonium in soils, filters, smears, and glass waste forms by measuring the uranium L-shell x-ray emissions associated with the decay of plutonium. In addition, the technique can simultaneously acquire spectra of samples and automatically analyze them for the amount of americium and .gamma.-ray emitting activation and fission products present. The samples are counted with a large area, thin-window, n-type germanium spectrometer which is equally efficient for the detection of low-energy x-rays (10-2000 keV), as well as high-energy .gamma. rays (>1 MeV). A 8192- or 16,384 channel analyzer is used to acquire the entire photon spectrum at one time. A dual-energy, time-tagged pulser, that is injected into the test input of the preamplifier to monitor the energy scale, and detector resolution. The L x-ray portion of each spectrum is analyzed by a linear-least-squares spectral fitting technique. The .gamma.-ray portion of each spectrum is analyzed by a standard Ge .gamma.-ray analysis program. This method can be applied to any analysis involving x- and .gamma.-ray analysis in one spectrum and is especially useful when interferences in the x-ray region can be identified from the .gamma.-ray analysis and accommodated during the x-ray analysis.

14. Spectral methods for exterior elliptic problems

NASA Technical Reports Server (NTRS)

Canuto, C.; Hariharan, S. I.; Lustman, L.

1984-01-01

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

15. Numerical constructions involving Chebyshev polynomials

Lyakhovsky, V. D.

2017-02-01

We propose a new algorithm for the character expansion of tensor products of finite-dimensional irreducible representations of simple Lie algebras. The algorithm produces valid results for the algebras B 3, C 3, and D 3. We use the direct correspondence between Weyl anti-invariant functions and multivariate second-kind Chebyshev polynomials. We construct the triangular trigonometric polynomials for the algebra D 3.

16. Chebyshev-like generalized Shapiro filters for high-accuracy flow computations

Falissard, F.

2017-05-01

This paper presents Chebyshev-like generalized Shapiro (CS) filters with improved spectral-like resolution compared to existing generalized Shapiro filters. These new filters combine the advantages of Shapiro filters, i.e. arbitrary accuracy order, no-dispersion, full damping of 2Δ-waves, and the advantages of Chebyshev filters, i.e. purely dissipative response function with equal ripples satisfying an arbitrary Chebyshev criterion in passband. Thanks to the formalism of generalized Shapiro filters, general formulas are derived for arbitrary accuracy orders and arbitrary Chebyshev criterion. A python script is provided in appendix to compute CS filter coefficients. Computations based on the Euler equations assess the benefit of CS filters compared to the standard Shapiro filters. Since CS filters differ from Shapiro filters only by their coefficients, they can easily and advantageously be implemented in computational solvers already making use of generalized Shapiro filters.

17. Hybrid least squares multivariate spectral analysis methods

DOEpatents

Haaland, David M.

2002-01-01

A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following estimation or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The "hybrid" method herein means a combination of an initial classical least squares analysis calibration step with subsequent analysis by an inverse multivariate analysis method. A "spectral shape" herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The "shape" can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

18. Hybrid least squares multivariate spectral analysis methods

DOEpatents

Haaland, David M.

2004-03-23

A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following prediction or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The hybrid method herein means a combination of an initial calibration step with subsequent analysis by an inverse multivariate analysis method. A spectral shape herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The shape can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

19. Spectral Methods for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zang, T. A.; Streett, C. L.; Hussaini, M. Y.

1994-01-01

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral

20. Spectral Methods for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zang, T. A.; Streett, C. L.; Hussaini, M. Y.

1994-01-01

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral

1. Data Outlier Detection using the Chebyshev Theorem

SciTech Connect

Amidan, Brett G.; Ferryman, Thomas A.; Cooley, Scott K.

2005-05-12

During data collection and analysis, it is often necessary to identify and possibly remove outliers that exist. It is often critical to have an objective method of identifying outliers to be removed. There are many automated outlier detection methods, however, many are limited by assumptions of a distribution or they require upper and lower pre-defined boundaries in which the data should exist. If there is a known distribution for the data, then using that distribution can aid in finding outliers. Often, a distribution is not known, or the experimenter does not want to make an assumption about a certain distribution. Also, enough information may not exist about a set of data to be able to determine reliable upper and lower boundaries. For these cases, an outlier detection method, using the empirical data and based upon Chebyshev's inequality, was formed. This method also allows for detection of multiple outliers, not just one at a time.

2. SPECTRAL RELATIVE ABSORPTION DIFFERENCE METHOD

SciTech Connect

Salaymeh, S.

2010-06-17

When analyzing field data, the uncertainty in the background continuum emission produces the majority of error in the final gamma-source analysis. The background emission typically dominates an observed spectrum in terms of counts and is highly variable spatially and temporally. The majority of the spectral shape of the background continuum is produced by combinations of cosmic rays, {sup 40}K, {sup 235}U, and {sup 220}Rn, and the continuum is similar in shape to the 15%-20% level for most field observations. However, the goal of spectroscopy analysis is to pick up subtle peaks (<%5) upon this large background. Because the continuum is falling off as energy increases, peak detection algorithms must first define the background surrounding the peak. This definition is difficult when the range of background shapes is considered. The full spectral template matching algorithms are heavily weighted to solving for the background continuum as it produces significant counts over much of the energy range. The most appropriate background mitigation technique is to take a separate background observation without the source of interest. But, it is frequently not possible to record a background observation in the exact location before (or after) a source has been detected. Thus, one uses approximate backgrounds that rely on spatially nearby locations or similar environments. Since the error in many field observations is dominated by the background, a technique that is less sensitive to the background would be quite beneficial. We report the result of an initial investigation into a novel observation scheme for gamma-emission detection in high background environments. Employing low resolution, NaI, detectors, we examine the different between the direct emission and the 'spectral-shadow' that the gamma emission produces when passed through a thin absorber. For this detection scheme to be competitive, it is required to count and analyze individual gamma-events. We describe the

3. Spectral element methods: Algorithms and architectures

NASA Technical Reports Server (NTRS)

Fischer, Paul; Ronquist, Einar M.; Dewey, Daniel; Patera, Anthony T.

1988-01-01

Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered: the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.

4. Spectral ratio method for measuring emissivity

USGS Publications Warehouse

Watson, K.

1992-01-01

The spectral ratio method is based on the concept that although the spectral radiances are very sensitive to small changes in temperature the ratios are not. Only an approximate estimate of temperature is required thus, for example, we can determine the emissivity ratio to an accuracy of 1% with a temperature estimate that is only accurate to 12.5 K. Selecting the maximum value of the channel brightness temperatures is an unbiased estimate. Laboratory and field spectral data are easily converted into spectral ratio plots. The ratio method is limited by system signal:noise and spectral band-width. The images can appear quite noisy because ratios enhance high frequencies and may require spatial filtering. Atmospheric effects tend to rescale the ratios and require using an atmospheric model or a calibration site. ?? 1992.

5. IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory.

PubMed

Romero, M; de Madrid, A P; Mañoso, C; Vinagre, B M

2013-07-01

This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

6. Standard methods for spectral estimation and prewhitening

SciTech Connect

Stearns, S.D.

1986-07-01

A standard FFT periodogram-averaging method for power spectral estimation is described in detail, with examples that the reader can use to verify his own software. The parameters that must be specified in order to repeat a given spectral estimate are listed. A standard technique for prewhitening is also described, again with repeatable examples and a summary of the parameters that must be specified.

7. Numerical studies for flow and heat transfer of the Powell-Eyring fluid thin film over an unsteady stretching sheet with internal heat generation using the chebyshev finite difference method

Khader, M. M.; Megahed, A. M.

2013-05-01

An analysis is carried out to study the unsteady two-dimensional Powell-Eyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of a similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of nonlinear ordinary differential equations. A numerical solution of the resulting nonlinear differential equations is found by using an efficient Chebyshev finite difference method. A comparison of numerical results is made with the earlier published results for limiting cases. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.

8. Improved Chebyshev series ephemeris generation capability of GTDS

NASA Technical Reports Server (NTRS)

Liu, S. Y.; Rogers, J.; Jacintho, J. J.

1980-01-01

An improved implementation of the Chebyshev ephemeris generation capability in the operational version of the Goddard Trajectory Determination System (GTDS) is described. Preliminary results of an evaluation of this orbit propagation method for three satellites of widely different orbit eccentricities are also discussed in terms of accuracy and computing efficiency with respect to the Cowell integration method. An empirical formula is deduced for determining an optimal fitting span which would give reasonable accuracy in the ephemeris with a reasonable consumption of computing resources.

9. A comparative image analysis of radial Fourier-Chebyshev moments

Li, Bo

2017-08-01

On the basis of the discrete Fourier functions and the discrete Chebyshev polynomials, a new set of radial orthogonal moment functions were presented. The new moments construct a new discrete orthogonal plane, and take a new sampling method that overcomes the default of classical method, which can be effectively used in the image analysis. The experimental results show that the new radial moments are superior to the conventional moments in image reconstruction and computing efficiency.

10. Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

11. A point interaction for the discrete Schrödinger operator and generalized Chebyshev polynomials

Yafaev, D. R.

2017-06-01

We consider semi-infinite Jacobi matrices corresponding to a point interaction for the discrete Schrödinger operator. Our goal is to find explicit expressions for the spectral measure, the resolvent, and other spectral characteristics of such Jacobi matrices. It turns out that the spectral analysis of this toy problem leads to a new class of orthogonal polynomials generalizing the classical Chebyshev polynomials.

12. A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

13. A spectral mimetic least-squares method

SciTech Connect

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.

14. A fast and well-conditioned spectral method for singular integral equations

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

15. A spectral Phase-Amplitude method for propagating a wave function to large distances

Rawitscher, George

2015-06-01

The phase and amplitude (Ph-A) of a wave function vary slowly with distance, in contrast to the wave function that can be highly oscillatory. Hence the Ph-A representation of a wave function requires far fewer computational mesh points than the wave function itself. In 1930 Milne presented an equation for the phase and the amplitude functions (which is different from the one developed by Calogero), and in 1962 Seaton and Peach solved these equations iteratively. The objective of the present study is to implement Seaton and Peach's iteration procedure with a spectral Chebyshev expansion method, and at the same time present a non-iterative analytic solution to an approximate version of the iterative equations. The iterations converge rapidly for the case of attractive potentials. Two numerical examples are given: (1) for a potential that decreases with distance as 1 /r3, and (2) a Coulomb potential ∝ 1 / r. In both cases the whole radial range of [0-2000] requires only between 25 and 100 mesh points and the corresponding accuracy is between 10-3 and 10-6. The 0th iteration (which is the WKB approximation) gives an accuracy of 10-2. This spectral method permits one to calculate a wave function out to large distances reliably and economically.

16. A numerical investigation of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet via rational Chebyshev functions

Parand, Kourosh; Mahdi Moayeri, Mohammad; Latifi, Sobhan; Delkhosh, Mehdi

2017-07-01

In this paper, a spectral method based on the four kinds of rational Chebyshev functions is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. First, by using the quasilinearization method (QLM), the model which is a nonlinear ordinary differential equation is converted to a sequence of linear ordinary differential equations (ODEs). By applying the proposed method on the ODEs in each iteration, the equations are converted to a system of linear algebraic equations. The results indicate the high accuracy and convergence of our method. Moreover, the effects of the Eyring-Powell fluid material parameters are discussed.

17. Logarithmic compression methods for spectral data

DOEpatents

Dunham, Mark E.

2003-01-01

A method is provided for logarithmic compression, transmission, and expansion of spectral data. A log Gabor transformation is made of incoming time series data to output spectral phase and logarithmic magnitude values. The output phase and logarithmic magnitude values are compressed by selecting only magnitude values above a selected threshold and corresponding phase values to transmit compressed phase and logarithmic magnitude values. A reverse log Gabor transformation is then performed on the transmitted phase and logarithmic magnitude values to output transmitted time series data to a user.

18. Methods for peptide identification by spectral comparison

PubMed Central

Liu, Jian; Bell, Alexander W; Bergeron, John JM; Yanofsky, Corey M; Carrillo, Brian; Beaudrie, Christian EH; Kearney, Robert E

2007-01-01

Background Tandem mass spectrometry followed by database search is currently the predominant technology for peptide sequencing in shotgun proteomics experiments. Most methods compare experimentally observed spectra to the theoretical spectra predicted from the sequences in protein databases. There is a growing interest, however, in comparing unknown experimental spectra to a library of previously identified spectra. This approach has the advantage of taking into account instrument-dependent factors and peptide-specific differences in fragmentation probabilities. It is also computationally more efficient for high-throughput proteomics studies. Results This paper investigates computational issues related to this spectral comparison approach. Different methods have been empirically evaluated over several large sets of spectra. First, we illustrate that the peak intensities follow a Poisson distribution. This implies that applying a square root transform will optimally stabilize the peak intensity variance. Our results show that the square root did indeed outperform other transforms, resulting in improved accuracy of spectral matching. Second, different measures of spectral similarity were compared, and the results illustrated that the correlation coefficient was most robust. Finally, we examine how to assemble multiple spectra associated with the same peptide to generate a synthetic reference spectrum. Ensemble averaging is shown to provide the best combination of accuracy and efficiency. Conclusion Our results demonstrate that when combined, these methods can boost the sensitivity and specificity of spectral comparison. Therefore they are capable of enhancing and complementing existing tools for consistent and accurate peptide identification. PMID:17227583

19. Advanced spectral methods for climatic time series

USGS Publications Warehouse

Ghil, M.; Allen, M.R.; Dettinger, M.D.; Ide, K.; Kondrashov, D.; Mann, M.E.; Robertson, A.W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.

2002-01-01

The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal- to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.

20. Fourier-Legendre spectral methods for incompressible channel flow

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1984-01-01

An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

1. Multidomain spectral solution of the Euler gas-dynamics equations

NASA Technical Reports Server (NTRS)

Kopriva, David A.

1991-01-01

The present interfacial treatments for Euler gasdynamic equation computations via the multidomain Chebyshev spectral collocation method are applicable both at subdomain corners and in overlapping or patched subdomains, for interfaces located in the sub-, super-, or transonic regions of a flow. The results thus obtained are found to be (1) spectrally accurate, (2) both more accurate and more efficient than a single-domain calculation, and (3) potentially more accurate and efficient than a single-domain calculation. Interfacial wave reflection is insignificant.

2. Spectral solution of the viscous blunt body problem. 2: Multidomain approximation

NASA Technical Reports Server (NTRS)

Kopriva, David A.

1994-01-01

We present steady solutions of high speed viscous flows over blunt bodies using a multidomain Chebyshev spectral collocation method. The region with the shock layer is divided into subdomains so that internal layers can be well-resolved. In the interiors of the subdomains, the solution is approximated by Chebyshev collocation. At interfaces between subdomains, the advective terms are upwinded and the viscous terms are treated by a penalty method. The method is applied to five flows, the Mach number range 5-25 and Reynolds number range 2,000 - 83,000, based on nose radius. Results are compared to experimental data and to a finite difference result.

3. Solution of the One-Dimensional Consolidation Equation for Saturated Clays Using a Spectral Method

Sepulveda, N.

2003-12-01

The nonlinear, one-dimensional consolidation equation of fully saturated clays interbedded in an aquifer, derived by Gibson and others in 1967, is solved using a spectral method. This equation considers the variation of soil compressibility and permeability during consolidation and recasts Darcy's law so that the relative velocity of the soil skeleton and the pore fluid are related to the excess pore fluid pressure gradient. The spectral solution presented herein uses the matrix representation with Chebyshev collocation to compute the spatial derivative of functions that depend on void ratio, vertical hydraulic conductivity, and the vertical gradient of effective stress. A fourth-order Runge-Kutta algorithm is used to solve the derivative of the void ratio with respect to time. The spectral method requires neither the linearization of the originally nonlinear equation nor the convergence of iterative processes of traditional numerical methods such as finite differences and finite elements. The solution identifies temporal changes in void ratio within the clay lenses occurring in the aquifer system. The compaction is calculated from void ratio changes accumulated throughout the simulated time periods. Laboratory data were used to obtain the mean value for the soil grain density and depth-dependent profiles for aquifer compressibility, hydraulic conductivity, and initial vertical distribution of void ratio for each clay lens. The vertical gradient of the effective stress, needed in the consolidation equation, was derived and the resulting expression was evaluated by using the depth-dependent void ratio profile and drawdown data from a well hydrograph. Compactions and expansions of the clay lens resulting from temporal variations in drawdown due to ground-water withdrawals and recharge periods were simulated for two observation wells in the Santa Clara Valley, California. The solution of the one-dimensional consolidation equation generated temporal changes in void

4. LORENE: Spectral methods differential equations solver

Gourgoulhon, Eric; Grandclément, Philippe; Marck, Jean-Alain; Novak, Jérôme; Taniguchi, Keisuke

2016-08-01

LORENE (Langage Objet pour la RElativité NumériquE) solves various problems arising in numerical relativity, and more generally in computational astrophysics. It is a set of C++ classes and provides tools to solve partial differential equations by means of multi-domain spectral methods. LORENE classes implement basic structures such as arrays and matrices, but also abstract mathematical objects, such as tensors, and astrophysical objects, such as stars and black holes.

5. Implicit Spectral Methods for Wave Propagation Problems

Wineberg, Stephen B.; McGrath, Joseph F.; Gabl, Edward F.; Ridgway Scott, L.; Southwell, Charles E.

1991-12-01

The numerical solution of a non-linear wave equation can be obtained by using spectral methods to resolve the unknown in space and the standard Crank-Nicolson differencing scheme to advance the solution in time. We have analyzed iterative techniques for solving the non-linear equations that arise from such implicit time-stepping schemes for the K-dV and the KP equations. We derived predictor—corrector method that retain the full accuracy of the implicit method with minimal stability restrictions on the size of the time step. Some numerical examples show the propagation of interacting solitons.

6. Evolutionary Computing Methods for Spectral Retrieval

NASA Technical Reports Server (NTRS)

Terrile, Richard; Fink, Wolfgang; Huntsberger, Terrance; Lee, Seugwon; Tisdale, Edwin; VonAllmen, Paul; Tinetti, Geivanna

2009-01-01

A methodology for processing spectral images to retrieve information on underlying physical, chemical, and/or biological phenomena is based on evolutionary and related computational methods implemented in software. In a typical case, the solution (the information that one seeks to retrieve) consists of parameters of a mathematical model that represents one or more of the phenomena of interest. The methodology was developed for the initial purpose of retrieving the desired information from spectral image data acquired by remote-sensing instruments aimed at planets (including the Earth). Examples of information desired in such applications include trace gas concentrations, temperature profiles, surface types, day/night fractions, cloud/aerosol fractions, seasons, and viewing angles. The methodology is also potentially useful for retrieving information on chemical and/or biological hazards in terrestrial settings. In this methodology, one utilizes an iterative process that minimizes a fitness function indicative of the degree of dissimilarity between observed and synthetic spectral and angular data. The evolutionary computing methods that lie at the heart of this process yield a population of solutions (sets of the desired parameters) within an accuracy represented by a fitness-function value specified by the user. The evolutionary computing methods (ECM) used in this methodology are Genetic Algorithms and Simulated Annealing, both of which are well-established optimization techniques and have also been described in previous NASA Tech Briefs articles. These are embedded in a conceptual framework, represented in the architecture of the implementing software, that enables automatic retrieval of spectral and angular data and analysis of the retrieved solutions for uniqueness.

7. Stochastic dynamic models and Chebyshev splines

PubMed Central

Fan, Ruzong; Zhu, Bin; Wang, Yuedong

2015-01-01

In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. PMID:26045632

8. The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

9. Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

NASA Technical Reports Server (NTRS)

Balachandar, S.; Yuen, D. A.

1994-01-01

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

10. Relaxation schemes for spectral multigrid methods

NASA Technical Reports Server (NTRS)

Phillips, Timothy N.

1987-01-01

The effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined. Iterative methods are an attractive alternative to direct methods because Fourier transform techniques enable the discrete matrix-vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations. Preconditioning is found to be essential for acceptable rates of convergence. Preconditioners based on second-order finite difference methods are used. A comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary. The investigations show that iterations based on incomplete LU decompositions provide the most efficient methods for solving these algebraic systems.

11. A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations

Tarman, Hakan I.; Berberoğlu, Halil

2009-04-01

A novel algorithm implementing Chebyshev spectral collocation (pseudospectral) method in combination with Newton's method is proposed for the nonlinear two-point boundary value problem (BVP) arising in solving propagation equations in fiber Raman amplifier. Moreover, an algorithm to train the known linear solution for use as a starting solution for the Newton iteration is proposed and successfully implemented. The exponential accuracy obtained by the proposed Chebyshev pseudospectral method is demonstrated on a case of the Raman propagation equations with strong nonlinearities. This is in contrast to algebraic accuracy obtained by typical solvers used in the literature. The resolving power and the efficiency of the underlying Chebyshev grid are demonstrated in comparison to a known BVP solver.

12. Spectral method for a kinetic swarming model

SciTech Connect

Gamba, Irene M.; Haack, Jeffrey R.; Motsch, Sebastien

2015-04-28

Here we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as there is a distribution dependent collision invariant to satisfy when computing the interaction term. We use a spectral representation linked with a discrete constrained optimization to compute these interactions. To test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the Vicsek model. Lastly, we observe that the kinetic model captures key features such as vortex formation and traveling waves.

13. Spectral method for a kinetic swarming model

DOE PAGES

Gamba, Irene M.; Haack, Jeffrey R.; Motsch, Sebastien

2015-04-28

Here we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as there is a distribution dependent collision invariant to satisfy when computing the interaction term. We use a spectral representation linked with a discrete constrained optimization to compute these interactions. To test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the Vicsek model. Lastly, we observe that the kinetic model captures key features such as vortex formation and traveling waves.

14. Parallel algorithms for the spectral transform method

SciTech Connect

Foster, I.T.; Worley, P.H.

1994-04-01

The spectral transform method is a standard numerical technique for solving partial differential equations on a sphere and is widely used in atmospheric circulation models. Recent research has identified several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the different algorithms has previously been attempted. In this paper, we describe these different parallel algorithms and report on computational experiments that we have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations or a sphere; considerable care was taken to ensure that the experiments provide a fair comparison of the different algorithms and that the results are relevant to global models. We focus on hypercube- and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional FFTs and other parallel transforms.

15. Spectral methods in edge-diffraction theories

SciTech Connect

Arnold, J.M. )

1992-12-01

Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries and caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are throughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [Proc. IEEE 62, 1468 (1974)] for circular apertures is deduced. 34 refs., 1 fig.

16. Parallel algorithms for the spectral transform method

SciTech Connect

Foster, I.T.; Worley, P.H.

1997-05-01

The spectral transform method is a standard numerical technique for solving partial differential equations on a sphere and is widely used in atmospheric circulation models. Recent research has identified several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the different algorithms has previously been attempted. In this paper, the authors describe these different parallel algorithms and report on computational experiments that they have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations on a sphere; considerable care was taken to ensure that the experiments provide a fair comparison of the different algorithms and that the results are relevant to global models. The authors focus on hypercube- and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but they also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional fast Fourier transforms (FFTs) and other parallel transforms.

17. Iterative spectral methods and spectral solutions to compressible flows

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1982-01-01

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

18. On spectral relaxation method approach for steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating, viscous dissipation and suction/injection

Motsa, Sandile S.; Makukula, Zodwa G.

2013-03-01

In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations.

19. A new spectral method to compute FCN

Zhang, M.; Huang, C. L.

2014-12-01

Free core nutation (FCN) is a rotational modes of the earth with fluid core. All traditional theoretical methods produce FCN period near 460 days with PREM, while the precise observations (VLBI + SG tides) say it should be near 430 days. In order to fill this big gap, astronomers and geophysicists give various assumptions, e.g., increasing core-mantle-boundary (CMB) flattening by about 5%, a strong coupling between nutation and geomagnetic field near CMB, viscous coupling, or topographical coupling etc. Do we really need these unproved assumptions? or is it only the problem of these traditional theoretical methods themselves? Earth models (e.g. PREM) provide accurate and robust profiles of physical parameters, like density and Lame parameters, but their radial derivatives, which are also used in all traditional methods to calculate normal modes (e.g.. FCN), nutation and tides of non-rigid earth theoretically, are not so trustable as the parameters themselves. A new multiple layer spectral method is proposed and applied to the computation of normal modes, to avoid these problems. This new method can solve not only one order ellipsoid but also irregular asymmetric 3D earth model. Our primary result of the FCN period is 435 sidereal days.

20. On obtaining spectrally accurate solutions of linear differential equations with complex interfaces using the immersed interface method

Ray, Sudipta; Saha, Sandeep

2016-11-01

Numerical solution of engineering problems with interfacial discontinuities requires exact implementation of the jump conditions else the accuracy deteriorates significantly; particularly, achieving spectral accuracy has been limited due to complex interface geometry and Gibbs phenomenon. We adopt a novel implementation of the immersed-interface method that satisfies the jump conditions at the interfaces exactly, in conjunction with the Chebyshev-collocation method. We consider solutions to linear second order ordinary and partial differential equations having a discontinuity in their zeroth and first derivatives across an interface traced by a complex curve. The solutions obtained demonstrate the ability of the proposed method to achieve spectral accuracy for discontinuous solutions across tortuous interfaces. The solution methodology is illustrated using two model problems: (i) an ordinary differential equation with jump conditions forced by an infinitely differentiable function, (ii) Poisson's equation having a discontinuous solution across interfaces that are ellipses of varying aspect ratio. The use of more polynomials in the direction of the major axis than the minor axis of the ellipse increases the convergence rate of the solution.

1. Spectral solution of the viscous blunt-body problem

NASA Technical Reports Server (NTRS)

Kopriva, David A.

1993-01-01

The viscous blunt-body problem is solved with a shock-fitted Chebyshev spectral method. No explicit artificial viscosity or filtering is needed to obtain smooth, converged solutions. The method is applied to two problems. First, results for the flow over a right circular cylinder in the Mach number range of 5.5-6.0 are compared with experimental data. Second, a solution for a Mach 25 flow over a hyperbolic cone is compared with a viscous shock-layer calculation.

2. A multi-domain spectral computation of three-dimensional laminar horseshoe vortex flow using incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Tan, C. S.

1989-01-01

Multidomain spectral methods are presently used to numerically simulate a strut-wall intersection's laminar horseshoe vortex flow through direct solution of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Direct expansion in Chebyshev polynomials and spectral element method spatial discretization of flow dependence are used to achieve high-order accuracy, and minimal dispersion errors. Low and moderate Reynolds number results are presented to illustrate the method application.

3. The iterative solution of the problem of orbit determination using Chebyshev series

NASA Technical Reports Server (NTRS)

Feagin, T.

1975-01-01

A method of orbit determination is investigated which employs Picard iteration and Chebyshev series. The method is applied to the problem of determining the orbit of an earth satellite from range and range-rate observations contaminated by noise. It is shown to be readily applicable and to possess linear convergence.

4. Two-dimensional Chebyshev pseudospectral modelling of cardiac propagation.

PubMed

Zhan, Z; Ng, K T

2000-05-01

Bidomain or monodomain modelling has been used widely to study various issues related to action potential propagation in cardiac tissue. In most of these previous studies, the finite difference method is used to solve the partial differential equations associated with the model. Though the finite difference approach has provided useful insight in many cases, adequate discretisation of cardiac tissue with realistic dimensions often requires a large number of nodes, making the numerical solution process difficult or impossible with available computer resources. Here, a Chebyshev pseudospectral method is presented that allows a significant reduction in the number of nodes required for a given solution accuracy. The new method is used to solve the governing nonlinear partial differential equation for the monodomain model representing a two-dimensional homogeneous sheet of cardiac tissue. The unknown transmembrane potential is expanded in terms of Chebyshev polynomial trial functions and the equation is enforced at the Gauss-Lobatto grid points. Spatial derivatives are obtained using the fast Fourier transform and the solution is advanced in time using an explicit technique. Numerical results indicate that the pseudospectral approach allows the number of nodes to be reduced by a factor of sixteen, while still maintaining the same error performance. This makes it possible to perform simulations with the same accuracy using about twelve times less CPU time and memory.

5. On the convexity of N-Chebyshev sets

Borodin, Petr A.

2011-10-01

We define N-Chebyshev sets in a Banach space X for every positive integer N (when N=1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N\\ge 3 is odd and X is smooth uniformly convex.

6. Spectral Methods Using Rational Basis Functions on an Infinite Interval

Boyd, John P.

1987-03-01

By using the map y = L cot( t) where L is a constant, differential equations on the interval yɛ [- ∞, ∞] can be transformed into tɛ [0, π] and solved by an ordinary Fourier series. In this article, earlier work by Grosch and Orszag ( J. Comput. Phys.25, 273 (1977)), Cain, Ferziger, and Reynolds ( J. Comput. Phys.56, 272 (1984)), and Boyd ( J. Comput. Phys.25, 43 (1982); 57, 454 (1985); SIAM J. Numer. Anal. (1987)) is extended in several ways. First, the series of orthogonal rational functions converge on the exterior of bipolar coordinate surfaces in the complex y-plane. Second, Galerkin's method will convert differential equations with polynomial or rational coefficients into banded matrix problems. Third, with orthogonal rational functions it is possible to obtain exponential convergence even for u( y) that asymptote to a constant although this behavior would wreck alternatives such as Hermite or sinc expansions. Fourth, boundary conditions are usually "natural" rather than "essential" in the sense that the singularities of the differential equation will force the numerical solution to have the correct behavior at infinity even if no constraints are imposed on the basis functions. Fifth, mapping a finite interval to an infinite one and then applying the rational Chebyshev functions gives an exponentially convergent method for functions with bounded endpoint singularities. These concepts are illustrated by five numerical examples.

7. Spectral properties and dynamics of gold nanorods revealed by EMCCD-based spectral phasor method.

PubMed

Chen, Hongtao; Gratton, Enrico; Digman, Michelle A

2015-04-01

Gold nanorods (NRs) with tunable plasmon-resonant absorption in the near-infrared region have considerable advantages over organic fluorophores as imaging agents due to their brightness and lack of photobleaching. However, the luminescence spectral properties of NRs have not been fully characterized at the single particle level due to lack of proper analytic tools. Here, we present a spectral phasor analysis method that allows investigations of NRs' spectra at single particle level showing the spectral variance and providing spatial information during imaging. The broad phasor distribution obtained by the spectral phasor analysis indicates that spectra of NRs are different from particle to particle. NRs with different spectra can be identified in images with high spectral resolution. The spectral behaviors of NRs under different imaging conditions, for example, different excitation powers and wavelengths, were revealed by our laser-scanning multiphoton microscope using a high-resolution spectrograph with imaging capability. Our results prove that the spectral phasor method is an easy and efficient tool in hyper-spectral imaging analysis to unravel subtle changes of the emission spectrum. We applied this method to study the spectral dynamics of NRs during direct optical trapping and by optothermal trapping. Interestingly, different spectral shifts were observed in both trapping phenomena.

8. Spectral Properties and Dynamics of Gold Nanorods Revealed by EMCCD Based Spectral-Phasor Method

PubMed Central

Chen, Hongtao; Digman, Michelle A.

2015-01-01

Gold nanorods (NRs) with tunable plasmon-resonant absorption in the near-infrared region have considerable advantages over organic fluorophores as imaging agents. However, the luminescence spectral properties of NRs have not been fully explored at the single particle level in bulk due to lack of proper analytic tools. Here we present a global spectral phasor analysis method which allows investigations of NRs' spectra at single particle level with their statistic behavior and spatial information during imaging. The wide phasor distribution obtained by the spectral phasor analysis indicates spectra of NRs are different from particle to particle. NRs with different spectra can be identified graphically in corresponding spatial images with high spectral resolution. Furthermore, spectral behaviors of NRs under different imaging conditions, e.g. different excitation powers and wavelengths, were carefully examined by our laser-scanning multiphoton microscope with spectral imaging capability. Our results prove that the spectral phasor method is an easy and efficient tool in hyper-spectral imaging analysis to unravel subtle changes of the emission spectrum. Moreover, we applied this method to study the spectral dynamics of NRs during direct optical trapping and by optothermal trapping. Interestingly, spectral shifts were observed in both trapping phenomena. PMID:25684346

9. Method to analyze remotely sensed spectral data

SciTech Connect

Stork, Christopher L.; Van Benthem, Mark H.

2009-02-17

A fast and rigorous multivariate curve resolution (MCR) algorithm is applied to remotely sensed spectral data. The algorithm is applicable in the solar-reflective spectral region, comprising the visible to the shortwave infrared (ranging from approximately 0.4 to 2.5 .mu.m), midwave infrared, and thermal emission spectral region, comprising the thermal infrared (ranging from approximately 8 to 15 .mu.m). For example, employing minimal a priori knowledge, notably non-negativity constraints on the extracted endmember profiles and a constant abundance constraint for the atmospheric upwelling component, MCR can be used to successfully compensate thermal infrared hyperspectral images for atmospheric upwelling and, thereby, transmittance effects. Further, MCR can accurately estimate the relative spectral absorption coefficients and thermal contrast distribution of a gas plume component near the minimum detectable quantity.

10. Chebyshev-based technique for automated restoration of digital copies of faded photographic prints

Uchaev, Dmitry V.; Uchaev, Denis V.; Malinnikov, Vasiliy A.

2017-01-01

We present a technique for automated restoration of digital images obtained from faded photographic prints. The proposed defading technique uses our early proposed image contrast enhancement algorithm based on a contrast measure of images in the Chebyshev moment transform domain. Obtained experimental results demonstrate some advantages of the technique as compared to other widely used image enhancement methods.

11. Computations of a laminar backward-facing step flow at Re=800 with a spectral domain decomposition method

Keskar, Jayant; Lyn, D. A.

1999-02-01

The two-dimensional laminar incompressible flow over a backward-facing step is computed using a spectral domain decomposition approach. A minimum number of subdomains (two) is used; high resolution being achieved by increasing the order of the basis Chebyshev polynomial. Results for the case of a Reynolds number of 800 are presented and compared in detail with benchmark computations. Stable accurate steady flow solutions were obtained using substantially fewer nodes than in previously reported simulations. In addition, the problem of outflow boundary conditions was examined on a shortened domain. Because of their more global nature, spectral methods are particularly sensitive to imposed boundary conditions, which may be exploited in examining the effect of artificial (non-physical) outflow boundary conditions. Two widely used set of conditions were tested: pseudo stress-free conditions and zero normal gradient conditions. Contrary to previous results using the finite volume approach, the latter is found to yield a qualitatively erroneous yet stable flow-field. Copyright

12. Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations

DTIC Science & Technology

2002-05-01

are given by xj = x+ hξj. (1.3) For the example given in Figure 1.1, the upper limit of j is n = 6. In a terminology consistent with Henrici [3...University of Cincinnati, 1996. [3] P. Henrici . Discrete variable methods in ordinary differential equations. John Wiley & Sons Inc., New York, 1962. [4] D

13. Subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization

Motamarri, Phani; Gavini, Vikram

2014-09-01

We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using higher-order spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single framework and is applicable to both pseudopotential as well as all-electron calculations. The key ideas involved in the development of this method include: (i) employing a higher-order spectral finite-element basis that is amenable to mesh adaption; (ii) using a Chebyshev filter to construct a subspace, which is an approximation to the occupied eigenspace in a given self-consistent field iteration; (iii) using a localization procedure to construct a nonorthogonal localized basis spanning the Chebyshev filtered subspace; and (iv) using a Fermi-operator expansion in terms of the subspace-projected Hamiltonian represented in the nonorthogonal localized basis to compute relevant quantities like the density matrix, electron density, and band energy. We demonstrate the accuracy and efficiency of the proposed approach on benchmark systems involving pseudopotential calculations on aluminum nanoclusters up to 3430 atoms and on alkane chains up to 7052 atoms, as well as all-electron calculations on silicon nanoclusters up to 3920 electrons. The benchmark studies revealed that accuracies commensurate with chemical accuracy can be obtained with the proposed method, and a subquadratic-scaling with system size was observed for the range of materials systems studied. In particular, for the alkane chains—representing an insulating material—close to linear scaling is observed, whereas, for aluminum nanoclusters—representing a metallic material—the scaling is observed to be O (N1.46). For all-electron calculations on silicon nanoclusters, the scaling with the number of electrons is computed to be O (N1.75). In all the benchmark systems, significant computational savings have been realized with the proposed approach, with

14. The Spectral Element Method for Geophysical Flows

Taylor, Mark

1998-11-01

We will describe SEAM, a Spectral Element Atmospheric Model. SEAM solves the 3D primitive equations used in climate modeling and medium range forecasting. SEAM uses a spectral element discretization for the surface of the globe and finite differences in the vertical direction. The model is spectrally accurate, as demonstrated by a variety of test cases. It is well suited for modern distributed-shared memory computers, sustaining over 24 GFLOPS on a 240 processor HP Exemplar. This performance has allowed us to run several interesting simulations in full spherical geometry at high resolution (over 22 million grid points).

15. Single scattering from nonspherical Chebyshev particles: A compendium of calculations

NASA Technical Reports Server (NTRS)

Wiscombe, W. J.; Mugnai, A.

1986-01-01

A large set of exact calculations of the scattering from a class of nonspherical particles known as Chebyshev particles' has been performed. Phase function and degree of polarization in random orientation, and parallel and perpendicular intensities in fixed orientations, are plotted for a variety of particles shapes and sizes. The intention is to furnish a data base against which both experimental data, and the predictions of approximate methods, can be tested. The calculations are performed with the widely-used Extended Boundary Condition Method. An extensive discussion of this method is given, including much material that is not easily available elsewhere (especially the analysis of its convergence properties). An extensive review is also given of all extant methods for nonspherical scattering calculations, as well as of the available pool of experimental data.

16. Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

17. Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

18. INSTRUMENTS AND METHODS OF INVESTIGATION: Spectral and spectral-frequency methods of investigating atmosphereless bodies of the Solar system

Busarev, Vladimir V.; Prokof'eva-Mikhailovskaya, Valentina V.; Bochkov, Valerii V.

2007-06-01

A method of reflectance spectrophotometry of atmosphereless bodies of the Solar system, its specificity, and the means of eliminating basic spectral noise are considered. As a development, joining the method of reflectance spectrophotometry with the frequency analysis of observational data series is proposed. The combined spectral-frequency method allows identification of formations with distinctive spectral features, and estimations of their sizes and distribution on the surface of atmospherelss celestial bodies. As applied to investigations of asteroids 21 Lutetia and 4 Vesta, the spectral frequency method has given us the possibility of obtaining fundamentally new information about minor planets.

19. Parallel computation with the spectral element method

SciTech Connect

Ma, Hong

1995-12-01

Spectral element models for the shallow water equations and the Navier-Stokes equations have been successfully implemented on a data parallel supercomputer, the Connection Machine model CM-5. The nonstaggered grid formulations for both models are described, which are shown to be especially efficient in data parallel computing environment.

20. Digital spectral separation methods and systems for bioluminescence imaging.

PubMed

Wang, Ge; Shen, Haiou; Liu, Ying; Cong, Alex; Cong, Wenxiang; Wang, Yue; Dubey, Purnima

2008-02-04

We propose a digital spectral separation (DSS) system and methods to extract spectral information optimally from a weak multi-spectral signal such as in the bioluminescent imaging (BLI) studies. This system utilizes our newly invented spatially-translated spectral-image mixer (SSM), which consists of dichroic beam splitters, a mirror, and a DSS algorithm. The DSS approach overcomes the shortcomings of the data acquisition scheme used for the current BLI systems. Primarily, using our DSS scheme, spectral information will not be filtered out. Accordingly, truly parallel multi-spectral multi-view acquisition is enabled for the first time to minimize experimental time and optimize data quality. This approach also permits recovery of the bioluminescent signal time course, which is useful to study the kinetics of multiple bioluminescent probes using multi-spectral bioluminescence tomography (MSBT).

1. Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D4 symmetry group; Interpolation within a squircle, Part I

Li, Shan; Boyd, John P.

2014-02-01

A domain is invariant under the eight-element D4 symmetry group if it is unchanged by reflection with respect to the x and y axes and also the diagonal line x=y. Previous treatments of group theory for spectral methods have generally demanded a semester's worth of group theory. We show this is unnecessary by providing explicit recipes for creating grids, etc. We show how to decompose an arbitrary function into six symmetry-invariant components, and thereby split the interpolation problem into six independent subproblems. We also show how to make symmetry-invariant basis functions from products of Chebyshev polynomials, from Zernike polynomials and from radial basis functions (RBFs) of any species. These recipes are completely general, and apply to any domain that is invariant under the dihedral group D4. These concepts are illustrated by RBF pseudospectral solutions of the Poisson equation in a domain bounded by a squircle, the square-with-rounded corners defined by x2ν+y2ν-1=0 where here ν=2. We also apply Chebyshev polynomials to compute eigenmodes of the Helmholtz equation on the square and show each mode belongs to one and only one of the six D4 classes. [F. Albert Cotton, in: Chemical Applications of Group Theory, John Wiley, New York, 1963, p. vii]Chebyshev polynomials in Cartesian coordinates. Znm(x,y), the Zernike polynomials. Radial basis functions (RBFs). We shall show how to rearrange each basis into six disjoint sets which are eigenfunctions of the operations of the group. We shall then explain how the interpolation problem with N points can be split into four problems of size N/8 and two problems of size N/4 with an enormous reduction of cost.First, though, we shall provide a brief overview of the D4 symmetry group.

2. Interference method for measuring central moments of spectral lines

SciTech Connect

Kozhevatov, I.E.; Kulikova, E.Kh.; Cheragin, N.P.

1995-04-01

A method of unconventional spectral analysis, which was developed for simultaneous measurements of integral parameters of spectral lines such as an area under the line, and its shift, half-width, asymmetry, etc., is substantiated. The basic concepts of the method are described and examples of its use with two- and multibeam interferometers are given.

3. A method of determining spectral analytical dye densities

NASA Technical Reports Server (NTRS)

Scarpace, F. L.; Friederichs, G. A.

1978-01-01

A straightforward method for the user of color imagery to determine the spectral analytical density of dyes present in the processed imagery is presented. The method involves exposing a large number of different color patches on the film which span the gamut of the film's imaging capabilities. From integral spectral density measurements at 16 to 19 different wavelengths, the unit spectral dye curves for each of the three dyes present were determined in two different types of color films. A discussion of the use of these spectral dye densities to determine the transformation between integral density measurements and analytical density is presented.

4. Methods of Spectral Analysis in C++ (MOSAIC)

Engesser, Michael

2016-06-01

Stellar spectroscopic classification is most often still done by hand. MOSAIC is a project focused on the collection and classification of astronomical spectra using a computerized algorithm. The code itself attempts to accurately classify stellar spectra according to the broad spectral classes within the Morgan-Keenan system of spectral classification, based on estimated temperature and the relative abundances of certain notable elements (Hydrogen, Helium, etc.) in the stellar atmosphere. The methodology includes calibrating the wavelength for pixels across the image by using the wavelength dispersion of pixels inherent with the spectrograph used. It then calculates the location of the peak in the star's Planck spectrum in order to roughly classify the star. Fitting the graph to a blackbody curve is the final step for a correct classification. Future work will involve taking a closer look at emission lines and luminosity classes.

5. Spectral Methods for Time Dependent Problems

DTIC Science & Technology

1990-09-01

0,27r), s _u> We observe that bNw(x) is nothing but the trigonometric interpolant of w(x) at the equidis- tant points x = x,: N 2N i x I x¢V)(x).=x,. = E...trigonometric interpolation provides us with an excellent vehicle to perform approxi- mate discretizations with high (= spectral) accuracy, of...The pseudospectral approximation gives us an alternative procedure: construct the trigono- metric interpolant N 1 2N (1.2.20) OArw(x) = E i-v(k)e ’ x

6. Evaluation of AMOEBA: a spectral-spatial classification method

USGS Publications Warehouse

Jenson, Susan K.; Loveland, Thomas R.; Bryant, J.

1982-01-01

Muitispectral remotely sensed images have been treated as arbitrary multivariate spectral data for purposes of clustering and classifying. However, the spatial properties of image data can also be exploited. AMOEBA is a clustering and classification method that is based on a spatially derived model for image data. In an evaluation test, Landsat data were classified with both AMOEBA and a widely used spectral classifier. The test showed that irrigated crop types can be classified as accurately with the AMOEBA method as with the generally used spectral method ISOCLS; the AMOEBA method, however, requires less computer time.

7. A spectral and morphologic method for white blood cell classification

Wang, Qian; Chang, Li; Zhou, Mei; Li, Qingli; Liu, Hongying; Guo, Fangmin

2016-10-01

The identification of white blood cells is important as it provides an assay for diagnosis of various diseases. To overcome the complexity and inaccuracy of traditional methods based on light microscopy, we proposed a spectral and morphologic method based on hyperspectral blood images. We applied mathematical morphology-based methods to extract spatial information and supervised method is employed for spectral analysis. Experimental results show that white blood cells could be segmented and classified into five types with an overall accuracy of more than 90%. Moreover, the experiments including spectral features reached higher accuracy than the spatial-only cases, with a maximum improvement of nearly 20%. By combing both spatial and spectral features, the proposed method provides higher classification accuracy than traditional methods.

8. A Spectral Method for the Equal Width Equation

García-Archilla, Bosco

1996-05-01

A spectral discretization of the equal width equation (EWE) is presented. The method is shown to be convergent and nonlinearly stable. Time-stepping is performed with high-order Adams methods. The spectral accuracy of the scheme reveals some features of the EWE that the methods previously used could not bare out properly. For instance, we may now study the changes in amplitude and velocity of solitary waves after collisions.

9. Spectral analysis methods for automatic speech recognition applications

Parinam, Venkata Neelima Devi

In this thesis, we evaluate the front-end of Automatic Speech Recognition (ASR) systems, with respect to different types of spectral processing methods that are extensively used. A filter bank approach for front end spectral analysis is one of the common methods used for spectral analysis. In this work we describe and evaluate spectral analysis based on Mel and Gammatone filter banks. These filtering methods are derived from auditory models and are thought to have some advantages for automatic speech recognition work. Experimentally, however, we show that direct use of FFT spectral values is just as effective as using either Mel or Gammatone filter banks, provided that the features extracted from the FFT spectral values take into account a Mel or Mel-like frequency scale. It is also shown that trajectory features based on sliding block of spectral features, computed using either FFT or filter bank spectral analysis are considerably more effective, in terms of ASR accuracy, than are delta and delta-delta terms often used for ASR. Although there is no major performance disadvantage to using a filter bank, simplicity of analysis is a reason to eliminate this step in speech processing. These assertions hold for both clean and noisy speech.

10. Power Spectral Density Error Analysis of Spectral Subtraction Type of Speech Enhancement Methods

Händel, Peter

2006-12-01

A theoretical framework for analysis of speech enhancement algorithms is introduced for performance assessment of spectral subtraction type of methods. The quality of the enhanced speech is related to physical quantities of the speech and noise (such as stationarity time and spectral flatness), as well as to design variables of the noise suppressor. The derived theoretical results are compared with the outcome of subjective listening tests as well as successful design strategies, performed by independent research groups.

11. FNAS/Rapid Spectral Inversion Methods

NASA Technical Reports Server (NTRS)

Poularikas, Alexander

1997-01-01

The purpose of this investigation was to study methods and ways for rapid inversion programs involving the correlated k-method, and to study the infrared observations of Saturn from the Cassini orbiter.

12. Domain decomposition preconditioners for the spectral collocation method

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

13. Application of the Spectral Element Method to Acoustic Radiation

NASA Technical Reports Server (NTRS)

Doyle, James F.; Rizzi, Stephen A. (Technical Monitor)

2000-01-01

This report summarizes research to develop a capability for analysis of interior noise in enclosed structures when acoustically excited by an external random source. Of particular interest was the application to the study of noise and vibration transmission in thin-walled structures as typified by aircraft fuselages. Three related topics are focused upon. The first concerns the development of a curved frame spectral element, the second shows how the spectral element method for wave propagation in folded plate structures is extended to problems involving curved segmented plates. These are of significance because by combining these curved spectral elements with previously presented flat spectral elements, the dynamic response of geometrically complex structures can be determined. The third topic shows how spectral elements, which incorporate the effect of fluid loading on the structure, are developed for analyzing acoustic radiation from dynamically loaded extended plates.

14. Black hole evolution by spectral methods

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

2000-10-01

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

15. Research of spectral curvature correction method for hyperspectral images

Li, Lin; Hu, Yong; Wang, Yueming

2011-08-01

The hyperspectral imager is able to acquire space and spectral information of ground object simultaneously. When using a prism splitting mode, different wavelengths of light will disperse nonlinearly in spectral dimension after going through the slit and the prism. Due to the longer slit and different angles of incidence, when going through the slit and the prism, the same wavelength of light will curve in space dimension. For SWIR bands, the maximum shift is more than 1.5 bandwidth. The shift cannot be ignored, for is alters the pixel spectral and reduces match accuracies between space and spectral information. In this paper, a correction method of non-uniform spectral radiance in hyperspectral image is put forward. First, the laboratory spectral calibration is performed to acquire center wavelength and full width half maximum (FWHM) of each band as well as each pixel. Secondly, for each band, the mean of center wavelength which is calculated according to the results of the spectral calibration is regarded as each pixel's adjusted center wavelength. For each band and each pixel, calculate the ratio coefficient based on adjacent bands, then establish a ratio coefficient form of full pixels. At last, correct the image by looking up the form. By using MNF transformation, a corrected image can be well evaluated, a brightness gradient of the images has been removed and the phenomenon of image spectral radiance mixing has been reduced greatly, especially at the edge of the image.

16. The chain collocation method: A spectrally accurate calculus of forms

Rufat, Dzhelil; Mason, Gemma; Mullen, Patrick; Desbrun, Mathieu

2014-01-01

Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.

17. A combined Galerkin/collocation spectral method for transient solution of flow past a spherical droplet

SciTech Connect

Nguyen, H.D.; Paik, S. ); Chung, J.N. . Dept. of Mechanical and Materials Engineering)

1992-01-01

A spectral model, based on the stream function and vorticity, is developed in order to calculate the time-dependent solution of flow past a spherical droplet. Both Chebyshev and Legendre polynomials are used to expand the stream fiinction and vorticity in the radial and angular directions, respectively, along with the backward Euler approximation to advance in time. Consistent treatment of boundary conditions is made to resolve the lack of vorticity boundary conditions by means of the influence matrix technique. The computed flow field, the drag coefficient, and the interfacial velocity are presented for Reynolds numbers in the range from 0.5 to 50 for both continuous and dispersed phases with viscosity ratios of 1 and 3. Comparison of the present results to those found in the literature indicate that the model is capable of predicting the correct nature of the flow associated with a droplet.

18. Complex Chebyshev-polynomial-based unified model (CCPBUM) neural networks

Jeng, Jin-Tsong; Lee, Tsu-Tian

1998-03-01

In this paper, we propose complex Chebyshev Polynomial Based unified model neural network for the approximation of complex- valued function. Based on this approximate transformable technique, we have derived the relationship between the single-layered neural network and multi-layered perceptron neural network. It is shown that the complex Chebyshev Polynomial Based unified model neural network can be represented as a functional link network that are based on Chebyshev polynomial. We also derived a new learning algorithm for the proposed network. It turns out that the complex Chebyshev Polynomial Based unified model neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional complex feedforward/recurrent neural network.

19. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

20. Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains

Hatano, Naomichi; Feinberg, Joshua

2016-12-01

We study Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as a function of energy. For Hermitian models, the expansion produces this energy-dependent function numerically in one run of the algorithm. This is in strong contrast to the standard transfer-matrix method, which produces the inverse localization length for a fixed energy in each run. For non-Hermitian models, as in the transfer-matrix method, our algorithm computes the inverse localization length for a fixed (complex) energy. We also find a formula of the Chebyshev-polynomial expansion of the density of states of non-Hermitian models. As explained in detail, our algorithm for non-Hermitian models may be the only available efficient algorithm for finding the density of states of models with interactions.

1. Single-grid spectral collocation for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte

1988-01-01

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

2. The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

Borzov, V. V.; Damaskinsky, E. V.

2014-10-01

In the previous works of Borzov and Damaskinsky ["Chebyshev-Koornwinder oscillator," Theor. Math. Phys. 175(3), 765-772 (2013)] and ["Ladder operators for Chebyshev-Koornwinder oscillator," in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

3. The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

SciTech Connect

Borzov, V. V.; Damaskinsky, E. V.

2014-10-15

In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

4. Spectral methods for multiscale plasma-physics simulations

Delzanno, Gian Luca; Manzini, Gianmarco; Vencels, Juris; Markidis, Stefano; Roytershteyn, Vadim

2016-10-01

In this talk, we present the SpectralPlasmaSolver (SPS) simulation method for the numerical approximation of the Vlasov-Maxwell equations. SPS either uses spectral methods both in physical and velocity space or combines spectral methods for the velocity space and a Discontinuous Galerkin (DG) discretization in space. The spectral methods are based on generalized Hermite's functions or Legendre polynomials, thus resulting in a time-dependent hyperbolic system for the spectral coefficients. The DG method is applied to numerically solve this system after a characteristic decomposition that properly ensures the upwinding in the scheme. This numerical approach can be seen as a generalization of the method of moment expansion and makes it possible to incorporate microscopic kinetic effects in a macroscale fluid-like behavior. The numerical approximation error for a given computational cost and the computational costs for a prescribed accuracy are orders of magnitude less than those provided by the standard PIC method. Moreover, conservation of physical quantities like mass, momentum, and energy can be proved theoretically. Finally, numerical examples are shown to prove the effectiveness of the approach.

5. Spectral multigrid methods with applications to transonic potential flow

NASA Technical Reports Server (NTRS)

Streett, C. L.; Zang, T. A.; Hussaini, M. Y.

1983-01-01

Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil.

6. A Spectral Conjugate Gradient Method for Unconstrained Optimization

SciTech Connect

Birgin, E. G. Martinez, J. M.

2001-07-01

A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak-Ribiere and the Fletcher-Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented.

7. A note on spectral properties of some gradient methods

di Serafino, Daniela; Ruggiero, Valeria; Toraldo, Gerardo; Zanni, Luca

2016-10-01

Starting from the work by Barzilai and Borwein, gradient methods have gained a great amount of attention, and efficient low-cost schemes are available nowadays. The acceleration strategies used by these methods are based on the definition of effective steplength updating rules, which capture spectral properties of the Hessian of the objective function. The methods arising from this idea represent effective computational tools, extremely appealing for a variety of large-scale optimization problems arising in applications. In this work we discuss the spectral properties of some recently proposed gradient methods with the aim of providing insight into their computational effectiveness. Numerical experiments supporting and illustrating the theoretical analysis are provided.

8. Nonconforming mortar element methods: Application to spectral discretizations

NASA Technical Reports Server (NTRS)

Maday, Yvon; Mavriplis, Cathy; Patera, Anthony

1988-01-01

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

9. Spectral analysis method for detecting an element

DOEpatents

Blackwood, Larry G [Idaho Falls, ID; Edwards, Andrew J [Idaho Falls, ID; Jewell, James K [Idaho Falls, ID; Reber, Edward L [Idaho Falls, ID; Seabury, Edward H [Idaho Falls, ID

2008-02-12

A method for detecting an element is described and which includes the steps of providing a gamma-ray spectrum which has a region of interest which corresponds with a small amount of an element to be detected; providing nonparametric assumptions about a shape of the gamma-ray spectrum in the region of interest, and which would indicate the presence of the element to be detected; and applying a statistical test to the shape of the gamma-ray spectrum based upon the nonparametric assumptions to detect the small amount of the element to be detected.

10. Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.

PubMed

Xie, Jiaquan; Huang, Qingxue; Yang, Xia

2016-01-01

In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.

11. A novel variable resolution global spectral method on the sphere

Janakiraman, S.; Nanjundiah, Ravi S.; Vasudeva Murthy, A. S.

2012-04-01

A variable resolution global spectral method is created on the sphere using High resolution Tropical Belt Transformation (HTBT). HTBT belongs to a class of map called reparametrisation maps. HTBT parametrisation of the sphere generates a clustering of points in the entire tropical belt; the density of the grid point distribution decreases smoothly in the domain outside the tropics. This variable resolution method creates finer resolution in the tropics and coarser resolution at the poles. The use of FFT procedure and Gaussian quadrature for the spectral computations retains the numerical efficiency available with the standard global spectral method. Accuracy of the method for meteorological computations are demonstrated by solving Helmholtz equation and non-divergent barotropic vorticity equation on the sphere.

12. Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

13. Adaptive mesh strategies for the spectral element method

NASA Technical Reports Server (NTRS)

Mavriplis, Catherine

1992-01-01

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

14. [Physical meaning of temperature measured by spectral line intensity method].

PubMed

Zhao, Wen-Hua; Tang, Huang-Zai; Shen, Yan; Shi, Yong; Hou, Ling-Yun

2007-11-01

The difference between electron temperature and excitation temperature is analyzed in the aspect of statistics thermodynamics. It is presented clearly that the temperature acquired by spectral line intensity method is not free electron temperature, but internal electronic excitation temperature of heavy particle. Under thermal equilibrium condition, the excitation temperature is equal to the electron temperature, while under non-thermal equilibrium condition, the excitation temperature is not equal to the electron temperature. In the study of arc jet plume in vacuum chamber, spectral line intensity method was employed to measure the apparent excitation temperature of arc jet plume, and Langmuir probe was employed to measure the electron temperature of arcjet plume. The big difference between the excitation temperature and the electron temperature proved that the temperature acquired by spectral line intensity method is not free electron temperature.

15. Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

16. Non-Equilibrium Allele Frequency Spectra Via Spectral Methods

PubMed Central

Hey, Jody; Chen, Kevin

2011-01-01

A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related populations require high-performance algorithms to determine the likelihood of different demographic scenarios that could have shaped the observed neutral single nucleotide polymorphism (SNP) allele frequency spectrum. In many areas of applied mathematics, Fourier Transforms and Spectral Methods are firmly established tools to analyze spectra of signals and model their dynamics as solutions of certain Partial Differential Equations (PDEs). When spectral methods are applicable, they have excellent error properties and are the fastest possible in high dimension; see [15]. In this paper we present an explicit numerical solution, using spectral methods, to the forward Kolmogorov equations for a Wright-Fisher process with migration of K populations, influx of mutations, and multiple population splitting events. PMID:21376069

17. Spectral methods for the Euler equations. I - Fourier methods and shock capturing

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

1985-01-01

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collociation methods are put into historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock-capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem.

18. Spectral methods for the Euler equations: Fourier methods and shock-capturing

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

1984-01-01

Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one dimensional, periodic astrophysical ""nozzle'' problem.

19. High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Li, Weidong

2017-09-01

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

20. Methods for spectral image analysis by exploiting spatial simplicity

DOEpatents

Keenan, Michael R.

2010-05-25

Several full-spectrum imaging techniques have been introduced in recent years that promise to provide rapid and comprehensive chemical characterization of complex samples. One of the remaining obstacles to adopting these techniques for routine use is the difficulty of reducing the vast quantities of raw spectral data to meaningful chemical information. Multivariate factor analysis techniques, such as Principal Component Analysis and Alternating Least Squares-based Multivariate Curve Resolution, have proven effective for extracting the essential chemical information from high dimensional spectral image data sets into a limited number of components that describe the spectral characteristics and spatial distributions of the chemical species comprising the sample. There are many cases, however, in which those constraints are not effective and where alternative approaches may provide new analytical insights. For many cases of practical importance, imaged samples are "simple" in the sense that they consist of relatively discrete chemical phases. That is, at any given location, only one or a few of the chemical species comprising the entire sample have non-zero concentrations. The methods of spectral image analysis of the present invention exploit this simplicity in the spatial domain to make the resulting factor models more realistic. Therefore, more physically accurate and interpretable spectral and abundance components can be extracted from spectral images that have spatially simple structure.

1. Methods for spectral image analysis by exploiting spatial simplicity

DOEpatents

Keenan, Michael R.

2010-11-23

Several full-spectrum imaging techniques have been introduced in recent years that promise to provide rapid and comprehensive chemical characterization of complex samples. One of the remaining obstacles to adopting these techniques for routine use is the difficulty of reducing the vast quantities of raw spectral data to meaningful chemical information. Multivariate factor analysis techniques, such as Principal Component Analysis and Alternating Least Squares-based Multivariate Curve Resolution, have proven effective for extracting the essential chemical information from high dimensional spectral image data sets into a limited number of components that describe the spectral characteristics and spatial distributions of the chemical species comprising the sample. There are many cases, however, in which those constraints are not effective and where alternative approaches may provide new analytical insights. For many cases of practical importance, imaged samples are "simple" in the sense that they consist of relatively discrete chemical phases. That is, at any given location, only one or a few of the chemical species comprising the entire sample have non-zero concentrations. The methods of spectral image analysis of the present invention exploit this simplicity in the spatial domain to make the resulting factor models more realistic. Therefore, more physically accurate and interpretable spectral and abundance components can be extracted from spectral images that have spatially simple structure.

2. A new measuring method to determine material spectral emissivity

Smetana, W.; Reicher, R.

1998-05-01

Emissivity is a measure of how well a real surface can radiate energy as compared with a blackbody. This characteristic radiative number is usually determined by means of optical pyrometry. By contrast an indirect measurement method has been developed which enables the determination of the normal spectral emissivity of various materials at a specific wavelength. A heat flow induced in a test body by the absorbed irradiation of a laser beam may be correlated with the spectral emissivity of its surface. The theory of the measuring principle is discussed and the feasibility of the method evaluated by means of practical experiments utilizing a thermopile built up using a thick film technique.

3. Impact of computational methods and spectral models on the retrieval of optical properties via spectral optimization.

PubMed

Huang, Shaohui; Li, Yonghong; Shang, Shaoping; Shang, Shaoling

2013-03-11

Spectral optimization algorithm (SOA) is a well-accepted scheme for the retrieval of water constituents from the measurement of ocean color radiometry. It defines an error function between the input and output remote sensing reflectance spectrum, with the latter modeled with a few variables that represent the optically active properties, while the variables are solved numerically by minimizing the error function. In this paper, with data from numerical simulations and field measurements as input, we evaluate four computational methods for minimization (optimization) for their efficiency and accuracy on solutions, and illustrate impact of bio-optical models on the retrievals. The four optimization routines are the Levenberg-Marquardt (LM), the Generalized Reduced Gradient (GRG), the Downhill Simplex Method (Amoeba), and the Simulated Annealing-Downhill Simplex (i.e. SA + Amoeba, hereafter abbreviated as SAA). The Garver-Siegel-Maritorena SOA model is used as a base to test these computational methods. It is observed that 1) LM is the fastest method, but SAA has the largest number of valid retrievals; 2) the quality of final solutions are strongly influenced by the forms of spectral models (or eigen functions); and 3) dynamically-varying eigen functions are necessary to obtain smaller errors for both reflectance spectrum and retrievals. Results of this study provide helpful guidance for the selection of a computational method and spectral models if an SOA scheme is to be used to process ocean color images.

4. The spectral cell method in nonlinear earthquake modeling

Giraldo, Daniel; Restrepo, Doriam

2017-08-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3 ) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

5. Improvements in the spectral difference method for measuring ultrasonic attenuation.

PubMed

Insana, M; Zagzebski, J; Madsen, E

1983-10-01

The accuracy of the spectral difference method for measuring ultrasonic attenuation has been investigated using tissue-mimicking phantoms. Attenuation coefficients of the phantom materials were measured using a narrow-band substitution technique and compared with the results of the spectral difference method. Agreement within +/-10 percent was typical for measurements in homogeneous materials. The best agreement between the spectral difference and substitution techniques was obtained when effects due to transducer beam diffraction were taken into account in the analysis. This was found for two types of homogeneous tissue-mimicking materials, both having speed of sound and attenuation properties similar to human liver but each with different backscatter properties. The effects of inhomogeneous tissues interposed between the transducer and the interrogated volume were also studied by simulating these conditions in phantoms. Experimental techniques which minimize the effects of perturbations introduced by these inhomogeneities are suggested.

6. Spectral estimation of plasma fluctuations. I. Comparison of methods

SciTech Connect

Riedel, K.S.; Sidorenko, A. ); Thomson, D.J. )

1994-03-01

The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of the periodogram estimate by averaging the spectrum over a frequency bandwidth. As the bandwidth increases, the variance decreases, but the bias error increases. The plasma spectra vary by over four orders of magnitude, and therefore, using a spectral window is necessary. The smoothed tapered periodogram is compared with the adaptive multiple taper methods and hybrid methods. It is found that a hybrid method, which uses four orthogonal tapers and then applies a kernel smoother, performs best. For 300 point data segments, even an optimized smoothed tapered periodogram has a 24% larger relative RMSE than the hybrid method. Two new adaptive multitaper weightings which outperform Thomson's original adaptive weighting are presented.

7. The spectral-element method, Beowulf computing, and global seismology.

PubMed

Komatitsch, Dimitri; Ritsema, Jeroen; Tromp, Jeroen

2002-11-29

The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines. This combination of hardware and software enables us to simulate broadband seismograms without intrinsic restrictions on the level of heterogeneity or the frequency content.

8. Spectral anomaly methods for aerial detection using KUT nuisance rejection

Detwiler, R. S.; Pfund, D. M.; Myjak, M. J.; Kulisek, J. A.; Seifert, C. E.

2015-06-01

This work discusses the application and optimization of a spectral anomaly method for the real-time detection of gamma radiation sources from an aerial helicopter platform. Aerial detection presents several key challenges over ground-based detection. For one, larger and more rapid background fluctuations are typical due to higher speeds, larger field of view, and geographically induced background changes. As well, the possible large altitude or stand-off distance variations cause significant steps in background count rate as well as spectral changes due to increased gamma-ray scatter with detection at higher altitudes. The work here details the adaptation and optimization of the PNNL-developed algorithm Nuisance-Rejecting Spectral Comparison Ratios for Anomaly Detection (NSCRAD), a spectral anomaly method previously developed for ground-based applications, for an aerial platform. The algorithm has been optimized for two multi-detector systems; a NaI(Tl)-detector-based system and a CsI detector array. The optimization here details the adaptation of the spectral windows for a particular set of target sources to aerial detection and the tailoring for the specific detectors. As well, the methodology and results for background rejection methods optimized for the aerial gamma-ray detection using Potassium, Uranium and Thorium (KUT) nuisance rejection are shown. Results indicate that use of a realistic KUT nuisance rejection may eliminate metric rises due to background magnitude and spectral steps encountered in aerial detection due to altitude changes and geographically induced steps such as at land-water interfaces.

9. A TV-constrained decomposition method for spectral CT

Guo, Xiaoyue; Zhang, Li; Xing, Yuxiang

2017-03-01

Spectral CT is attracting more and more attention in medicine, industrial nondestructive testing and security inspection field. Material decomposition is an important issue to a spectral CT to discriminate materials. Because of the spectrum overlap of energy channels, as well as the correlation of basis functions, it is well acknowledged that decomposition step in spectral CT imaging causes noise amplification and artifacts in component coefficient images. In this work, we propose materials decomposition via an optimization method to improve the quality of decomposed coefficient images. On the basis of general optimization problem, total variance minimization is constrained on coefficient images in our overall objective function with adjustable weights. We solve this constrained optimization problem under the framework of ADMM. Validation on both a numerical dental phantom in simulation and a real phantom of pig leg on a practical CT system using dual-energy imaging is executed. Both numerical and physical experiments give visually obvious better reconstructions than a general direct inverse method. SNR and SSIM are adopted to quantitatively evaluate the image quality of decomposed component coefficients. All results demonstrate that the TV-constrained decomposition method performs well in reducing noise without losing spatial resolution so that improving the image quality. The method can be easily incorporated into different types of spectral imaging modalities, as well as for cases with energy channels more than two.

10. Coupling finite element and spectral methods: First results

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Debit, Naima; Maday, Yvon

1987-01-01

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

11. [An improved low spectral distortion PCA fusion method].

PubMed

Peng, Shi; Zhang, Ai-Wu; Li, Han-Lun; Hu, Shao-Xing; Meng, Xian-Gang; Sun, Wei-Dong

2013-10-01

Aiming at the spectral distortion produced in PCA fusion process, the present paper proposes an improved low spectral distortion PCA fusion method. This method uses NCUT (normalized cut) image segmentation algorithm to make a complex hyperspectral remote sensing image into multiple sub-images for increasing the separability of samples, which can weaken the spectral distortions of traditional PCA fusion; Pixels similarity weighting matrix and masks were produced by using graph theory and clustering theory. These masks are used to cut the hyperspectral image and high-resolution image into some sub-region objects. All corresponding sub-region objects between the hyperspectral image and high-resolution image are fused by using PCA method, and all sub-regional integration results are spliced together to produce a new image. In the experiment, Hyperion hyperspectral data and Rapid Eye data were used. And the experiment result shows that the proposed method has the same ability to enhance spatial resolution and greater ability to improve spectral fidelity performance.

12. Application of the Spectral Element Method to Interior Noise Problems

NASA Technical Reports Server (NTRS)

Doyle, James F.

1998-01-01

The primary effort of this research project was focused the development of analytical methods for the accurate prediction of structural acoustic noise and response. Of particular interest was the development of curved frame and shell spectral elements for the efficient computational of structural response and of schemes to match this to the surrounding fluid.

13. The convergence of spectral methods for nonlinear conservation laws

NASA Technical Reports Server (NTRS)

1987-01-01

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows.

14. Spectral method for obtaining three-dimensional magnetohydrodynamic equilibria

SciTech Connect

Hirshman, S.P.; Lee, D.K.

1985-07-01

A description is given of a new code, MOMCON (spectral moments with constraints), that obtains three-dimensional ideal magnetohydrodynamic (MHD) equilibria in a fixed toroidal domain using a Fourier expansion for the inverse coordinates (R,Z) representing nested magnetic surfaces. A set of nonlinear coupled ordinary differential equations for the spectral coefficients of (R,Z) is solved using an accelerated steepest descent method. A stream function lambda is introduced to improve the mode convergence properties of the Fourier series for R and Z. Constraint equations relating the m greater than or equal to 2 moments of R and Z are solved to define a unique poloidal angle.

15. Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

Khosravian-Arab, Hassan; Dehghan, Mehdi; Eslahchi, M. R.

2017-06-01

This paper is intended to provide exponentially accurate Galerkin, Petrov-Galerkin and pseudo-spectral methods for fractional differential equations on a semi-infinite interval. We start our discussion by introducing two new non-classical Lagrange basis functions: NLBFs-1 and NLBFs-2 which are based on the two new families of the associated Laguerre polynomials: GALFs-1 and GALFs-2 obtained recently by the authors in [28]. With respect to the NLBFs-1 and NLBFs-2, two new non-classical interpolants based on the associated- Laguerre-Gauss and Laguerre-Gauss-Radau points are introduced and then fractional (pseudo-spectral) differentiation (and integration) matrices are derived. Convergence and stability of the new interpolants are proved in detail. Several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives (and integrals) of some functions. Moreover, the pseudo-spectral, Galerkin and Petrov-Galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones. Some useful comments from the numerical point of view on Galerkin and Petrov-Galerkin methods are listed at the end.

16. Spectral curvature correction method based on inverse distance weighted interpolation

Jing, Juanjuan; Zhou, Jinsong; Li, Yacan; Feng, Lei

2016-10-01

Spectral curvature (smile effect) is universally existed in dispersive imaging spectrometer. Since most image processing systems considered all spatial pixels having the same wavelength, spectral curvature destroys the response consistence of the radiation energy in spatial dimension, it is necessary to correct the spectral curvature based on the spectral calibration data of the imaging spectrometer. Interpolation is widely used in resampling the measured spectra at the non-offset wavelength, but it is not versatile because the accuracy is different due to the spectral resolution changed. In the paper, we introduce the inverse distance weighted(IDW) method in spectrum resampling. First, calculate the Euclidean distance between the non-offset wavelength and the points near to it, the points number can be two, three, four or five, as many as you define. Then use the Euclidean distance to calculate the weight value of these points. Finally calculate the radiation of non-offset wavelength using the weight value and its corresponding radiation. The results turned out to be effective with the practical data acquired by the instrument, and it has the characteristics of versatility, simplicity, and fast.

17. Solving incompressible flow problems with parallel spectral element methods

SciTech Connect

Ma, Hong

1994-10-01

Parallel spectral element models are built for the Navier-Stokes equations and the shallow water equations with nonstaggered grid formulations. The optimized computational efficiency of these parallel spectral element models comes not only from the exponential convergence of their numerical solutions, but also from their efficient usage of the powerful vector-processing units of the latest parallel architectures. Furthermore, the communication cost of the spectral element model is lower than that of the h-type finite element model, partly because many fewer redundant nodal values have to be stored. The nonstaggered grid formulations perform well in iterative procedures which are highly in parallel. Implementations of these models are carried out on the Connection Machine systems. The present work shows that the high-order domain decomposition methods can be efficiently applied in a data parallel programming environment.

18. A review on spectral processing methods for geological remote sensing

2016-05-01

In this work, many of the fundamental and advanced spectral processing methods available to geologic remote sensing are reviewed. A novel categorization scheme is proposed that groups the techniques into knowledge-based and data-driven approaches, according to the type and availability of reference data. The two categories are compared and their characteristics and geologic outcomes are contrasted. Using an oil-sand sample scanned through the sisuCHEMA hyperspectral imaging system as a case study, the effectiveness of selected processing techniques from each category is demonstrated. The techniques used to bridge between the spectral data and other geoscience products are then discussed. Subsequently, the hybridization of the two approaches is shown to yield some of the most robust processing techniques available to multi- and hyperspectral remote sensing. Ultimately, current and future challenges that spectral analysis are expected to overcome and some potential trends are highlighted.

19. Spectral grouping using the Nyström method.

PubMed

Fowlkes, Charless; Belongie, Serge; Chung, Fan; Malik, Jitendra

2004-02-01

Spectral graph theoretic methods have recently shown great promise for the problem of image segmentation. However, due to the computational demands of these approaches, applications to large problems such as spatiotemporal data and high resolution imagery have been slow to appear. The contribution of this paper is a method that substantially reduces the computational requirements of grouping algorithms based on spectral partitioning making it feasible to apply them to very large grouping problems. Our approach is based on a technique for the numerical solution of eigenfunction problems known as the Nyström method. This method allows one to extrapolate the complete grouping solution using only a small number of samples. In doing so, we leverage the fact that there are far fewer coherent groups in a scene than pixels.

20. Friedmann's equations in all dimensions and Chebyshev's theorem

SciTech Connect

Chen, Shouxin; Gibbons, Gary W.; Li, Yijun; Yang, Yisong E-mail: gwg1@damtp.cam.ac.uk E-mail: yisongyang@nyu.edu

2014-12-01

This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time t and conformal time η of the Friedmann equations in all dimensions and with an arbitrary cosmological constant Λ. More precisely, it is shown that for spatially flat universes an explicit integration in t may always be carried out, and that, in the non-flat situation and when Λ is zero and the ratio w of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension n of space and w obey some specific relations among an infinite family. The situation for explicit integration in η is complementary to that in t. More precisely, it is shown in the flat-universe case with Λ ≠ 0 that an explicit integration in η can be carried out if and only if w and n obey similar relations among a well-defined family which we specify, and that, when Λ = 0, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.

1. Subroutines for convolution sums of Chebyshev and Fourier series

Delic, G.; Malherbe, S. M.

1988-02-01

Title of program: CCFS Catalogue number: ABBO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland (see application form in this issue) Computer: IBM 3083J24; Installation: University of the Witwatersrand Computer Centre Operating system: VM/SP HPO 4.2 Programming language used: FORTRAN VS LEVEL 1.4.1, LANGLVL (77) High speed storage required: 27412 bytes for OPT (0) compile No. of bits in a byte: 8 Peripherals used: card reader, line printer No. of cards in combined program and test deck: 682 Nature of the problem Numerical calculation of the coefficients for a single series obtained as the product of two series. Method of solution Application of standard results for Chebyshev polynomials and Fourier series. Restrictions on the complexity of the problem Length of the series is not limited in the subroutine package but is limited to 41 terms in the main driver, I/O and test programs. Typical running times Dependent on required range and accuracy: for the test cases it is 0.15 s.

2. Circulating tumor cell detection using photoacoustic spectral methods

Strohm, Eric M.; Berndl, Elizabeth S. L.; Kolios, Michael C.

2014-03-01

A method to detect and differentiate circulating melanoma tumor cells (CTCs) from blood cells using ultrasound and photoacoustic signals with frequencies over 100 MHz is presented. At these frequencies, the acoustic wavelength is similar to the dimensions of a cell, which results in unique features in the signal; periodically varying minima and maxima occur throughout the power spectrum. The spacing between minima depends on the ratio of the size to sound speed of the cell. Using a 532 nm pulsed laser and a 375 MHz center frequency wide-bandwidth transducer, the ultrasound and photoacoustic signals were measured from single cells. A total of 80 cells were measured, 20 melanoma cells, 20 white blood cells (WBCs) and 40 red blood cells (RBCs). The photoacoustic spectral spacing Δf between minima was 95 +/- 15 MHz for melanoma cells and greater than 230 MHz for RBCs. No photoacoustic signal was detected from WBCs. The ultrasonic spectral spacing between minima was 46 +/- 9 MHz for melanoma cells and 98 +/- 11 for WBCs. Both photoacoustic and ultrasound signals were detected from melanoma cells, while only ultrasound signals were detected from WBCs. RBCs showed distinct photoacoustic spectral variations in comparison to any other type of cell. Using the spectral spacing and signal amplitudes, each cell type could be grouped together to aid in cell identification. This method could be used for label-free counting and classifying cells in a sample.

3. Spectral element method implementation on GPU for Lamb wave simulation

Kudela, Pawel; Wandowski, Tomasz; Radzienski, Maciej; Ostachowicz, Wieslaw

2017-04-01

Parallel implementation of the time domain spectral element method on GPU (Graphics Processing Unit) is presented. The proposed spectral element method implementation is based on sparse matrix storage of local shape function derivatives calculated at Gauss-Lobatto-Legendre points. The algorithm utilizes two basic operations: multiplication of sparse matrix by vector and element-by-element vectors multiplication. Parallel processing is performed on the degree of freedom level. The assembly of resultant force is done by the aid of a mesh coloring algorithm. The implementation enables considerable computation speedup as well as a simulation of complex structural health monitoring systems based on anomalies of propagating Lamb waves. Hence, the complexity of various models can be tested and compared in order to be as close to reality as possible by using modern computers. A comparative example of a composite laminate modeling by using homogenization of material properties in one layer of 3D brick spectral elements with composite in which each ply is simulated by separate layer of 3D brick spectral elements is described. Consequences of application of each technique are explained. Further analysis is performed for composite laminate with delamination. In each case piezoelectric transducer as well as glue layer between actuator and host structure is modeled.

4. Effective numerical method of spectral analysis of quantum graphs

2017-05-01

We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrödinger operators with real-valued periodic electric potentials as Hamiltonians and with Kirchhoff and Neumann conditions at the vertices. Our method is based on the spectral parameter power series method, which leads to a series representation of the dispersion equation, which is suitable for both analytical and numerical calculations. Several important examples demonstrate the effectiveness of our method for some periodic graphs of interest that possess potentials usually found in quantum mechanics.

5. A Spectral Time-Domain Method for Computational Electrodynamics

Lambers, James V.

2009-09-01

We present a new approach to the numerical solution of Maxwell's equations in the case of spatially-varying electric permittivity and/or magnetic permeability, based on Krylov subspace spectral (KSS) methods. KSS methods for scalar equations compute each Fourier coefficient of the solution using techniques developed by Gene Golub and Gérard Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral, rather than physical, domain. We show how they can be generalized to coupled systems of equations, such as Maxwell's equations, by choosing appropriate basis functions that, while induced by this coupling, still allow efficient and robust computation of the Fourier coefficients of each spatial component of the electric and magnetic fields. We also discuss the implementation of appropriate boundary conditions for simulation on infinite computational domains, and how discontinuous coefficients can be handled.

6. Incompressible Spectral-Element Method-Derivation of Equations

DTIC Science & Technology

1993-04-01

expansion functions. Not all orthogonal expansion functions provide high accuracy; however, the eigenfunctions of a singlar Sturm - Liouville operator allow...orthogonal functions p(x), q(x), w(x) = functions in Sturm - Liouville equation P = p/p + IV-V, dynamic pressure Pn = a system of orthogonal polynomials of...truncated series in approximating functions. 1.2 Sturm - Liouville Problems The importance of Sturm - Liouville problems for spectral methods lies in the fact

7. Spectral methods and sum acceleration algorithms. Final report

SciTech Connect

Boyd, J.

1995-03-01

The principle investigator pursued his investigation of numerical algorithms during the period of the grant. The attached list of publications is so lengthy that it is impossible to describe them in detail. However, the author calls attention to the four articles on sequence acceleration and fourteen more on spectral methods, which fulfill the goals of the original proposal. He also continued his research on nonlinear waves, and wrote a dozen papers on this, too.

8. Spectral method for pricing options in illiquid markets

Pindza, Edson; Patidar, Kailash C.

2012-09-01

We present a robust numerical method to solve a problem of pricing options in illiquid markets. The governing equation is described by a nonlinear Black-Scholes partial differential equation (BS-PDE) of the reaction-diffusion-advection type. To discretise this BS-PDE numerically, we use a spectral method in the asset (spatial) direction and couple it with a fifth order RADAU method for the discretisation in the time direction. Numerical experiments illustrate that our approach is very efficient for pricing financial options in illiquid markets.

9. Terminal Convergence Approximation Modified Chebyshev Picard Iteration for Efficient Orbit Propagation

Probe, A.; Macomber, B.; Kim, D.; Woollands, R.; Junkins, J.

2014-09-01

Modified Chebyshev Picard Iteration (MCPI) is a numerical method for approximating solutions of Ordinary Differential Equations (ODEs). MCPI uses Picard Iteration with Orthogonal Chebyshev Polynomial basis functions to recursively update approximate time histories of system states. Unlike stepping numerical integrators, such as explicit Runge-Kutta methods, MCPI approximates large segments of the trajectory by evaluating the forcing function at multiple nodes along the current approximation during each iteration. Importantly, the Picard sequence theoretically converges to the solution over large time intervals if the forces are continuous and once differentiable. Orthogonality of the basis functions and a vector-matrix formulation allow for low overhead cost, efficient iterations, and parallel evaluation of the forcing function. Despite these advantages MCPI only achieves a geometric rate of convergence. Depending on the quality of the starting approximation, MCPI sometimes requires more function evaluations than competing methods; for parallel applications, this is not a serious drawback, but may be for some serial applications. To improve efficiency, the Terminal Convergence Approximation Modified Chebyshev Picard Iteration (TCA-MCPI) was developed. TCA-MCPI takes advantage of the property that once moderate accuracy of the approximating trajectory has been achieved, the subsequent displacement of nodes asymptotically approaches zero. Applying judicious approximation methods to the force function at each node in the terminal convergence iterations is shown to dramatically reduce the computational cost to achieve accurate convergence. To illustrate this approach we consider high-order spherical-harmonic gravity for high accuracy orbital propagation. When combined with a starting approximation from the 2-body solution TCA-MCPI, is shown to outperform 2 current state-of-practice integration methods for astrodynamics. This paper presents the development of TCA

10. Atomic spectral methods for molecular electronic structure calculations.

PubMed

Langhoff, P W; Boatz, J A; Hinde, R J; Sheehy, J A

2004-11-15

Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive

11. A plane rational map with Chebyshev-like dynamics

Liu, Han

This paper concerns a specific rational map of two complex variables whose dynamics are closely related to those of the well known one variable Chebyshev map. The goal is to obtain a complete description of the dynamics of the map, something that is rarely possible for such examples and then go on to study dynamics of some nearby perturbations.

12. Least-Squares Adaptive Control Using Chebyshev Orthogonal Polynomials

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Burken, John; Ishihara, Abraham

2011-01-01

This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.

13. Radon transforms and Gegenbauer-Chebyshev integrals, I

Rubin, Boris

2017-06-01

We suggest new modifications of the Helgason's support theorem and description of the kernel for the hyperplane Radon transform and its dual. The assumptions for functions are formulated in integral terms and close to minimal. The proofs rely on the properties of the Gegenbauer-Chebyshev integrals which generalize Abel type fractional integrals on the positive half-line.

14. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

15. An Improved Spectral Background Subtraction Method Based on Wavelet Energy.

PubMed

Zhao, Fengkui; Wang, Jian; Wang, Aimin

2016-12-01

Most spectral background subtraction methods rely on the difference in frequency response of background compared with characteristic peaks. It is difficult to extract accurately the background components from the spectrum when characteristic peaks and background have overlaps in frequency domain. An improved background estimation algorithm based on iterative wavelet transform (IWT) is presented. The wavelet entropy principle is used to select the best wavelet basis. A criterion based on wavelet energy theory to determine the optimal iteration times is proposed. The case of energy dispersive X-ray spectroscopy is discussed for illustration. A simulated spectrum with a prior known background and an experimental spectrum are tested. The processing results of the simulated spectrum is compared with non-IWT and it demonstrates the superiority of the IWT. It has great significance to improve the accuracy for spectral analysis.

16. Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

SciTech Connect

Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H.

1996-12-31

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

17. Adaptive Spectral Estimation Methods in Color Flow Imaging.

PubMed

Karabiyik, Yucel; Ekroll, Ingvild Kinn; Eik-Nes, Sturla H; Avdal, Jorgen; Lovstakken, Lasse

2016-11-01

Clutter rejection for color flow imaging (CFI) remains a challenge due to either a limited amount of temporal samples available or nonstationary tissue clutter. This is particularly the case for interleaved CFI and B-mode acquisitions. Low velocity blood signal is attenuated along with the clutter due to the long transition band of the available clutter filters, causing regions of biased mean velocity estimates or signal dropouts. This paper investigates how adaptive spectral estimation methods, Capon and blood iterative adaptive approach (BIAA), can be used to estimate the mean velocity in CFI without prior clutter filtering. The approach is based on confining the clutter signal in a narrow spectral region around the zero Doppler frequency while keeping the spectral side lobes below the blood signal level, allowing for the clutter signal to be removed by thresholding in the frequency domain. The proposed methods are evaluated using computer simulations, flow phantom experiments, and in vivo recordings from the common carotid and jugular vein of healthy volunteers. Capon and BIAA methods could estimate low blood velocities, which are normally attenuated by polynomial regression filters, and may potentially give better estimation of mean velocities for CFI at a higher computational cost. The Capon method decreased the bias by 81% in the transition band of the used polynomial regression filter for small packet size ( N=8 ) and low SNR (5 dB). Flow phantom and in vivo results demonstrate that the Capon method can provide color flow images and flow profiles with lower variance and bias especially in the regions close to the artery walls.

18. Adaptive Spectral Estimation Methods in Color Flow Imaging.

PubMed

Karabiyik, Yucel; Ekroll, Ingvild Kinn; Eik-Nes, Sturla; Avdal, Jorgen; Lovstakken, Lasse

2016-07-28

Clutter rejection for color flow imaging (CFI) remains a challenge due to either limited amount of temporal samples available or non-stationary tissue clutter. This is particularly the case for interleaved CFI and B-mode acquisitions. Low velocity blood signal is attenuated along with the clutter due to the long transition band of the available clutter filters, causing regions of biased mean velocity estimates or signal dropouts. This work investigates how adaptive spectral estimation methods, the Capon and BIAA, can be used to estimate the mean velocity in CFI without prior clutter filtering. The approach is based on confining the clutter signal in a narrow spectral region around the zero Doppler frequency while keeping the spectral side lobes below the blood signal level, allowing for the clutter signal to be removed by thresholding in the frequency domain. The proposed methods are evaluated using computer simulations, flow phantom experiments and in-vivo recordings from the common carotid and jugular vein of healthy volunteers. Capon and BIAA methods could estimate low blood velocities which are normally attenuated by polynomial regression filters, and may potentially give better estimation of mean velocities for CFI at a higher computational cost. The Capon method decreased the bias by 81% in the transition band of the used polynomial regression filter for small packet size (N=8) and low SNR (5 dB). Flow phantom and invivo results demonstrate that the Capon method can provide color flow images and flow profiles with lower variance and bias especially in the regions close to the artery walls.

19. Spectral analysis of mammographic images using a multitaper method

SciTech Connect

Wu Gang; Mainprize, James G.; Yaffe, Martin J.

2012-02-15

Purpose: Power spectral analysis in radiographic images is conventionally performed using a windowed overlapping averaging periodogram. This study describes an alternative approach using a multitaper technique and compares its performance with that of the standard method. This tool will be valuable in power spectrum estimation of images, whose content deviates significantly from uniform white noise. The performance of the multitaper approach will be evaluated in terms of spectral stability, variance reduction, bias, and frequency precision. The ultimate goal is the development of a useful tool for image quality assurance. Methods: A multitaper approach uses successive data windows of increasing order. This mitigates spectral leakage allowing one to calculate a reduced-variance power spectrum. The multitaper approach will be compared with the conventional power spectrum method in several typical situations, including the noise power spectra (NPS) measurements of simulated projection images of a uniform phantom, NPS measurement of real detector images of a uniform phantom for two clinical digital mammography systems, and the estimation of the anatomic noise in mammographic images (simulated images and clinical mammograms). Results: Examination of spectrum variance versus frequency resolution and bias indicates that the multitaper approach is superior to the conventional single taper methods in the prevention of spectrum leakage and variance reduction. More than four times finer frequency precision can be achieved with equivalent or less variance and bias. Conclusions: Without any shortening of the image data length, the bias is smaller and the frequency resolution is higher with the multitaper method, and the need to compromise in the choice of regions of interest size to balance between the reduction of variance and the loss of frequency resolution is largely eliminated.

20. Application of Block Krylov Subspace Spectral Methods to Maxwell's Equations

Lambers, James V.

2009-10-01

Ever since its introduction by Kane Yee over forty years ago, the finite-difference time-domain (FDTD) method has been a widely-used technique for solving the time-dependent Maxwell's equations. This paper presents an alternative approach to these equations in the case of spatially-varying electric permittivity and/or magnetic permeability, based on Krylov subspace spectral (KSS) methods. These methods have previously been applied to the variable-coefficient heat equation and wave equation, and have demonstrated high-order accuracy, as well as stability characteristic of implicit time-stepping schemes, even though KSS methods are explicit. KSS methods for scalar equations compute each Fourier coefficient of the solution using techniques developed by Gene Golub and Gérard Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral, rather than physical, domain. We show how they can be generalized to coupled systems of equations, such as Maxwell's equations, by choosing appropriate basis functions that, while induced by this coupling, still allow efficient and robust computation of the Fourier coefficients of each spatial component of the electric and magnetic fields. We also discuss the implementation of appropriate boundary conditions for simulation on infinite computational domains, and how discontinuous coefficients can be handled.

1. Application of Block Krylov Subspace Spectral Methods to Maxwell's Equations

SciTech Connect

Lambers, James V.

2009-10-08

Ever since its introduction by Kane Yee over forty years ago, the finite-difference time-domain (FDTD) method has been a widely-used technique for solving the time-dependent Maxwell's equations. This paper presents an alternative approach to these equations in the case of spatially-varying electric permittivity and/or magnetic permeability, based on Krylov subspace spectral (KSS) methods. These methods have previously been applied to the variable-coefficient heat equation and wave equation, and have demonstrated high-order accuracy, as well as stability characteristic of implicit time-stepping schemes, even though KSS methods are explicit. KSS methods for scalar equations compute each Fourier coefficient of the solution using techniques developed by Gene Golub and Gerard Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral, rather than physical, domain. We show how they can be generalized to coupled systems of equations, such as Maxwell's equations, by choosing appropriate basis functions that, while induced by this coupling, still allow efficient and robust computation of the Fourier coefficients of each spatial component of the electric and magnetic fields. We also discuss the implementation of appropriate boundary conditions for simulation on infinite computational domains, and how discontinuous coefficients can be handled.

2. A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

3. High temperature spectral emissivity measurement using integral blackbody method

Pan, Yijie; Dong, Wei; Lin, Hong; Yuan, Zundong; Bloembergen, Pieter

2016-10-01

Spectral emissivity is a critical material's thermos-physical property for heat design and radiation thermometry. A prototype instrument based upon an integral blackbody method was developed to measure material's spectral emissivity above 1000 °. The system was implemented with an optimized commercial variable-high-temperature blackbody, a high speed linear actuator, a linear pyrometer, and an in-house designed synchronization circuit. A sample was placed in a crucible at the bottom of the blackbody furnace, by which the sample and the tube formed a simulated blackbody which had an effective total emissivity greater than 0.985. During the measurement, the sample was pushed to the end opening of the tube by a graphite rod which was actuated through a pneumatic cylinder. A linear pyrometer was used to monitor the brightness temperature of the sample surface through the measurement. The corresponding opto-converted voltage signal was fed and recorded by a digital multi-meter. A physical model was proposed to numerically evaluate the temperature drop along the process. Tube was discretized as several isothermal cylindrical rings, and the temperature profile of the tube was measurement. View factors between sample and rings were calculated and updated along the whole pushing process. The actual surface temperature of the sample at the end opening was obtained. Taking advantages of the above measured voltage profile and the calculated true temperature, spectral emissivity under this temperature point was calculated.

4. Tomographic fluorescence reconstruction by a spectral projected gradient pursuit method

Ye, Jinzuo; An, Yu; Mao, Yamin; Jiang, Shixin; Yang, Xin; Chi, Chongwei; Tian, Jie

2015-03-01

In vivo fluorescence molecular imaging (FMI) has played an increasingly important role in biomedical research of preclinical area. Fluorescence molecular tomography (FMT) further upgrades the two-dimensional FMI optical information to three-dimensional fluorescent source distribution, which can greatly facilitate applications in related studies. However, FMT presents a challenging inverse problem which is quite ill-posed and ill-conditioned. Continuous efforts to develop more practical and efficient methods for FMT reconstruction are still needed. In this paper, a method based on spectral projected gradient pursuit (SPGP) has been proposed for FMT reconstruction. The proposed method was based on the directional pursuit framework. A mathematical strategy named the nonmonotone line search was associated with the SPGP method, which guaranteed the global convergence. In addition, the Barzilai-Borwein step length was utilized to build the new step length of the SPGP method, which was able to speed up the convergence of this gradient method. To evaluate the performance of the proposed method, several heterogeneous simulation experiments including multisource cases as well as comparative analyses have been conducted. The results demonstrated that, the proposed method was able to achieve satisfactory source localizations with a bias less than 1 mm; the computational efficiency of the method was one order of magnitude faster than the contrast method; and the fluorescence reconstructed by the proposed method had a higher contrast to the background than the contrast method. All the results demonstrated the potential for practical FMT applications with the proposed method.

5. A spectral method for spatial downscaling | Science Inventory ...

EPA Pesticide Factsheets

Complex computer models play a crucial role in air quality research. These models are used to evaluate potential regulatory impacts of emission control strategies and to estimate air quality in areas without monitoring data. For both of these purposes, it is important to calibrate model output with monitoring data to adjust for model biases and improve spatial prediction. In this paper, we propose a new spectral method to study and exploit complex relationships between model output and monitoring data. Spectral methods allow us to estimate the relationship between model output and monitoring data separately at different spatial scales, and to use model output for prediction only at the appropriate scales. The proposed method is computationally efficient and can be implemented using standard software. We apply the method to compare Community Multiscale Air Quality (CMAQ) model output with ozone measurements in the United States in July, 2005. We find that CMAQ captures large-scale spatial trends, but has low correlation with the monitoring data at small spatial scales. The National Exposure Research Laboratory′s (NERL′s)Atmospheric Modeling Division (AMAD) conducts research in support of EPA′s mission to protect human health and the environment. AMAD′s research program is engaged in developing and evaluating predictive atmospheric models on all spatial and temporal scales for forecasting the Nation′s air quality and for assessing ch

6. Time spectral method for rotorcraft flow with vorticity confinement

Butsuntorn, Nawee

2008-10-01

This thesis shows that simulation of helicopter flows can adhere to engineering accuracy without the need of massive computing resources or long turnaround time by choosing an alternative framework for rotorcraft simulation. The method works in both hovering and forward flight regimes. The new method has shown to be more computationally efficient and sufficiently accurate. By utilizing the periodic nature of the rotorcraft flow field, the Fourier based Time Spectral method lends itself to the problem and significantly increases the rate of convergence compared to traditional implicit time integration schemes such as the second order backward difference formula (BDF). A Vorticity Confinement method has been explored and has been shown to work well in subsonic and transonic simulations. Vortical structure can be maintained after long distances without resorting to the traditional mesh refinement technique.

7. Regularized discriminative spectral regression method for heterogeneous face matching.

PubMed

Huang, Xiangsheng; Lei, Zhen; Fan, Mingyu; Wang, Xiao; Li, Stan Z

2013-01-01

Face recognition is confronted with situations in which face images are captured in various modalities, such as the visual modality, the near infrared modality, and the sketch modality. This is known as heterogeneous face recognition. To solve this problem, we propose a new method called discriminative spectral regression (DSR). The DSR maps heterogeneous face images into a common discriminative subspace in which robust classification can be achieved. In the proposed method, the subspace learning problem is transformed into a least squares problem. Different mappings should map heterogeneous images from the same class close to each other, while images from different classes should be separated as far as possible. To realize this, we introduce two novel regularization terms, which reflect the category relationships among data, into the least squares approach. Experiments conducted on two heterogeneous face databases validate the superiority of the proposed method over the previous methods.

8. PSD computations using Welch's method. [Power Spectral Density (PSD)

SciTech Connect

Solomon, Jr, O M

1991-12-01

This report describes Welch's method for computing Power Spectral Densities (PSDs). We first describe the bandpass filter method which uses filtering, squaring, and averaging operations to estimate a PSD. Second, we delineate the relationship of Welch's method to the bandpass filter method. Third, the frequency domain signal-to-noise ratio for a sine wave in white noise is derived. This derivation includes the computation of the noise floor due to quantization noise. The signal-to-noise ratio and noise flood depend on the FFT length and window. Fourth, the variance the Welch's PSD is discussed via chi-square random variables and degrees of freedom. This report contains many examples, figures and tables to illustrate the concepts. 26 refs.

9. Spatial-spectral method for classification of hyperspectral images.

PubMed

Bian, Xiaoyong; Zhang, Tianxu; Yan, Luxin; Zhang, Xiaolong; Fang, Houzhang; Liu, Hai

2013-03-15

Spatial-spectral approach with spatially adaptive classification of hyperspectral images is proposed. The rotation-invariant spatial texture information for each object is exploited and incorporated into the classifier by using the modified local Gabor binary pattern to distinguish different types of classes of interest. The proposed method can effectively suppress anisotropic texture in spatially separate classes as well as improve the discrimination among classes. Moreover, it becomes more robust with the within-class variation. Experimental results on the classification of three real hyperspectral remote sensing images demonstrate the effectiveness of the proposed approach.

10. Method for evaluating moisture tensions of soils using spectral data

NASA Technical Reports Server (NTRS)

Peterson, John B. (Inventor)

1982-01-01

A method is disclosed which permits evaluation of soil moisture utilizing remote sensing. Spectral measurements at a plurality of different wavelengths are taken with respect to sample soils and the bidirectional reflectance factor (BRF) measurements produced are submitted to regression analysis for development therefrom of predictable equations calculated for orderly relationships. Soil of unknown reflective and unknown soil moisture tension is thereafter analyzed for bidirectional reflectance and the resulting data utilized to determine the soil moisture tension of the soil as well as providing a prediction as to the bidirectional reflectance of the soil at other moisture tensions.

11. A Fourier-Legendre spectral element method in polar coordinates

Qiu, Zhouhua; Zeng, Zhong; Mei, Huan; Li, Liang; Yao, Liping; Zhang, Liangqi

2012-01-01

In this paper, a new Fourier-Legendre spectral element method based on the Galerkin formulation is proposed to solve the Poisson-type equations in polar coordinates. The 1/ r singularity at r = 0 is avoided by using Gauss-Radau type quadrature points. In order to break the time-step restriction in the time-dependent problems, the clustering of collocation points near the pole is prevented through the technique of domain decomposition in the radial direction. A number of Poisson-type equations subject to the Dirichlet or Neumann boundary condition are computed and compared with the results in literature, which reveals a desirable result.

12. Thermoacoustic tomography forward modeling with the spectral element method.

PubMed

Lim, Kim Hwa; Lee, Joon-Ho; Liu, Qing Huo

2008-01-01

A thermoacoustic tomography (TAT) forward solver based on the spectral element method (SEM) with perfectly matched layer absorbing boundary condition has been developed. The TAT forward solver is intended to model acoustically inhomogeneous media with high accuracy in the frequency domain. The high-order basis functions used in the SEM are Gauss-Lobatto-Legendre (GLL) polynomials. Due to the orthogonality of the GLL basis functions and GLL quadrature integration, the mass matrix is diagonal and the stiffness matrix is sparse. Thus, the proposed method greatly reduces the memory requirement and computational time in comparison with the conventional finite element method (FEM). Numerical results show that the high-order SEM is able to achieve the same accuracy as the FEM but with a much smaller number of unknowns. Therefore, the TAT forward solver based on SEM is able to simulate a large-scale and realistic TAT problem.

13. Near-infrared spectral methods for noninvasively measuring blood glucose

Fei, Sun; Kong, Deyi; Mei, Tao; Tao, Yongchun

2004-05-01

Determination of blood glucose concentrations in diabetic patients is a frequently occurring procedure and an important tool for diabetes management. Use of noninvasive detection techniques can relieve patients from the pain of frequent finger pokes and avoid the infection of disease via blood. This thesis discusses current research and analyzes the advantages and shortages of different measurement methods, including: optical methods (Transmission, Polarimetry and scattering), then, we give emphasis to analyze the technology of near-infrared (NIR) spectra. NIR spectral range 700 nm ~2300 nm was used because of its good transparency for biological tissue and presence of glucose absorption band. In this work, we present an outline of noninvasive blood glucose measurement. A near-infrared light beam is passed through the finger, and the spectral components of the emergent beam are measured using spectroscopic techniques. The device includes light sources having the wavelengths of 600 nm - 1800 nm to illuminate the tissue. Receptors associated with the light sources for receiving light and generating a transmission signal representing the light transmitted are also provided. Once a transmission signal is received by receptors, and the high and low values from each of the signals are stored in the device. The averaged values are then analyzed to determine the glucose concentration, which is displayed on the device.

14. 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.

15. The Spectral Ewald method for singly periodic domains

Saffar Shamshirgar, Davoud; Tornberg, Anna-Karin

2017-10-01

We present a fast and spectrally accurate method for efficient computation of the three dimensional Coulomb potential with periodicity in one direction. The algorithm is FFT-based and uses the so-called Ewald decomposition, which is naturally most efficient for the triply periodic case. In this paper, we show how to extend the triply periodic Spectral Ewald method to the singly periodic case, such that the cost of computing the singly periodic potential is only marginally larger than the cost of computing the potential for the corresponding triply periodic system. In the Fourier space contribution of the Ewald decomposition, a Fourier series is obtained in the periodic direction with a Fourier integral over the non-periodic directions for each discrete wave number. We show that upsampling to resolve the integral is only needed for modes with small wave numbers. For the zero wave number, this Fourier integral has a singularity. For this mode, we effectively need to solve a free-space Poisson equation in two dimensions. A very recent idea by Vico et al. makes it possible to use FFTs to solve this problem, allowing us to unify the treatment of all modes. An adaptive 3D FFT can be established to apply different upsampling rates locally. The computational cost for other parts of the algorithm is essentially unchanged as compared to the triply periodic case, in total yielding only a small increase in both computational cost and memory usage for this singly periodic case.

16. Fourier time spectral method for subsonic and transonic flows

Zhan, Lei; Liu, Feng; Papamoschou, Dimitri

2016-06-01

The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

17. An improved Chebyshev distance metric for clustering medical images

Mousa, Aseel; Yusof, Yuhanis

2015-12-01

A metric or distance function is a function which defines a distance between elements of a set. In clustering, measuring the similarity between objects has become an important issue. In practice, there are various similarity measures used and this includes the Euclidean, Manhattan and Minkowski. In this paper, an improved Chebyshev similarity measure is introduced to replace existing metrics (such as Euclidean and standard Chebyshev) in clustering analysis. The proposed measure is later realized in analyzing blood cancer images. Results demonstrate that the proposed measure produces the smallest objective function value and converge at the lowest number of iteration. Hence, it can be concluded that the proposed distance metric contribute in producing better clusters.

18. Spectral ordering techniques for incomplete LU preconditoners for CG methods

NASA Technical Reports Server (NTRS)

Clift, Simon S.; Simon, Horst D.; Tang, Wei-Pai

1995-01-01

The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.

19. Spectral methods applied to fluidized-bed combustors

SciTech Connect

Brown, R.C.; Raines, T.S.; Thiede, T.D.

1995-11-01

The goal of this research is to characterize coals and sorbents during the normal operation of an industrial-scale circulating fluidized bed (CFB) boiler. The method determines coal or sorbent properties based on the analysis of transient CO{sub 2} or SO{sub 2} emissions from the boiler. Fourier Transform Infrared (FTIR) spectroscopy is used to qualitatively and quantitatively analyze the gaseous products of combustion. Spectral analysis applied to the transient response of CO{sub 2} and SO{sub 2} resulting from introduction of a batch of coal or limestone into the boiler yields characteristic time constants from which combustion or sorbent models are developed. The method is non-intrusive and is performed under realistic combustion conditions. Results are presented from laboratory studies and power plant monitoring.

20. A Data Transfer Fusion Method for Discriminating Similar Spectral Classes

PubMed Central

Wang, Qingyan; Zhang, Junping

2016-01-01

Hyperspectral data provide new capabilities for discriminating spectrally similar classes, but such class signatures sometimes will be difficult to analyze. To incorporate reliable useful information could help, but at the same time, may also lead increased dimensionality of the feature vector making the hyperspectral data larger than expected. It is challenging to apply discriminative information from these training data to testing data that are not in the same feature space and with different data distributions. A data fusion method based on transfer learning is proposed, in which transfer learning is introduced into boosting algorithm, and other out-date data are used to instruct hyperspectral image classification. In order to validate the method, experiments are conducted on EO-1 Hyperion hyperspectral data and ROSIS hyperspectral data. Significant improvements have been achieved in terms of accuracy compared to the results generated by conventional classification approaches. PMID:27854238

1. Spectral analysis methods for vehicle interior vibro-acoustics identification

2009-02-01

Noise has various effects on comfort, performance and health of human. Sound are analysed by human brain based on the frequencies and amplitudes. In a dynamic system, transmission of sound and vibrations depend on frequency and direction of the input motion and characteristics of the output. It is imperative that automotive manufacturers invest a lot of effort and money to improve and enhance the vibro-acoustics performance of their products. The enhancement effort may be very difficult and time-consuming if one relies only on 'trial and error' method without prior knowledge about the sources itself. Complex noise inside a vehicle cabin originated from various sources and travel through many pathways. First stage of sound quality refinement is to find the source. It is vital for automotive engineers to identify the dominant noise sources such as engine noise, exhaust noise and noise due to vibration transmission inside of vehicle. The purpose of this paper is to find the vibro-acoustical sources of noise in a passenger vehicle compartment. The implementation of spectral analysis method is much faster than the 'trial and error' methods in which, parts should be separated to measure the transfer functions. Also by using spectral analysis method, signals can be recorded in real operational conditions which conduce to more consistent results. A multi-channel analyser is utilised to measure and record the vibro-acoustical signals. Computational algorithms are also employed to identify contribution of various sources towards the measured interior signal. These achievements can be utilised to detect, control and optimise interior noise performance of road transport vehicles.

2. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of

3. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of

4. Spectral Sensitivity Measured with Electroretinogram Using a Constant Response Method

PubMed Central

Rocha, Fernando Allan de Farias; Gomes, Bruno Duarte; Silveira, Luiz Carlos de Lima; Martins, Sonia Limara; Aguiar, Renata Genaro; de Souza, John Manuel; Ventura, Dora Fix

2016-01-01

A new method is presented to determine the retinal spectral sensitivity function S(λ) using the electroretinogram (ERG). S(λ)s were assessed in three different species of myomorph rodents, Gerbils (Meriones unguiculatus), Wistar rats (Ratus norvegicus), and mice (Mus musculus). The method, called AC Constant Method, is based on a computerized automatic feedback system that adjusts light intensity to maintain a constant-response amplitude to a flickering stimulus throughout the spectrum, as it is scanned from 300 to 700 nm, and back. The results are presented as the reciprocal of the intensity at each wavelength required to maintain a constant peak to peak response amplitude. The resulting S(λ) had two peaks in all three rodent species, corresponding to ultraviolet and M cones, respectively: 359 nm and 511 nm for mice, 362 nm and 493 nm for gerbils, and 362 nm and 502 nm for rats. Results for mouse and gerbil were similar to literature reports of S(λ) functions obtained with other methods, confirming that the ERG associated to the AC Constant-Response Method was effective to obtain reliable S(λ) functions. In addition, due to its fast data collection time, the AC Constant Response Method has the advantage of keeping the eye in a constant light adapted state. PMID:26800521

5. Bivariate Chebyshev Expansion of the Pacejka's Tyre Model

López, Alberto; Vélez, Pilar; Moriano, Cristina

2007-09-01

Pacejka's tyre model is widely used and well-known by the community of automotive engineers. The magic formula basically describes the brake force, side force and self-aligning torque in terms of the longitudinal slip and slip angle, with corrections due to the variation of the load force and camber angle. Obtaining continuous approximate solutions in Chebyshev series expansions of full vehicle dynamics can help in the real time solving of vehicle equations, for collision avoidance purposes. We contribute to solve the specific problem of the tyre's model expansion and its integration with the longitudinal, lateral and vertical behaviour of the car. The present work describes the approximation of the magic formula with Chebyshev's series development of rational polynomials, maintaining a moderate error of the model respect to the original formula, with a triple objective: firstly to obtain a very fast processing of the formula, secondly to allow the inclusion of the formula in DAE systems of vehicular dynamic modelling solved continuously, not numerically, by means of the expansion of the complete system in Chebyshev's series, and thirdly, the final expressions can be evaluated, integrated and derived easily.

6. A new automated spectral feature extraction method and its application in spectral classification and defective spectra recovery

Wang, Ke; Guo, Ping; Luo, A.-Li

2017-03-01

Spectral feature extraction is a crucial procedure in automated spectral analysis. This procedure starts from the spectral data and produces informative and non-redundant features, facilitating the subsequent automated processing and analysis with machine-learning and data-mining techniques. In this paper, we present a new automated feature extraction method for astronomical spectra, with application in spectral classification and defective spectra recovery. The basic idea of our approach is to train a deep neural network to extract features of spectra with different levels of abstraction in different layers. The deep neural network is trained with a fast layer-wise learning algorithm in an analytical way without any iterative optimization procedure. We evaluate the performance of the proposed scheme on real-world spectral data. The results demonstrate that our method is superior regarding its comprehensive performance, and the computational cost is significantly lower than that for other methods. The proposed method can be regarded as a new valid alternative general-purpose feature extraction method for various tasks in spectral data analysis.

7. How Accurately Do Spectral Methods Estimate Effective Elastic Thickness?

Perez-Gussinye, M.; Lowry, A. R.; Watts, A. B.; Velicogna, I.

2002-12-01

The effective elastic thickness, Te, is an important parameter that has the potential to provide information on the long-term thermal and mechanical properties of the the lithosphere. Previous studies have estimated Te using both forward and inverse (spectral) methods. While there is generally good agreement between the results obtained using these methods, spectral methods are limited because they depend on the spectral estimator and the window size chosen for analysis. In order to address this problem, we have used a multitaper technique which yields optimal estimates of the bias and variance of the Bouguer coherence function relating topography and gravity anomaly data. The technique has been tested using realistic synthetic topography and gravity. Synthetic data were generated assuming surface and sub-surface (buried) loading of an elastic plate with fractal statistics consistent with real data sets. The cases of uniform and spatially varying Te are examined. The topography and gravity anomaly data consist of 2000x2000 km grids sampled at 8 km interval. The bias in the Te estimate is assessed from the difference between the true Te value and the mean from analyzing 100 overlapping windows within the 2000x2000 km data grids. For the case in which Te is uniform, the bias and variance decrease with window size and increase with increasing true Te value. In the case of a spatially varying Te, however, there is a trade-off between spatial resolution and variance. With increasing window size the variance of the Te estimate decreases, but the spatial changes in Te are smeared out. We find that for a Te distribution consisting of a strong central circular region of Te=50 km (radius 600 km) and progressively smaller Te towards its edges, the 800x800 and 1000x1000 km window gave the best compromise between spatial resolution and variance. Our studies demonstrate that assumed stationarity of the relationship between gravity and topography data yields good results even in

8. 1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind

Dragoljub Pavlović, Vlastimir; Stanojko Dončov, Nebojša; Gradimir Ćirić, Dejan

2013-11-01

Christoffel-Darboux formula for Chebyshev continual orthogonal polynomials of the first kind is proposed to find a mathematical solution of approximation problem of a one-dimensional (1D) filter function in the z domain. Such an approach allows for the generation of a linear phase selective 1D low-pass digital finite impulse response (FIR) filter function in compact explicit form by using an analytical method. A new difference equation and structure of corresponding linear phase 1D low-pass digital FIR filter are given here. As an example, one extremely economic 1D FIR filter (with four adders and without multipliers) is designed by the proposed technique and its characteristics are presented. Global Christoffel-Darboux formula for orthonormal Chebyshev polynomials of the first kind and for two independent variables for generating linear phase symmetric two-dimensional (2D) FIR digital filter functions in a compact explicit representative form, by using an analytical method, is proposed in this paper. The formula can be most directly applied for mathematically solving the approximation problem of a filter function of even and odd order. Examples of a new class of extremely economic linear phase symmetric selective 2D FIR digital filters obtained by the proposed approximation technique are presented.

9. Scalable implementation of spectral methods for the Dirac equation

SciTech Connect

Wells, J.C.

1998-10-01

The author discusses the implementation and performance on massively parallel, distributed-memory computers of a message-passing program to solve the time-dependent dirac equation in three Cartesian coordinates. Luses pseudo-spectral methods to obtain a discrete representation of the dirac spinor wavefunction and all coordinate-space operators. Algorithms for the solution of the discrete equations are iterative and depend critically on the dirac hamiltonian-wavefunction product, which he implements as a series of parallel matrix products using MPI. He investigated two communication algorithms, a ring algorithm and a collective-communication algorithm, and present performance results for each on a Paragon-MP (1024 nodes) and a Cray T3E-900 (512 nodes). The ring algorithm achieves very good performance, scaling up to the maximum number of nodes on each machine. However, the collective-communication algorithm scales effectively only on the Paragon.

10. Propane spectral resolution enhancement by the maximum entropy method

NASA Technical Reports Server (NTRS)

Bonavito, N. L.; Stewart, K. P.; Hurley, E. J.; Yeh, K. C.; Inguva, R.

1990-01-01

The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard FFT estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2 to the 18th data sample interferogram, giving a maximum unapodized resolution of 0.06/cm. This estimate was then interpolated by zero filling an additional 2 to the 18th points, and the final resolution was taken to be 0.06/cm. Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45/cm region of the spectrum for several increasing record lengths of interferogram data beginning at 2 to the 10th. It is found that over this region the MEM estimate with 2 to the 16th data samples is in close agreement with the FFT estimate using 2 to the 18th samples.

11. Method for detection and imaging over a broad spectral range

DOEpatents

Yefremenko, Volodymyr; Gordiyenko, Eduard; Pishko, legal representative, Olga; Novosad, Valentyn; Pishko, deceased; Vitalii

2007-09-25

A method of controlling the coordinate sensitivity in a superconducting microbolometer employs localized light, heating or magnetic field effects to form normal or mixed state regions on a superconducting film and to control the spatial location. Electron beam lithography and wet chemical etching were applied as pattern transfer processes in epitaxial Y--Ba--Cu--O films. Two different sensor designs were tested: (i) a 3 millimeter long and 40 micrometer wide stripe and (ii) a 1.25 millimeters long, and 50 micron wide meandering-like structure. Scanning the laser beam along the stripe leads to physical displacement of the sensitive area, and, therefore, may be used as a basis for imaging over a broad spectral range. Forming the superconducting film as a meandering structure provides the equivalent of a two-dimensional detector array. Advantages of this approach are simplicity of detector fabrication, and simplicity of the read-out process requiring only two electrical terminals.

12. Spectral (Finite) Volume Method for One Dimensional Euler Equations

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.

13. Propane spectral resolution enhancement by the maximum entropy method

NASA Technical Reports Server (NTRS)

Bonavito, N. L.; Stewart, K. P.; Hurley, E. J.; Yeh, K. C.; Inguva, R.

1990-01-01

The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard FFT estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2 to the 18th data sample interferogram, giving a maximum unapodized resolution of 0.06/cm. This estimate was then interpolated by zero filling an additional 2 to the 18th points, and the final resolution was taken to be 0.06/cm. Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45/cm region of the spectrum for several increasing record lengths of interferogram data beginning at 2 to the 10th. It is found that over this region the MEM estimate with 2 to the 16th data samples is in close agreement with the FFT estimate using 2 to the 18th samples.

14. Spectral finite-element methods for parametric constrained optimization problems.

SciTech Connect

Anitescu, M.; Mathematics and Computer Science

2009-01-01

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.

15. A spectral method for the computation of propeller acoustics

Schulten, J. B. H. M.

1987-10-01

An analytical description of the acoustic field of a propeller in a uniform flow is derived. Instead of applying the usual Ffowcs Williams-Hawkings version of the acoustic analogy, sources are formulated on a surface enclosing the propeller and its adjacent nonlinear flow field. This approach, which avoids the laborious evaluation of quadrupole source terms, is to be considered as a generalization of the Kirchhoff-Helmholtz theorem of acoustics. By describing the fundamental solution as a spectral Fourier-Bessel decomposition, the resulting sound field is readily given the appropriate series of harmonic amplitudes. The method is validated by a comparison of numerical results with experimental data of a propeller in an acoustic wind tunnel. A good agreement in amplitude and phase is found between theory and experiment.

16. Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

NASA Technical Reports Server (NTRS)

Streett, C. L.

1987-01-01

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

17. Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods

2017-05-01

We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the concept of spectral vanishing viscosity (SVV). For the global spectral method, SVV is very effective and the computational cost is O (N2), which is essentially the same as for the standard Burgers equation. We also develop a local discontinuous Galerkin (LDG) spectral element method to improve the accuracy around discontinuities, and we again stabilize the LDG method with the SVV operator. Finally, we solve numerically the inviscid fractional Burgers equation both with the spectral and the spectral element LDG methods. We study systematically the stability and convergence of both methods and determine the effectiveness of each method for different parameters.

18. Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities

Kärhä, Petri; Vaskuri, Anna; Mäntynen, Henrik; Mikkonen, Nikke; Ikonen, Erkki

2017-08-01

Spectral irradiance data are often used to calculate colorimetric properties, such as color coordinates and color temperatures of light sources by integration. The spectral data may contain unknown correlations that should be accounted for in the uncertainty estimation. We propose a new method for estimating uncertainties in such cases. The method goes through all possible scenarios of deviations using Monte Carlo analysis. Varying spectral error functions are produced by combining spectral base functions, and the distorted spectra are used to calculate the colorimetric quantities. Standard deviations of the colorimetric quantities at different scenarios give uncertainties assuming no correlations, uncertainties assuming full correlation, and uncertainties for an unfavorable case of unknown correlations, which turn out to be a significant source of uncertainty. With 1% standard uncertainty in spectral irradiance, the expanded uncertainty of the correlated color temperature of a source corresponding to the CIE Standard Illuminant A may reach as high as 37.2 K in unfavorable conditions, when calculations assuming full correlation give zero uncertainty, and calculations assuming no correlations yield the expanded uncertainties of 5.6 K and 12.1 K, with wavelength steps of 1 nm and 5 nm used in spectral integrations, respectively. We also show that there is an absolute limit of 60.2 K in the error of the correlated color temperature for Standard Illuminant A when assuming 1% standard uncertainty in the spectral irradiance. A comparison of our uncorrelated uncertainties with those obtained using analytical methods by other research groups shows good agreement. We re-estimated the uncertainties for the colorimetric properties of our 1 kW photometric standard lamps using the new method. The revised uncertainty of color temperature is a factor of 2.5 higher than the uncertainty assuming no correlations.

19. Martian Radiative Transfer Modeling Using the Optimal Spectral Sampling Method

NASA Technical Reports Server (NTRS)

Eluszkiewicz, J.; Cady-Pereira, K.; Uymin, G.; Moncet, J.-L.

2005-01-01

The large volume of existing and planned infrared observations of Mars have prompted the development of a new martian radiative transfer model that could be used in the retrievals of atmospheric and surface properties. The model is based on the Optimal Spectral Sampling (OSS) method [1]. The method is a fast and accurate monochromatic technique applicable to a wide range of remote sensing platforms (from microwave to UV) and was originally developed for the real-time processing of infrared and microwave data acquired by instruments aboard the satellites forming part of the next-generation global weather satellite system NPOESS (National Polarorbiting Operational Satellite System) [2]. As part of our on-going research related to the radiative properties of the martian polar caps, we have begun the development of a martian OSS model with the goal of using it to perform self-consistent atmospheric corrections necessary to retrieve caps emissivity from the Thermal Emission Spectrometer (TES) spectra. While the caps will provide the initial focus area for applying the new model, it is hoped that the model will be of interest to the wider Mars remote sensing community.

20. A spectral boundary integral method for flowing blood cells

Zhao, Hong; Isfahani, Amir H. G.; Olson, Luke N.; Freund, Jonathan B.

2010-05-01

A spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated. The blood cells are modeled as finite-deformation elastic membranes containing a higher viscosity fluid than the surrounding plasma, but the solver itself is independent of the particular constitutive model employed for the cell membranes. The surface integrals developed for solving the viscous flow, and thereby the motion of the massless membrane, are evaluated using an O(NlogN) particle-mesh Ewald (PME) approach. The cell shapes, which can become highly distorted under physiologic conditions, are discretized with spherical harmonics. The resolution of these global basis functions is, of course, excellent, but more importantly they facilitate an approximate de-aliasing procedure that stabilizes the simulations without adding any numerical dissipation or further restricting the permissible numerical time step. Complex geometry no-slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine. The implementation is verified against solutions for axisymmetric flows reported in the literature, and its accuracy is demonstrated by comparison against exact solutions for relaxing surface deformations. It is also used to simulate flow of blood cells at 30% volume fraction in tubes between 4.9 and 16.9 μm in diameter. For these, it is shown to reproduce the well-known non-monotonic dependence of the effective viscosity on the tube diameter.

1. Gravitational collapse of scalar fields via spectral methods

SciTech Connect

Oliveira, H. P. de; Rodrigues, E. L.; Skea, J. E. F.

2010-11-15

In this paper we present a new numerical code based on the Galerkin method to integrate the field equations for the spherical collapse of massive and massless scalar fields. By using a spectral decomposition in terms of the radial coordinate, the field equations were reduced to a finite set of ordinary differential equations in the space of modes associated with the Galerkin expansion of the scalar field, together with algebraic sets of equations connecting modes associated with the metric functions. The set of ordinary differential equations with respect to the null coordinate is then integrated using an eighth-order Runge-Kutta method. The numerical tests have confirmed the high accuracy and fast convergence of the code. As an application we have evaluated the whole spectrum of black hole masses which ranges from infinitesimal to large values obtained after varying the amplitude of the initial scalar field distribution. We have found strong numerical evidence that this spectrum is described by a nonextensive distribution law.

2. Effect of method and parameters of spectral analysis on selected indices of simulated Doppler spectra.

PubMed

Kaluzynski, K; Palko, T

1993-05-01

The sensitivity of Doppler spectral indices (mean frequency, maximum frequency, spectral broadening index and turbulence intensity) to the conditions of spectral analysis (estimation method, data window, smoothing window or model order) increases with decreasing signal bandwidth and growing index complexity. The bias of spectral estimate has a more important effect on these indices than its variance. A too low order, in the case of autoregressive modeling and minimum variance methods, and excessive smoothing, in the case of the FFT method, result in increased errors of Doppler spectral indices. There is a trade-off between the errors resulting from a short data window and those due to insufficient temporal resolution.

3. Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173-193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

4. The use of the spectral method within the fast adaptive composite grid method

SciTech Connect

McKay, S.M.

1994-12-31

The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.

5. A method of determining spectral dye densities in color films

NASA Technical Reports Server (NTRS)

Friederichs, G. A.; Scarpace, F. L.

1977-01-01

A mathematical analysis technique called characteristic vector analysis, reported by Simonds (1963), is used to determine spectral dye densities in multiemulsion film such as color or color-IR imagery. The technique involves examining a number of sets of multivariate data and determining linear transformations of these data to a smaller number of parameters which contain essentially all of the information contained in the original set of data. The steps involved in the actual procedure are outlined. It is shown that integral spectral density measurements of a large number of different color samples can be accurately reconstructed from the calculated spectral dye densities.

6. A method of determining spectral dye densities in color films

NASA Technical Reports Server (NTRS)

Friederichs, G. A.; Scarpace, F. L.

1977-01-01

A mathematical analysis technique called characteristic vector analysis, reported by Simonds (1963), is used to determine spectral dye densities in multiemulsion film such as color or color-IR imagery. The technique involves examining a number of sets of multivariate data and determining linear transformations of these data to a smaller number of parameters which contain essentially all of the information contained in the original set of data. The steps involved in the actual procedure are outlined. It is shown that integral spectral density measurements of a large number of different color samples can be accurately reconstructed from the calculated spectral dye densities.

7. Rapid simulation of spatial epidemics: a spectral method.

PubMed

Brand, Samuel P C; Tildesley, Michael J; Keeling, Matthew J

2015-04-07

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel.

8. Two-Time Green's Functions and the Spectral Density Method in Nonextensive Classical Statistical Mechanics

Cavallo, A.; Cosenza, F.; de Cesare, L.

2001-12-01

The two-time retarded and advanced Green's function technique is formulated in nonextensive classical statistical mechanics within the optimal Lagrange multiplier framework. The main spectral properties are presented and a spectral decomposition for the spectral density is obtained. Finally, the nonextensive version of the spectral density method is given and its effectiveness is tested by exploring the equilibrium properties of a classical ferromagnetic spin chain.

9. The generalized fractional order of the Chebyshev functions on nonlinear boundary value problems in the semi-infinite domain

Parand, Kourosh; Delkhosh, Mehdi

2017-09-01

A new collocation method, namely the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) collocation method, is given for solving some nonlinear boundary value problems in the semi-infinite domain, such as equations of the unsteady isothermal flow of a gas, the third grade fluid, the Blasius, and the field equation determining the vortex profile. The method reduces the solution of the problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of the method, the numerical results of the present method are compared with several numerical results.

10. Good Interpolation Points: Learning from Chebyshev, Fekete, Haar and Lebesgue

Cuyt, Annie; Ibrahimoglu, B. Ali; Yaman, Irem

2011-09-01

The search for sets of good interpolation points is highly motivated by the fact that, due to the finite precision of digital computers, valid results can only be expected when the interpolation problem is well-conditioned. The conditioning of polynomial interpolation and of rational interpolation with preassigned poles is measured by the respective Lebesgue constants. Here we summarize the main results with respect to the Lebesgue constant for polynomial interpolation and we present the best Lebesgue constants in existence for rational interpolation with preassigned poles. The new results are based on a fairly unknown rational analogue of the Chebyshev orthogonal polynomials. We compare with the results obtained in [1] and [2].

11. Method and apparatus for measuring film spectral properties

SciTech Connect

Forrest, S.R.; Burrows, P.E.; Garbuzov, D.Z.; Bulovic, V.

1999-12-21

Film spectral properties are measured by projecting chopped monochromatic light onto a luminescent film sample deposited on a substrate, and coupling through use of immersion oil the reflection of light therefrom to a light detector.

12. Method and apparatus for measuring film spectral properties

DOEpatents

Forrest, Stephen R.; Burrows, Paul E.; Garbuzov, Dmitri Z.; Bulovic, Vladimir

1999-12-21

Film spectral properties are measured by projecting chopped monochromatic light onto a luminescent film sample deposited on a substrate, and coupling through use of immersion oil the reflection of light therefrom to a light detector.

13. Towards spectral geometric methods for Euclidean quantum gravity

Panine, Mikhail; Kempf, Achim

2016-04-01

The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.

14. An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

2014-09-01

Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the

15. Chebyshev acceleration for lambda mode calculations

SciTech Connect

Belchior, A. Jr.; Moreira, J.M.L. )

1992-01-01

Coordenadoria para Projetos Especals (COPESP) has been making an effort to develop a power distribution mapping system utilizing self-powered neutron detectors. The scheme adopted to estimate the power distribution is based on an expansion of lambda modes for a given reactor state. Two-dimensional lambda modes were obtained previously with a modified version of the CITATION code. The method was based on the orthogonality properties of the lambda modes. Several modes could be obtained, but the convergence was slow because of the lack of an appropriate accelerating scheme in the CITATION code for calculating lambda modes. This work presents the acceleration scheme implemented into the CITATION code to obtain lambda modes.

16. New spectral methods in cloud and aerosol remote sensing applications

Schmidt, K. Sebastian; McBride, Patrick; Pilewskie, Peter; Feingold, Graham; Jiang, Hongli

2010-05-01

We present new remote sensing techniques that rely on spectral observations of clouds and aerosols in the solar wavelength range. As a first example, we show how the effects of heterogeneous clouds, aerosols of changing optical properties, and the surface within one pixel can be distinguished by means of their spectral signatures. This example is based on data from the Gulf of Mexico Atmospheric Composition and Climate Study (GoMACCS, Houston, Texas, 2006), Large Eddy Simulations (LES) of polluted boundary layer clouds, and 3-dimensional radiative transfer calculations. In a second example, we show that the uncertainty of cloud retrievals can be improved considerably by exploiting the spectral information around liquid water absorption features in the near-infrared wavelength range. This is illustrated with spectral transmittance data from the NOAA International Chemistry Experiment in the Arctic LOwer Troposphere (ICEALOT, 2008). In contrast to reflected radiance, transmitted radiance is only weakly sensitive to cloud effective drop radius, and only cloud optical thickness can be obtained from the standard dual-channel technique. We show that effective radius and liquid water path can also be retrieved with the new spectral approach, and validate our results with microwave liquid water path measurements.

17. Characterizing Intra-Die Spatial Correlation Using Spectral Density Fitting Method

Fu, Qiang; Luk, Wai-Shing; Tao, Jun; Yan, Changhao; Zeng, Xuan

In this paper, a spectral domain method named the SDF (Spectral Density Fitting) method for intra-die spatial correlation function extraction is presented. Based on theoretical analysis of random field, the spectral density, as the spectral domain counterpart of correlation function, is employed to estimate the parameters of the correlation function effectively in the spectral domain. Compared with the existing extraction algorithm in the original spatial domain, the SDF method can obtain the same quality of results in the spectral domain. In actual measurement process, the unavoidable measurement error with arbitrary frequency components would greatly confound the extraction results. A filtering technique is further developed to diminish the high frequency components of the measurement error and recover the data from noise contamination for parameter estimation. Experimental results have shown that the SDF method is practical and stable.

18. Spectral multigrid methods for the solution of homogeneous turbulence problems

NASA Technical Reports Server (NTRS)

Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.

1987-01-01

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

19. PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise

SciTech Connect

Abdulle, Assyr; Vilmart, Gilles

2013-06-01

A partitioned implicit–explicit orthogonal Runge–Kutta method (PIROCK) is proposed for the time integration of diffusion–advection–reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm.

20. Spectral/HP Element Method With Hierarchical Reconstruction for Solving Hyperbolic Conservation Laws

SciTech Connect

Xu, Zhiliang; Lin, Guang

2009-12-01

Hierarchical reconstruction (HR) has been successfully applied to prevent oscillations in solutions computed by finite volume, discontinuous Galerkin, spectral volume schemes when solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element methods for solving hyperbolic conservation laws. We show that HR preserves the order of accuracy of spectral/hp element methods for smooth solutions and generate essentially non-oscillatory solution profiles for shock wave problems.

1. A spectral KRMI conjugate gradient method under the strong-Wolfe line search

Khadijah, Wan; Rivaie, Mohd.; Mamat, Mustafa; Jusoh, Ibrahim

2016-06-01

In this paper, a modification of spectral conjugate gradient (CG) method is proposed which combines the advantages of the spectral CG method and the RMIL method namely as spectral Khadijah-Rivaie-Mustafa-Ibrahim (SKRMI) to solve unconstrained optimization problems. Based on inexact line searches, the objective function generates a sufficient descent direction and the global convergence property for the proposed method has been proved. Moreover, the method reduces to the standard RMIL method if exact line search is applied. Numerical results are also presented to examine the efficiency of the proposed method.

2. Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

2017-02-01

Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

3. A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

4. Analysis of the superconducting coplanar waveguide by combining spectral domain method and phenomenological equivalence method

Kong, K.-S.; Kuo, C. W.; Kitazawa, T.; Itoh, T.

1990-09-01

A new appraoch to calculating the conductor loss of a superconducting coplanar waveguide (CPW) by combining the spectral domain method (SDM) and the phenomenological equivalence method (PEM) is presented. The inductance of the CPW is first accurately calculated by the modified SDM. The derivative of the inductance is then numerically calculated to obtain the geometric factor. The dimensions of the equivalent strip are obtained and the conductor loss is calculated from the equivalent strip. The method has the potential of extending the applicability of PEM to other transmission-line structures.

5. Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves.

PubMed

Bayındır, Cihan

2016-02-25

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions.

6. Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

7. Analysis of superconducting patch antennas using the spectral domain method

SciTech Connect

Itoh, Kiyohiko; Fukasawa, Toru; Ishii, Nozomu

1994-12-31

In this paper, the authors analyze electrical small HTS (High-Tc Superconductors) patch antennas using the modified spectral domain moment method (SDMM). Although it is assumed that a patch and a ground plane are perfect electric conductors (PECs) in the conventional SDMM, they can compute the performance of not only HTS patch antennas but also patch antennas with a conducting loss, by exchanging the boundary conditions on the conductors for {Epsilon}{sub t} = Z{sub s}J{sub s}, where {Epsilon}{sub t} is the tangential {Epsilon} field, Z{sub s} is surface impedance on the conductors, and J{sub s} is surface impedance on the conductors, and J{sub s} is surface current density. Z{sub s} of HTS is determined by using the three-fluid model in the analysis. This paper presents the numerical results for a 2.8GHz HTS patch antenna with 12mm length and 1.5mm width, on the grounded dielectric substrate with thickness d = 0.5mm, {epsilon}{sub r} = 25 and tan {delta} = 0. As the result, one can see that efficiency of the HTS patch is improved, for example, 3.8 times at T = 0(K) and 2.9 times at T = 77(K) improvement are obtained from the analysis. As regards the input impedance when a patch is proved, the peak at the resonance of the Cu patch is much smaller than the PEC patch, because the resonance is weaker as a conducting loss is larger, Therefore, the peak of the HTS patch is larger than that of the Cu patch, and is smaller than that of the PEC patch. This tendency is dependent on Z{sub s} of HTS, that is, this peak is larger as a real part of Z{sub s} is smaller. The authors also show that the resonance frequency of the HTS patch is shifted as temperature is changing. There are conducting losses, a dielectric loss and surface wave losses as factors degrading radiation efficiency. They examine the loss mechanism of the HTS patch for the various substrate thickness, d.

8. An Improved Variational Method for Hyperspectral Image Pansharpening with the Constraint of Spectral Difference Minimization

Huang, Z.; Chen, Q.; Shen, Y.; Chen, Q.; Liu, X.

2017-09-01

Variational pansharpening can enhance the spatial resolution of a hyperspectral (HS) image using a high-resolution panchromatic (PAN) image. However, this technology may lead to spectral distortion that obviously affect the accuracy of data analysis. In this article, we propose an improved variational method for HS image pansharpening with the constraint of spectral difference minimization. We extend the energy function of the classic variational pansharpening method by adding a new spectral fidelity term. This fidelity term is designed following the definition of spectral angle mapper, which means that for every pixel, the spectral difference value of any two bands in the HS image is in equal proportion to that of the two corresponding bands in the pansharpened image. Gradient descent method is adopted to find the optimal solution of the modified energy function, and the pansharpened image can be reconstructed. Experimental results demonstrate that the constraint of spectral difference minimization is able to preserve the original spectral information well in HS images, and reduce the spectral distortion effectively. Compared to original variational method, our method performs better in both visual and quantitative evaluation, and achieves a good trade-off between spatial and spectral information.

9. On the cross-stream spectral method for the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Zorumski, William E.; Hodge, Steven L.

1993-01-01

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

10. Orbital Tori Construction Using Trajectory Following Spectral Methods

DTIC Science & Technology

2010-09-01

Global Positioning System IGS International GNSS Service KAM Kolmogorov-Arnold-Moser LAGEOS Laser Geodynamics Satellites MCS Master Control Station MEO...considerable detail on the spectral lines of the Simplified General Perturbations Satellite Orbit Model 4 (SGP4) model and show how it correlates to its full...suggests a mismatch in frequency identification, but equal or greater contributors to the error are more than likely the loss of higher-order harmonic

11. Spectral element methods for transitional flows, in complex geometries.

SciTech Connect

Fischer, P. F.; Kruse, G. W.; Loth, F.; Mathematics and Computer Science; Juniata Coll.; Univ. of Illinois

2002-01-01

We describe the development and implementation of an efficient spectral element code for simulating transitional flows in complex three-dimensional domains. Critical to this effort is the use of geometrically nonconforming elements that allow localized refinement in regions of interest, coupled with a stabilized high-order time-split formulation of the semi-discrete Navier-Stokes equations. Simulations of transition in a model of an arteriovenous graft illustrate the potential of this approach in biomechanical applications.

12. Spectral: Solving Schroedinger and Wheeler-DeWitt equations in the positive semi-axis by the spectral method

Corrêa Silva, E. V.; Monerat, G. A.; de Oliveira Neto, G.; Ferreira Filho, L. G.

2014-01-01

The Galerkin spectral method can be used for approximate calculation of eigenvalues and eigenfunctions of unidimensional Schroedinger-like equations such as the Wheeler-DeWitt equation. The criteria most commonly employed for checking the accuracy of results is the conservation of norm of the wave function, but some other criteria might be used, such as the orthogonality of eigenfunctions and the variation of the spectrum with varying computational parameters, e.g. the number of basis functions used in the approximation. The package Spectra, which implements the spectral method in Maple language together with a number of testing tools, is presented. Alternatively, Maple may interact with the Octave numerical system without the need of Octave programming by the user.

13. An efficient and secure Diffie-Hellman key agreement protocol based on Chebyshev chaotic map

Yoon, Eun-Jun; Jeon, Il-Soo

2011-06-01

This paper proposes a new efficient and secure Diffie-Hellman key agreement protocol based on Chebyshev chaotic map. The proposed key agreement protocol uses the semi-group property of Chebyshev polynomials to agree Diffie-Hellman based session key. The proposed protocol provides strong security compared with the previous related protocols. In addition, the proposed protocol does not require any timestamp information and greatly reduces computational costs between communication parties. As a result, the proposed protocol is more practical and provides computational/communicational efficiency compare with several previously proposed key agreement protocols based on Chebyshev chaotic map.

14. A new fractional Chebyshev FDM: an application for solving the fractional differential equations generated by optimisation problem

2015-10-01

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge-Kutta method is given.

15. The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

Degasperis, Antonio; Conforti, Matteo; Baronio, Fabio; Wabnitz, Stefan; Lombardo, Sara

2011-06-01

The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.

16. A spectral-spatial kernel-based method for hyperspectral imagery classification

Li, Li; Ge, Hongwei; Gao, Jianqiang

2017-02-01

Spectral-based classification methods have gained increasing attention in hyperspectral imagery classification. Nevertheless, the spectral cannot fully represent the inherent spatial distribution of the imagery. In this paper, a spectral-spatial kernel-based method for hyperspectral imagery classification is proposed. Firstly, the spatial feature was extracted by using area median filtering (AMF). Secondly, the result of the AMF was used to construct spatial feature patch according to different window sizes. Finally, using the kernel technique, the spectral feature and the spatial feature were jointly used for the classification through a support vector machine (SVM) formulation. Therefore, for hyperspectral imagery classification, the proposed method was called spectral-spatial kernel-based support vector machine (SSF-SVM). To evaluate the proposed method, experiments are performed on three hyperspectral images. The experimental results show that an improvement is possible with the proposed technique in most of the real world classification problems.

17. Quantum state-to-state cross sections for atom-diatom reactions: A Chebyshev real wave-packet approach

SciTech Connect

Lin Shiying; Guo Hua

2006-08-15

We describe the implementation of a quantum mechanical method to calculate state-to-state differential cross sections for atom-diatom reactive scattering processes. The key ingredient of this approach is the efficient and accurate propagation of a real scattering wave packet in the Chebyshev order domain, from which the S-matrix elements can be extracted. This approach is implemented with Open MP and applied to compute differential and integral cross sections for the direct H+H{sub 2} abstraction reaction and the more challenging N({sup 2}D)+H{sub 2} insertion reaction.

18. A comparison of numerical methods for the Rayleigh equation in unbounded domains

NASA Technical Reports Server (NTRS)

Liou, W. W.; Morris, P. J.

1991-01-01

A second-order finite difference and two spectral methods, including a Chebyshev tau and a Chebyshev collocation method were implemented to determine the linear hydrodynamic stability of an unbounded shear flow. The velocity profile of the basic flow in the stability analysis mimicks that of a one-stream free mixing layer. Local and global eigenvalue solution methods are used to determine individual eigenvalues and the eigenvalue spectrum, respectively. The calculated eigenvalue spectrum includes a discrete mode, a continuous spectrum associated with the equation singularity and a continuous spectrum associated with the domain unboundedness. The efficiency and the accuracy of these discretization methods in the prediction of the eigensolutions of the discrete mode were evaluated by comparison with a conventional shooting procedure. Their capabilities in mapping out the continuous eigenvalue spectra are also discussed.

19. Color constancy - A method for recovering surface spectral reflectance

NASA Technical Reports Server (NTRS)

Maloney, L. T.; Wandell, B. A.

1986-01-01

An algorithm has been developed for estimating the surface reflectance functions of objects in a scene with incomplete knowledge of the spectral power distribution of the ambient light. An image processing system employing this algorithm can assign colors that are constant despite changes in the lighting of the scene; this capability is essential to correct color rendering in photography, TV, and in the construction of artificial visual systems for robotics. Attention is given to the way in which constraints on lights and surfaces in the environment make color-constancy possible for a visual system, and the algorithm's implications for human color vision are discussed.

20. A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

1. Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

2. Analysis of the spectral vanishing viscosity method for periodic conservation laws

NASA Technical Reports Server (NTRS)

1988-01-01

The convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid Burgers' equation is analyzed. It is proven that this kind of vanishing viscosity is responsible for a spectral decay of those Fourier coefficients located toward the end of the computed spectrum; consequently, the discretization error is shown to be spectrally small independent of whether the underlying solution is smooth or not. This in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments.

3. [Correction method for infrared spectral emissivity measurement system based on integrating sphere reflectometer].

PubMed

Zhang, Yu-Feng; Dai, Jing-Min; Zhang, Yu; Pan, Wei-Dong; Zhang, Lei

2013-08-01

In view of the influence of non-ideal reference standard on spectral emissivity measurement, by analyzing the principle of infrared emissivity measurement system based on integrating sphere reflectometer, a calibration method suitable for measuring spectral emissivity system using the reflection measurement was proposed. By fitting a spectral reflectance curve of the reference standard sample to the given reflectance data, the correction coefficient of measurement system was computed. Then the output voltage curve of reference standard sample was corrected by this coefficient. The system error caused by the imperfection of reference standard was eliminated. The correction method was applied to the spectral emissivity measurement system based on integrating sphere reflectometer. The results measured by the corrected system and the results measured by energy comparison measurement were compared to verify the feasibility and effectivity of this correction method in improving the accuracy of spectral emissivity measurement.

4. [A method of hyperspectral quantificational identification of minerals based on infrared spectral artificial immune calculation].

PubMed

Liu, Qing-Jie; Jing, Lin-Hai; Li, Xin-Wu; Bi, Jian-Tao; Wang, Meng-Fei; Lin, Qi-Zhong

2013-04-01

Rapid identification of minerals based on near infrared (NIR) and shortwave infrared (SWIR) hyperspectra is vital to remote sensing mine exploration, remote sensing minerals mapping and field geological documentation of drill core, and have leaded to many identification methods including spectral angle mapping (SAM), spectral distance mapping (SDM), spectral feature fitting(SFF), linear spectral mixture model (LSMM), mathematical combination feature spectral linear inversion model(CFSLIM) etc. However, limitations of these methods affect their actual applications. The present paper firstly gives a unified minerals components spectral inversion (MCSI) model based on target sample spectrum and standard endmember spectral library evaluated by spectral similarity indexes. Then taking LSMM and SAM evaluation index for example, a specific formulation of unified MCSI model is presented in the form of a kind of combinatorial optimization. And then, an artificial immune colonial selection algorithm is used for solving minerals feature spectral linear inversion model optimization problem, which is named ICSFSLIM. Finally, an experiment was performed to use ICSFSLIM and CFSLIM to identify the contained minerals of 22 rock samples selected in Baogutu in Xinjiang China. The mean value of correctness and validness identification of ICSFSLIM are 34.22% and 54.08% respectively, which is better than that of CFSLIM 31.97% and 37.38%; the correctness and validness variance of ICSFSLIM are 0.11 and 0.13 smaller than that of CFSLIM, 0.15 and 0.25, indicating better identification stability.

5. The research of a new test method about dynamic target infrared spectral signature

Wu, Jiang-hui; Gao, Jiao-bo; Chen, Qing; Luo, Yan-ling; Li, Jiang-jun; Gao, Ze-dong; Wang, Nan; Gao, Meng

2014-11-01

The research on infrared spectral target signature shows great military importance in the domain of IR detection Recognition, IRCM, IR image guide and ir stealth etc. The measurements of infrared spectral of tactical targets have been a direct but effective technique in providing signatures for both analysis and simulation to missile seeker designers for many years. In order to deal with the problem of dynamic target infrared spectral signature, this paper presents a new method for acquiring and testing ir spectral radiation signatures of dynamic objects, which is based on an IR imager guiding the target and acquiring the scene at the same time, a FOV chopping scan infrared spectral radiometer alternatively testing the target and its background around ir spectral signature.ir imager and spectral radiometer have the same optical axis. The raw test data was processed according to a new deal with method. Principles and data processing methods were described in detail, test error also analyzed. Field test results showed that the method described in the above is right; the test error was reduced smaller, and can better satisfy the needs of acquiring dynamic target ir spectral signature.

6. Color reproduction of human skin by spectral reflectance using RGB images and the Wiener estimation method

Sato, Kiyomi; Miyazawa, Shota; Funamizu, Hideki; Yuasa, Tomonori; Nishidate, Izumi; Aizu, Yoshihisa

2017-04-01

Skin measurements based on spectral reflectance are widely studied in the fields of medical care and cosmetics. It has the advantage that several skin properties can be estimated in the non-invasive and non-contacting manner. In this study, we demonstrate the color reproduction of human skin by spectral reflectance using RGB images and the Wiener estimation method.

7. A statistical evaluation of spectral fingerprinting methods using analysis of variance and principal component analysis

USDA-ARS?s Scientific Manuscript database

Six methods were compared with respect to spectral fingerprinting of a well-characterized series of broccoli samples. Spectral fingerprints were acquired for finely-powdered solid samples using Fourier transform-infrared (IR) and Fourier transform-near infrared (NIR) spectrometry and for aqueous met...

8. On spectral multigrid methods for the time-dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1985-01-01

A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.

9. A Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results

NASA Technical Reports Server (NTRS)

Larsen, Curtis E.; Irvine, Tom

2013-01-01

A comprehensive review of the available methods for estimating fatigue damage from variable amplitude loading is presented. The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for random processes relevant to real structures such as in offshore or aerospace applications. Beginning with the Rayleigh (or narrow band) approximation, attempts at improved approximations or corrections to the Rayleigh approximation are examined by comparison to rainflow analysis of time histories simulated from psd functions representative of simple theoretical and real world applications. Spectral methods investigated include corrections by Wirsching and Light, Ortiz and Chen, the Dirlik formula, and the Single-Moment method, among other more recent proposed methods. Good agreement is obtained between the spectral methods and the time-domain rainflow identification for most cases, with some limitations. Guidelines are given for using the several spectral methods to increase confidence in the damage estimate.

10. A Real-Time Infrared Ultra-Spectral Signature Classification Method via Spatial Pyramid Matching

PubMed Central

Mei, Xiaoguang; Ma, Yong; Li, Chang; Fan, Fan; Huang, Jun; Ma, Jiayi

2015-01-01

The state-of-the-art ultra-spectral sensor technology brings new hope for high precision applications due to its high spectral resolution. However, it also comes with new challenges, such as the high data dimension and noise problems. In this paper, we propose a real-time method for infrared ultra-spectral signature classification via spatial pyramid matching (SPM), which includes two aspects. First, we introduce an infrared ultra-spectral signature similarity measure method via SPM, which is the foundation of the matching-based classification method. Second, we propose the classification method with reference spectral libraries, which utilizes the SPM-based similarity for the real-time infrared ultra-spectral signature classification with robustness performance. Specifically, instead of matching with each spectrum in the spectral library, our method is based on feature matching, which includes a feature library-generating phase. We calculate the SPM-based similarity between the feature of the spectrum and that of each spectrum of the reference feature library, then take the class index of the corresponding spectrum having the maximum similarity as the final result. Experimental comparisons on two publicly-available datasets demonstrate that the proposed method effectively improves the real-time classification performance and robustness to noise. PMID:26205263

11. A Real-Time Infrared Ultra-Spectral Signature Classification Method via Spatial Pyramid Matching.

PubMed

Mei, Xiaoguang; Ma, Yong; Li, Chang; Fan, Fan; Huang, Jun; Ma, Jiayi

2015-07-03

The state-of-the-art ultra-spectral sensor technology brings new hope for high precision applications due to its high spectral resolution. However, it also comes with new challenges, such as the high data dimension and noise problems. In this paper, we propose a real-time method for infrared ultra-spectral signature classification via spatial pyramid matching (SPM), which includes two aspects. First, we introduce an infrared ultra-spectral signature similarity measure method via SPM, which is the foundation of the matching-based classification method. Second, we propose the classification method with reference spectral libraries, which utilizes the SPM-based similarity for the real-time infrared ultra-spectral signature classification with robustness performance. Specifically, instead of matching with each spectrum in the spectral library, our method is based on feature matching, which includes a feature library-generating phase. We calculate the SPM-based similarity between the feature of the spectrum and that of each spectrum of the reference feature library, then take the class index of the corresponding spectrum having the maximum similarity as the final result. Experimental comparisons on two publicly-available datasets demonstrate that the proposed method effectively improves the real-time classification performance and robustness to noise.

12. Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation.

PubMed

Wei, Yunxia; Chen, Yanping; Shi, Xiulian; Zhang, Yuanyuan

2016-01-01

We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text] (d denotes the space dimensions) as the collocation points. The error analysis in [Formula: see text]-norm and [Formula: see text]-norm theoretically justifies the exponential convergence of spectral collocation method in multidimensional space. We give two numerical examples in order to illustrate the validity of the proposed Jacobi spectral collocation method.

13. Development and validation of a new fallout transport method using variable spectral winds. Doctoral thesis

SciTech Connect

Hopkins, A.T.

1984-09-01

The purpose of this research was to develop and validate a fallout prediction method using variable transport calculations. The new method uses National Meteorological Center (NMC) spectral coefficients to compute wind vectors along the space- and time-varying trajectories of falling particles. The method was validated by comparing computed and actual cloud trajectories from a Mount St. Helens volcanic eruption and a high dust cloud. In summary, this research demonstrated the feasibility of using spectral coefficients for fallout transport calculations, developed a two-step smearing model to treat variable winds, and showed that uncertainties in spectral winds do not contribute significantly to the error in computed dose rate.

14. Establishing a method to measure bone structure using spectral CT

Ramyar, M.; Leary, C.; Raja, A.; Butler, A. P. H.; Woodfield, T. B. F.; Anderson, N. G.

2017-03-01

Combining bone structure and density measurement in 3D is required to assess site-specific fracture risk. Spectral molecular imaging can measure bone structure in relation to bone density by measuring macro and microstructure of bone in 3D. This study aimed to optimize spectral CT methodology to measure bone structure in excised bone samples. MARS CT with CdTe Medipix3RX detector was used in multiple energy bins to calibrate bone structure measurements. To calibrate thickness measurement, eight different thicknesses of Aluminium (Al) sheets were scanned one in air and the other around a falcon tube and then analysed. To test if trabecular thickness measurements differed depending on scan plane, a bone sample from sheep proximal tibia was scanned in two orthogonal directions. To assess the effect of air on thickness measurement, two parts of the same human femoral head were scanned in two conditions (in the air and in PBS). The results showed that the MARS scanner (with 90μm voxel size) is able to accurately measure the Al (in air) thicknesses over 200μm but it underestimates the thicknesses below 200μm because of partial volume effect in Al-air interface. The Al thickness measured in the highest energy bin is overestimated at Al-falcon tube interface. Bone scanning in two orthogonal directions gives the same trabecular thickness and air in the bone structure reduced measurement accuracy. We have established a bone structure assessment protocol on MARS scanner. The next step is to combine this with bone densitometry to assess bone strength.

15. Quality Parameters Defined by Chebyshev Polynomials in Cold Rolling Process Chain

Judin, Mika; Nylander, Jari; Larkiola, Jari; Verho, Martti

2011-05-01

The thickness profile of hot strip is of importance to profile, flatness and shape of the final cold rolled product. In this work, strip thickness and flatness profiles are decomposed into independent components by solving Chebyshev polynomials coefficients using matrix calculation. Four terms are used to characterize most common shapes of thickness and flatness profile. The calculated Chebyshev coefficients from different line measurements are combined together and analysed using neural network tools. The most common types of shapes are classified.

16. Quality Parameters Defined by Chebyshev Polynomials in Cold Rolling Process Chain

SciTech Connect

Judin, Mika; Nylander, Jari; Larkiola, Jari; Verho, Martti

2011-05-04

The thickness profile of hot strip is of importance to profile, flatness and shape of the final cold rolled product. In this work, strip thickness and flatness profiles are decomposed into independent components by solving Chebyshev polynomials coefficients using matrix calculation. Four terms are used to characterize most common shapes of thickness and flatness profile. The calculated Chebyshev coefficients from different line measurements are combined together and analysed using neural network tools. The most common types of shapes are classified.

17. Estimates of the trace of the inverse of a symmetric matrix using the modified Chebyshev algorithm

Meurant, Gérard

2009-07-01

In this paper we study how to compute an estimate of the trace of the inverse of a symmetric matrix by using Gauss quadrature and the modified Chebyshev algorithm. As auxiliary polynomials we use the shifted Chebyshev polynomials. Since this can be too costly in computer storage for large matrices we also propose to compute the modified moments with a stochastic approach due to Hutchinson (Commun Stat Simul 18:1059-1076, 1989).

18. Research on method of infrared spectral imaging based on thermal imager

Huan, Ke-wei; Shi, Xiao-guang; Wu, Wei; Zheng, Feng; Liu, Xiao-xi

2011-08-01

In recent years, technology of thermal imager and spectral imaging is becoming mature, and the application of them is increased. The method is based on the blackbody radiation theory, make use of the infrared thermal imager to collect and analysis the thermal images, distill the temperature value of different pixel of the thermal images, use Matlab to deal blackbody radiation emitted curve fitting according with the temperature value of different pixels, and get the values of the degree of radiation emitted at the same wavelength from the different pixels, then make spectral imaging (1μm~10μm) according to the values. At last, do analysis to spectral imaging of different spectral bands; discuss the limitations of using this method to achieve spectral imaging.

19. A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions

PubMed Central

Bhrawy, A. H.; Alghamdi, M. A.

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. PMID:25057507

20. Research on method of geometry and spectral calibration of pushbroom dispersive hyperspectral imager

He, Zhiping; Shu, Rong; Wang, Jianyu

2012-11-01

Development and application of airborne and aerospace hyperspectral imager press for high precision geometry and spectral calibration of pixels of image cube. The research of geometry and spectral calibration of pushbroom hyperspectral imager, its target is giving the coordinate of angle field of view and center wavelength of each detect unit in focal plane detector of hyperspectral imager, and achieves the high precision, full field of view, full channel geometry and spectral calibration. It is importance for imaging quantitative and deep application of hyperspectal imager. The paper takes the geometry and spectral calibration of pushbroom dispersive hyperspectral imager as case study, and research on the constitution and analysis of imaging mathematical model. Aimed especially at grating-dispersive hyperspectral imaging, the specialty of the imaging mode and dispersive method has been concretely analyzed. Based on the analysis, the theory and feasible method of geometry and spectral calibration of dispersive hyperspectral imager is set up. The key technique has been solved is As follows: 1). the imaging mathematical model and feasible method of geometry and spectral calibration for full pixels of image cube has been set up, the feasibility of the calibration method has been analyzed. 2). the engineering model and method of the geometry and spectral calibration of pushbroom dispersive hyperspectral imager has been set up and the calibration equipment has been constructed, and the calibration precision has been analyzed.

1. [Method of Remote Sensing Identification for Mineral Types Based on Multiple Spectral Characteristic Parameters Matching].

PubMed

Wei, Jing; Ming, Yan-fang; Han, Liu-sheng; Ren, Zhong-liang; Guo, Ya-min

2015-10-01

The traditional mineral mapping methods with remote sensing data, based on spectral reflectance matching techniques, shows low accuracy, for obviously being affected by the image quality, atmospheric and other factors. A new mineral mapping method based on multiple types of spectral characteristic parameters is presented in this paper. Various spectral characteristic parameters are used together to enhanced the stability in the situation of atmosphere and environment background affecting. AVIRIS (Airborne Visible Infrared Imaging Spectrometer) data of Nevada Cuprite are selected to determine the mineral types with this method. Typical mineral spectral data are also obtained from USGS (United States Geological Survey) spectral library to calculate the spectral characteristic parameters. A mineral identification model based on multiple spectral characteristic parameters is built by analyzing the various characteristic parameters, and is applied in the mineral mapping experiment in Cuprite area. The mineral mapping result produced by Clark et al. in 1995 is used to evaluate the effect of this method, results show, that mineral mapping results with this method can obtain a high precision, the overall mineral identification accuracy is 78.96%.

2. Change Detection Method with Spatial and Spectral Information from Deep Learning

Lyu, Haobo; Lu, Hui

2017-04-01

Change detection is a key application of remote sensing technology. For multi-spectral images, the available spatial information and useful spectral information is both helpful for data analysis, especially change detection tasks. However, it is difficult that how to learn the changed features from spatial and spectral information meantime in one model. In this paper, we proposed a new method which combines 2-dimensional Convolutional Neural Network and 1-dimensional Recurrent Neural Network for learn changed feature. Compared with only using spectral information, the spatial information will be helpful to overcome temporal spectral variance issues. Our method extracts the spatial difference and spectral difference meantime, and these change information will be balanced in final memory cell of our model, and the leaned change information will be exploited to character change features for change detection. Finally, experiments are performed on two multi-temporal datasets, and the results show superior performance on detecting changes with spatial information and spectral information. Index Terms— Change detection, multi-temporal images, recurrent neural network, convolutional neural network , deep learning, spatial information, spectral information

3. [Selection of interpolation methods used to mitigate spectral misregistration of imaging spectrometers].

PubMed

Chen, Xu; Xiang, Yang; Feng, Yu-Tao

2011-04-01

Spectral curvature destroys the co-registration of the spectra measured by dispersion imaging spectrometer. Using interpolation to re-sample the measured spectra at the non-offset mid-wavelengths can mitigate the spectral misregistration. It is very important to select an optimum interpolation method. The performances of six common interpolation methods are evaluated by comparing the residual errors in the corrected spectral radiance. The results indicate that, four-point cubic Lagrange interpolation and cubic spline interpolation are better than other four interpolation methods (linear Interpolation, three points quadratic polynomial interpolation, five points four-order Lagrange interpolation and cubic Hermite interpolation). For spectral offset of 10% deltalambda (deltalambda = 5 nm), the normalized errors in measured spectral radiance is PV = 0.06, that is reduced to PV < 0.022 after interpolation with cubic Lagrange interpolation or cubic spline interpolation, but for other four methods they are PV > 0.035. Furthermore, for lower spectral resolution (deltalambda > 5 nm), cubic Lagrange interpolation is a little better than cubic spline interpolation; while for higher spectral resolution (deltalambda < 5 nm), cubic spline interpolation is a little better.

4. [Calculation of spectral shifts of the mutants of bacteriorhodopsin by QM/MM methods].

PubMed

Orekhov, F S; Shaĭtan, A K; Shaĭtan, K V

2012-01-01

In the present work spectral shifts of adsorption maxima for the number of mutants of bacteriorhodopsin have been calculated using QM/MM hybrid methodology. Along with this calculation an analysis of possible mechanisms of spectral modulation has been performed. Also we have carried out a comparative analysis of modern quantum chemical methods in respect of the level of optical spectra predictability they allow. We have shown that modern hybrid quantum chemical methods reach an acceptable level of preciseness when applied in the calculation of spectral shifts even if the absolute values of adsorption maxima predicted by these methods are underestimated. The number of rules has been found linking the value of spectral shift with the structural rearrangement in the apoprotein. The methods we were using as well as those rules we have found out both may be useful for development of nanoelectronical devices based on mutant species of bacteriorhodopsin (memory elements, optical triggers etc.).

5. On the Convergence of Galerkin Spectral Methods for a Bioconvective Flow

de Aguiar, R.; Climent-Ezquerra, B.; Rojas-Medar, M. A.; Rojas-Medar, M. D.

2017-03-01

Convergence rates of the spectral Galerkin method are obtained for a system consisting of the Navier-Stokes equation coupled with a linear convection-diffusion equation modeling the concentration of microorganisms in a culture fluid.

6. Spectral methods and cluster structure in correlation-based networks

Heimo, Tapio; Tibély, Gergely; Saramäki, Jari; Kaski, Kimmo; Kertész, János

2008-10-01

We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and focus specifically on the spectral properties of weight W=|-δ and diffusion matrices D=W/sj-δ, where C is the correlation matrix and si=∑jW the strength of node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix are ranked in descending order. As in the earlier observations, the first eigenvector stands for a measure of the market correlations. Its components are, to first approximation, equal to the strengths of the nodes and there is a second order, roughly linear, correction. The high ranking eigenvectors, excluding the highest ranking one, are usually assigned to market sectors and industrial branches. Our study shows that both for weight and diffusion matrices the eigenpair analysis is not capable of easily deducing the cluster structure of the network without a priori knowledge. In addition we have studied the clustering of stocks using the asset graph approach with and without spectrum based noise filtering. It turns out that asset graphs are quite insensitive to noise and there is no sharp percolation transition as a function of the ratio of bonds included, thus no natural threshold value for that ratio seems to exist. We suggest that these observations can be of use for other correlation based networks as well.

7. Method for hyperspectral imagery exploitation and pixel spectral unmixing

NASA Technical Reports Server (NTRS)

Lin, Ching-Fang (Inventor)

2003-01-01

An efficiently hybrid approach to exploit hyperspectral imagery and unmix spectral pixels. This hybrid approach uses a genetic algorithm to solve the abundance vector for the first pixel of a hyperspectral image cube. This abundance vector is used as initial state in a robust filter to derive the abundance estimate for the next pixel. By using Kalman filter, the abundance estimate for a pixel can be obtained in one iteration procedure which is much fast than genetic algorithm. The output of the robust filter is fed to genetic algorithm again to derive accurate abundance estimate for the current pixel. The using of robust filter solution as starting point of the genetic algorithm speeds up the evolution of the genetic algorithm. After obtaining the accurate abundance estimate, the procedure goes to next pixel, and uses the output of genetic algorithm as the previous state estimate to derive abundance estimate for this pixel using robust filter. And again use the genetic algorithm to derive accurate abundance estimate efficiently based on the robust filter solution. This iteration continues until pixels in a hyperspectral image cube end.

8. The nephelometric method of determining light attenuation in the ultraviolet and visible spectral bands

Toropova, T. P.

1980-03-01

An analysis of the variability of the shape of the scattering indicatrix of the atmospheric boundary layer in the spectral range of 304 to 710 nm is presented. The accuracy of determining attenuation using the indicatrix measured at various angles is evaluated; it is shown that in the application of the nephelometric method in the examined spectral region it is shown that in the application of the nephelometric method in the examined spectral region it is more advantageous to utilize the indicatrix measurements preformed at angles of 40-50 deg, which produce a mean magnitude of error not exceeding 10-15%.

9. Source depth estimation of self-potential anomalies by spectral methods

Di Maio, Rosa; Piegari, Ester; Rani, Payal

2017-01-01

Spectral analysis of the self-potential (SP) field for geometrically simple anomalous bodies is studied. In particular, three spectral techniques, i.e. Periodogram (PM), Multi Taper (MTM) and Maximum Entropy (MEM) methods, are proposed to derive the depth of the anomalous bodies. An extensive numerical analysis at varying the source parameters outlines that MEM is successful in determining the source depth with a percent error less than 5%. The application of the proposed spectral approach to the interpretation of field datasets has provided depth estimations of the SP anomaly sources in very good agreement with those obtained by other numerical methods.

10. Computationally efficient algorithms for incorporation of hydrodynamic and excluded volume interactions in Brownian dynamics simulations: A comparative study of the Krylov subspace and Chebyshev based techniques

2014-05-01

Excluded volume and hydrodynamic interactions play a central role in macromolecular dynamics under equilibrium and non-equilibrium settings. The high computational cost of incorporating the influence of hydrodynamic interaction in meso-scale simulation of polymer dynamics has motivated much research on development of high fidelity and cost efficient techniques. Among them, the Chebyshev polynomial based techniques and the Krylov subspace methods are most promising. To this end, in this study we have developed a series of semi-implicit predictor-corrector Brownian dynamics algorithms for bead-spring chain micromechanical model of polymers that utilizes either the Chebyshev or the Krylov framework. The efficiency and fidelity of these new algorithms in equilibrium (radius of gyration and diffusivity) and non-equilibrium conditions (transient planar extensional flow) are demonstrated with particular emphasis on the new enhancements of the Chebyshev polynomial and the Krylov subspace methods. In turn, the algorithm with the highest efficiency and fidelity, namely, the Krylov subspace method, is used to simulate dilute solutions of high molecular weight polystyrene in uniaxial extensional flow. Finally, it is demonstrated that the bead-spring Brownian dynamics simulation with appropriate inclusion of excluded volume and hydrodynamic interactions can quantitatively predict the observed extensional hardening of polystyrene dilute solutions over a broad molecular weight range.

11. Application of spectral methods for high-frequency financial data to quantifying states of market participants

Sato, Aki-Hiro

2008-06-01

Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A 382 (2007) 258-270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore, it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and numerically. It is confirmed that these spectral distances are connected with distributions for behavioural parameters of the market participants from numerical simulation. This concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioural parameters of the market participants.

12. Quantitative method to assess caries via fluorescence imaging from the perspective of autofluorescence spectral analysis

Chen, Q. G.; Zhu, H. H.; Xu, Y.; Lin, B.; Chen, H.

2015-08-01

A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565-750 nm. The spectral parameter, defined as the ratio of wavebands at 565-750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as <0.66, 0.66-1.06, 1.06-1.62, and >1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems.

13. On modelling three-dimensional piezoelectric smart structures with boundary spectral element method

2017-05-01

The computational efficiency of the boundary element method in elastodynamic analysis can be significantly improved by employing high-order spectral elements for boundary discretisation. In this work, for the first time, the so-called boundary spectral element method is utilised to formulate the piezoelectric smart structures that are widely used in structural health monitoring (SHM) applications. The resultant boundary spectral element formulation has been validated by the finite element method (FEM) and physical experiments. The new formulation has demonstrated a lower demand on computational resources and a higher numerical stability than commercial FEM packages. Comparing to the conventional boundary element formulation, a significant reduction in computational expenses has been achieved. In summary, the boundary spectral element formulation presented in this paper provides a highly efficient and stable mathematical tool for the development of SHM applications.

14. Postprocessing Fourier spectral methods: The case of smooth solutions

SciTech Connect

Garcia-Archilla, B.; Novo, J.; Titi, E.S.

1998-11-01

A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is analyzed and a refined postprocessing technique is proposed.

15. A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation

Gong, Yuezheng; Wang, Qi; Wang, Yushun; Cai, Jiaxiang

2017-01-01

A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrödinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref. [56] to prove that the optimal rate of convergence of the new method is in the order of O (N-r +τ2) in the discrete L2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and τ is the time step size. A fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method. Numerical examples are presented to show the efficiency and accuracy of the new method.

16. A DFFD simulation method combined with the spectral element method for solid-fluid-interaction problems

Chen, Li-Chieh; Huang, Mei-Jiau

2017-02-01

A 2D simulation method for a rigid body moving in an incompressible viscous fluid is proposed. It combines one of the immersed-boundary methods, the DFFD (direct forcing fictitious domain) method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid-structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. A pseudo body force is imposed within the solid domain to enforce the rigid body motion and a Lagrangian mesh composed of triangular elements is employed for tracing the rigid body. In particular, a so called sub-cell scheme is proposed to smooth the discontinuity at the fluid-solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures.

17. Spectrum-based method to generate good decoy libraries for spectral library searching in peptide identifications.

PubMed

Cheng, Chia-Ying; Tsai, Chia-Feng; Chen, Yu-Ju; Sung, Ting-Yi; Hsu, Wen-Lian

2013-05-03

As spectral library searching has received increasing attention for peptide identification, constructing good decoy spectra from the target spectra is the key to correctly estimating the false discovery rate in searching against the concatenated target-decoy spectral library. Several methods have been proposed to construct decoy spectral libraries. Most of them construct decoy peptide sequences and then generate theoretical spectra accordingly. In this paper, we propose a method, called precursor-swap, which directly constructs decoy spectral libraries directly at the "spectrum level" without generating decoy peptide sequences by swapping the precursors of two spectra selected according to a very simple rule. Our spectrum-based method does not require additional efforts to deal with ion types (e.g., a, b or c ions), fragment mechanism (e.g., CID, or ETD), or unannotated peaks, but preserves many spectral properties. The precursor-swap method is evaluated on different spectral libraries and the results of obtained decoy ratios show that it is comparable to other methods. Notably, it is efficient in time and memory usage for constructing decoy libraries. A software tool called Precursor-Swap-Decoy-Generation (PSDG) is publicly available for download at http://ms.iis.sinica.edu.tw/PSDG/.

18. Spectral methods for some singularly perturbed third order ordinary differential equations

Temsah, R.

2008-01-01

Spectral methods with interface point are presented to deal with some singularly perturbed third order boundary value problems of reaction-diffusion and convection-diffusion types. First, linear equations are considered and then non-linear equations. To solve non-linear equations, Newton?s method of quasi-linearization is applied. The problem is reduced to two systems of ordinary differential equations. And, then, each system is solved using spectral collocation methods. Our numerical experiments show that the proposed methods are produce highly accurate solutions in little computer time when compared with the other methods available in the literature.

19. Multi-spectral temperature measurement method for gas turbine blade

Gao, Shan; Feng, Chi; Wang, Lixin; Li, Dong

2016-02-01

One of the basic methods to improve both the thermal efficiency and power output of a gas turbine is to increase the firing temperature. However, gas turbine blades are easily damaged in harsh high-temperature and high-pressure environments. Therefore, ensuring that the blade temperature remains within the design limits is very important. There are unsolved problems in blade temperature measurement, relating to the emissivity of the blade surface, influences of the combustion gases, and reflections of radiant energy from the surroundings. In this study, the emissivity of blade surfaces has been measured, with errors reduced by a fitting method, influences of the combustion gases have been calculated for different operational conditions, and a reflection model has been built. An iterative computing method is proposed for calculating blade temperatures, and the experimental results show that this method has high precision.

20. Spectral methods applied to fluidized bed combustors. Final report

SciTech Connect

Brown, R.C.; Christofides, N.J.; Junk, K.W.; Raines, T.S.; Thiede, T.D.

1996-08-01

The objective of this project was to develop methods for characterizing fuels and sorbents from time-series data obtained during transient operation of fluidized bed boilers. These methods aimed at determining time constants for devolatilization and char burnout using carbon dioxide (CO{sub 2}) profiles and from time constants for the calcination and sulfation processes using CO{sub 2} and sulfur dioxide (SO{sub 2}) profiles.

1. Modified Spectral Fatigue Methods for S-N Curves With MIL-HDBK-5J Coefficients

NASA Technical Reports Server (NTRS)

Irvine, Tom; Larsen, Curtis

2016-01-01

The rainflow method is used for counting fatigue cycles from a stress response time history, where the fatigue cycles are stress-reversals. The rainflow method allows the application of Palmgren-Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The fatigue damage may also be calculated from a stress response power spectral density (PSD) using the semi-empirical Dirlik, Single Moment, Zhao-Baker and other spectral methods. These methods effectively assume that the PSD has a corresponding time history which is stationary with a normal distribution. This paper shows how the probability density function for rainflow stress cycles can be extracted from each of the spectral methods. This extraction allows for the application of the MIL-HDBK-5J fatigue coefficients in the cumulative damage summation. A numerical example is given in this paper for the stress response of a beam undergoing random base excitation, where the excitation is applied separately by a time history and by its corresponding PSD. The fatigue calculation is performed in the time domain, as well as in the frequency domain via the modified spectral methods. The result comparison shows that the modified spectral methods give comparable results to the time domain rainflow counting method.

2. Stepwise method based on Wiener estimation for spectral reconstruction in spectroscopic Raman imaging.

PubMed

Chen, Shuo; Wang, Gang; Cui, Xiaoyu; Liu, Quan

2017-01-23

Raman spectroscopy has demonstrated great potential in biomedical applications. However, spectroscopic Raman imaging is limited in the investigation of fast changing phenomena because of slow data acquisition. Our previous studies have indicated that spectroscopic Raman imaging can be significantly sped up using the approach of narrow-band imaging followed by spectral reconstruction. A multi-channel system was built to demonstrate the feasibility of fast wide-field spectroscopic Raman imaging using the approach of simultaneous narrow-band image acquisition followed by spectral reconstruction based on Wiener estimation in phantoms. To further improve the accuracy of reconstructed Raman spectra, we propose a stepwise spectral reconstruction method in this study, which can be combined with the earlier developed sequential weighted Wiener estimation to improve spectral reconstruction accuracy. The stepwise spectral reconstruction method first reconstructs the fluorescence background spectrum from narrow-band measurements and then the pure Raman narrow-band measurements can be estimated by subtracting the estimated fluorescence background from the overall narrow-band measurements. Thereafter, the pure Raman spectrum can be reconstructed from the estimated pure Raman narrow-band measurements. The result indicates that the stepwise spectral reconstruction method can improve spectral reconstruction accuracy significantly when combined with sequential weighted Wiener estimation, compared with the traditional Wiener estimation. In addition, qualitatively accurate cell Raman spectra were successfully reconstructed using the stepwise spectral reconstruction method from the narrow-band measurements acquired by a four-channel wide-field Raman spectroscopic imaging system. This method can potentially facilitate the adoption of spectroscopic Raman imaging to the investigation of fast changing phenomena.

3. The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential

Baskakov, A. G.; Polyakov, D. M.

2017-01-01

The paper is concerned with the spectral properties of second- order differential operators defined by periodic and quasi-periodic boundary conditions. We obtain asymptotic formulae for the eigenvalues, derive estimates of projections, give estimates for the equiconvergence of spectral decompositions, find sufficient conditions for operators to be spectral, and write down an asymptotic expansion for the semigroup of operators generated by the negative of the differential operator under consideration. Our estimates involve coefficients of the Fourier potential. The main results of the paper are obtained by using the method of similar operators. Bibliography: 34 titles.

4. Extension of a spectral time-stepping domain decomposition method for dispersive and dissipative wave propagation.

PubMed

Botts, Jonathan; Savioja, Lauri

2015-04-01

For time-domain modeling based on the acoustic wave equation, spectral methods have recently demonstrated promise. This letter presents an extension of a spectral domain decomposition approach, previously used to solve the lossless linear wave equation, which accommodates frequency-dependent atmospheric attenuation and assignment of arbitrary dispersion relations. Frequency-dependence is straightforward to assign when time-stepping is done in the spectral domain, so combined losses from molecular relaxation, thermal conductivity, and viscosity can be approximated with little extra computation or storage. A mode update free from numerical dispersion is derived, and the model is confirmed with a numerical experiment.

5. Daniell method for power spectral density estimation in atomic force microscopy

SciTech Connect

Labuda, Aleksander

2016-03-15

An alternative method for power spectral density (PSD) estimation—the Daniell method—is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion—the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum.

6. FOCUSR: feature oriented correspondence using spectral regularization--a method for precise surface matching.

PubMed

Lombaert, Herve; Grady, Leo; Polimeni, Jonathan R; Cheriet, Farida

2013-09-01

Existing methods for surface matching are limited by the tradeoff between precision and computational efficiency. Here, we present an improved algorithm for dense vertex-to-vertex correspondence that uses direct matching of features defined on a surface and improves it by using spectral correspondence as a regularization. This algorithm has the speed of both feature matching and spectral matching while exhibiting greatly improved precision (distance errors of 1.4 percent). The method, FOCUSR, incorporates implicitly such additional features to calculate the correspondence and relies on the smoothness of the lowest-frequency harmonics of a graph Laplacian to spatially regularize the features. In its simplest form, FOCUSR is an improved spectral correspondence method that nonrigidly deforms spectral embeddings. We provide here a full realization of spectral correspondence where virtually any feature can be used as an additional information using weights on graph edges, but also on graph nodes and as extra embedded coordinates. As an example, the full power of FOCUSR is demonstrated in a real-case scenario with the challenging task of brain surface matching across several individuals. Our results show that combining features and regularizing them in a spectral embedding greatly improves the matching precision (to a submillimeter level) while performing at much greater speed than existing methods.

7. FOCUSR: Feature Oriented Correspondence using Spectral Regularization–A Method for Precise Surface Matching

PubMed Central

Lombaert, Herve; Grady, Leo; Polimeni, Jonathan R.; Cheriet, Farida

2013-01-01

Existing methods for surface matching are limited by the trade-off between precision and computational efficiency. Here we present an improved algorithm for dense vertex-to-vertex correspondence that uses direct matching of features defined on a surface and improves it by using spectral correspondence as a regularization. This algorithm has the speed of both feature matching and spectral matching while exhibiting greatly improved precision (distance errors of 1.4%). The method, FOCUSR, incorporates implicitly such additional features to calculate the correspondence and relies on the smoothness of the lowest-frequency harmonics of a graph Laplacian to spatially regularize the features. In its simplest form, FOCUSR is an improved spectral correspondence method that nonrigidly deforms spectral embeddings. We provide here a full realization of spectral correspondence where virtually any feature can be used as additional information using weights on graph edges, but also on graph nodes and as extra embedded coordinates. As an example, the full power of FOCUSR is demonstrated in a real case scenario with the challenging task of brain surface matching across several individuals. Our results show that combining features and regularizing them in a spectral embedding greatly improves the matching precision (to a sub-millimeter level) while performing at much greater speed than existing methods. PMID:23868776

8. Tracking perturbations in Boolean networks with spectral methods

Kesseli, Juha; Rämö, Pauli; Yli-Harja, Olli

2005-08-01

In this paper we present a method for predicting the spread of perturbations in Boolean networks. The method is applicable to networks that have no regular topology. The prediction of perturbations can be performed easily by using a presented result which enables the efficient computation of the required iterative formulas. This result is based on abstract Fourier transform of the functions in the network. In this paper the method is applied to show the spread of perturbations in networks containing a distribution of functions found from biological data. The advances in the study of the spread of perturbations can directly be applied to enable ways of quantifying chaos in Boolean networks. Derrida plots over an arbitrary number of time steps can be computed and thus distributions of functions compared with each other with respect to the amount of order they create in random networks.

9. A spectral method for halo particle definition in intense mismatched beams

SciTech Connect

Dorf, Mikhail A.; Davidson, Ronald C.; Startsev, Edward A.

2011-04-15

An advanced spectral analysis of a mismatched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.

10. New Spectral Method for Halo Particle Definition in Intense Mis-matched Beams

SciTech Connect

Dorf, Mikhail A.; Davidson, Ronald C.; Startsev, Edward A.

2011-04-27

An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.

11. Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid

PubMed Central

Xu, Zhenli; Cai, Wei

2009-01-01

This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from 𝒪(M2N4) to 𝒪(MN4), where N2 is the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method. PMID:20414359

12. Weak turbulence simulations with the Hermite-Fourier spectral method

Vencels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco; Roytershteyn, Vadim; Markidis, Stefano

2015-11-01

Recently, a new (transform) method based on a Fourier-Hermite (FH) discretization of the Vlasov-Maxwell equations has been developed. The resulting set of moment equations is discretized implicitly in time with a Crank-Nicolson scheme and solved with a nonlinear Newton-Krylov technique. For periodic boundary conditions, this discretization delivers a scheme that conserves the total mass, momentum and energy of the system exactly. In this work, we apply the FH method to study a problem of Langmuir turbulence, where a low signal-to-noise ratio is important to follow the turbulent cascade and might require a lot of computational resources if studied with PIC. We simulate a weak (low density) electron beam moving in a Maxwellian plasma and subject to an instability that generates Langmuir waves and a weak turbulence field. We also discuss some optimization techniques to optimally select the Hermite basis in terms of its shift and scaling argument, and show that this technique improve the overall accuracy of the method. Finally, we discuss the applicability of the HF method for studying kinetic plasma turbulence. This work was funded by LDRD under the auspices of the NNSA of the U.S. by LANL under contract DE-AC52-06NA25396 and by EC through the EPiGRAM project (grant agreement no. 610598. epigram-project.eu).

13. A method extracting solar cell parameters from spectral response by inverse laplace transform

Tuominen, E.; Acerbis, M.; Hovinen, A.; Siirtola, T.; Sinkkonen, J.

1997-01-01

A mathematical method to interpret spectral responses measured from solar cells has been developed. Taking an inverse Laplace transform from the spectral response of a solar cell the spatial dependent collection efficiency of the cell can be obtained. Several important material parameters of the solar cell can be extracted from this function. Applying this method the properties of the solar cell can be investigated without applying characterization methods to the cell itself. We have applied the method both to simulated solar cells andto real solar cells.

14. Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors.

PubMed

Kawamoto, Tatsuro; Kabashima, Yoshiyuki

2015-06-01

Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

15. Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors

Kawamoto, Tatsuro; Kabashima, Yoshiyuki

2015-06-01

Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

16. Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

17. Single-domain spectral method for black hole puncture data

SciTech Connect

Ansorg, Marcus; Bruegmann, Bernd; Tichy, Wolfgang

2004-09-15

We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudospectral method applied in a single spatial domain. Introducing appropriate coordinates, these methods exhibit rapid convergence of the conformal factor and lead to highly accurate solutions. As an application we investigate small mass ratios of binary black holes and compare these with the corresponding test mass limit that we obtain through a semianalytical limiting procedure. In particular, we compare the binding energy of puncture data in this limit with that of a test particle in the Schwarzschild spacetime and find that it deviates by 50% from the Schwarzschild result at the innermost stable circular orbit of Schwarzschild, if the ADM mass at each puncture is used to define the local black hole masses.

18. Generalized spectral method for near-field optical microscopy

SciTech Connect

Jiang, B.-Y.; Zhang, L. M.; Basov, D. N.; Fogler, M. M.; Castro Neto, A. H.

2016-02-07

Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.

19. Generalized spectral method for near-field optical microscopy

Jiang, B.-Y.; Zhang, L. M.; Castro Neto, A. H.; Basov, D. N.; Fogler, M. M.

2016-02-01

Electromagnetic interaction between a sub-wavelength particle (the "probe") and a material surface (the "sample") is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.

20. GPU Accelerated Spectral Element Methods: 3D Euler equations

Abdi, D. S.; Wilcox, L.; Giraldo, F.; Warburton, T.

2015-12-01

A GPU accelerated nodal discontinuous Galerkin method for the solution of three dimensional Euler equations is presented. The Euler equations are nonlinear hyperbolic equations that are widely used in Numerical Weather Prediction (NWP). Therefore, acceleration of the method plays an important practical role in not only getting daily forecasts faster but also in obtaining more accurate (high resolution) results. The equation sets used in our atomospheric model NUMA (non-hydrostatic unified model of the atmosphere) take into consideration non-hydrostatic effects that become more important with high resolution. We use algorithms suitable for the single instruction multiple thread (SIMT) architecture of GPUs to accelerate solution by an order of magnitude (20x) relative to CPU implementation. For portability to heterogeneous computing environment, we use a new programming language OCCA, which can be cross-compiled to either OpenCL, CUDA or OpenMP at runtime. Finally, the accuracy and performance of our GPU implementations are veried using several benchmark problems representative of different scales of atmospheric dynamics.

1. Structural, spectral analysis of ambroxol using DFT methods

Rajesh, P.; Gunasekaran, S.; Manikandan, A.

2017-09-01

The FT-IR and FT-Raman spectra of Ambroxol are recorded in the region 4000-450 cm-1 and 4000-50 cm-1 respectively. Theoretical calculations were performed by density functional theory (DFT) method using 6-31G(2d,3p) basis set. The complete vibrational assignments of wavenumbers were made on the basis of potential energy distribution (PED). The results of the calculations were applied to the simulated spectra of the title compound, which show excellent agreement with the observed spectra. The frontier orbital energy gap and dipole moment, illustrates the high reactivity of the title molecule. Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analysed using natural bond orbital (NBO) analysis. Molecular electrostatic potential (MEP), the electronic properties were performed by time-dependent DFT (TD-DFT) approach, and HOMO-LUMO energy levels are also constructed.

2. A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity

SciTech Connect

Feng, W. M.; Yu, P.; Hu, Shenyang Y.; Liu, Z. K.; Du, Q.; Chen , L.Q.

2009-02-01

In recent years, Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences. To further improve their effectiveness, we recently developed a new adaptive Fourier-spectral semi-implicit method (AFSIM) for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm. In this paper, we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous, anisotropic elasticity. Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes. It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.

3. Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

4. Spectral responsivity calibrations of two types of pyroelectric radiometers using three different methods

Zeng, J.; Eppeldauer, G. P.; Hanssen, L. M.; Podobedov, V. B.

2012-06-01

Spectral responsivity calibrations of two different types of pyroelectric radiometers have been made in the infrared region up to 14 μm in power mode using three different calibration facilities at NIST. One pyroelectric radiometer is a temperature-controlled low noise-equivalent-power (NEP) single-element pyroelectric radiometer with an active area of 5 mm in diameter. The other radiometer is a prototype using the same type of pyroeletric detector with dome-input optics, which was designed to increase absorptance and to minimize spectral structures to obtain a constant spectral responsivity. Three calibration facilities at NIST were used to conduct direct and indirect responsivity calibrations tied to absolute scales in the infrared spectral regime. We report the calibration results for the single-element pyroelectric radiometer using a new Infrared Spectral Comparator Facility (IRSCF) for direct calibration. Also, a combined method using the Fourier Transform Infrared Spectrophotometry (FTIS) facility and single wavelength laser tie-points are described to calibrated standard detectors with an indirect approach. For the dome-input pyroelectric radiometer, the results obtained from another direct calibration method using a circular variable filter (CVF) spectrometer and the FTIS are also presented. The inter-comparison of different calibration methods enables us to improve the responsivity uncertainty performed by the different facilities. For both radiometers, consistent results of the spectral power responsivity have been obtained applying different methods from 1.5 μm to 14 μm with responsivity uncertainties between 1 % and 2 % (k = 2). Relevant characterization results, such as spatial uniformity, linearity, and angular dependence of responsivity, are shown. Validation of the spectral responsivity calibrations, uncertainty sources, and improvements for each method will also be discussed.

5. A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

SciTech Connect

Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.

2013-06-15

Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods.

6. Estimating ecological indicators of karst rocky desertification by linear spectral unmixing method

Zhang, Xia; Shang, Kun; Cen, Yi; Shuai, Tong; Sun, Yanli

2014-09-01

Coverage rates of vegetation and exposed bedrock are two key indicators of karst rocky desertification. In this study, the abundances of vegetation and exposed rock were retrieved from a hyperspectral Hyperion image using linear spectral unmixing method. The results were verified using the spectral indices of karst rocky desertification (KRDSI) and an integrated LAI spectral index: modified chlorophyll absorption ratio index (MCARI2). The abundances showed significant linear correlations with KRDSI and MCARI2. The coefficients of determination (R2) were 0.93, 0.66, and 0.84 for vegetation, soil, and rock, respectively, indicating that the abundances of vegetation and bedrock can characterize their coverage rates to a certain extent. Finally, the abundances of vegetation and bedrock were graded and integrated to evaluate rocky desertification in a typical karst region. This study suggests that spectral unmixing algorithm and hyperspectral remote sensing imagery can be used to monitor and evaluate karst rocky desertification.

7. Study of femtosecond laser spectrally resolved interferometry distance measurement based on excess fraction method

Ji, Rongyi; Hu, Kun; Li, Yao; Gao, Shuyuan; Zhou, Weihu

2017-02-01

Spectrally resolved interferometry (SRI) technology is a high precision laser interferometry technology, whose short non-ambiguity range (NAR) increases the precision requirement of pre-measurement in absolute distance measurement. In order to improve NAR of femtosecond laser SRI, the factors affecting NAR are studied in measurement system, and synthetic NAR method is presented based on excess fraction method to solve this question. A theoretical analysis is implemented and two Fabry-Perot Etalons with different free spectral range are selected to carry out digital simulation experiments. The experiment shows that NAR can be improved using synthetic NAR method and the precision is the same with that of fundamental femtosecond laser SRI.

8. A comparison of vortex and pseudo-spectral methods at high Reynolds numbers

Leonard, Anthony; van Rees, Wim; Koumoutsakos, Petros

2010-11-01

We validate the hybrid particle-mesh vortex method against a pseudo-spectral method in simulations of the Taylor-Green vortex and colliding vortex tubes at Re = 1600 - 10,000. The spectral method uses the smooth filter introduced in [1]. In the case of the Taylor-Green vortex, we observe very good agreement in the evolution of the vortical structures albeit small discrepancies in the energy spectrum only for the smallest length scales. In the collision of two anti-parallel vortex tubes at Re = 10 000, there is very good agreement between the two methods in terms of the simulated vortical structures throughout the first reconnection of the tubes. The maximum error in the effective viscosity is below 2.5% and 1% for the vortex method and the pseudo-spectral method respectively. At later times the agreement between the two methods in the vortical structures deteriorates even though there is good agreement in the energy spectrum. Both methods resolve an unexpected vortex breakdown during the second reconnection of the vortex tubes.[4pt] [1] Hou, T. and Li, R., 2007. Computing nearly singular solutions using pseudo-spectral methods. J. of Comput. Phys., 226:379-397.

9. Binding characteristics of salbutamol with DNA by spectral methods.

PubMed

Bi, Shuyun; Pang, Bo; Zhao, Tingting; Wang, Tianjiao; Wang, Yu; Yan, Lili

2013-07-01

Salbutamol interacting with deoxyribonucleic acid (DNA) was examined by fluorescence, UV absorption, viscosity measurements, and DNA melting techniques. The binding constants and binding sites were obtained at different temperatures by fluorescence quenching. The Stern-Volmer plots showed that the quenching of fluorescence of salbutamol by DNA was a static quenching. To probe the binding mode, various analytical methods were performed and the results were as follows: hyperchromic effect was shown in the absorption spectra of salbutamol upon addition of DNA; there was no appreciable increase in melting temperature of DNA when salbutamol was presented in DNA solution; the fluorescence intensity of salbutamol-DNA decrease with the increasing ionic strength; the relative viscosity of DNA did not change in the presence of salbutamol; the binding constant of salbutamol with double strand DNA (dsDNA) was much higher than that of it with single strand DNA (ssDNA). All these results indicated that the binding mode of salbutamol to DNA should be groove binding. The thermodynamic parameters suggested that hydrogen bond or van der Waals force might play an important role in salbutamol binding to DNA. According to the Förster energy transference theory, the binding distance between the acceptor and donor was 3.70 nm.

10. Binding characteristics of salbutamol with DNA by spectral methods

Bi, Shuyun; Pang, Bo; Zhao, Tingting; Wang, Tianjiao; Wang, Yu; Yan, Lili

2013-07-01

Salbutamol interacting with deoxyribonucleic acid (DNA) was examined by fluorescence, UV absorption, viscosity measurements, and DNA melting techniques. The binding constants and binding sites were obtained at different temperatures by fluorescence quenching. The Stern-Volmer plots showed that the quenching of fluorescence of salbutamol by DNA was a static quenching. To probe the binding mode, various analytical methods were performed and the results were as follows: hyperchromic effect was shown in the absorption spectra of salbutamol upon addition of DNA; there was no appreciable increase in melting temperature of DNA when salbutamol was presented in DNA solution; the fluorescence intensity of salbutamol-DNA decrease with the increasing ionic strength; the relative viscosity of DNA did not change in the presence of salbutamol; the binding constant of salbutamol with double strand DNA (dsDNA) was much higher than that of it with single strand DNA (ssDNA). All these results indicated that the binding mode of salbutamol to DNA should be groove binding. The thermodynamic parameters suggested that hydrogen bond or van der Waals force might play an important role in salbutamol binding to DNA. According to the Förster energy transference theory, the binding distance between the acceptor and donor was 3.70 nm.

11. Semi-implicit spectral deferred correction methods for ordinary differential equations

SciTech Connect

Minion, Michael L.

2002-10-06

A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The stability and accuracy of the resulting ODE methods are explored analytically and numerically. The SISDC methods are intended to be combined with the method of lines approach to yield a flexible framework for creating higher-order semi-implicit methods for partial differential equations. A discussion and numerical examples of the SISDC method applied to advection-diffusion type equations are included. The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.

12. A novel edge-preserving nonnegative matrix factorization method for spectral unmixing

Bao, Wenxing; Ma, Ruishi

2015-12-01

Spectral unmixing technique is one of the key techniques to identify and classify the material in the hyperspectral image processing. A novel robust spectral unmixing method based on nonnegative matrix factorization(NMF) is presented in this paper. This paper used an edge-preserving function as hypersurface cost function to minimize the nonnegative matrix factorization. To minimize the hypersurface cost function, we constructed the updating functions for signature matrix of end-members and abundance fraction respectively. The two functions are updated alternatively. For evaluation purpose, synthetic data and real data have been used in this paper. Synthetic data is used based on end-members from USGS digital spectral library. AVIRIS Cuprite dataset have been used as real data. The spectral angle distance (SAD) and abundance angle distance(AAD) have been used in this research for assessment the performance of proposed method. The experimental results show that this method can obtain more ideal results and good accuracy for spectral unmixing than present methods.

13. Performance evaluation of spectral analysis and Werner deconvolution interpretation techniques in magnetic method

2017-03-01

Determining the depth of anomalous geological subsurface structure is an important parameter in any of geophysical methods. Though, numerous magnetic interpretation techniques are available in literature for locating depth to the causative source, no specific information is found on the performance of any of the techniques. Werner deconvolution and Spectral methods are widely used to determine the approximate depth to the causative sources, which are then used in modeling methods. An attempt has been made in this study to evaluate the performance of Werner and spectral methods. Synthetic magnetic anomalies are generated over sheet, dyke and fault models for different combinations of geometric dimensions of the bodies and magnetization angles. These anomalies were interpreted with the two methods: Werner deconvolution and Spectral analysis. The error percentages are calculated as the difference between the theoretical and interpreted values. In addition, the results are discussed for their performance. It is observed that Werner method yields more reasonable values for depth compared to spectral methods particularly when body widths are more and deep seated or faulting is deep. In case of dyke model, the Werner method determines width also reliably.

14. [The method of time series modeling and its application in the spectral analysis of lubricating oil].

PubMed

Gan, M; Zuo, H; Yang, Z; Jiang, Y

2000-02-01

In this paper, we discuss the applications of time series modeling method in the analysis of lubricating oil of mechanical equipment. We obtained satisfactory results by applying AR model to perform time series modeling and forecasting analysis to the collected spectral analysis data of the air engine. So we have built a practical method for state monitoring and trouble forecasting of mechanical equipment.

15. Finite and spectral cell method for wave propagation in heterogeneous materials

Joulaian, Meysam; Duczek, Sascha; Gabbert, Ulrich; Düster, Alexander

2014-09-01

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1-3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].

16. A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

17. Application of the MUSIC method for spectral estimation to a model system

1993-04-01

The multiple signal classification method (MUSIC) for spectral estimation is applied to data generated for three cases of a simple model system, based on five harmonic frequencies. The results are compared to the exact spectrum as well as to the results obtained with the Fourier transform method. The effect of the parameters required to be set in the application of the MUSIC methods as well as the effect of signal-to-noise ratio on the spectral estimate and its error are studied. Spectral resolution is discussed. It is found here that MUSIC tends to yield very good estimates of the frequencies but that relative amplitudes of lines and line shapes are not generally estimated.

18. High-capacity quantum key distribution using Chebyshev-map values corresponding to Lucas numbers coding

Lai, Hong; Orgun, Mehmet A.; Pieprzyk, Josef; Li, Jing; Luo, Mingxing; Xiao, Jinghua; Xiao, Fuyuan

2016-11-01

We propose an approach that achieves high-capacity quantum key distribution using Chebyshev-map values corresponding to Lucas numbers coding. In particular, we encode a key with the Chebyshev-map values corresponding to Lucas numbers and then use k-Chebyshev maps to achieve consecutive and flexible key expansion and apply the pre-shared classical information between Alice and Bob and fountain codes for privacy amplification to solve the security of the exchange of classical information via the classical channel. Consequently, our high-capacity protocol does not have the limitations imposed by orbital angular momentum and down-conversion bandwidths, and it meets the requirements for longer distances and lower error rates simultaneously.

19. Improved Fault Classification in Series Compensated Transmission Line: Comparative Evaluation of Chebyshev Neural Network Training Algorithms.

PubMed

Vyas, Bhargav Y; Das, Biswarup; Maheshwari, Rudra Prakash

2016-08-01

This paper presents the Chebyshev neural network (ChNN) as an improved artificial intelligence technique for power system protection studies and examines the performances of two ChNN learning algorithms for fault classification of series compensated transmission line. The training algorithms are least-square Levenberg-Marquardt (LSLM) and recursive least-square algorithm with forgetting factor (RLSFF). The performances of these algorithms are assessed based on their generalization capability in relating the fault current parameters with an event of fault in the transmission line. The proposed algorithm is fast in response as it utilizes postfault samples of three phase currents measured at the relaying end corresponding to half-cycle duration only. After being trained with only a small part of the generated fault data, the algorithms have been tested over a large number of fault cases with wide variation of system and fault parameters. Based on the studies carried out in this paper, it has been found that although the RLSFF algorithm is faster for training the ChNN in the fault classification application for series compensated transmission lines, the LSLM algorithm has the best accuracy in testing. The results prove that the proposed ChNN-based method is accurate, fast, easy to design, and immune to the level of compensations. Thus, it is suitable for digital relaying applications.

20. Research on high resolution spectral method of hyperspectral LiDAR

Li, Feng; Jiang, Chenghao; Zhu, Jingguo; Li, Menglin; Meng, Zhe

2016-10-01

Hyperspectral LiDAR using supercontinuum laser as light source, applying spectroscopic technology gets backscattered reflectance of different wavelengths, and can acquire both the geometry and spectral information on the target. Due to the development of the photoelectric sensor, hyperspectral LiDAR has fewer spectral channels, which limits its application in physical properties detection. To solve this problem, this paper proposes a new method based on the micro mirror array. By blaze grating, the supercontinuum laser is grating into monochromatic light in space, first projected to the micro mirror array, by controlling the micro mirror array flip, specific spectrum and reflection to corresponding photoelectric sensor channels, improve the spectral resolution. The micro mirror array photoelectric sensor resolution is much higher than the number of channels, through this method, can greatly improve the spectral resolution. In this paper, based on the micro mirror array, the simulation design is carried out and the feasibility of the method is verified by experiments. The simulation and experimental results show that the spectral resolution can be improved greatly by controlling the turning of the micro mirror.

1. Color image segmentation using watershed and Nyström method based spectral clustering

Bai, Xiaodong; Cao, Zhiguo; Yu, Zhenghong; Zhu, Hu

2011-11-01

Color image segmentation draws a lot of attention recently. In order to improve efficiency of spectral clustering in color image segmentation, a novel two-stage color image segmentation method is proposed. In the first stage, we use vector gradient approach to detect color image gradient information, and watershed transformation to get the pre-segmentation result. In the second stage, Nyström extension based spectral clustering is used to get the final result. To verify the proposed algorithm, it is applied to color images from the Berkeley Segmentation Dataset. Experiments show our method can bring promising results and reduce the runtime significantly.

2. The analysis of toxic connections content in water by spectral methods

Plotnikova, I. V.; Chaikovskaya, O. N.; Sokolova, I. V.; Artyushin, V. R.

2017-08-01

The current state of ecology means the strict observance of measures for the utilization of household and industrial wastes that is connected with very essential expenses of means and time. Thanks to spectroscopic devices usage the spectral methods allow to carry out the express quantitative and qualitative analysis in a workplace and field conditions. In a work the application of spectral methods by studying the degradation of toxic organic compounds after preliminary radiation of various sources is shown. Experimental data of optical density of water at various influences are given.

3. A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

4. Application of Modified Chebyshev Picard Iteration to Differential Correction for Improved Robustness and Computation Time

Swenson, Travis; Woollands, Robyn; Junkins, John; Lo, Martin

2017-01-01

A novel application of Modified Chebyshev Picard Iteration (MCPI) to differential correction is presented. By leveraging the Chebyshev basis functions of MCPI, interpolation in 1 dimension may be used to target plane crossing events, instead of integrating the 42 dimensional variational equation required for standard step integrators. This results in dramatically improved performance over traditional differential correctors. MCPI was tested against the Runge-Kutta 7/8 integrator on over 45,000 halo orbits in three different three-body problems, and was found to be up to an order of magnitude faster, while simultaneously increasing robustness.

5. Application of Modified Chebyshev Picard Iteration to Differential Correction for Improved Robustness and Computation Time

Swenson, Travis; Woollands, Robyn; Junkins, John; Lo, Martin

2017-09-01

A novel application of Modified Chebyshev Picard Iteration (MCPI) to differential correction is presented. By leveraging the Chebyshev basis functions of MCPI, interpolation in 1 dimension may be used to target plane crossing events, instead of integrating the 42 dimensional variational equation required for standard step integrators. This results in dramatically improved performance over traditional differential correctors. MCPI was tested against the Runge-Kutta 7/8 integrator on over 45,000 halo orbits in three different three-body problems, and was found to be up to an order of magnitude faster, while simultaneously increasing robustness.

6. Data processing method applying principal component analysis and spectral angle mapper for imaging spectroscopic sensors

García-Allende, P. B.; Conde, O. M.; Mirapeix, J.; Cubillas, A. M.; López-Higuera, J. M.

2007-07-01

A data processing method for hyperspectral images is presented. Each image contains the whole diffuse reflectance spectra of the analyzed material for all the spatial positions along a specific line of vision. This data processing method is composed of two blocks: data compression and classification unit. Data compression is performed by means of Principal Component Analysis (PCA) and the spectral interpretation algorithm for classification is the Spectral Angle Mapper (SAM). This strategy of classification applying PCA and SAM has been successfully tested on the raw material on-line characterization in the tobacco industry. In this application case the desired raw material (tobacco leaves) should be discriminated from other unwanted spurious materials, such as plastic, cardboard, leather, candy paper, etc. Hyperspectral images are recorded by a spectroscopic sensor consisting of a monochromatic camera and a passive Prism- Grating-Prism device. Performance results are compared with a spectral interpretation algorithm based on Artificial Neural Networks (ANN).

7. Wave propagation numerical models in damage detection based on the time domain spectral element method

Ostachowicz, W.; Kudela, P.

2010-06-01

A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.

8. Site Characterization in the Urban Area of Tijuana, B. C., Mexico by Means of: H/V Spectral Ratios, Spectral Analysis of Surface Waves, and Random Decrement Method

Tapia-Herrera, R.; Huerta-Lopez, C. I.; Martinez-Cruzado, J. A.

2009-05-01

Results of site characterization for an experimental site in the metropolitan area of Tijuana, B. C., Mexico are presented as part of the on-going research in which time series of earthquakes, ambient noise, and induced vibrations were processed with three different methods: H/V spectral ratios, Spectral Analysis of Surface Waves (SASW), and the Random Decrement Method, (RDM). Forward modeling using the wave propagation stiffness matrix method (Roësset and Kausel, 1981) was used to compute the theoretical SH/P, SV/P spectral ratios, and the experimental H/V spectral ratios were computed following the conventional concepts of Fourier analysis. The modeling/comparison between the theoretical and experimental H/V spectral ratios was carried out. For the SASW method the theoretical dispersion curves were also computed and compared with the experimental one, and finally the theoretical free vibration decay curve was compared with the experimental one obtained with the RDM. All three methods were tested with ambient noise, induced vibrations, and earthquake signals. Both experimental spectral ratios obtained with ambient noise as well as earthquake signals agree quite well with the theoretical spectral ratios, particularly at the fundamental vibration frequency of the recording site. Differences between the fundamental vibration frequencies are evident for sites located at alluvial fill (~0.6 Hz) and at sites located at conglomerate/sandstones fill (0.75 Hz). Shear wave velocities for the soft soil layers of the 4-layer discrete soil model ranges as low as 100 m/s and up to 280 m/s. The results with the SASW provided information that allows to identify low velocity layers, not seen before with the traditional seismic methods. The damping estimations obtained with the RDM are within the expected values, and the dominant frequency of the system also obtained with the RDM correlates within the range of plus-minus 20 % with the one obtained by means of the H/V spectral

9. An Extension of the Time-Spectral Method to Overset Solvers

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas

2013-01-01

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

10. A combined spatial-spectral method for automated white blood cells segmentation

Li, Qingli; Wang, Yiting; Liu, Hongying; Wang, Jianbiao; Guo, Fangmin

2013-12-01

To overcome the shortcomings in the traditional white blood cells (WBCs) identification methods based on the color or gray images captured by light microscopy, a microscopy hyperspectral imaging system was used to analyze the blood smears. The system was developed by coupling an acousto-optic tunable filter (AOTF) adapter to a microscopy and driven by a SPF Model AOTF controller, which can capture hyperspectral images from 550 nm to 1000 nm with the spectral resolution 2-5 nm. Moreover, a combined spatial-spectral algorithm is proposed to segment the nuclei and cytoplasm of WBCs from the microscopy hyperspectral images. The proposed algorithm is based on the pixel-wise improved spectral angle mapper (ISAM) segmentation, followed by the majority voting within the active contour model regions. Experimental results show that the accuracy of the proposed algorithm is 91.06% (nuclei) and 85.59% (cytoplasm), respectively, which is higher than that of the spectral information divergence (SID) algorithm because the new method can jointly use both the spectral and spatial information of blood cells.

11. [Study on the absolute spectral irradiation calibration method for far ultraviolet spectrometer in remote sensing].

PubMed

Yu, Lei; Lin, Guan-Yu; Chen, Bin

2013-01-01

The present paper studied spectral irradiation responsivities calibration method which can be applied to the far ultraviolet spectrometer for upper atmosphere remote sensing. It is difficult to realize the calibration for far ultraviolet spectrometer for many reasons. Standard instruments for far ultraviolet waveband calibration are few, the degree of the vacuum experiment system is required to be high, the stabilities of the experiment are hardly maintained, and the limitation of the far ultraviolet waveband makes traditional diffuser and the integrating sphere radiance calibration method difficult to be used. To solve these problems, a new absolute spectral irradiance calibration method was studied, which can be applied to the far ultraviolet calibration. We build a corresponding special vacuum experiment system to verify the calibration method. The light source system consists of a calibrated deuterium lamp, a vacuum ultraviolet monochromater and a collimating system. We used the calibrated detector to obtain the irradiance responsivities of it. The three instruments compose the calibration irradiance source. We used the "calibration irradiance source" to illuminate the spectrometer prototype and obtained the spectral irradiance responsivities. It realized the absolute spectral irradiance calibration for the far ultraviolet spectrometer utilizing the calibrated detector. The absolute uncertainty of the calibration is 7.7%. The method is significant for the ground irradiation calibration of the far ultraviolet spectrometer in upper atmosphere remote sensing.

12. A quaternion-based spectral clustering method for color image segmentation

Li, Xiang; Jin, Lianghai; Liu, Hong; He, Zeng

2011-11-01

Spectral clustering method has been widely used in image segmentation. A key issue in spectral clustering is how to build the affinity matrix. When it is applied to color image segmentation, most of the existing methods either use Euclidean metric to define the affinity matrix, or first converting color-images into gray-level images and then use the gray-level images to construct the affinity matrix (component-wise method). However, it is known that Euclidean distances can not represent the color differences well and the component-wise method does not consider the correlation between color channels. In this paper, we propose a new method to produce the affinity matrix, in which the color images are first represented in quaternion form and then the similarities between color pixels are measured by quaternion rotation (QR) mechanism. The experimental results show the superiority of the new method.

13. High-Order Spectral Volume Method for 2D Euler Equations

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Zhang, Laiping; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The Spectral Volume (SV) method is extended to the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. Solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.

14. Development and Validation of a New Fallout Transport Method Using Variable Spectral Winds

Hopkins, Arthur Thomas

A new method has been developed to incorporate variable winds into fallout transport calculations. The method uses spectral coefficients derived by the National Meteorological Center. Wind vector components are computed with the coefficients along the trajectories of falling particles. Spectral winds are used in the two-step method to compute dose rate on the ground, downwind of a nuclear cloud. First, the hotline is located by computing trajectories of particles from an initial, stabilized cloud, through spectral winds, to the ground. The connection of particle landing points is the hotline. Second, dose rate on and around the hotline is computed by analytically smearing the falling cloud's activity along the ground. The feasibility of using specgtral winds for fallout particle transport was validated by computing Mount St. Helens ashfall locations and comparing calculations to fallout data. In addition, an ashfall equation was derived for computing volcanic ash mass/area on the ground. Ashfall data and the ashfall equation were used to back-calculate an aggregated particle size distribution for the Mount St. Helens eruption cloud. Further validation was performed by comparing computed and actual trajectories of a high explosive dust cloud (DIRECT COURSE). Using an error propagation formula, it was determined that uncertainties in spectral wind components produce less than four percent of the total dose rate variance. In summary, this research demonstrated the feasibility of using spectral coefficients for fallout transport calculations, developed a two-step smearing model to treat variable winds, and showed that uncertainties in spectral winds do not contribute significantly to the error in computed dose rate.

15. Study on Raman spectral imaging method for simultaneous estimation of ingredients concentration in food powder

USDA-ARS?s Scientific Manuscript database

This study investigated the potential of point scan Raman spectral imaging method for estimation of different ingredients and chemical contaminant concentration in food powder. Food powder sample was prepared by mixing sugar, vanillin, melamine and non-dairy cream at 5 different concentrations in a ...

16. Spectral method for characterization of avalanche photodiode working as single-photon detector.

PubMed

Cavalcanti, Maria Daniela Santabaia; Mendonça, Fábio Alencar; Ramos, Rubens Viana

2011-09-01

In this Letter, a new method for avalanche photodiode characterization, based on the spectral analysis of the photocurrent produced during an avalanche, is proposed. The theory is developed, and an experimental characterization of an avalanche photodiode working in the Geiger mode with CW laser is performed.

17. Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

NASA Technical Reports Server (NTRS)

Casarin, Mario

1996-01-01

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

18. Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems

Marchandise, Emilie; Chevaugeon, Nicolas; Remacle, Jean-Francois

2008-06-01

In this paper, we analyze the spatial and spectral superconvergence properties of one-dimensional hyperbolic conservation law by a discontinuous Galerkin (DG) method. The analyses combine classical mathematical arguments with MATLAB experiments. Some properties of the DG schemes are discovered using discrete Fourier analyses: superconvergence of the numerical wave numbers, Radau structure of the X spatial error.

19. Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

NASA Technical Reports Server (NTRS)

Casarin, Mario

1996-01-01

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

20. Finite-difference, spectral and Galerkin methods for time-dependent problems

NASA Technical Reports Server (NTRS)

1983-01-01

Finite difference, spectral and Galerkin methods for the approximate solution of time dependent problems are surveyed. A unified discussion on their accuracy, stability and convergence is given. In particular, the dilemma of high accuracy versus stability is studied in some detail.

1. Spectral collocation methods using sine functions for a rotating Bose-Einstein condensation in optical lattices

Chen, Huei-Shuang; Chang, Shing-Lin; Chien, Cheng-Sheng

2012-02-01

We study spectral-Galerkin methods (SGM) and spectral collocation methods (SCM) for parameter-dependent problems, where the Fourier sine functions are used as the basis functions. When the SGM and the SCM are incorporated in the context of a Taylor predictor-inexact Newton corrector continuation algorithm for tracing solution curves of the Gross-Pitaevskii equation (GPE), they can efficiently provide accurate numerical solutions for the GPE. We show how the inexact Newton method outperforms the classical Newton method in the continuation algorithm. In our numerical experiments, the centered difference method (CDM), the SGM and SCM are exploited to compute energy levels and wave functions of a rotating Bose-Einstein condensation (BEC) and a rotating BEC in optical lattices in 2D. Sample numerical results are reported.

2. Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

DOE PAGES

Smallwood, D. O.

1996-01-01

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

3. Direct numerical simulations of a reacting turbulent mixing layer by a pseudospectral-spectral element method

NASA Technical Reports Server (NTRS)

Mcmurtry, Patrick A.; Givi, Peyman

1992-01-01

An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.

4. Testing the accuracy and stability of spectral methods in numerical relativity

SciTech Connect

Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.

2007-01-15

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test.

5. Variational multiscale turbulence modelling in a high order spectral element method

SciTech Connect

Wasberg, Carl Erik Gjesdal, Thor Reif, Bjorn Anders Pettersson Andreassen, Oyvind

2009-10-20

In the variational multiscale (VMS) approach to large eddy simulation (LES), the governing equations are projected onto an a priori scale partitioning of the solution space. This gives an alternative framework for designing and analyzing turbulence models. We describe the implementation of the VMS LES methodology in a high order spectral element method with a nodal basis, and discuss the properties of the proposed scale partitioning. The spectral element code is first validated by doing a direct numerical simulation of fully developed plane channel flow. The performance of the turbulence model is then assessed by several coarse grid simulations of channel flow at different Reynolds numbers.

6. A complex guided spectral transform Lanczos method for studying quantum resonance states

DOE PAGES

Yu, Hua-Gen

2014-12-28

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the originalmore » Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.« less

7. A complex guided spectral transform Lanczos method for studying quantum resonance states

SciTech Connect

Yu, Hua-Gen

2014-12-28

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.

8. Spectral methods based on new formulations for coupled Stokes and Darcy equations

Wang, Weiwei; Xu, Chuanju

2014-01-01

In this paper we consider the numerical solution of the Stokes and Darcy coupled equations, which frequently appears in porous media modeling. The main contribution of this work is as follows: First, we introduce a new formulation for the Stokes/Darcy coupled equations, subject respectively to the Beavers-Joseph-Saffman interface condition and an alternative matching interface condition. Secondly, we prove the well-posedness of these weak problems by using the classical saddle point theory. Thirdly, some spectral approximations to the weak problems are proposed and analyzed, and some error estimates are provided. It is found that the new formulations significantly simplify the error analysis and numerical implementation. Finally, some two-dimensional spectral and spectral element numerical examples are provided to demonstrate the efficiency of our methods.

9. An Investigation of Three Methods for Determining Young Star Spectral Types

Bruhns, Sara; Prato, Lisa A.

2015-01-01

We present an investigation of several spectral typing techniques applied to 6 young, low-mass binary systems in the Taurus star-forming region (2 Myr). Spectra of resolution ~2000 were taken in the K band at Keck II using NIRC2 in grism spectroscopy mode where adaptive optics allowed us to resolve subarcsecond separations. We tested three different methods to determine spectral type to compare and contrast the strengths and weaknesses of each method. First, we used fits to standard star spectra to determine spectral types, extinctions, and K-band excesses. This method resulted in anomalously high extinctions not supported in the literature. It was also often difficult to distinguish between best fits. Second, we used the equivalent width ratios of IRTF SpeX standards to determine linear relationships onto which we plotted the equivalent width ratios of our sample stars. This method was complicated by low signal to noise in weak lines and the presence of significant circumstellar material around some of our sample of young stars, which may have inconsistently veiled and skewed our results. Third, we used K-band spectral indices and solar metallicity models to infer effective temperatures for our sample. This promising approach, applicable for the M-type stars in our sample, yields effective temperatures of several hundred degrees Kelvin lower than the other methods. Our main goal in this work is to highlight the uncertainties inherent in the typical procedures used for determining young star spectral types and encourage a concerted effort to define a more accurate and precise approach to the measurement of pre-main sequence effective temperature. Temperature is a fundamental stellar property without which our calibration of young star evolution, and by inference planet formation, is highly uncertain, even in the face of precisely measured stellar masses.

10. Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics.

PubMed

Cavallo, A; Cosenza, F; De Cesare, L

2008-05-01

We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.

11. Method for Removing Spectral Contaminants to Improve Analysis of Raman Imaging Data

PubMed Central

Zhang, Xun; Chen, Sheng; Ling, Zhe; Zhou, Xia; Ding, Da-Yong; Kim, Yoon Soo; Xu, Feng

2017-01-01

The spectral contaminants are inevitable during micro-Raman measurements. A key challenge is how to remove them from the original imaging data, since they can distort further results of data analysis. Here, we propose a method named “automatic pre-processing method for Raman imaging data set (APRI)”, which includes the adaptive iteratively reweighted penalized least-squares (airPLS) algorithm and the principal component analysis (PCA). It eliminates the baseline drifts and cosmic spikes by using the spectral features themselves. The utility of APRI is illustrated by removing the spectral contaminants from a Raman imaging data set of a wood sample. In addition, APRI is computationally efficient, conceptually simple and potential to be extended to other methods of spectroscopy, such as infrared (IR), nuclear magnetic resonance (NMR), X-Ray Diffraction (XRD). With the help of our approach, a typical spectral analysis can be performed by a non-specialist user to obtain useful information from a spectroscopic imaging data set. PMID:28054587

12. Development and validation of a new fallout transport method using variable spectral winds

SciTech Connect

Hopkins, A.T.

1984-01-01

A new method was developed to incorporate variable winds into fallout transport calculations. The method uses spectral coefficients derived by the National Meteorological Center. Wind vector components are computed with the coefficients along the trajectories of falling particles. Spectral winds are used in the two-step method to compute dose rate on the ground, downwind of a nuclear cloud. First, the hotline is located by computing trajectories of particles from an initial, stabilized cloud, through spectral winds to the ground. The connection of particle landing points is the hotline. Second, dose rate on and around the hotline is computed by analytically smearing the falling cloud's activity along the ground. The feasibility of using spectral winds for fallout particle transport was validated by computing Mount St. Helens ashfall locations and comparing calculations to fallout data. In addition, an ashfall equation was derived for computing volcanic ash mass/area on the ground. Ashfall data and the ashfall equation were used to back-calculate an aggregated particle size distribution for the Mount St. Helens eruption cloud.

13. A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA

Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan

2016-11-01

The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.

14. High-precision solution to the moving load problem using an improved spectral element method

Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li

2017-06-01

In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

15. 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.

16. Energy conserving discontinuous Galerkin spectral element method for the Vlasov-Poisson system

Madaule, Éric; Restelli, Marco; Sonnendrücker, Eric

2014-12-01

We propose a new, energy conserving, spectral element, discontinuous Galerkin method for the approximation of the Vlasov-Poisson system in arbitrary dimension, using Cartesian grids. The method is derived from the one proposed in [4], with two modifications: energy conservation is obtained by a suitable projection operator acting on the solution of the Poisson problem, rather than by solving multiple Poisson problems, and all the integrals appearing in the finite element formulation are approximated with Gauss-Lobatto quadrature, thereby yielding a spectral element formulation. The resulting method has the following properties: exact energy conservation (up to errors introduced by the time discretization), stability (thanks to the use of upwind numerical fluxes), high order accuracy and high locality. For the time discretization, we consider both Runge-Kutta methods and exponential integrators, and show results for 1D and 2D cases (2D and 4D in phase space, respectively).

17. From Chebyshev to Bernstein: A Tour of Polynomials Small and Large

ERIC Educational Resources Information Center

Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin

2006-01-01

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

18. Determination of rare-earth elements in Luna 16 regolith sample by chemical spectral method

NASA Technical Reports Server (NTRS)

Stroganova, N. S.; Ryabukhin, V. A.; Laktinova, N. V.; Ageyeva, L. V.; Galkina, I. P.; Gatinskaya, N. G.; Yermakov, A. N.; Karyakin, A. V.

1974-01-01

An analysis was made of regolith from layer A of the Luna 16 sample for rare earth elements, by a chemical spectral method. Chemical and ion exchange concentrations were used to determine the content of 12 elements and Y at the level 0.001 to 0.0001 percent with 10 to 15 percent reproducibility of the emission determination. Results within the limits of reproducibility agree with data obtained by mass spectra, activation, and X-ray fluorescent methods.

19. A GPU parallelized spectral method for elliptic equations in rectangular domains

Chen, Feng; Shen, Jie

2013-10-01

We design and implement a polynomial-based spectral method on graphic processing units (GPUs). The key to success lies in the seamless integration of the matrix diagonalization technique and the new generation CUDA tools. The method is applicable to elliptic equations in rectangular domains with general boundary condition. We show remarkable speedups of up to 15 times in the 2-D case and more than 35 times in the 3-D case.

20. Determination of rare-earth elements in Luna 16 regolith sample by chemical spectral method

NASA Technical Reports Server (NTRS)

Stroganova, N. S.; Ryabukhin, V. A.; Laktinova, N. V.; Ageyeva, L. V.; Galkina, I. P.; Gatinskaya, N. G.; Yermakov, A. N.; Karyakin, A. V.

1974-01-01

An analysis was made of regolith from layer A of the Luna 16 sample for rare earth elements, by a chemical spectral method. Chemical and ion exchange concentrations were used to determine the content of 12 elements and Y at the level 0.001 to 0.0001 percent with 10 to 15 percent reproducibility of the emission determination. Results within the limits of reproducibility agree with data obtained by mass spectra, activation, and X-ray fluorescent methods.

1. Strong and Weak Lagrange-Galerkin Spectral Element Methods for the Shallow Water Equations

DTIC Science & Technology

2003-02-01

Galerkin Spectral Element Methods for the Shallow Water Equations F . X. GIRALDO Naval Research Laboratory Monterey, CA 93943, U.S.A...edged. 0898-1221/03/\$ - see front matter © 2003 Published by Elsevier Science Ltd. PII: 80898-1221(02)00330-9 Typeset by ANfS-TEX 98 F . X...resulting operator is then discretized using the standard finite-element method. This is the approach used by Bercovier and Pironneau [4], Bermejo [5

2. Regularization Method And Its Application In Problem Of Determination A Radial Distribution Of Spectral Lines

SciTech Connect

Vuceljic, M. J.

2007-04-23

There are a lot of methods dealing with the problems how to get the local radial intensity from a measured lateral intensity of the spectral line. All of them need some a priori information and often a preliminary filtering of the signal. Thus, it is always a question about loosing the useful information of the signal. One of the methods for determination radial intensity is a Tikhonov regularization method. This method requires minimum a priori information such as: the intensity is a monotone positive function. To check applicability limitations of the method, some model functions have been introduced. Special attention was devoted to the model function with the fine structure.

3. Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

NASA Technical Reports Server (NTRS)

Vanel, Florence O.

1995-01-01

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the

4. Axisymmetric fully spectral code for hyperbolic equations

Panosso Macedo, Rodrigo; Ansorg, Marcus

2014-11-01

We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta (“SDIRK”-) method. In this paper, the SDIRK-method is also used to solve issue (ii). The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space-time in so-called hyperboloidal slices and reproduce some recent results available in the literature.

5. Stress drop of earthquakes from the Multi-Window Spectral Ratio method in a regional network

D'Alessio, M. A.; Imanishi, K.; Ellsworth, W. L.

2006-12-01

Insight into the mechanics of faulting comes from seismologically determined parameters such as earthquake stress drop. To produce higher precision estimates of stress drop on regional networks like the Parkfield HRSN borehole network, we use the multi-window spectral ratio (MWSR) method to determine the corner frequency and relative moment of earthquake pairs. This method assumes that the frequency distribution of spectral power is the same for direct arrivals and later arriving scattered energy. By taking the power spectra of individual time windows, we collect multiple, quasi-independent estimates of the power spectra for a given earthquake. For pairs of earthquakes located within a few hundred meters of one another, the ratio of their power spectra at a given station provides better estimates of their relative moments and corner frequencies by eliminating some of the path-dependent effects. We calculate the spectral ratio for each time window at each station in a regional borehole network and stack the ratios to cancel out noise and determine a robust estimate of the true power spectral ratio. Systematic differences between the spectral ratio at stations with different azimuths can be interpreted as evidence for directivity in the earthquake pulses or frequency- dependent attenuation along the source-receiver path. Because the method is based on a collection of quasi- independent spectral ratio observations, we can quantify the uncertainty in the estimates of corner frequency and moment for each earthquake pair. We use a bootstrap analysis with noise selected from the distribution of scatter from individual time windows about the mean spectral ratio to quantify the range of moment and corner frequencies that fit each station. By assuming that the earthquakes are simple circular cracks, we convert these parameters into stress drop with estimates of uncertainty. We evaluate the reliability of the technique in a regional network for different earthquake spacings

6. Multi-component spectral analysis of extended sources with a likelihood method

Naumann, Christopher Lindsay; Jacholkowska, Agnieszka

2012-12-01

The spectral and morphological analysis for gamma-ray sources with multiple emission components remains a major challenge for Cherenkov telescopes due to background emission from diffuse gamma rays. Current methods of background suppression, based on the bin-by-bin subtraction of OFF-source data do not allow an analysis of the various background components. As an alternative, we present an approach based on an event-by-event likelihood fit of ON-source data, using a combined spectral model for the source emission as well as the gamma-like background obtained from fits of the OFF-source data. Multiple emission components are separated by successive fits in different energy regimes and spectral variation inside the extended source is derived. The performance of this approach is evaluated by toy Monte-Carlo studies. For the application to real data, two well-studied H.E.S.S. sources are re-examined: the extragalactic point-source PKS 2155-304 and the extended pulsar wind nebula HESS J1825-137. For the latter, radial variation of the emission spectral index was evaluated with the likelihood method, confirming earlier findings by the H.E.S.S. collaboration [1].

7. A wavelet-based computational method for solving stochastic Itô–Volterra integral equations

SciTech Connect

2015-10-01

This paper presents a computational method based on the Chebyshev wavelets for solving stochastic Itô–Volterra integral equations. First, a stochastic operational matrix for the Chebyshev wavelets is presented and a general procedure for forming this matrix is given. Then, the Chebyshev wavelets basis along with this stochastic operational matrix are applied for solving stochastic Itô–Volterra integral equations. Convergence and error analysis of the Chebyshev wavelets basis are investigated. To reveal the accuracy and efficiency of the proposed method some numerical examples are included.

8. A new spectral method using legendre wavelets for shallow water model in limited-area

Yin, Fukang; Song, Junqiang; Wu, Jianping; Cao, Xiaoqun

2017-02-01

This paper presents a new spectral method using Legendre wavelets (named LWSTCM), which complete the stepping in spectral space while deal with boundary conditions in grid-point space by collocation method, for the numerical solution of shallow water model in limited-area. In order to deal with the overlapping boundaries, some proper schemes are considered for exchanging the information on the boundaries between sub-domains. 1-D advection equation is used to analysis the exponential convergence property and error characteristics of LWSTCM. Finally, we study LWSTCM on 2-D shallow water equations for a more realistic application. The numerical results are compared with existing numerical solutions found in the literature and demonstrate the validity and applicability of the presented method.

9. Reservoir hydrocarbon delineation using spectral decomposition: The application of S-Transform and empirical mode decomposition (EMD) method

Haris, A.; Morena, V.; Riyanto, A.; Zulivandama, S. R.

2017-07-01

Non-stationer signal from the seismic survey is difficult to be directly interpreted in time domain analysis. Spectral decomposition is one of the spectral analysis methods that can analyze the non-stationer signal in frequency domain. The Fast Fourier Transform method was commonly used for spectral decomposition analysis, however, this method had a limitation in the scaled window analysis and produced pure quality for low-frequency shadow. The S-Transform and Empirical the Mode Decomposition (EMD) is another method of spectral decomposition that can be used to enhanced low-frequency shadows. In this research, comparison of the S-Transform and the EMD methods that can show the difference imaging result of low-frequency shadows zone is applied to Eldo Field, Jambi Province. The spectral decomposition result based on the EMD method produced better imaging of low-frequency shadows zone in tuning thickness compared to S-Transform methods.

10. Spectral element method for elastic and acoustic waves in frequency domain

Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei; Liu, Na; Liu, Qing Huo

2016-12-01

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

11. [Study of near infrared spectral preprocessing and wavelength selection methods for endometrial cancer tissue].

PubMed

Zhao, Li-Ting; Xiang, Yu-Hong; Dai, Yin-Mei; Zhang, Zhuo-Yong

2010-04-01

Near infrared spectroscopy was applied to measure the tissue slice of endometrial tissues for collecting the spectra. A total of 154 spectra were obtained from 154 samples. The number of normal, hyperplasia, and malignant samples was 36, 60, and 58, respectively. Original near infrared spectra are composed of many variables, for example, interference information including instrument errors and physical effects such as particle size and light scatter. In order to reduce these influences, original spectra data should be performed with different spectral preprocessing methods to compress variables and extract useful information. So the methods of spectral preprocessing and wavelength selection have played an important role in near infrared spectroscopy technique. In the present paper the raw spectra were processed using various preprocessing methods including first derivative, multiplication scatter correction, Savitzky-Golay first derivative algorithm, standard normal variate, smoothing, and moving-window median. Standard deviation was used to select the optimal spectral region of 4 000-6 000 cm(-1). Then principal component analysis was used for classification. Principal component analysis results showed that three types of samples could be discriminated completely and the accuracy almost achieved 100%. This study demonstrated that near infrared spectroscopy technology and chemometrics method could be a fast, efficient, and novel means to diagnose cancer. The proposed methods would be a promising and significant diagnosis technique of early stage cancer.

12. Spectral element method for elastic and acoustic waves in frequency domain

SciTech Connect

Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei; Liu, Na; Liu, Qing Huo

2016-12-15

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

13. Rapid screening of guar gum using portable Raman spectral identification methods.

PubMed

Srivastava, Hirsch K; Wolfgang, Steven; Rodriguez, Jason D

2016-01-25

Guar gum is a well-known inactive ingredient (excipient) used in a variety of oral pharmaceutical dosage forms as a thickener and stabilizer of suspensions and as a binder of powders. It is also widely used as a food ingredient in which case alternatives with similar properties, including chemically similar gums, are readily available. Recent supply shortages and price fluctuations have caused guar gum to come under increasing scrutiny for possible adulteration by substitution of cheaper alternatives. One way that the U.S. FDA is attempting to screen pharmaceutical ingredients at risk for adulteration or substitution is through field-deployable spectroscopic screening. Here we report a comprehensive approach to evaluate two field-deployable Raman methods--spectral correlation and principal component analysis--to differentiate guar gum from other gums. We report a comparison of the sensitivity of the spectroscopic screening methods with current compendial identification tests. The ability of the spectroscopic methods to perform unambiguous identification of guar gum compared to other gums makes them an enhanced surveillance alternative to the current compendial identification tests, which are largely subjective in nature. Our findings indicate that Raman spectral identification methods perform better than compendial identification methods and are able to distinguish guar gum from other gums with 100% accuracy for samples tested by spectral correlation and principal component analysis. Published by Elsevier B.V.

14. Deterministic numerical solutions of the Boltzmann equation using the fast spectral method

Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao

2013-10-01

The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases

15. Spectral feature characterization methods for blood stain detection in crime scene backgrounds

Yang, Jie; Mathew, Jobin J.; Dube, Roger R.; Messinger, David W.

2016-05-01

Blood stains are one of the most important types of evidence for forensic investigation. They contain valuable DNA information, and the pattern of the stains can suggest specifics about the nature of the violence that transpired at the scene. Blood spectral signatures containing unique reflectance or absorption features are important both for forensic on-site investigation and laboratory testing. They can be used for target detection and identification applied to crime scene hyperspectral imagery, and also be utilized to analyze the spectral variation of blood on various backgrounds. Non-blood stains often mislead the detection and can generate false alarms at a real crime scene, especially for dark and red backgrounds. This paper measured the reflectance of liquid blood and 9 kinds of non-blood samples in the range of 350 nm - 2500 nm in various crime scene backgrounds, such as pure samples contained in petri dish with various thicknesses, mixed samples with different colors and materials of fabrics, and mixed samples with wood, all of which are examined to provide sub-visual evidence for detecting and recognizing blood from non-blood samples in a realistic crime scene. The spectral difference between blood and non-blood samples are examined and spectral features such as "peaks" and "depths" of reflectance are selected. Two blood stain detection methods are proposed in this paper. The first method uses index to denote the ratio of "depth" minus "peak" over"depth" add"peak" within a wavelength range of the reflectance spectrum. The second method uses relative band depth of the selected wavelength ranges of the reflectance spectrum. Results show that the index method is able to discriminate blood from non-blood samples in most tested crime scene backgrounds, but is not able to detect it from black felt. Whereas the relative band depth method is able to discriminate blood from non-blood samples on all of the tested background material types and colors.

16. A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows

Min, Misun; Lee, Taehun

2011-01-01

We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.

17. A spectral-element discontinuous Galerkin lattice Boltzmann method for incompressible flows.

SciTech Connect

Min, M.; Lee, T.; Mathematics and Computer Science; City Univ. of New York

2011-01-01

We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.

18. Spectral Inverse Quantum (Spectral-IQ) Method for Modeling Mesoporous Systems: Application on Silica Films by FTIR

PubMed Central

Putz, Ana-Maria; Putz, Mihai V.

2012-01-01

The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature. PMID:23443102

19. [Research on Accuracy and Stability of Inversing Vegetation Chlorophyll Content by Spectral Index Method].

PubMed

Jiang, Hai-ling; Yang, Hang; Chen, Xiao-ping; Wang, Shu-dong; Li, Xue-ke; Liu, Kai; Cen, Yi

2015-04-01

Spectral index method was widely applied to the inversion of crop chlorophyll content. In the present study, PSR3500 spectrometer and SPAD-502 chlorophyll fluorometer were used to acquire the spectrum and relative chlorophyll content (SPAD value) of winter wheat leaves on May 2nd 2013 when it was at the jointing stage of winter wheat. Then the measured spectra were resampled to simulate TM multispectral data and Hyperion hyperspectral data respectively, using the Gaussian spectral response function. We chose four typical spectral indices including normalized difference vegetation index (NDVD, triangle vegetation index (TVI), the ratio of modified transformed chlorophyll absorption ratio index (MCARI) to optimized soil adjusted vegetation index (OSAVI) (MCARI/OSAVI) and vegetation index based on universal pattern decomposition (VIUPD), which were constructed with the feature bands sensitive to the vegetation chlorophyll. After calculating these spectral indices based on the resampling TM and Hyperion data, the regression equation between spectral indices and chlorophyll content was established. For TM, the result indicates that VIUPD has the best correlation with chlorophyll (R2 = 0.819 7) followed by NDVI (R2 = 0.791 8), while MCARI/OSAVI and TVI also show a good correlation with R2 higher than 0.5. For the simulated Hyperion data, VIUPD again ranks first with R2 = 0.817 1, followed by MCARI/OSAVI (R2 = 0.658 6), while NDVI and TVI show very low values with R2 less than 0.2. It was demonstrated that VIUPD has the best accuracy and stability to estimate chlorophyll of winter wheat whether using simulated TM data or Hyperion data, which reaffirms that VIUPD is comparatively sensor independent. The chlorophyll estimation accuracy and stability of MCARI/OSAVI also works well, partly because OSAVI could reduce the influence of backgrounds. Two broadband spectral indices NDVI and TVI are weak for the chlorophyll estimation of simulated Hyperion data mainly because of

20. A spectral measurement method for determining white OLED average junction temperatures

2016-09-01

The objective of this study was to investigate an indirect method of measuring the average junction temperature of a white organic light-emitting diode (OLED) based on temperature sensitivity differences in the radiant power emitted by individual emitter materials (i.e., "blue," "green," and "red"). The measured spectral power distributions (SPDs) of the white OLED as a function of temperature showed amplitude decrease as a function of temperature in the different spectral bands, red, green, and blue. Analyzed data showed a good linear correlation between the integrated radiance for each spectral band and the OLED panel temperature, measured at a reference point on the back surface of the panel. The integrated radiance ratio of the spectral band green compared to red, (G/R), correlates linearly with panel temperature. Assuming that the panel reference point temperature is proportional to the average junction temperature of the OLED panel, the G/R ratio can be used for estimating the average junction temperature of an OLED panel.

1. Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods

DOE PAGES

Jalas, S.; Dornmair, I.; Lehe, R.; ...

2017-03-20

Particle in Cell (PIC) simulations are a widely used tool for the investigation of both laser- and beam-driven plasma acceleration. It is a known issue that the beam quality can be artificially degraded by numerical Cherenkov radiation (NCR) resulting primarily from an incorrectly modeled dispersion relation. Pseudo-spectral solvers featuring infinite order stencils can strongly reduce NCR - or even suppress it - and are therefore well suited to correctly model the beam properties. For efficient parallelization of the PIC algorithm, however, localized solvers are inevitable. Arbitrary order pseudo-spectral methods provide this needed locality. Yet, these methods can again be pronemore » to NCR. Here in this paper, we show that acceptably low solver orders are sufficient to correctly model the physics of interest, while allowing for parallel computation by domain decomposition.« less

2. A Comparison of Analytical and Data Preprocessing Methods for Spectral Fingerprinting

PubMed Central

LUTHRIA, DEVANAND L.; MUKHOPADHYAY, SUDARSAN; LIN, LONG-ZE; HARNLY, JAMES M.

2013-01-01

Spectral fingerprinting, as a method of discriminating between plant cultivars and growing treatments for a common set of broccoli samples, was compared for six analytical instruments. Spectra were acquired for finely powdered solid samples using Fourier transform infrared (FT-IR) and Fourier transform near-infrared (NIR) spectrometry. Spectra were also acquired for unfractionated aqueous methanol extracts of the powders using molecular absorption in the ultraviolet (UV) and visible (VIS) regions and mass spectrometry with negative (MS−) and positive (MS+) ionization. The spectra were analyzed using nested one-way analysis of variance (ANOVA) and principal component analysis (PCA) to statistically evaluate the quality of discrimination. All six methods showed statistically significant differences between the cultivars and treatments. The significance of the statistical tests was improved by the judicious selection of spectral regions (IR and NIR), masses (MS+ and MS−), and derivatives (IR, NIR, UV, and VIS). PMID:21352644

3. Applications of spectral methods to turbulent magnetofluids in space and fusion research

NASA Technical Reports Server (NTRS)

Montgomery, D.; Voigt, R. G. (Editor); Gottlieb, D. (Editor); Hussaini, M. Y. (Editor)

1984-01-01

Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas.

4. A Quadrilateral Spectral Multidomain Penalty Method Model For High Reynolds Number Incompressible Stratified Flows

Escobar-Vargas, Jorge; Diamessis, Peter

2011-11-01

We present a spectral multidomain penalty method-based incompressible Navier Stokes solver for high Reynolds number stratified turbulent flows in doubly non-periodic domains. Within the solver, time is discretized with a fractional-step method, and, in space, a Gauss-Lobatto-Legendre collocation approach is used in discontinuous quadrilateral subdomains. Stability of the numerical scheme is guaranteed through a penalty scheme and spectral filtering, further buttressed by a overintegration-based dealiasing technique. The efficient iterative solution of the associated discrete pressure Poisson equation is ensured through a Kronecker product based computation of the null vector associated with the global matrix, plus a two-level preconditioner within a GMRES solver. Efficiency and accuracy of the Navier Stokes solver are assessed through the solution of the lid-driven cavity flow, Taylor vortex and double shear layer. The canonical lock exchange problem is also presented to assess the potential of the solver for the study of environmental stratified flows.

5. GW calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

DOE PAGES

Pham, T. Anh; Nguyen, Huy -Viet; Rocca, Dario; ...

2013-04-26

Inmore » a recent paper we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmon-pole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. Lastly, we demonstrate the efficiency of our approach by carrying out GW calculations for systems with several hundred valence electrons.« less

6. Spectral method for fast measurement of twisted nematic liquid crystal cell parameters.

PubMed

Pinzón, Plinio Jesús; Pérez, Isabel; Sánchez-Pena, José Manuel; Vázquez, Carmen

2014-08-10

We present an experimental approach for the fast measurement of twisted nematic (TN) liquid crystal (LC) cells' parameters. It is based on the spectral measurements of the light transmitted by the system polarizer-reference wave plate-LC cell-analyzer. The cell parameters are obtained by fitting the theoretical model to the experimental data. This method allows determining the rubbing angle, the twist angle and its sense, and the spectral dispersion of the LC cell retardation, simultaneously, with few measurements and without the need of applying voltage or any specific analytical conditions. The method is validated by characterizing two different TN cells with retardations of about 0.91 and 1.85 μm. The birefringence relative error is less than 1.3%.

7. Spectral transmittance of organic dye-doped glass films obtained by the solgel method

Nemoto, Shojiro; Hirokawa, Naoyuki

1996-06-01

The spectral transmittance of colored glass films synthesized by the solgel method is presented. The film was formed on a glass slide by dipping it into an organic dye-doped solution and, thereafter, by putting it into a furnace for solidification. Three dyes, Methylene Blue, Eosin, and Uranine, were used that exhibit transparent blue, pink, and yellow colors, respectively, when they are dissolved in the starting solution. We clarify how the spectral transmittance of the films varies with the solidification temperature. The films doped with two of the three dyes that exhibit violet, orange, and green colors are also synthesized, and their transmittance is measured. Moreover, the chemical durability of the films and the transmittance change caused by aging and illumination are examined. organic dye, solgel method.

8. A spectral method for action-angle representation of linear waves in plasmas

Hirota, M.

2009-11-01

Hamiltonian aspects of linear waves in plasmas are generally reviewed and discussed. Action-angle representation of linear waves is a fundamental problem, but it requires a careful mathematical consideration in the presence of continuum mode (continuous spectrum). We introduce a novel spectral technique that can treat continuous spectrum as well as discrete spectrum in a unified manner. Our method facilitates the derivation of action-angle variables, which is demonstrated for the Van Kampen mode in electrostatic plasma.

9. Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries

NASA Technical Reports Server (NTRS)

1989-01-01

The numerical analysis of spectral methods when non-constant coefficients appear in the equation, either due to the original statement of the equations or to take into account the deformed geometry, is presented. Particular attention is devoted to the optimality of the discretization even for low values of the discretization parameter. The effect of some overintegration is also addressed, in order to possibly improve the accuracy of the discretization.

10. A method for dynamic spectrophotometric measurements in vivo using principal component analysis-based spectral deconvolution.

PubMed

Zupancic, Gregor

2003-10-01

A method was developed for dynamic spectrophotometric measurements in vivo in the presence of non-specific spectral changes due to external disturbances. This method was used to measure changes in mitochondrial respiratory pigment redox states in photoreceptor cells of live, white-eyed mutants of the blowfly Calliphora vicina. The changes were brought about by exchanging the atmosphere around an immobilised animal from air to N2 and back again by a rapid gas exchange system. During an experiment reflectance spectra were measured by a linear CCD array spectrophotometer. This method involves the pre-processing steps of difference spectra calculation and digital filtering in one and two dimensions. These were followed by time-domain principal component analysis (PCA). PCA yielded seven significant time domain principal component vectors and seven corresponding spectral score vectors. In addition, through PCA we also obtained a time course of changes common to all wavelengths-the residual vector, corresponding to non-specific spectral changes due to preparation movement or mitochondrial swelling. In the final step the redox state time courses were obtained by fitting linear combinations of respiratory pigment difference spectra to each of the seven score vectors. The resulting matrix of factors was then multiplied by the matrix of seven principal component vectors to yield the time courses of respiratory pigment redox states. The method can be used, with minor modifications, in many cases of time-resolved optical measurements of multiple overlapping spectral components, especially in situations where non-specific external influences cannot be disregarded.

11. Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods

Zampieri, Elena; Pavarino, Luca F.

2006-01-01

A numerical approximation of the acoustic wave equation is presented. The spatial discretization is based on conforming spectral elements, whereas we use finite difference Newmark's explicit integration schemes for the temporal discretization. A rigorous stability analysis is developed for the discretized problem providing an upper bound for the time step [Delta]t. We present several numerical results concerning stability and convergence properties of the proposed numerical methods.

12. Spectral collocation and a two-level continuation scheme for dipolar Bose-Einstein condensates

Jeng, B.-W.; Chien, C.-S.; Chern, I.-L.

2014-01-01

We exploit the high accuracy of spectral collocation methods in the context of a two-level continuation scheme for computing ground state solutions of dipolar Bose-Einstein condensates (BEC), where the first kind Chebyshev polynomials and Fourier sine functions are used as the basis functions for the trial function space. The governing Gross-Pitaevskii equation (or Schrödinger equation) can be reformulated as a Schrödinger-Poisson (SP) type system [13]. The two-level continuation scheme is developed for tracing the first solution curves of the SP system, which in turn provide an appropriate initial guess for the Newton method to compute ground state solutions for 3D dipolar BEC. Extensive numerical experiments on 3D dipolar BEC and dipolar BEC in optical lattices are reported.

13. Quantification of minerals from ATR-FTIR spectra with spectral interferences using the MRC method

2017-06-01

A method for quantifying the individual components of mineral samples based on attenuated total reflectance - Fourier transform infrared spectroscopy (ATR-FTIR) is described, extending the constant ratio (CR) method to analytes absorbing in a common range of wavenumbers. Absorbance values in the spectral region where the analytes absorb relative to the absorbance of an internal standard absorbing at a wavenumber where the analytes do not absorb, permits the quantification of N analytes using measurements at N fixed wavenumbers. The method was tested for mixtures of albite, orthoclase, kaolin and quartz.

14. A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory

SciTech Connect

Nintcheu Fata, Sylvain; Gray, Leonard J

2009-01-01

This research is focused on the development of a fast spectral method to accelerate the solution of three-dimensional hypersingular boundary integral equations of potential theory. Based on a Galerkin approximation, the Fast Fourier Transform and local interpolation operators, the proposed method is a generalization of the Precorrected-FFT technique to deal with double-layer potential kernels, hypersingular kernels and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are included to illustrate the performance of the method.

15. Method for separation of homogeneous and inhomogeneous components of spectral broadening of rigid systems

SciTech Connect

Litvinyuk, I.V.

1997-01-30

A method is suggested that allows separation of the contributions from homogeneous and inhomogeneous broadening (IB) to a total spectral contour of rigid systems. Based upon a simple convolution model of inhomogeneous broadening, the method allows calculation of homogeneously broadened spectra and an inhomogeneous distribution function (IDF) from the measured excitation-wavelength-dependent fluorescence spectra of the system. The method is applied successfully to the solid solution of coumarin 334 (C334) in poly(methyl methacrylate) (PMMA) glass at 293 K. 16 refs., 5 figs.

16. A comparative study of the performance of different spectral estimation methods for classification of mental tasks.

PubMed

Diez, Pablo F; Laciar, Eric; Mut, Vicente; Avila, Enrique; Torres, Abel

2008-01-01

In this paper we compare three different spectral estimation techniques for the classification of mental tasks. These techniques are the standard periodogram, the Welch periodogram and the Burg method, applied to electroencephalographic (EEG) signals. For each one of these methods we compute two parameters: the mean power and the root mean square (RMS), in various frequency bands. The classification of the mental tasks was conducted with a linear discriminate analysis. The Welch periodogram and the Burg method performed better than the standard periodogram. The use of the RMS allows better classification accuracy than the obtained with the power of EEG signals.

17. Predicting the effective response of bulk polycrystalline ferroelectric ceramics via improved spectral phase field methods

Vidyasagar, A.; Tan, W. L.; Kochmann, D. M.

2017-09-01

Understanding the electromechanical response of bulk polycrystalline ferroelectric ceramics requires scale-bridging approaches. Recent advances in fast numerical methods to compute the homogenized mechanical response of materials with heterogeneous microstructure have enabled the solution of hitherto intractable systems. In particular, the use of a Fourier-based spectral method as opposed to the traditional finite element method has gained significant interest in the homogenization of periodic microstructures. Here, we solve the periodic, electro-mechanically-coupled boundary value problem at the mesoscale of polycrystalline ferroelectrics in order to extract the effective response of barium titanate (BaTiO3) and lead zirconate titanate (PZT) under applied electric fields. Results include the effective electric hysteresis and the associated butterfly curve of strain vs. electric field for mean stress-free electric loading. Computational predictions of the 3D polycrystalline response show convincing agreement with our experimental electric cycling and strain hysteresis data for PZT-5A. In addition to microstructure-dependent effective physics, we also show how finite-difference-based approximations in the spectral solution scheme significantly reduce instability and ringing phenomena associated with spectral techniques and lead to spatial convergence with h-refinement, which have been major challenges when modeling high-contrast systems such as polycrystals.

18. a High-Efficiency Fusion Method of Multi-Spectral Image and Panchromatic Image

Xue, X.; Wang, J. P.; Wang, H.; Xiang, F.

2013-07-01

With the development of modern remote sensing technology, a variety of earth observation satellites could continue to tremendously provide image data of different spatial resolution, time resolution, spectral resolution remote sensing, and the remote sensing data obtained is increasing with great capacity, which forms multi-source image pyramid in the same area. To play the advantages of a variety of remote sensing data, the application of remote sensing image fusion is a very important choice. When remote sensing data is large, fusion is large in computing capacity and time-consuming, so it is difficult to carry out rapid, real-time fusion. However, in some remote sensing applications, such as disaster prevention and relief quick, etc., timely fusion is required. Based on image fusion method of principal component analysis (PCA) and the advantage of parallel computing, a high-efficiency fusion method of multi-spectral image and panchromatic image is proposed. Beijing-1 Micro-satellite is a high-performance small satellite for earth observation，With Beijing-1 Micro-satellite remote sensing images as the experimental data, it is proved that good fusion results of multi-spectral image and panchromatic image can be obtained with the proposed method, and the fusion speed is also fast. At the same time, some measures of improving the efficiency of parallel image fusion are also discussed.

19. The automatic solution of partial differential equations using a global spectral method

Townsend, Alex; Olver, Sheehan

2015-10-01

A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and the one-dimensional ultraspherical spectral method. If a partial differential operator is of splitting rank 2, such as the operator associated with Poisson or Helmholtz, the corresponding PDE is solved via a generalized Sylvester matrix equation, and a bivariate polynomial approximation of the solution of degree (nx ,ny) is computed in O ((nxny) 3 / 2) operations. Partial differential operators of splitting rank ≥3 are solved via a linear system involving a block-banded matrix in O (min ⁡ (nx3 ny ,nx ny3)) operations. Numerical examples demonstrate the applicability of our 2D spectral method to a broad class of PDEs, which includes elliptic and dispersive time-evolution equations. The resulting PDE solver is written in MATLAB and is publicly available as part of CHEBFUN. It can resolve solutions requiring over a million degrees of freedom in under 60 seconds. An experimental implementation in the JULIA language can currently perform the same solve in 10 seconds.

20. Detection of the power lines in UAV remote sensed images using spectral-spatial methods.

PubMed

Bhola, Rishav; Krishna, Nandigam Hari; Ramesh, K N; Senthilnath, J; Anand, Gautham

2017-09-17

In this paper, detection of the power lines on images acquired by Unmanned Aerial Vehicle (UAV) based remote sensing is carried out using spectral-spatial methods. Spectral clustering was performed using Kmeans and Expectation Maximization (EM) algorithm to classify the pixels into the power lines and non-power lines. The spectral clustering methods used in this study are parametric in nature, to automate the number of clusters Davies-Bouldin index (DBI) is used. The UAV remote sensed image is clustered into the number of clusters determined by DBI. The k clustered image is merged into 2 clusters (power lines and non-power lines). Further, spatial segmentation was performed using morphological and geometric operations, to eliminate the non-power line regions. In this study, UAV images acquired at different altitudes and angles were analyzed to validate the robustness of the proposed method. It was observed that the EM with spatial segmentation (EM-Seg) performed better than the Kmeans with spatial segmentation (Kmeans-Seg) on most of the UAV images. Copyright © 2017 Elsevier Ltd. All rights reserved.