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.
Elimination of spurious eigenvalues in the Chebyshev tau spectral method
NASA Technical Reports Server (NTRS)
Mcfadden, G. B.; Murray, B. T.; Boisvert, R. F.
1989-01-01
Spectral methods have been used to great advantage in hydrodynamic stability calculations; the concepts are described in Orszag's seminal application of the Chebyshev tau method to the Orr-Sommerfeld equation for plane Poiseuille flow in 1971. Orszag discusses both the Chebyshev Galerkin and the Chebyshev tau methods, but presents results for the tau method, which is easier to implement than the Galerkin method. The tau method has the disadvantage that two unstable eigenvalues are produced that are artifacts of the discretization. An extremely simple modification to the Chebyshev tau method is presented which eliminates the spurious eigenvalues. First a simplified model of the Orr-Sommerfeld equation discussed by Gottlieb and Orszag was studied. Then the Chebyshev tau method is considered, which has two spurious eigenvalues, and then a modification which eliminates them is described. Finally, results for the Orr-Sommerfeld equation are considered where the modified tau method also eliminates the spurious eigenvalues. The simplicity of the modification makes it a convenient alternative to other approaches to the problem.
Elimination of spurious eigenvalues in the Chebyshev tau spectral method
NASA Technical Reports Server (NTRS)
Mcfadden, G. B.; Murray, B. T.; Boisvert, R. F.
1990-01-01
A very simple modification is presented for the Chebyshev tau method which can eliminate spurious eigenvalues, proceeding from a consideration of the vorticity-streamfunction reformulation of the Chebyshev tau method and the Chebyshev-Galerkin method, which have no spurious modes. Consideration of a model problem indicates that these two approaches are equivalent, and that they reduce to the present modification of the tau method. This modified tau method also eliminates spurious eigenvalues from the Orr-Sommerfeld equation.
Chebyshev-Fourier spectral methods in bipolar coordinates
NASA Astrophysics Data System (ADS)
Huang, Zhu; Boyd, John P.
2015-08-01
Bipolar coordinates provide an efficient cartography for a variety of geometries: the exterior of two disks or cylinders, a half-plane containing a disk, an eccentric annulus with a small disk offset from the center of an outer boundary that is a large circle, and so on. A pseudospectral method that employs a tensor product basis of Fourier functions in the cyclic coordinate η and Chebyshev polynomials in the quasi-radial coordinate ξ gives easy-to-program spectral accuracy. We show, however, that as the inner disk becomes more and more offset from the center of the outer boundary circle, the grid is increasingly non-uniform, and the rate of exponential convergence increasingly slow. One-dimensional coordinate mappings significantly reduce the non-uniformity. In spite of this non-uniformity, the Chebyshev-Fourier method is quite effective in an idealized model of the wind-driven ocean circulation, resolving both internal and boundary layers. Bipolar coordinates are also a good starting point for solving problems in a domain which is not one of the "bipolar-compatible" domains listed above, but is a sufficiently small perturbation of such. This is illustrated by applying boundary collocation with bipolar harmonics to solve Laplace's equation in a perturbed eccentric annulus in which the disk-shaped island has been replaced by an island bounded by an ellipse. Similarly a perturbed bipolar domain can be mapped to an eccentric annulus by a smooth change of coordinates.
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.
Zhao, Shengkai; Yedlin, M.J. )
1994-08-01
We present a new iterative Chebyshev spectral method for solving the elliptic equation [del] [center dot] ([sigma] [del]u) = f. We rewrite the equation in the form of a Poisson's equation [del][sup 2]u = (f - [del]u [center dot] [del][sigma]/[sigma]). In each iteration we compute the right-hand side terms from the guess values first. Then we solve the resultant Poisson equation by a direct method to obtain the updated values. Three numerical examples are presented. For the sam number of iterations, the accuracy of the present method is about 6-8 orders better than the Chebyshev spectral multigrid method. On a SPARC Station 2 computer, the CPU time of the new method is about one-third of the Chebyshev spectral multigrid method. To obtain the same accuracy, the CPU time of the present method is about one-tenth of the Chebyshev spectral multigrid method. 17 refs., 5 figs., 3 tabs.
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
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
A third-order multistep time discretization for a Chebyshev tau spectral method
NASA Astrophysics Data System (ADS)
Vreman, A. W.; Kuerten, J. G. M.
2016-01-01
A time discretization scheme based on the third-order backward difference formula has been embedded into a Chebyshev tau spectral method for the Navier-Stokes equations. The time discretization is a variant of the second-order backward scheme proposed by Krasnov et al. (2008) [3]. High-resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the Runge-Kutta scheme proposed by Spalart et al. (1991) [2]. It is shown that the Runge-Kutta scheme leads to a poor convergence of some third-order spatial derivatives in the direct vicinity of the wall, derivatives that represent the diffusion of wall-tangential vorticity. The convergence at the wall is shown to be significantly improved if the backward scheme is applied.
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
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
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.
Boundary conditions in Chebyshev and Legendre methods
NASA Technical Reports Server (NTRS)
Canuto, C.
1984-01-01
Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.
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.
NASA Astrophysics Data System (ADS)
Su, C.; Seriani, G.
2012-04-01
Many physical problems require the modelling of wave phenomena in media having variable properties, while highly accurate algorithms are needed in order to avoid unphysical effects. Often the property fluctuations may be very high compared to the minimum wavelength, leading to an extremely large problem, since a grid resolution down to the finest scales is required and the much larger wavelength scale of interest cannot be exploited in order to reduce the computational burden. Here, like in multiscale methods, efficiency can be increased only by solving the macroscopic behavior without solving explicitly the microscopic one. Spectral element methods (SEM) have excellent properties of accuracy and flexibility in describing complex models and are used as well for wave modelling. In the standard SEM approach, the computational domain is discretized by using very coarse meshes and constant-property elements, which makes it inappropriate for solving the above mentioned problem. A convenient solution approach is provided by a poly-grid Chebyshev spectral element method, which allows to overcome this limitation. The domain decomposition is built by using composite elements having a set of local grids, or poly-grid. The main grid is used for wave propagation, whereas the remaining auxiliary grids are used for describing the physical parameters. As a consequence, SEM accuracy and efficiency is maintained in wave field computations while dealing with small scale property fluctuations. Moreover, interfaces between different materials can be easily handled internally to each element without the need of their edges be aligned with the interfaces.
Chebyshev moment problems: Maximum entropy and kernel polynomial methods
Silver, R.N.; Roeder, H.; Voter, A.F.; Kress, J.D.
1995-12-31
Two Chebyshev recursion methods are presented for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). They are applicable to physical properties involving large numbers of eigenstates such as densities of states, spectral functions, thermodynamics, total energies for Monte Carlo simulations and forces for tight binding molecular dynamics. this paper emphasizes efficient algorithms.
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.
Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes
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.
Weighted Chebyshev distance classification method for hyperspectral imaging
NASA Astrophysics Data System (ADS)
Demirci, S.; Erer, I.; Ersoy, O.
2015-06-01
The main objective of classification is to partition the surface materials into non-overlapping regions by using some decision rules. For supervised classification, the hyperspectral imagery (HSI) is compared with the reflectance spectra of the material containing similar spectral characteristic. As being a spectral similarity based classification method, prediction of different level of upper and lower spectral boundaries of all classes spectral signatures across spectral bands constitutes the basic principles of the Multi-Scale Vector Tunnel Algorithm (MS-VTA) classification algorithm. The vector tunnel (VT) scaling parameters obtained from means and standard deviations of the class references are used. In this study, MS-VT method is improved and a spectral similarity based technique referred to as Weighted Chebyshev Distance (WCD) method for the supervised classification of HSI is introduced. This is also shown to be equivalent to the use of the WCD in which the weights are chosen as an inverse power of the standard deviation per spectral band. The use of WCD measures in terms of the inverse power of standard deviations and optimization of power parameter constitute the most important side of the study. The algorithms are trained with the same kinds of training sets, and their performances are calculated for the power of the standard deviation. During these studies, various levels of the power parameters are evaluated based on the efficiency of the algorithms for choosing the best values of the weights.
Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics
NASA Astrophysics Data System (ADS)
Junkins, John L.; Bani Younes, Ahmad; Woollands, Robyn M.; Bai, Xiaoli
2013-12-01
This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics. Using Chebyshev polynomials, as the orthogonal approximation basis, it is straightforward to distribute the computation of force functions needed in MCPI to generate the polynomial coefficients (approximating the path iterations) to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refines path estimates over large time intervals chosen to be within the domain of convergence of Picard iteration. The developed vector-matrix form makes MCPI methods computationally efficient and a more systematic approach is given, leading to a modest correction to results in the published dissertation by Bai. The power of MCPI methods for solving IVPs is clearly illustrated using a simple nonlinear differential equation with a known analytical solution. Compared with the most common integration scheme, the standard Runge-Kutta 4-5 method as implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, on a serial machine. MCPI performance is also compared to state of the art integrators such as the Runge-Kutta Nystrom 12(10) methods applied to the relevant orbit mechanics problems. The MCPI method is shown to be well-suited to solving these problems in serial processors with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. When used in conjunction with the recently developed local gravity approximations in conjunction with parallel computation, we anticipate MCPI will enable revolutionary speedups while ensuring
An error embedded method based on generalized Chebyshev polynomials
NASA Astrophysics Data System (ADS)
Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung
2016-02-01
In this paper, we develop an error embedded method based on generalized Chebyshev polynomials for solving stiff initial value problems. The solution and the error at each integration step are calculated by generalized Chebyshev polynomials of two consecutive degrees having overlapping zeros, which enables us to minimize overall computational costs. Further the errors at each integration step are embedded in the algorithm itself. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 6th order convergence and an almost L-stability. We assess the proposed method with several numerical results, showing that it uses larger time step sizes and is numerically more efficient.
Liu, Yi-Xin Zhang, Hong-Dong
2014-06-14
We present a fast and accurate numerical method for the self-consistent field theory calculations of confined polymer systems. It introduces an exponential time differencing method (ETDRK4) based on Chebyshev collocation, which exhibits fourth-order accuracy in temporal domain and spectral accuracy in spatial domain, to solve the modified diffusion equations. Similar to the approach proposed by Hur et al. [Macromolecules 45, 2905 (2012)], non-periodic boundary conditions are adopted to model the confining walls with or without preferential interactions with polymer species, avoiding the use of surface field terms and the mask technique in a conventional approach. The performance of ETDRK4 is examined in comparison with the operator splitting methods with either Fourier collocation or Chebyshev collocation. Numerical experiments show that our exponential time differencing method is more efficient than the operator splitting methods in high accuracy calculations. This method has been applied to diblock copolymers confined by two parallel flat surfaces.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Hedayatrasa, Saeid; Bui, Tinh Quoc; Zhang, Chuanzeng; Lim, Chee Wah
2014-02-01
Numerical modeling of the Lamb wave propagation in functionally graded materials (FGMs) by a two-dimensional time-domain spectral finite element method (SpFEM) is presented. The high-order Chebyshev polynomials as approximation functions are used in the present formulation, which provides the capability to take into account the through thickness variation of the material properties. The efficiency and accuracy of the present model with one and two layers of 5th order spectral elements in modeling wave propagation in FGM plates are analyzed. Different excitation frequencies in a wide range of 28-350 kHz are investigated, and the dispersion properties obtained by the present model are verified by reference results. The through thickness wave structure of two principal Lamb modes are extracted and analyzed by the symmetry and relative amplitude of the vertical and horizontal oscillations. The differences with respect to Lamb modes generated in homogeneous plates are explained. Zero-crossing and wavelet signal processing-spectrum decomposition procedures are implemented to obtain phase and group velocities and their dispersion properties. So it is attested how this approach can be practically employed for simulation, calibration and optimization of Lamb wave based nondestructive evaluation techniques for the FGMs. The capability of modeling stress wave propagation through the thickness of an FGM specimen subjected to impact load is also investigated, which shows that the present method is highly accurate as compared with other existing reference data.
Short-time Chebyshev wave packet method for molecular photoionization
NASA Astrophysics Data System (ADS)
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.
Hubbell rectangular source integral calculation using a fast Chebyshev wavelets method.
Manai, K; Belkadhi, K
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. PMID:27152913
Spectral multigrid methods for elliptic equations II
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1984-01-01
A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.
Spectral multigrid methods for elliptic equations 2
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1983-01-01
A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.
Modified Chebyshev-Picard Iteration Methods for Solution of Boundary Value Problems
NASA Astrophysics Data System (ADS)
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.
Pusa, M.; Leppaenen, J.
2012-07-01
The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides. (authors)
Spectral methods for time dependent problems
NASA Technical Reports Server (NTRS)
Tadmor, Eitan
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.
NASA Astrophysics Data System (ADS)
Parand, K.; Khaleqi, S.
2016-02-01
The Lane-Emden equation has been used to model several phenomena in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the rational Chebyshev function of Second kind (RCS) to solve the Lane-Emden equation over the semi-infinite interval [0,+∞[ . According to well-known results and comparing with previous methods, it can be said that this method is efficient and applicable.
3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method
NASA Astrophysics Data System (ADS)
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.
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.
Fast Chebyshev-polynomial method for simulating the time evolution of linear dynamical systems.
Loh, Y L; Taraskin, S N; Elliott, S R
2001-05-01
We present a fast method for simulating the time evolution of any linear dynamical system possessing eigenmodes. This method does not require an explicit calculation of the eigenvectors and eigenfrequencies, and is based on a Chebyshev polynomial expansion of the formal operator matrix solution in the eigenfrequency domain. It does not suffer from the limitations of ordinary time-integration methods, and can be made accurate to almost machine precision. Among its possible applications are harmonic classical mechanical systems, quantum diffusion, and stochastic transport theory. An example of its use is given for the problem of vibrational wave-packet propagation in a disordered lattice. PMID:11415044
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.
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.
Formanek, Martin; Vana, Martin; Houfek, Karel
2010-09-30
We compare efficiency of two methods for numerical solution of the time-dependent Schroedinger equation, namely the Chebyshev method and the recently introduced generalized Crank-Nicholson method. As a testing system the free propagation of a particle in one dimension is used. The space discretization is based on the high-order finite diferences to approximate accurately the kinetic energy operator in the Hamiltonian. We show that the choice of the more effective method depends on how many wave functions must be calculated during the given time interval to obtain relevant and reasonably accurate information about the system, i.e. on the choice of the time step.
Preconditioners for the spectral multigrid method
NASA Technical Reports Server (NTRS)
Phillips, T. N.; Zang, T. A.; Hussaini, M. Y.
1983-01-01
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 problems 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.
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.
Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations
Pusa, M.
2013-07-01
The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides. (authors)
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.
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.
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.
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.
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.
Multistage spectral relaxation method for solving the hyperchaotic complex systems.
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
Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
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
Zhou, Yunkai; Chelikowsky, James R.; Saad, Yousef
2014-10-01
First-principles density functional theory (DFT) calculations for the electronic structure problem require a solution of the Kohn–Sham equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.
Spectral methods for modeling supersonic chemically reacting flow fields
NASA Technical Reports Server (NTRS)
Drummond, J. P.; Hussaini, M. Y.; Zang, T. A.
1985-01-01
A numerical algorithm was developed for solving the equations describing chemically reacting supersonic flows. The algorithm employs a two-stage Runge-Kutta method for integrating the equations in time and a Chebyshev spectral method for integrating the equations in space. The accuracy and efficiency of the technique were assessed by comparison with an existing implicit finite-difference procedure for modeling chemically reacting flows. The comparison showed that the procedure presented yields equivalent accuracy on much coarser grids as compared to the finite-difference procedure with resultant significant gains in computational efficiency.
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.
Chebyshev Expansion Applied to Dissipative Quantum Systems.
Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich
2016-05-19
To determine the dynamics of a molecular aggregate under the influence of a strongly time-dependent perturbation within a dissipative environment is still, in general, a challenge. The time-dependent perturbation might be, for example, due to external fields or explicitly treated fluctuations within the environment. Methods to calculate the dynamics in these cases do exist though some of these approaches assume that the corresponding correlation functions can be written as a weighted sum of exponentials. One such theory is the hierarchical equations of motion approach. If the environment, however, is described by a complex spectral density or if its temperature is low, these approaches become very inefficient. Therefore, we propose a scheme based on a Chebyshev decomposition of the bath correlation functions and detail the respective quantum master equations within second-order perturbation theory in the environmental coupling. Similar approaches have recently been proposed for systems coupled to Fermionic reservoirs. The proposed scheme is tested for a simple two-level system and compared to existing results. Furthermore, the advantages and disadvantages of the present Chebyshev approach are discussed. PMID:26845380
NASA Astrophysics Data System (ADS)
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.
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.
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.
A spectral element method for the simulation of unsteady incompressible flows with heat transfer
NASA Technical Reports Server (NTRS)
Karniadakis, George E.; Patera, Anthony T.
1986-01-01
The spectral element method is a high-order finite element technique for solution of the Navier-Stokes and energy equations. In the isoparametric spectral element discretization, the domain is broken up into general brick elements, and the dependent and independent variables represented as high-order tensor-product Lagrangian interpolants through Chebyshev collocation points. The nonlinear and convective terms in the governing equations are treated with explicit collocation, while the pressure and diffusive contributions are handled implicitly using variational projection operators. The method is applied to flow past a cylinder, flow in grooved channels, and natural convection in an enclosure.
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.
Method of multivariate spectral analysis
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).
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.
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.
NASA Astrophysics Data System (ADS)
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.
A linear-scaling spectral-element method for computing electrostatic potentials.
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. PMID:19045386
On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media.
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. PMID:27119059
Shock capturing by the spectral viscosity method
NASA Technical Reports Server (NTRS)
Tadmor, Eitan
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.
Spectral Methods for Thesaurus Construction
NASA Astrophysics Data System (ADS)
Shimizu, Nobuyuki; Sugiyama, Masashi; Nakagawa, Hiroshi
Traditionally, popular synonym acquisition methods are based on the distributional hypothesis, and a metric such as Jaccard coefficients is used to evaluate the similarity between the contexts of words to obtain synonyms for a query. On the other hand, when one tries to compile and clean a thesaurus, one often already has a modest number of synonym relations at hand. Could something be done with a half-built thesaurus alone? We propose the use of spectral methods and discuss their relation to other network-based algorithms in natural language processing (NLP), such as PageRank and Bootstrapping. Since compiling a thesaurus is very laborious, we believe that adding the proposed method to the toolkit of thesaurus constructors would significantly ease the pain in accomplishing this task.
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.
Spectral Methods for Magnetic Anomalies
NASA Astrophysics Data System (ADS)
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
Spectral Methods in General Relativistic MHD Simulations
NASA Astrophysics Data System (ADS)
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.
Method of photon spectral analysis
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.
Method of photon spectral analysis
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.
Spectral methods for inviscid, compressible flows
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.; Salas, M. D.; Zang, T. A.
1983-01-01
Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.
Hybrid least squares multivariate spectral analysis methods
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.
Hybrid least squares multivariate spectral analysis methods
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.
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
SPECTRAL RELATIVE ABSORPTION DIFFERENCE METHOD
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
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.
Spectral ratio method for measuring emissivity
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.
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.
Best quadrature formula on Sobolev class with Chebyshev weight
NASA Astrophysics Data System (ADS)
Xie, Congcong
2008-05-01
Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f[set membership, variant]KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.
Efficient Conjunction Assessment using Modified Chebyshev Picard Iteration
NASA Astrophysics Data System (ADS)
Probe, A.; Macomber, B.; Read, J.; Woollands, R.; Masher, A.; Junkins, J.
Conjunction Assessment is one of the most important and computationally expensive components of modern SSA efforts. Timely warnings of potential conjunctions are critical for the protection of valuable space assets. Upgrades to the US Space Surveillance Network (SSN) such as the Space Surveillance Telescope and the new Space Fence become operational, the influx of newly trackable objects will exacerbate the current issues of computational tractability. Modified Chebyshev Picard Iteration (MCPI) is a numerical method for solving ordinary differential equations that can be utilized to efficiently proximate orbits with high accuracy. Unlike, more traditional stepping based integrators; MCPI uses recursive approximation using Chebyshev polynomials to estimate segments of an orbit. The end result of the propagation is orthogonal Chebyshev polynomial approximation of the orbital trajectory; this approximation is analytically differentiable and potentially accurate to machine precision. Once computed, these approximations provide an efficient method for evaluating and comparing the positions of space objects. The reduced cost of catalog propagation and subsequent conjunction probability analysis when using MCPI, allows for significant reduction in the cost to perform high fidelity conjunction assessment. A method for catalog propagation and conjunction assessment using MCPI is presented, along with results from implementation running in a compute cluster environment are presented.
Spectral multigrid methods for elliptic equations
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1981-01-01
An alternative approach which employs multigrid concepts in the iterative solution of spectral equations was examined. Spectral multigrid methods are described for self adjoint elliptic equations with either periodic or Dirichlet boundary conditions. For realistic fluid calculations the relevant boundary conditions are periodic in at least one (angular) coordinate and Dirichlet (or Neumann) in the remaining coordinates. Spectral methods are always effective for flows in strictly rectangular geometries since corners generally introduce singularities into the solution. If the boundary is smooth, then mapping techniques are used to transform the problem into one with a combination of periodic and Dirichlet boundary conditions. It is suggested that spectral multigrid methods in these geometries can be devised by combining the techniques.
Some Theoretical Aspects for Elastic Wave Modeling in a Recently Developed Spectral Element Method
NASA Astrophysics Data System (ADS)
Wang, X. M.; Seriani, G.; Lin, W. J.
2006-10-01
A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media and by the Galerkin approach applied to a partition, in small subdomains, of the original physical domain under investigation. In the present work some mathematical aspects of the method and of the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobbatto collocation points, used in reference element quadrature, are introduced. The related analytical integration formulas are obtained. The standard error estimations and expansion convergence are discussed. In order to improve the computation accuracy and efficiency, an element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence neither the global matrices, nor the effective force vector is assembled. When analytical formula are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without loosing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes spectral element methods much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The second part will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the modelling example comparison of the proposed spectral element method with a conventional finite-element method and a staggered pseudo-spectral method that is to be reported in the other work.
Spectral methods to detect surface mines
NASA Astrophysics Data System (ADS)
Winter, Edwin M.; Schatten Silvious, Miranda
2008-04-01
Over the past five years, advances have been made in the spectral detection of surface mines under minefield detection programs at the U. S. Army RDECOM CERDEC Night Vision and Electronic Sensors Directorate (NVESD). The problem of detecting surface land mines ranges from the relatively simple, the detection of large anti-vehicle mines on bare soil, to the very difficult, the detection of anti-personnel mines in thick vegetation. While spatial and spectral approaches can be applied to the detection of surface mines, spatial-only detection requires many pixels-on-target such that the mine is actually imaged and shape-based features can be exploited. This method is unreliable in vegetated areas because only part of the mine may be exposed, while spectral detection is possible without the mine being resolved. At NVESD, hyperspectral and multi-spectral sensors throughout the reflection and thermal spectral regimes have been applied to the mine detection problem. Data has been collected on mines in forest and desert regions and algorithms have been developed both to detect the mines as anomalies and to detect the mines based on their spectral signature. In addition to the detection of individual mines, algorithms have been developed to exploit the similarities of mines in a minefield to improve their detection probability. In this paper, the types of spectral data collected over the past five years will be summarized along with the advances in algorithm development.
NASA Astrophysics Data System (ADS)
Cai, Tao
2016-04-01
In this paper, we have described a 'stratified' semi-implicit spectral method to study compressible convection in Cartesian geometry. The full set of compressible hydrodynamic equations are solved in conservative forms. The numerical scheme is accurate and efficient, based on fast Fourier/sin/cos spectral transforms in the horizontal directions, Chebyshev spectral transform or second-order finite difference scheme in the vertical direction, and second order semi-implicit scheme in time marching of linear terms. We have checked the validity of both the fully pseudo-spectral scheme and the mixed finite-difference pseudo-spectral scheme by studying the onset of compressible convection. The difference of the critical Rayleigh number between our numerical result and the linear stability analysis is within two percent. Besides, we have computed the Mach numbers with different Rayleigh numbers in compressible convection. It shows good agreement with the numerical results of finite difference methods and finite volume method. This model has wide application in studying laminar and turbulent flow. Illustrative examples of application on horizontal convection, gravity waves, and long-lived vortex are given in this paper.
A spectral Phase-Amplitude method for propagating a wave function to large distances
NASA Astrophysics Data System (ADS)
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.
Quasioptimality of some spectral mixed methods
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Jayadeep; Demkowicz, L. F. Leszek F.
2004-05-01
In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectral mixed methods, including the Raviart-Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.
A spectral mimetic least-squares method
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
A spectral mimetic least-squares method
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.
Stochastic dynamic models and Chebyshev splines
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
Logarithmic compression methods for spectral data
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.
Advanced spectral methods for climatic time series
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.
Image contrast enhancement using Chebyshev wavelet moments
NASA Astrophysics Data System (ADS)
Uchaev, Dm. V.; Uchaev, D. V.; Malinnikov, V. A.
2015-12-01
A new algorithm for image contrast enhancement in the Chebyshev moment transform (CMT) domain is introduced. This algorithm is based on a contrast measure that is defined as the ratio of high-frequency to zero-frequency content in the bands of CMT matrix. Our algorithm enables to enhance a large number of high-spatial-frequency coefficients, that are responsible for image details, without severely degrading low-frequency contributions. To enhance high-frequency Chebyshev coefficients we use a multifractal spectrum of scaling exponents (SEs) for Chebyshev wavelet moment (CWM) magnitudes, where CWMs are multiscale realization of Chebyshev moments (CMs). This multifractal spectrum is very well suited to extract meaningful structures on images of natural scenes, because these images have a multifractal character. Experiments with test images show some advantages of the proposed algorithm as compared to other widely used image enhancement algorithms. The main advantage of our algorithm is the following: the algorithm very well highlights image details during image contrast enhancement.
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.
LORENE: Spectral methods differential equations solver
NASA Astrophysics Data System (ADS)
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.
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.
Fuzzy stochastic elements method. Spectral approach
NASA Astrophysics Data System (ADS)
Sniady, Pawel; Mazur-Sniady, Krystyna; Sieniawska, Roza; Zukowski, Stanislaw
2013-05-01
We study a complex dynamic problem, which concerns a structure with uncertain parameters subjected to a stochastic excitation. Formulation of such a problem introduces fuzzy random variables for parameters of the structure and fuzzy stochastic processes for the load process. The uncertainty has two sources, namely the randomness of structural parameters such as geometry characteristics, material and damping properties, load process and imprecision of the theoretical model and incomplete information or uncertain data. All of these have a great influence on the response of the structure. By analyzing such problems we describe the random variability using the probability theory and the imprecision by use of fuzzy sets. Due to the fact that it is difficult to find an analytic expression for the inversion of the stochastic operator in the stochastic differential equation, a number of approximate methods have been proposed in the literature which can be connected to the finite element method. To evaluate the effects of excitation in the frequency domain we use the spectral density function. The spectral analysis is widely used in stochastic dynamics field of linear systems for stationary random excitation. The concept of the evolutionary spectral density is used in the case of non-stationary random excitation. We solve the considered problem using fuzzy stochastic finite element method. The solution is based on the idea of a fuzzy random frequency response vector for stationary input excitation and a transient fuzzy random frequency response vector for the fuzzy non-stationary one. We use the fuzzy random frequency response vector and the transient fuzzy random frequency response vector in the context of spectral analysis in order to determine the influence of structural uncertainty on the fuzzy random response of the structure. We study a linear system with random parameters subjected to two particular cases of stochastic excitation in a frequency domain. The first one
Yatsyshin, Petr; Savva, Nikos; Kalliadasis, Serafim
2012-03-28
We propose a numerical scheme based on the Chebyshev pseudo-spectral collocation method for solving the integral and integro-differential equations of the density-functional theory and its dynamic extension. We demonstrate the exponential convergence of our scheme, which typically requires much fewer discretization points to achieve the same accuracy compared to conventional methods. This discretization scheme can also incorporate the asymptotic behavior of the density, which can be of interest in the investigation of open systems. Our scheme is complemented with a numerical continuation algorithm and an appropriate time stepping algorithm, thus constituting a complete tool for an efficient and accurate calculation of phase diagrams and dynamic phenomena. To illustrate the numerical methodology, we consider an argon-like fluid adsorbed on a Lennard-Jones planar wall. First, we obtain a set of phase diagrams corresponding to the equilibrium adsorption and compare our results obtained from different approximations to the hard sphere part of the free energy functional. Using principles from the theory of sub-critical dynamic phase field models, we formulate the time-dependent equations which describe the evolution of the adsorbed film. Through dynamic considerations we interpret the phase diagrams in terms of their stability. Simulations of various wetting and drying scenarios allow us to rationalize the dynamic behavior of the system and its relation to the equilibrium properties of wetting and drying. PMID:22462841
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.
Chebyshev Polynomials Are Not Always Optimal
NASA Technical Reports Server (NTRS)
Fischer, B.; Freund, E.
1989-01-01
The authors are concerned with the problem of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations, and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. In this note, the authors show that this is not true in general. Moreover, the authors derive sufficient conditions which guarantee that Chebyshev polynomials are optimal. Also, some numerical examples are presented.
A spectral method for spatial downscaling.
Reich, Brian J; Chang, Howard H; Foley, Kristen M
2014-12-01
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 article, 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. PMID:24965037
A Spectral Method for Spatial Downscaling
Reich, Brian J.; Chang, Howard H.; Foley, Kristen M.
2014-01-01
Summary 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 article, 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. PMID:24965037
A spectral projection method for transmission eigenvalues
NASA Astrophysics Data System (ADS)
Zeng, Fang; Sun, JiGuang; Xu, LiWei
2016-08-01
In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides if the region contains eigenvalue(s) or not. It is particularly suitable to test if zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.
Spectral method for a kinetic swarming model
NASA Astrophysics Data System (ADS)
Gamba, Irene M.; Haack, Jeffrey R.; Motsch, Sebastien
2015-09-01
In this paper 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. We observe that the kinetic model captures key features such as vortex formation and traveling waves.
Spectral method for a kinetic swarming model
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.
Parallel algorithms for the spectral transform method
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.
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.
NASA Astrophysics Data System (ADS)
Porter, Edward K.
2006-10-01
We introduce a new method for modelling the gravitational wave flux function of a test-mass particle inspiralling into an intermediate mass Schwarzschild black hole which is based on Chebyshev polynomials of the first kind. It is believed that these intermediate mass ratio inspiral events (IMRI) are expected to be seen in both the ground- and space-based detectors. Starting with the post-Newtonian expansion from black hole perturbation theory, we introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a model with faster convergence than either post-Newtonian- or Padé-based methods. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. We find that at the last stable orbit, the error between the Chebyshev approximation and a numerically calculated flux is reduced, <1.8%, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general >0.99, and smaller errors, <1/10%, in the estimation of the chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the intermediate test-mass case, the new Chebyshev template is superior to both PN and Padé approximant templates, especially at lower orders of approximation.
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.
Spectral Methods Using Rational Basis Functions on an Infinite Interval
NASA Astrophysics Data System (ADS)
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.
Spectral density method to Anderson-Holstein model
Chebrolu, Narasimha Raju Chatterjee, Ashok
2015-06-24
Two-parameter spectral density function of a magnetic impurity electron in a non-magnetic metal is calculated within the framework of the Anderson-Holstein model using the spectral density approximation method. The effect of electron-phonon interaction on the spectral function is investigated.
Method to analyze remotely sensed spectral data
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.
Spectral distributed Lagrange multiplier method: algorithm and benchmark tests
NASA Astrophysics Data System (ADS)
Dong, Suchuan; Liu, Dong; Maxey, Martin R.; Karniadakis, George Em
2004-04-01
We extend the formulation of the distributed Lagrange multiplier (DLM) approach for particulate flows to high-order methods within the spectral/ hp element framework. We implement the rigid-body motion constraint inside the particle via a penalty method. The high-order DLM method demonstrates spectral convergence rate, i.e. discretization errors decrease exponentially as the order of spectral polynomials increases. We provide detailed comparisons between the spectral DLM method, direct numerical simulations, and the force coupling method for a number of 2D and 3D benchmark flow problems. We also validate the spectral DLM method with available experimental data for a transient problem. The new DLM method can potentially be very effective in many-moving body problems, where a smaller number of grid points is required in comparison with low-order methods.
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.
NASA Astrophysics Data System (ADS)
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.
A broadband spectral inversion method for spatial heterodyne spectroscopy
NASA Astrophysics Data System (ADS)
Cai, Qisheng; Bin, Xiangli; Du, Shusong
2014-11-01
Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique with many advantages, such as high throughput, good robustness (no moving parts), and high resolving power. However, in the basic theory of SHS, the relationship between the wavenumber and the frequency of the interferogram is approximated to be linear. This approximation limits the spectral range of a spatial heterodyne spectrometer to a narrow band near the Littrow wavenumber. Several methods have been developed to extend the spectral range of the SHS. They use echelle gratings or tunable pilot mirrors to make a SHS instrument work at multiple narrow spectral bands near different Littrow wavenumbers. These solutions still utilize the linear relationship between the wavenumber and the frequency of the interferogram. But they need to separate different spectral bands, and this will increase the difficulty of post processing and the complexity of the SHS system. Here, we solve this problem from another perspective: making a SHS system work at one broad spectral band instead of multiple narrow spectral bands. As in a broad spectral range, the frequency of the interferogram will not be linear with respect to the wavenumber anymore. According to this non-linear relationship, we propose a broadband spectral inversion method based on the stationary phase theory. At first, we describe the principles and the basic characters of SHS. Then, the narrow band limitation is analyzed and the broadband spectral inversion method is elaborated. In the end, we present a parameter design example of the SHS system according to a given spectral range, and the effectiveness of this method is validated with a spectral simulation example. This broadband spectral inversion method can be applied to the existing SHS system without changing or inserting any moving components. This method retains the advantages of SHS and there is almost no increase in complexity for post processing.
Methods of Spectral Analysis in C++ (MOSAIC)
NASA Astrophysics Data System (ADS)
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.
Spectral methods for electromagnetic propagation and diffraction
NASA Astrophysics Data System (ADS)
Felsen, L. B.
1990-03-01
Analysis of source-excited time-harmonic and transient electromagnetic wave propagation in complicated environments, wave scattering by complicated targets, or wave penetration into complex structures generally requires decomposition of the incident field into elementary constituents, tracking each constituent through the environment or past the scatter, and recombining at the observer. The elementary constituents are spectral objects such as plane waves, cylindrical waves, conical waves, modal fields, ray field, etc. Under transient conditions, the recombination is conventionally performed first on the time-harmonic constituents, with frequency synthesis performed thereafter, but one may alternatively, by a less conventional approach, employ transient constituents (transient plane or cylindrical waves, etc.) and perform the remaining spatial synthesis thereafter. Viewed from this general perspective, there exists an enormous flexibility in the selection of the spectral objects, and of hybrid combinations, for analysis of a particular propagation or scattering problem. It is the objective of the proposed research to examine the various spectral options in their most fundamental terms, study the relation between them, and then assess which option best addresses a particular propagation or scattering phenomenon.
NASA Astrophysics Data System (ADS)
Chen, Hai-Wen; McGurr, Mike; Brickhouse, Mark
2015-11-01
We present a newly developed feature transformation (FT) detection method for hyper-spectral imagery (HSI) sensors. In essence, the FT method, by transforming the original features (spectral bands) to a different feature domain, may considerably increase the statistical separation between the target and background probability density functions, and thus may significantly improve the target detection and identification performance, as evidenced by the test results in this paper. We show that by differentiating the original spectral, one can completely separate targets from the background using a single spectral band, leading to perfect detection results. In addition, we have proposed an automated best spectral band selection process with a double-threshold scheme that can rank the available spectral bands from the best to the worst for target detection. Finally, we have also proposed an automated cross-spectrum fusion process to further improve the detection performance in lower spectral range (<1000 nm) by selecting the best spectral band pair with multivariate analysis. Promising detection performance has been achieved using a small background material signature library for concept-proving, and has then been further evaluated and verified using a real background HSI scene collected by a HYDICE sensor.
Inflationary reheating classes via spectral methods
NASA Astrophysics Data System (ADS)
Bassett, Bruce A.
1998-07-01
Inflationary reheating is almost completely controlled by the Floquet indices, μk. Using spectral theory, we demonstrate that the stability bands (where μk=0) of the Mathieu and Lamé equations are destroyed even in Minkowski spacetime, leaving a fractal Cantor set or a measure zero set of stable modes in the cases, where the inflaton evolves in an almost-periodic or stochastic manner, respectively. These two types of potential model the expected multi-field and quantum back reaction effects during reheating.
The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator
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.
Evaluation of AMOEBA: a spectral-spatial classification method
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.
NASA Astrophysics Data System (ADS)
Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.
2013-09-01
Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are
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. PMID:27504247
Spectral analysis methods for automatic speech recognition applications
NASA Astrophysics Data System (ADS)
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.
3D parallel computations of turbofan noise propagation using a spectral element method
NASA Astrophysics Data System (ADS)
Taghaddosi, Farzad
2006-12-01
A three-dimensional code has been developed for the simulation of tone noise generated by turbofan engine inlets using computational aeroacoustics. The governing equations are the linearized Euler equations, which are further simplified to a set of equations in terms of acoustic potential, using the irrotational flow assumption, and subsequently solved in the frequency domain. Due to the special nature of acoustic wave propagation, the spatial discretization is performed using a spectral element method, where a tensor product of the nth-degree polynomials based on Chebyshev orthogonal functions is used to approximate variations within hexahedral elements. Non-reflecting boundary conditions are imposed at the far-field using a damping layer concept. This is done by augmenting the continuity equation with an additional term without modifying the governing equations as in PML methods. Solution of the linear system of equations for the acoustic problem is based on the Schur complement method, which is a nonoverlapping domain decomposition technique. The Schur matrix is first solved using a matrix-free iterative method, whose convergence is accelerated with a novel local preconditioner. The solution in the entire domain is then obtained by finding solutions in smaller subdomains. The 3D code also contains a mean flow solver based on the full potential equation in order to take into account the effects of flow variations around the nacelle on the scattering of the radiated sound field. All aspects of numerical simulations, including building and assembling the coefficient matrices, implementation of the Schur complement method, and solution of the system of equations for both the acoustic and mean flow problems are performed on multiprocessors in parallel using the resources of the CLUMEQ Supercomputer Center. A large number of test cases are presented, ranging in size from 100 000-2 000 000 unknowns for which, depending on the size of the problem, between 8-48 CPU's are
[Spectral discrimination method information divergence combined with gradient angle].
Zhang, Xiu-bao; Yuan, Yan; Jing, Juan-juan; Sun, Cheng-ming; Wang, Qian
2011-03-01
The present paper proposes a spectral discrimination method combining spectral information divergence with spectral gradient angle (SID x tan(SGA(pi/2)) which overcomes the shortages of the existing methods which can not take the whole spectral shape and local characteristics into account simultaneously. Using the simulation spectra as input data, according to the interferogram acquirement principle and spectrum recovery algorithm of the temporally and spatially modulated Fourier transform imaging spectrometer (TSMFTIS), we simulated the distortion spectra recovery process of the TMSFTIS in different maximum mix ratio and distinguished the difference between the recovered spectra and the true spectrum by different spectral discrimination methods. The experiment results show that the SID x tan(SGA(pi/2)) can not only identify the similarity of the whole spectral shapes, but also distinguish local differences of the spectral characteristics. A comparative study was conducted among the different discrimination methods. The results have validated that the SID x tan(SGA(pi/2)) has a significant improvement in the discriminatory ability. PMID:21595255
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.
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.
A divisive spectral method for network community detection
NASA Astrophysics Data System (ADS)
Cheng, Jianjun; Li, Longjie; Leng, Mingwei; Lu, Weiguo; Yao, Yukai; Chen, Xiaoyun
2016-03-01
Community detection is a fundamental problem in the domain of complex network analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive spectral method for identifying community structures from networks which utilizes a sparsification operation to pre-process the networks first, and then uses a repeated bisection spectral algorithm to partition the networks into communities. The sparsification operation makes the community boundaries clearer and sharper, so that the repeated spectral bisection algorithm extract high-quality community structures accurately from the sparsified networks. Experiments show that the combination of network sparsification and a spectral bisection algorithm is highly successful, the proposed method is more effective in detecting community structures from networks than the others.
Comparison of spectral analysis methods for characterizing brain oscillations
van Vugt, Marieke K.; Sederberg, Per B.; Kahana, Michael J.
2007-01-01
Spectral analysis methods are now routinely used in electrophysiological studies of human and animal cognition. Although a wide variety of spectral methods has been used, the ways in which these methods differ are not generally understood. Here we use simulation methods to characterize the similarities and differences between three spectral analysis methods: wavelets, multitapers and Pepisode. Pepisode is a novel method that quantifies the fraction of time that oscillations exceed amplitude and duration thresholds. We show that wavelets and Pepisode used side-by-side helps to disentangle length and amplitude of a signal. Pepisode is especially sensitive to fluctuations around its thresholds, puts frequencies on a more equal footing, and is sensitive to long but low-amplitude signals. In contrast, multitaper methods are less sensitive to weak signals, but are very frequency-specific. If frequency-specificity is not essential, then wavelets and Pepisode are recommended. PMID:17292478
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.
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.
Spectral radiative property control method based on filling solution
NASA Astrophysics Data System (ADS)
Jiao, Y.; Liu, L. H.; Hsu, P.-f.
2014-01-01
Controlling thermal radiation by tailoring spectral properties of microstructure is a promising method, can be applied in many industrial systems and have been widely researched recently. Among various property tailoring schemes, geometry design of microstructures is a commonly used method. However, the existing radiation property tailoring is limited by adjustability of processed microstructures. In other words, the spectral radiative properties of microscale structures are not possible to change after the gratings are fabricated. In this paper, we propose a method that adjusts the grating spectral properties by means of injecting filling solution, which could modify the thermal radiation in a fabricated microstructure. Therefore, this method overcomes the limitation mentioned above. Both mercury and water are adopted as the filling solution in this study. Aluminum and silver are selected as the grating materials to investigate the generality and limitation of this control method. The rigorous coupled-wave analysis is used to investigate the spectral radiative properties of these filling solution grating structures. A magnetic polaritons mechanism identification method is proposed based on LC circuit model principle. It is found that this control method could be used by different grating materials. Different filling solutions would enable the high absorption peak to move to longer or shorter wavelength band. The results show that the filling solution grating structures are promising for active control of spectral radiative properties.
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.
Spectral multigrid methods with applications to transonic potential flow
NASA Technical Reports Server (NTRS)
Streett, C. L.; Zang, T. A.; Hussaini, M. Y.
1985-01-01
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.
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.
Spectral analysis method for detecting an element
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.
Friedmann's equations in all dimensions and Chebyshev's theorem
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.
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.
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.
Spatio-spectral Maximum Entropy Method. I. Formulation and Test
NASA Astrophysics Data System (ADS)
Bong, Su-Chan; Lee, Jeongwoo; Gary, Dale E.; Yun, Hong Sik
2006-01-01
The spatio-spectral maximum entropy method (SSMEM) has been developed by Komm and coworkers in 1997 for use with solar multifrequency interferometric observation. In this paper we further improve the formulation of the SSMEM to establish it as a tool for astronomical imaging spectroscopy. We maintain their original idea that spectral smoothness at neighboring frequencies can be used as an additional a priori assumption in astrophysical problems and that this can be implemented by adding a spectral entropy term to the usual maximum entropy method (MEM) formulation. We, however, address major technical difficulties in introducing the spectral entropy into the imaging problem that are not encountered in the conventional MEM. These include calculation of the spectral entropy in a generally frequency-dependent map grid, simultaneous adjustment of the temperature variables and Lagrangian multipliers in the spatial and spectral domain, and matching the solutions to the observational constraints at a large number of frequencies. We test the performance of the SSMEM in comparison with the conventional MEM.
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.
Methods for spectral image analysis by exploiting spatial simplicity
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.
Methods for spectral image analysis by exploiting spatial simplicity
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.
NASA Astrophysics Data System (ADS)
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
Radon transforms and Gegenbauer-Chebyshev integrals, I
NASA Astrophysics Data System (ADS)
Rubin, Boris
2016-04-01
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.
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.
[High Precision Spectral Calibration Method of Fourier Interferometric Spectrometer].
Lin, Jun; Shao, Jun; Song, Chao-yu; Li, Yun-wei; Lei, Yu-fei
2015-12-01
The Fourier interferometric spectrometer (FIS) acquires the interference data information of the spectrum and during the spectrum data processing, a series of spectrum reconstruction will be performed on the interference information to obtain the final spectrum information data. The spectral calibration is the key step to spectrum reconstruction of FIS, which directly determines accuracy and availability of the spectrum results. This paper introduces the basic ideas and calibration accuracy about the spectral calibration for the FIS and puts forward a new spectral calibration method based on calculating the precise value of the total optical path difference (TOPD). The TOPD of FIS is difficult to be precisely measured, but it is the core and key to the spectral calibration. In order to calculate the precise TOPD, this paper proposes the idea how to traverse the TOPD and analyzes the spectrum drift. During the calibration, all the possible values of the TOPD participate in the spectrum reconstruction flow to carry out spectrum recovery and analysis. Ultimately the TOPD with the minimum spectrum drift will be achieved, namely solution value of the TOPD. This method can accurately resolve the TOPD of the FIS and then calibrate the spectrum with high accuracy. In addition, the paper introduces the detailed and complete spectral calibration flow and obtains the center wavelength value of every band and wavenumber resolution. Moreover, the paper designs the main parameters of the typical FIS and generates its simulation interference data. Using the above method to calibrate the simulation data, the analysis and verification of the spectral calibration results proves that the calibration precision of wavenumber resolution achieves 0.000 25 cm⁻¹ or above. PMID:26964245
Spectral anomaly methods for aerial detection using KUT nuisance rejection
NASA Astrophysics Data System (ADS)
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.
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.
The convergence of spectral methods for nonlinear conservation laws
NASA Technical Reports Server (NTRS)
Tadmor, Eitan
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.
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.
A review on spectral processing methods for geological remote sensing
NASA Astrophysics Data System (ADS)
Asadzadeh, Saeid; de Souza Filho, Carlos Roberto
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.
Hyperspectral image-based methods for spectral diversity
NASA Astrophysics Data System (ADS)
Sotomayor, Alejandro; Medina, Ollantay; Chinea, J. D.; Manian, Vidya
2015-05-01
Hyperspectral images are an important tool to assess ecosystem biodiversity. To obtain more precise analysis of biodiversity indicators that agree with indicators obtained using field data, analysis of spectral diversity calculated from images have to be validated with field based diversity estimates. The plant species richness is one of the most important indicators of biodiversity. This indicator can be measured in hyperspectral images considering the Spectral Variation Hypothesis (SVH) which states that the spectral heterogeneity is related to spatial heterogeneity and thus to species richness. The goal of this research is to capture spectral heterogeneity from hyperspectral images for a terrestrial neo tropical forest site using Vector Quantization (VQ) method and then use the result for prediction of plant species richness. The results are compared with that of Hierarchical Agglomerative Clustering (HAC). The validation of the process index is done calculating the Pearson correlation coefficient between the Shannon entropy from actual field data and the Shannon entropy computed in the images. One of the advantages of developing more accurate analysis tools would be the extension of the analysis to larger zones. Multispectral image with a lower spatial resolution has been evaluated as a prospective tool for spectral diversity.
Circulating tumor cell detection using photoacoustic spectral methods
NASA Astrophysics Data System (ADS)
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.
A Spectral Adaptive Mesh Refinement Method for the Burgers equation
NASA Astrophysics Data System (ADS)
Nasr Azadani, Leila; Staples, Anne
2013-03-01
Adaptive mesh refinement (AMR) is a powerful technique in computational fluid dynamics (CFD). Many CFD problems have a wide range of scales which vary with time and space. In order to resolve all the scales numerically, high grid resolutions are required. The smaller the scales the higher the resolutions should be. However, small scales are usually formed in a small portion of the domain or in a special period of time. AMR is an efficient method to solve these types of problems, allowing high grid resolutions where and when they are needed and minimizing memory and CPU time. Here we formulate a spectral version of AMR in order to accelerate simulations of a 1D model for isotropic homogenous turbulence, the Burgers equation, as a first test of this method. Using pseudo spectral methods, we applied AMR in Fourier space. The spectral AMR (SAMR) method we present here is applied to the Burgers equation and the results are compared with the results obtained using standard solution methods performed using a fine mesh.
Spectral method for pricing options in illiquid markets
NASA Astrophysics Data System (ADS)
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.
Calculating the spectrum of anisotropic waveguides using a spectral method.
Zharnikov, T V; Syresin, D E; Hsu, C-J
2013-09-01
The computation of the spectrum of a waveguide with arbitrary anisotropy with spatial dependence is a challenging task due to the coupling between axial and azimuthal harmonics. This problem is tackled in cylindrical coordinates by extending a spectral method for the general case. By considering the matrix representation of the operator on the right-hand side of the governing equations, the latter are exactly reformulated as an infinite set of integro-differential equations. Essential part of this study is taking into account the coupling of different harmonics, which becomes evident from the kernels of these equations. Provided a waveguide is translationally invariant in the axial direction, the coupling of axial harmonics vanishes. A practical approximation and truncation procedure yields a generalized eigenvalue problem, which can be solved numerically to obtain the entire spectrum of the operator and to construct the dispersion curves for the eigenmodes. The spectral method is tested against the results from the measurements of dispersion curves for the monopole, dipole, and quadrupole normal modes of scaled boreholes in tilted transverse isotropy anisotropic rock sample. Besides, the comparison of dispersion curves calculated by the spectral method and those computed from the synthetic data is discussed. PMID:23967909
Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials
NASA Astrophysics Data System (ADS)
Shakiba, Ali; Hooshmandasl, Mohammad Reza; Meybodi, Mohsen Alambardar
2016-06-01
In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples.
Power spectrum of the fluctuation of Chebyshev's prime counting function
NASA Astrophysics Data System (ADS)
Lan, Boon Leong; Yong, Shaohen
2006-02-01
The one-sided power spectrum of the fluctuation of Chebyshev's weighted prime counting function is numerically estimated based on samples of the fluctuating function of different sizes. The power spectrum is also estimated analytically for large frequency based on Riemann hypothesis and the exact formula for the fluctuating function in terms of all the non-trivial Riemann zeroes. Our analytical estimate is consistent with our numerical estimate of a 1/f2 power spectrum.
Bivariate Chebyshev Expansion of the Pacejka's Tyre Model
NASA Astrophysics Data System (ADS)
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.
On a spectral method for forward gravity field modelling
NASA Astrophysics Data System (ADS)
Root, B. C.; Novák, P.; Dirkx, D.; Kaban, M.; van der Wal, W.; Vermeersen, L. L. A.
2016-07-01
This article reviews a spectral forward gravity field modelling method that was initially designed for topographic/isostatic mass reduction of gravity data. The method transforms 3D spherical density models into gravitational potential fields using a spherical harmonic representation. The binomial series approximation in the approach, which is crucial for its computational efficiency, is examined and an error analysis is performed. It is shown that, this method cannot be used for density layers in crustal and upper mantle regions, because it results in large errors in the modelled potential field. Here, a correction is proposed to mitigate this erroneous behaviour. The improved method is benchmarked with a tesseroid gravity field modelling method and is shown to be accurate within ±4 mGal for a layer representing the Moho density interface, which is below other errors in gravity field studies. After the proposed adjustment the method can be used for the global gravity modelling of the complete Earth's density structure.
Spatial and Spectral Methods for Weed Detection and Localization
NASA Astrophysics Data System (ADS)
Vioix, Jean-Baptiste; Douzals, Jean-Paul; Truchetet, Frédéric; Assémat, Louis; Guillemin, Jean-Philippe
2002-12-01
This study concerns the detection and localization of weed patches in order to improve the knowledge on weed-crop competition. A remote control aircraft provided with a camera allowed to obtain low cost and repetitive information. Different processings were involved to detect weed patches using spatial then spectral methods. First, a shift of colorimetric base allowed to separate the soil and plant pixels. Then, a specific algorithm including Gabor filter was applied to detect crop rows on the vegetation image. Weed patches were then deduced from the comparison of vegetation and crop images. Finally, the development of a multispectral acquisition device is introduced. First results for the discrimination of weeds and crops using the spectral properties are shown from laboratory tests. Application of neural networks were mostly studied.
Spectral analysis of mammographic images using a multitaper method
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.
Application of Block Krylov Subspace Spectral Methods to Maxwell's Equations
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.
Tomographic fluorescence reconstruction by a spectral projected gradient pursuit method
NASA Astrophysics Data System (ADS)
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.
PSD computations using Welch's method. [Power Spectral Density (PSD)
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.
Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods
NASA Astrophysics Data System (ADS)
Garbanzo-Salas, Marcial; Hocking, Wayne. K.
2015-09-01
In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.
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.
NASA Astrophysics Data System (ADS)
Zhou, Xiran; Liu, Jun; Liu, Shuguang; Cao, Lei; Zhou, Qiming; Huang, Huawen
2014-02-01
High spatial resolution and spectral fidelity are basic standards for evaluating an image fusion algorithm. Numerous fusion methods for remote sensing images have been developed. Some of these methods are based on the intensity-hue-saturation (IHS) transform and the generalized IHS (GIHS), which may cause serious spectral distortion. Spectral distortion in the GIHS is proven to result from changes in saturation during fusion. Therefore, reducing such changes can achieve high spectral fidelity. A GIHS-based spectral preservation fusion method that can theoretically reduce spectral distortion is proposed in this study. The proposed algorithm consists of two steps. The first step is spectral modulation (SM), which uses the Gaussian function to extract spatial details and conduct SM of multispectral (MS) images. This method yields a desirable visual effect without requiring histogram matching between the panchromatic image and the intensity of the MS image. The second step uses the Gaussian convolution function to restore lost edge details during SM. The proposed method is proven effective and shown to provide better results compared with other GIHS-based methods.
Automated method for RNFL segmentation in spectral domain OCT
NASA Astrophysics Data System (ADS)
Paranjape, Amit S.; Elmaanaoui, Badr; Dewelle, Jordan; Rylander, H. Grady; Milner, Thomas E.
2008-02-01
We introduce a method based on optical reflectivity changes to segment the retinal nerve fiber layer (RNFL) in images recorded using swept source spectral domain optical coherence tomography (OCT). The segmented image is used to determine the RNFL thickness. Simple filtering followed by edge detecting techniques can successfully be applied to segment the RNFL from recorded images and estimate RNFL thickness. The method is computationally more efficient than previously reported approaches. Higher computational efficiency allows faster segmentation and provides the ophthalmologist segmented retinal images that better utilize advantages of spectral domain OCT instrumentation. OCT B-scan and fundus images of the retina are recorded for 5 patients. The segmentation method is applied on B-scan images recorded from all patients. An expert ophthalmologist separately demarcates the RNFL layer in the OCT images from the same patients in each B-scan image. Results from automated image processing software are compared to the boundary demarcated by the expert ophthalmologist. The absolute error between the boundaries demarcated by the expert and the algorithm is expressed in terms of area and is used as an error metric. Ability of the algorithm to accurately segment the RNFL in comparison with an expert ophthalmologist is reported.
Semi-spectral method for the Wigner equation
NASA Astrophysics Data System (ADS)
Furtmaier, O.; Succi, S.; Mendoza, M.
2016-01-01
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into L2 (Rd) basis functions in momentum-space to obtain a system of first-order advection-reaction equations. The resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew-hermitian reaction matrix as a generator of unitary rotations. The method is validated for the case of particles subject to a one-dimensional (an-)harmonic and Morse potential using finite-differences for the advection part. Thereby, we verify the second order of convergence and observe non-classical behavior in the evolution of the Wigner function.
Global seismic waveform tomography based on the spectral element method.
NASA Astrophysics Data System (ADS)
Capdeville, Y.; Romanowicz, B.; Gung, Y.
2003-04-01
Because seismogram waveforms contain much more information on the earth structure than body wave time arrivals or surface wave phase velocities, inversion of complete time-domain seismograms should allow much better resolution in global tomography. In order to achieve this, accurate methods for the calculation of forward propagation of waves in a 3D earth need to be utilized, which presents theoretical as well as computational challenges. In the past 8 years, we have developed several global 3D S velocity models based on long period waveform data, and a normal mode asymptotic perturbation formalism (NACT, Li and Romanowicz, 1996). While this approach is relatively accessible from the computational point of view, it relies on the assumption of smooth heterogeneity in a single scattering framework. Recently, the introduction of the spectral element method (SEM) has been a major step forward in the computation of seismic waveforms in a global 3D earth with no restrictions on the size of heterogeneities (Chaljub, 2000). While this method is computationally heavy when the goal is to compute large numbers of seismograms down to typical body wave periods (1-10 sec), it is much more accessible when restricted to low frequencies (T>150sec). When coupled with normal modes (e.g. Capdeville et al., 2000), the numerical computation can be restricted to a spherical shell within which heterogeneity is considered, further reducing the computational time. Here, we present a tomographic method based on the non linear least square inversion of time domain seismograms using the coupled method of spectral elements and modal solution. SEM/modes are used for both the forward modeling and to compute partial derivatives. The parametrisation of the model is also based on the spectral element mesh, the "cubed sphere" (Sadourny, 1972), which leads to a 3D local polynomial parametrization. This parametrization, combined with the excellent earth coverage resulting from the full 3D theory used
Near-infrared spectral methods for noninvasively measuring blood glucose
NASA Astrophysics Data System (ADS)
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.
Application of spectral subtraction method on enhancement of electrolarynx speech.
Liu, Hanjun; Zhao, Qin; Wan, Mingxi; Wang, Supin
2006-07-01
Although electrolarynx (EL) serves as an important method of phonation for the laryngectomees, the resulting speech is of poor intelligibility due to the presence of a steady background noise caused by the instrument, even worse in the case of additive noise. This paper investigates the problem of EL speech enhancement by taking into account the frequency-domain masking properties of the human auditory system. One approach is incorporating an auditory masking threshold (AMT) for parametric adaptation in a subtractive-type enhancement process. The other is the supplementary AMT (SAMT) algorithm, which applies a cross-correlation spectral subtraction (CCSS) approach as a post-processing scheme to enhancing EL speech dealt with the AMT method. The performance of these two algorithms was evaluated as compared to the power spectral subtraction (PSS) algorithm. The best performance of EL speech enhancement was associated with the SAMT algorithm, followed by the AMT algorithm and the PSS algorithm. Acoustic and perceptual analyses indicated that the AMT and SAMT algorithms achieved the better performances of noise reduction and the enhanced EL speech was more pleasant to human listeners as compared to the PSS algorithm. PMID:16875235
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.
Fourier time spectral method for subsonic and transonic flows
NASA Astrophysics Data System (ADS)
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.
Fourier time spectral method for subsonic and transonic flows
NASA Astrophysics Data System (ADS)
Zhan, Lei; Liu, Feng; Papamoschou, Dimitri
2016-01-01
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.
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.
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
Spectral analysis methods for vehicle interior vibro-acoustics identification
NASA Astrophysics Data System (ADS)
Hosseini Fouladi, Mohammad; Nor, Mohd. Jailani Mohd.; Ariffin, Ahmad Kamal
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.
Multi-Dimensional Spectral Difference Method for Unstructured Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
2005-01-01
A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.
Spectral Sensitivity Measured with Electroretinogram Using a Constant Response Method
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
Spectral Sensitivity Measured with Electroretinogram Using a Constant Response Method.
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
How Accurately Do Spectral Methods Estimate Effective Elastic Thickness?
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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
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.
Spectral finite-element methods for parametric constrained optimization problems.
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.
Method for detection and imaging over a broad spectral range
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.
Genetic Algorithms: A New Method for Neutron Beam Spectral Characterization
David W. Freeman
2000-06-04
A revolutionary new concept for solving the neutron spectrum unfolding problem using genetic algorithms (GAs) has recently been introduced. GAs are part of a new field of evolutionary solution techniques that mimic living systems with computer-simulated chromosome solutions that mate, mutate, and evolve to create improved solutions. The original motivation for the research was to improve spectral characterization of neutron beams associated with boron neutron capture therapy (BNCT). The GA unfolding technique has been successfully applied to problems with moderate energy resolution (up to 47 energy groups). Initial research indicates that the GA unfolding technique may well be superior to popular unfolding methods in common use. Research now under way at Kansas State University is focused on optimizing the unfolding algorithm and expanding its energy resolution to unfold detailed beam spectra based on multiple foil measurements. Indications are that the final code will significantly outperform current, state-of-the-art codes in use by the scientific community.
Scalable implementation of spectral methods for the Dirac equation
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.
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.
Magnetic depths to basalts: extension of spectral depths method
NASA Astrophysics Data System (ADS)
Clifton, Roger
2015-11-01
Although spectral depth determination has played a role in magnetic interpretation for over four decades, automating the procedure has been inhibited by the need for manual intervention. This paper introduces the concept of a slope spectrum of an equivalent layer, to be used in an automated depth interpretation algorithm suitable for application to very large datasets such as the complete Northern Territory aeromagnetic grid. In order to trace the extensive basalts across the Northern Territory, profiles of spectral depths have been obtained at 5 km intervals across the NT stitched grid of total magnetic intensity (TMI). Each profile is a graph from 0 to 1000 m of the probability of a magnetic layer occurring at each depth. Automating the collection of the 50 000 profiles required the development of a formula that relates slopes along the power spectrum to depths to an equivalent magnetic layer. Model slabs were populated with a large number of randomly located dipoles and their power spectra correlated with modelled depth to provide the formula. Depth profiles are too noisy to be used singly, but when a series of depth profiles are lined up side-by-side as a transect, significant magnetic layers can be traced for large distances. Transects frequently show a second layer. The formula is quite general in its derivation and would apply to any mid-latitude area where significant magnetic bodies can be modelled as extensive layers. Because the method requires a radial power spectrum, it fails to provide signal at depths much shallower than the flight line spacing. The method is convenient for a fast first pass at depth estimation, but its horizontal resolution is rather coarse and errors can be quite large.
Tracking discontinuities in hyperbolic conservation laws with spectral accuracy
NASA Astrophysics Data System (ADS)
Touil, H.; Hussaini, M. Y.; Sussman, M.
2007-08-01
It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite-order convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1988; J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, New York, 2001; C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin Heidelberg, 2006]). If a discontinuity or a shock is present in the solution, this advantage is lost. There have been attempts to recover exponential convergence in such cases with rather limited success. The aim of this paper is to propose a discontinuous spectral element method coupled with a level set procedure, which tracks discontinuities in the solution of nonlinear hyperbolic conservation laws with spectral convergence in space. Spectral convergence is demonstrated in the case of the inviscid Burgers equation and the one-dimensional Euler equations.
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.
Calculation of infrared system operating distance by spectral bisection method
NASA Astrophysics Data System (ADS)
Zhao, Yu; Wu, Ping; Sun, Wenfang
2014-03-01
During the transmission of infrared radiation, the atmospheric transmittance could be a complex parameter due to the absorbing and scattering of atmosphere, as well as the influences from the environment and transmission distance. With the help of a spectral bisection method, a new assessing formula and solution is raised by calculating the operating distance of infrared system. In the small segments, MODTRAN can be used to figure out the percentage of penetration, which is called by advanced program, so as to get the infrared radiation in those segments. The calculated data of the segments were summed up and used to calculate the operating distance of the infrared system. Compared with the conventional calculation methods that the transmittance was used as a constant or a average, The calculation precise of the operating distance is highly increased by this method the results of all small segments by comparing with the traditional methods. The whole computing process becomes more clear and effective by taking the influences from visibility of atmosphere, altitude, targets zenith angle and spatial frequency into consideration, and by building an instant monitoring system of the operating distance. The final computing result and real effecting distance are based on the general simulation for penetration rate and the tendency of operating distance in all conditions.
Use of new spectral analysis methods in gamma spectra deconvolution
NASA Astrophysics Data System (ADS)
Pinault, Jean Louis
1991-07-01
A general deconvolution method applicable to X and gamma ray spectrometry is proposed. Using new spectral analysis methods, it is applied to an actual case: the accurate on-line analysis of three elements (Ca, Si, Fe) in a cement plant using neutron capture gamma rays. Neutrons are provided by a low activity (5 μg) 252Cf source; the detector is a BGO 3 in. × 8 in. scintillator. The principle of the method rests on the Fourier transform of the spectrum. The search for peaks and determination of peak areas are worked out in the Fourier representation, which enables separation of background and peaks and very efficiently discriminates peaks, or elements represented by several peaks. First the spectrum is transformed so that in the new representation the full width at half maximum (FWHM) is independent of energy. Thus, the spectrum is arranged symmetrically and transformed into the Fourier representation. The latter is multiplied by a function in order to transform original Gaussian into Lorentzian peaks. An autoregressive filter is calculated, leading to a characteristic polynomial whose complex roots represent both the location and the width of each peak, provided that the absolute value is lower than unit. The amplitude of each component (the area of each peak or the sum of areas of peaks characterizing an element) is fitted by the weighted least squares method, taking into account that errors in spectra are independent and follow a Poisson law. Very accurate results are obtained, which would be hard to achieve by other methods. The DECO FORTRAN code has been developed for compatible PC microcomputers. Some features of the code are given.
Gravitational collapse of scalar fields via spectral methods
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.
Extraction of sea ice concentration based on spectral unmixing method
NASA Astrophysics Data System (ADS)
Zhang, Dong; Ke, Changqing; Sun, Bo; Lei, Ruibo; Tang, Xueyuan
2011-01-01
The traditional methods to derive sea ice concentration are mainly from low resolution microwave data, which is disadvantageous to meet the grid size requirement of high resolution climate models. In this paper, moderate resolution imaging spectroradiometer (MODIS)/Terra calibrated radiances Level-1B (MOD02HKM) data with 500 m resolution in the vicinity of the Abbot Ice Shelf, Antarctica, is unmixed, respectively, by two neural networks to extract the sea ice concentration. After two different neural network models and MODIS potential open water algorithm (MPA) are introduced, a MOD02HKM image is unmixed using these neural networks and sea ice concentration maps are derived. At the same time, sea ice concentration for the same area is extracted by MPA from MODIS/Terra sea ice extent (MOD29) data with 1 km resolution. Comparisons among sea ice concentration results of the three algorithms showed that a spectral unmixing method is suitable for the extraction of sea ice concentration with high resolution and the accuracy of radial basis function neural network is better than that of backpropagation.
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.
The use of the spectral method within the fast adaptive composite grid method
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.
Rapid simulation of spatial epidemics: a spectral method.
Brand, Samuel P C; Tildesley, Michael J; Keeling, Matthew J
2015-04-01
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. PMID:25659478
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.
Method and apparatus for measuring film spectral properties
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.
A comparison of spectral estimation methods for the analysis of sibilant fricatives
Reidy, Patrick F.
2015-01-01
It has been argued that, to ensure accurate spectral feature estimates for sibilants, the spectral estimation method should include a low-variance spectral estimator; however, no empirical evaluation of estimation methods in terms of feature estimates has been given. The spectra of /s/ and /ʃ/ were estimated with different methods that varied the pre-emphasis filter and estimator. These methods were evaluated in terms of effects on two features (centroid and degree of sibilance) and on the detection of four linguistic contrasts within these features. Estimation method affected the spectral features but none of the tested linguistic contrasts. PMID:25920873
Finite Frequency Upper Mantle Tomography Using the Spectral Element Method
NASA Astrophysics Data System (ADS)
Lekic, V.; Romanowicz, B.
2007-12-01
In the past quarter century, global tomography based on ray theory and first-order perturbation methods has imaged long-wavelength velocity heterogeneities of the Earth's mantle. While these models have contributed significantly to our understanding of mantle circulation, the development of higher resolution images of the Earth's interior holds tremendous promise for understanding the nature of the observed heterogeneities. This endeavor confronts us with two challenges. First, it requires extracting a far greater amount of information from the available seismograms than is generally used. Second, the approximate techniques upon which global tomographers have traditionally relied become inadequate when dealing with short-wavelength heterogeneity. We have developed a novel hybrid approach to long-period waveform tomography in which forward-modeling is performed using the Coupled Spectral Element Method (CSEM: Capdeville et al., 2003), which can accurately model seismic wave propagation in a 3D earth with both short and long wavelength structure, while in the inversion step, the sensitivity kernels are calculated using an approximate, non-linear normal mode summation approach (NACT: Li and Romanowicz, 1995). Our dataset consists of complete 3-component time domain seismograms filtered at periods greater than 80 s for 100 earthquakes observed at well over 100 stations of the IRIS/GSN, GEOSCOPE, GEOFON and various regional broadband networks. Modeling is performed in an iterative fashion, and convergence is achieved as long as the sign of the sensitivity kernels is correct. A further advantage of this hybrid approach is that it allows us - for the first time in global tomography - to accurately account for the effects of crustal structure on the observed seismograms. We illustrate these effects and the consequences of common assumptions such as linear crustal corrections. We present a preliminary model of velocity and radial anisotropy variations in the upper 800 km of
Towards spectral geometric methods for Euclidean quantum gravity
NASA Astrophysics Data System (ADS)
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.
Global mantle waveform tomography using the Spectral Element Method
NASA Astrophysics Data System (ADS)
Romanowicz, B. A.; French, S.; Masson, Y.; Jiménez-Pérez, H.
2015-12-01
In the past 20 years, we developed several generations of global mantle shear velocity models based entirely on time domain waveform inversion. This implies computations of synthetics in 3D earth models. Initially, the method of choice relied on normal mode perturbation theory, within which we built the framework of our inversion methodology. The latter includes, among others, windowing of waveforms to bring out contribution of weak amplitude phases, (e,g, Sdiff), and a fast converging quasi-Newton inversion with an approximate Hessian calculated using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995). Recently, the Spectral Element Method (SEM) was introduced in global seismology as a powerful numerical method to compute the seismic wavefield accurately in arbitrary 3D models (Komatitsch and Vilotte, 1998; Komatitsch and Tromp, 2002). Implementing the numerical SEM synthetics was straightforward, albeit with significantly increased cost of computation. In order to advance mantle imaging at the global scale, we introduced computational efficiencies, such as (1) substituting a fine layered crustal model by an equivalent, smooth, "homogeneized" crust designed to fit a global surface wave dispersion dataset, (2) continuing quasi-Newton inversion using NACT rather than adjoints, which involved the development of an efficient matrix assembly method (French et al., 2015), and (3) stepping progressively from long to short periods. The resulting models (Lekic and Romanowicz, 2011; French et al., 2013; French and Romanowicz, 2014), in particular, confirm the presence of deep mantle plumes beneath many major hotspots (French and Romanowicz, 2015). We discuss the choice of inverse approach, and illustrate the stability of our global models, in view of the use of NACT kernels, with respect to the choice of the starting model. Global inversion remains a challenge as higher resolution implies reaching higher frequencies to capture more of the scattered
NASA Astrophysics Data System (ADS)
Gebhart, Steven C.; Stokes, David L.; Vo-Dinh, Tuan; Mahadevan-Jansen, Anita
2005-03-01
Multiple methodologies exist to implement spectral imaging for tissue demarcation and disease diagnosis. In this paper, benchtop acousto-optic tunable filter (AOTF), liquid-crystal tunable filter (LCTF) and Fourier interferometric spectral imaging systems were quantitatively compared in terms of imaging speed of soft tissue autofluorescence. Optical throughput, image signal-to-noise ratio (SNR), and collagen autofluorescence imaging in chicken breast were assessed. Within this comparison, the Fourier system possessed the largest optical throughput (~50%) relative to the tunable-filter imaging systems; however, its throughput advantage failed to correlate to improved image SNR over the LCTF system. Further, while the autofluorescence imaging capability of the Fourier system exceeded that of the LCTF system for comparable total image integration times, the LCTF is capable of producing equivalent autofluorescence SNR with superior SNR when interrogations at only a few wavelengths are required and the random access filter tuning of the LCTF can be exploited. Therefore, the simple, rugged design and random-access filter-tuning capability of LCTF-based spectral imaging makes it best-suited for clinical development of soft tissue autofluorescence imaging.
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.
New spectral methods in cloud and aerosol remote sensing applications
NASA Astrophysics Data System (ADS)
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.
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.
Towards oscillation-free implementation of the immersed boundary method with spectral-like methods
Fang Jiannong; Diebold, Marc; Higgins, Chad; Parlange, Marc B.
2011-09-10
Highlights: {yields} A radial basis function based smoothing technique is introduced. {yields} It is more general and easier to implement compared to other techniques. {yields} With this technique, a combined immersed boundary and spectral method is developed. {yields} It is shown that the proposed method works better in terms of reducing the non-physical Gibbs oscillation. - Abstract: It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with the intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows.
Assessing Mantle Models with the Spectral-Element Method
NASA Astrophysics Data System (ADS)
Tromp, J.; Komatitsch, D.; Ritsema, J.; Allen, R.
2001-12-01
We have developed and implemented a spectral-element method (SEM) to simulate seismic wave propagation throughout the entire globe. Our SEM incorporates the effects of fluid-solid boundaries, attenuation, anisotropy, the oceans, rotation, self-gravitation and 3-D mantle and crustal heterogeneity. The method is implemented on a massively parallel PC cluster computer using message-passing software (MPI). The effects of crustal thickness, anisotropy, and attenuation on surface waves are quite dramatic. Self-gravitation and, in particular, the presence of a water layer slow the Rayleigh wave down. For spherically symmetric Earth models the SEM is in excellent agreement with normal-mode synthetics at periods greater than 20~seconds. We use the SEM to assess the quality of mantle model S20RTS, developed by Ritsema and colleagues, and Iceland model ICEMAN, developed by Allen and colleagues. The effects of 3-D heterogeneity can be spectacular. For example, along oceanic paths from Fiji-Tonga to Western North America or Japan the Rayleigh wave arrives more than a minute earlier than in PREM, and the Love wave exhibits very little dispersion, unlike in PREM. These effects are largely due to the fact that the oceanic crust is much thinner than in PREM. For a set of well-recorded earthquakes we use the SEM to determine how well model S20RTS fits the travel-time data. Because the SEM synthetics are essentially exact at periods greater than 20~seconds, this facilitates a difficult test for a 3-D model. For Iceland we are investigating whether or not a narrow plume can explain the differential travel-time data used to constrain the model. The width of the plume is so small that standard ray theory may be inadequate for waves with periods greater than 20~seconds. Due to finite-frequency effects, a ray that `misses' the plume can still be significantly affected by its presence. The question is whether a thin plume, which is preferred in geodynamic models, can explain the data as
New method for evaluation of finite-energy few-electron spectral function expressions
NASA Astrophysics Data System (ADS)
Carmelo, J. M. P.; Penc, K.; Sacramento, P. D.; Claessen, R.
2004-04-01
We present a method for the calculation of few-electron spectral functions of the one-dimen- sional Hubbard model which relies on a pseudofermion description introduced recently in Ref. [6]. The spectral functions are expressed as a convolution of pseudofermion dynamical correlation functions. Our general method involves the direct evaluation of the matrix elements of pseudofermion operators between the ground state and the excited states. We briefly discuss the application of our general method to the study of the unusual finite-energy spectral properties observed in the quasi-one-dimensional organic conductor TTF-TCNQ. Key words. correlation effects spectral properties organic conductors
Spectral/HP Element Method With Hierarchical Reconstruction for Solving Hyperbolic Conservation Laws
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.
A spectral KRMI conjugate gradient method under the strong-Wolfe line search
NASA Astrophysics Data System (ADS)
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.
Spectral imaging method for material classification and inspection of printed circuit boards
NASA Astrophysics Data System (ADS)
Ibrahim, Abdelhameed; Tominaga, Shoji; Horiuchi, Takahiko
2010-05-01
We propose a spectral imaging method for material classification and inspection of raw printed circuit boards (PCBs). The method is composed of two steps (1) estimation the PCB surface-spectral reflectances and (2) unsupervised classification of the reflectance data to make the inspection of PCB easy and efficient. First, we develop a spectral imaging system that captures high dynamic range images of a raw PCB with spatially and spectrally high resolutions in the region of visible wavelength. The surface-spectral reflectance is then estimated at every pixel point from multiple spectral images, based on the reflection characteristics of different materials. Second, the surface-spectral reflectance data are classified into several groups, according to the number of PCB materials. We develop an unsupervised classification algorithm incorporating both spectral information and spatial information, based on the Nyström approximation of the normalized cut method. The initial seeds for the Nyström procedure are effectively chosen using a guidance module based on the K-means algorithm. Low-dimensional spectral features are efficiently extracted from the original high-dimensional spectral reflectance data. The feasibility of the proposed method is examined in experiments using real PCBs in detail.
Quality Parameters Defined by Chebyshev Polynomials in Cold Rolling Process Chain
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.
Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1
NASA Astrophysics Data System (ADS)
Deckers, Karl; van Deun, Joris; Bultheel, Adhemar
2008-06-01
In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [-1,1] to arbitrary complex poles outside [-1,1] . The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [-1,1] .
Estimates of the trace of the inverse of a symmetric matrix using the modified Chebyshev algorithm
NASA Astrophysics Data System (ADS)
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).
Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves.
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
Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves
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
[Comparison among remotely sensed image fusion methods based on spectral response function].
Dou, Wen; Sun, Hong-quan; Chen, Yun-hao
2011-03-01
Remotely sensed image fusion is a critical issue, and many methods have been developed to inject features from a high spatial resolution panchromatic sensor into low spatial resolution multi-spectral images, trying to preserve spectral signatures while improving spatial resolution of multi-spectral images. However, no explicit physical information of the detection system has been taken into account in usual methods, which might lead to undesirable effects such as severe spectral distortion. Benefiting from the proper decomposition of the image fusion problem by a concise image fusion mathematical model, the present paper focuses on comparing reasonable modulation coefficient of spatial details based on analysis of the spectral response function (SRF). According to the classification of former methods, three modulation coefficients based on SRF of sensors were concluded, which lead to three image fusion methods incorporating spatial detail retrieved by Gaussian high-pass filter. All these methods were validated on Ikonos data compared to GS and HPM method. PMID:21595232
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.
Comparison of spectral CT imaging methods based a photon-counting detector: Experimental study
NASA Astrophysics Data System (ADS)
Lee, Youngjin; Lee, Seungwan; Kim, Hee-Joung
2016-04-01
Photon-counting detectors allow spectral computed tomography (CT) imaging using energy-resolved information from a polychromatic X-ray spectrum. The spectral CT images based on the photon-counting detectors are dependent on the energy ranges defined by energy bins for image acquisition. In this study, K-edge and energy weighting imaging methods were experimentally implemented by using a spectral CT system with a cadmium zinc telluride (CZT)-based photon-counting detector. The spectral CT images were obtained by various energy bins and compared in terms of CNR improvement for investigating the effect of energy bins and the efficiency of the spectral CT imaging methods. The results showed that the spectral CT image quality was improved by using the particular energy bins, which were optimized for each spectral CT imaging method and target material. The CNR improvement was different for the spectral CT imaging methods and target materials. It can be concluded that an appropriate selection of imaging method for each target material and the optimization of energy bin can maximize the quality of spectral CT images.
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.
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.
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.
Analysis of the spectral vanishing viscosity method for periodic conservation laws
NASA Technical Reports Server (NTRS)
Maday, Yvon; Tadmor, Eitan
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.
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. PMID:24159891
NASA Astrophysics Data System (ADS)
Desai, Ranjit P.; Menon, Jai P.
1998-12-01
A large class of high-speed visualization applications use image acquisition and 3D volume reconstruction techniques in cylindrical sampling grids; these include real-time 3D medical reconstruction, and reverse engineering. This paper presents the novel use of Chebyshev bases in such cylindrical grid- based volume applications, to allow efficient computation of cross-sectional planes of interest and partial volumes without the computationally expensive step of volume rendering, for subsequent transmission in constrained bitrate environments. This has important consequences for low-bitrate applications such as video-conferencing and internet-based visualization environments, where interaction and fusion between independently sampled heterogenous data streams (images, video and 3D volumes) from multiple sources is beginning to play an important part. Volumes often embody widely varying physical signals such as those acquired by X-rays, ultrasound sensors in addition to standard c.c.d. cameras. Several benefits of Chebyshev expansions such as fast convergence, bounded error, computational efficiency, and their optimality for cylindrical grids are taken into account. In addition, our method exploits knowledge about the sampling strategy (e.g. position and trajectory of the sensor) used to acquire the original ensemble of images, which in turn makes the overall approach very amenable to internet-based low-bitrate applications.
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
The research of a new test method about dynamic target infrared spectral signature
NASA Astrophysics Data System (ADS)
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.
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.
A Real-Time Infrared Ultra-Spectral Signature Classification Method via Spatial Pyramid Matching
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
A Real-Time Infrared Ultra-Spectral Signature Classification Method via Spatial Pyramid Matching.
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
Analysis of spectral radiative heat transfer using discrete exchange factor method
NASA Astrophysics Data System (ADS)
Zhang, Yinqiu; Naraghi, M. H. N.
1993-09-01
A solution technique is developed for spectral radiative heat-transfer problems. The formulation is based on the discrete exchange factor (DEF) method and uses Edward's (1976) wide band model to obtain spectral data. The results of the analyses of three cases were found to be in excellent agreement with those of the zonal method and differ by less than 5 percent from those of the discrete-ordinates method.
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.
A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions
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
Research on method of geometry and spectral calibration of pushbroom dispersive hyperspectral imager
NASA Astrophysics Data System (ADS)
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.
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%. PMID:26904833
An empirical method for correcting the detector spectral response in energy-resolved CT
NASA Astrophysics Data System (ADS)
Schmidt, Taly Gilat
2012-03-01
Energy-resolving photon-counting detectors have the potential for improved material decomposition compared to dual-kVp approaches. However, material decomposition accuracy is limited by the nonideal spectral response of the detectors. This work proposes an empirical method for correcting the nonideal spectral response, including spectrum-tailing effects. Unlike previous correction methods which relied on synchrotron measurements, the proposed method can be performed on the scanner. The proposed method estimates a spectral-response matrix by performing x-ray projection measurements through a range of known thicknesses of two or more calibration materials. Once estimated, the spectral-response matrix is incorporated into conventional material decomposition algorithms. A simulation study investigated preliminary feasibility of the proposed method. The spectral-response matrix was estimated using simulated projection measurements through PMMA, aluminum, and gadolinium. An energy-resolved acquisition of a thorax phantom with gadolinium in the blood pool was simulated assuming a five-bin detector with realistic spectral response. Energy-bin data was decomposed into Compton, photoelectric, and gadolinium basis projections with and without the proposed correction method. Basis images were reconstructed by filtered backprojection. Results demonstrated that the nonideal spectral response reduced the ability to distinguish gadolinium from materials such as bone, while images reconstructed with the proposed correction method successfully depicted the contrast agent. The proposed correction method reduced errors from 9% to 0.6% in the Compton image, 90% to 0.6% in the photoelectric image and from 40% to 6% in the gadolinium image when using a three-material calibration. Overall, results support feasibility of the proposed spectral-response correction method.
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.
On the Convergence of Galerkin Spectral Methods for a Bioconvective Flow
NASA Astrophysics Data System (ADS)
de Aguiar, R.; Climent-Ezquerra, B.; Rojas-Medar, M. A.; Rojas-Medar, M. D.
2016-06-01
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.
[Calculation of spectral shifts of the mutants of bacteriorhodopsin by QM/MM methods].
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.). PMID:22594277
A method to correct for spectral artifacts in optical-CT dosimetry
Pierquet, Michael; Jordan, Kevin; Oldham, Mark
2011-01-01
The recent emergence of radiochromic dosimeters with low inherent light-scattering presents the possibility of fast 3D dosimetry using broad-beam optical computed tomography (optical-CT). Current broad beam scanners typically employ either a single or a planar array of light-emitting diodes (LED) for the light source. The spectrum of light from LED sources is polychromatic and this, in combination with the non-uniform spectral absorption of the dosimeter, can introduce spectral artifacts arising from preferential absorption of photons at the peak absorption wavelengths in the dosimeter. Spectral artifacts can lead to large errors in the reconstructed attenuation coefficients, and hence dose measurement. This work presents an analytic method for correcting for spectral artifacts which can be applied if the spectral characteristics of the light source, absorbing dosimeter, and imaging detector are known or can be measured. The method is implemented here for a PRESAGE® dosimeter scanned with the DLOS telecentric scanner (Duke Large field-of-view Optical-CT Scanner). Emission and absorption profiles were measured with a commercial spectrometer and spectrophotometer, respectively. Simulations are presented that show spectral changes can introduce errors of 8% for moderately attenuating samples where spectral artifacts are less pronounced. The correction is evaluated by application to a 16 cm diameter PRESAGE® cylindrical dosimeter irradiated along the axis with two partially overlapping 6 × 6 cm fields of different doses. The resulting stepped dose distribution facilitates evaluation of the correction as each step had different spectral contributions. The spectral artifact correction was found to accurately correct the reconstructed coefficients to within ~1.5%, improved from ~7.5%, for normalized dose distributions. In conclusion, for situations where spectral artifacts cannot be removed by physical filters, the method shown here is an effective correction. Physical
Yokoya, Naoto; Miyamura, Norihide; Iwasaki, Akira
2010-08-20
Hyperspectral imaging sensors suffer from spectral and spatial misregistrations due to optical-system aberrations and misalignments. These artifacts distort spectral signatures that are specific to target objects and thus reduce classification accuracy. The main objective of this work is to detect and correct spectral and spatial misregistrations of hyperspectral images. The Hyperion visible near-infrared subsystem is used as an example. An image registration method based on phase correlation demonstrates the accurate detection of the spectral and spatial misregistrations. Cubic spline interpolation using estimated properties makes it possible to modify the spectral signatures. The accuracy of the proposed postlaunch estimation of the Hyperion characteristics is comparable to that of the prelaunch measurements, which enables the accurate onboard calibration of hyperspectral sensors. PMID:20733628
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. PMID:25314714
NASA Astrophysics Data System (ADS)
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.
Postprocessing Fourier spectral methods: The case of smooth solutions
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.