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1

B-spline Collocation with Domain Decomposition Method

NASA Astrophysics Data System (ADS)

A global B-spline collocation method has been previously developed and successfully implemented by the present authors for solving elliptic partial differential equations in arbitrary complex domains. However, the global B-spline approximation, which is simply reduced to Bezier approximation of any degree p with C0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order in the global method would be more prominent in domains of large dimension. For the increased collocation points, it may also lead to the ill-conditioning problem. In this study, overlapping domain decomposition of multiplicative Schwarz algorithm is combined with the global method. Our objective is two-fold that improving the accuracy with the combination technique, and also investigating influence of the combination technique to the employed B-spline basis orders with respect to the obtained accuracy. It was shown that the combination method produced higher accuracy with the B-spline basis of much lower order than that needed in implementation of the initial method. Hence, the approximation stability of the B-spline collocation method was also increased.

Hidayat, M. I. P.; Ariwahjoedi, B.; Parman, S.

2013-04-01

2

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Kojima, Fumio

1990-01-01

3

Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere

: numerical weather prediction; finite element; semiLagrangian semiimplicit; Rossby stability; staggered present a finite elementbased method, which dis cretizes the shallow water equations (SWEs) in time, for solving the shallow water equations (SWEs) in spherical co ordinates. A quadratic spline collocation

Christara, Christina C.

4

Quintic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation

NASA Astrophysics Data System (ADS)

In this paper, the quintic B-spline collocation scheme is implemented to find numerical solution of the Kuramoto-Sivashinsky equation. The scheme is based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are also shown graphically and are compared with results given in the literature.

Mittal, R. C.; Arora, Geeta

2010-10-01

5

Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation

NASA Astrophysics Data System (ADS)

A second-order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended Fisher-Kolmogorov equation. With the help of Lyapunov functional, a bound in maximum norm is derived for the semidiscrete solution. Optimal error estimates are established for the semidiscrete case. Finally, using the monomial basis functions we present the numerical results in which the integration in time is performed using RADAU 5 software library.

Danumjaya, P.; Pani, Amiya K.

2005-02-01

6

NASA Astrophysics Data System (ADS)

Physical processes with memory and hereditary properties can be best described by fractional differential equations due to the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.

Li, Xinxiu

2012-10-01

7

BACOL: B-Spline Adaptive COLlocation Software for 1-D Parabolic PDEs

and temporal error estimates. The software implements a spline collocation method at Gaussian points, with a B-splineBACOL: B-Spline Adaptive COLlocation Software for 1-D Parabolic PDEs R. WANG and P. KEAST Dalhousie, Performance Additional Key Words and Phrases: 1-D Parabolic PDEs, B-splines, collocation, high

Keast, Patrick

8

Discrete-time orthogonal spline collocation methods for Schrodinger-type problems

Time-dependent Schrodinger and vibration problems are of much physical and engineering significance. In this dissertation, we study the fully discrete high-order approximate solution of initial-boundary value problems for linear and nonlinear Schrodinger equations and vibration equation in two space variables on a unit square. We employ orthogonal spline collocation (OSC) with C1 piecewise polynomials of arbitrary degree r\\/ge3 in each

Bingkun Li

1998-01-01

9

Quartic B-spline collocation method applied to Korteweg de Vries equation

NASA Astrophysics Data System (ADS)

The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+?uux+?uxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L?-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L?-norm are also increase.

Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md

2014-07-01

10

NASA Astrophysics Data System (ADS)

In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L?andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.

Mittal, R. C.; Jain, R. K.

2012-12-01

11

1 Quadratic spline collocation for onedimensional linear parabolic partial differential equations general linear parabolic partial differential equations (PDEs) in one space dimen sion are developed. The methods combine quadraticspline collocation for the space discretization and classical finite differences

Christara, Christina C.

12

NASA Astrophysics Data System (ADS)

A numerical method is proposed for solving singularly perturbed one-dimensional parabolic convection-diffusion problems. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and B-spline collocation method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O(([Delta]x)2+[Delta]t). An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. Several numerical experiments have been carried out in support of the theoretical results. Comparisons of the numerical solutions are performed with an upwind finite difference scheme on a piecewise uniform mesh and exponentially fitted method on a uniform mesh to demonstrate the efficiency of the method.

Kadalbajoo, Mohan K.; Gupta, Vikas; Awasthi, Ashish

2008-10-01

13

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effectiveness and accuracy of B-spline collocation for solving differential equations include which points to use for collocation, what degree B-spline to use and what level of continuity to maintain. Success using higher degree B-spline curves having higher continuity at the knots, as opposed to more traditional approaches using orthogonal collocation, have recently been investigated along with collocation at the Greville points for linear (1D) and rectangular (2D) geometries. The development of automatic knot insertion techniques to provide sufficient accuracy for B-spline collocation has been underway. The present article reviews recent progress for the application of B-spline collocation to fluid motion equations as well as new work in developing a novel adaptive knot insertion algorithm for a 1D convection-diffusion model equation.

Johnson, Richard Wayne

2003-05-01

14

A fourth order spline collocation approach for a business cycle model

NASA Astrophysics Data System (ADS)

A collocation approach, based on a fourth order cubic B-splines is presented for the numerical solution of a Kaleckian business cycle model formulated by a nonlinear delay differential equation. The equation is approximated and the nonlinearity is handled by employing an iterative scheme arising from Newton's method. It is shown that the model exhibits a conditionally dynamical stable cycle. The fourth-order rate of convergence of the scheme is verified numerically for different special cases.

Sayfy, A.; Khoury, S.; Ibdah, H.

2013-10-01

15

to functions basis collocation spline dratic quadratic on based methods element finite other with used be also from arising systems linear for analyzed and developed been have methods colloca element finite for work related The equations. differential of discretization element finite type spline quadratic

Christara, Christina C.

16

NASA Astrophysics Data System (ADS)

A boundary value problem for linear partial differential algebraic systems of equations with multiple characteristic curves is examined. It is assumed that the pencil of matrix functions associated with this system is smoothly equivalent to a special canonic form. The spline collocation is used to construct for this problem a difference scheme of an arbitrary approximation order with respect to each independent variable. Sufficient conditions are found for this scheme to be absolutely stable.

Gaidomak, S. V.

2013-09-01

17

Collocation and Galerkin Time-Stepping Methods

NASA Technical Reports Server (NTRS)

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Huynh, H. T.

2011-01-01

18

NASA Astrophysics Data System (ADS)

A mixed approach, based on cubic B-spline collocation and asymptotic boundary conditions (ABCs), is presented for the numerical solution of an extended class of two-point linear boundary value problems (BVPs) over an infinite interval as well as a system of BVPs. The condition at infinity is reduced to an asymptotic boundary condition that approaches the required value at infinity over a large finite interval. The resulting problem is handled using an adaptive spline collocation approach constructed over uniform meshes. The rate of convergence is verified numerically to be of fourth-order. The efficiency and applicability of the method are demonstrated by applying the strategy to a number of examples. The numerical solutions are compared with existing analytical solutions.

Khoury, S.; Ibdah, H.; Sayfy, A.

2013-10-01

19

Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

NASA Astrophysics Data System (ADS)

We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.

Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo

2014-04-01

20

B-spline Method in Fluid Dynamics

NASA Technical Reports Server (NTRS)

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier; Shariff, Karim; Mansour, Nagi N. (Technical Monitor)

2001-01-01

21

A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

Johnson, Richard Wayne; Landon, Mark Dee

1999-07-01

22

A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics

The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

M. D. Landon; R. W. Johnson

1999-07-01

23

An enhanced splined saddle method

NASA Astrophysics Data System (ADS)

We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)], 10.1063/1.2916716. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C60 fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time.

Ghasemi, S. Alireza; Goedecker, Stefan

2011-07-01

24

An enhanced splined saddle method.

We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)]. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C(60) fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time. PMID:21744889

Ghasemi, S Alireza; Goedecker, Stefan

2011-07-01

25

Splines and the Galerkin method for solving the integral equations of scattering theory

NASA Astrophysics Data System (ADS)

This paper investigates the Galerkin method with cubic B-spline approximants to solve singular integral equations that arise in scattering theory. We stress the relationship between the Galerkin and collocation methods.The error bound for cubic spline approximates has a convergence rate of O(h4), where h is the mesh spacing. We test the utility of the Galerkin method by solving both two- and three-body problems. We demonstrate, by solving the Amado-Lovelace equation for a system of three identical bosons, that our numerical treatment of the scattering problem is both efficient and accurate for small linear systems.

Brannigan, M.; Eyre, D.

1983-06-01

26

A tensor product b-spline method for 3D multi-block elliptic grid generation

We formulate a tensor product b-spline method for multi-block numerical grid generation. The Cartesian coordinate functions for a block are represented as a sum of tensor product b-spline basis functions defined on a parameter space for the block. The tensor product b-spline basis functions are constructed so that the basis functions and their first partials are continuous on the parameter space. The coordinate functions inherit this smoothness: a grid computed by evaluating the coordinate functions along constant parameter lines leads to smooth grid lines with smoothly varying tangents. The expansion coefficients for the coordinate functions are computed by solving the usual elliptic grid generation equations using simple collocation. This assures that the computed grid has the smoothness and resolution expected for an elliptic grid with appropriate control. An important result of the formulation is that the dimension of the collocation equations is the number of distinct knots for the tensor product b-spline basis functions. Combining this results with the smoothness of the b-spline representation makes it possible to reduce the dimension of the tensor product method with respect to the finite difference method, simply by using fewer knots than grid points. We formulate the expansion of the Cartesian coordinate functions as a sum of tensor product b-spline basis functions, and then we derive the collocation and boundary condition equations for the usual elliptic grid generation equations. We investigate the structure of the system of equations for the expansion coefficients and then formulate a solution algorithm to compute the coefficients. Finally, we describe the implementation of the method in a 2D multi-block grid code and discuss the performance of the method for several grids. 3 refs., 11 figs.

Manke, J.W.

1988-12-01

27

Multivariate spline methods in surface fitting

NASA Technical Reports Server (NTRS)

The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.

Guseman, L. F., Jr. (principal investigator); Schumaker, L. L.

1984-01-01

28

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

NASA Astrophysics Data System (ADS)

In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and following the isogeometric paradigm, we map them on domains which are (piecewise) spline or NURBS geometries. We analyze their geometric and topological structure, as related to the connectivity of the underlying mesh, and we present degrees of freedom together with their physical interpretation. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.

Buffa, A.; Sangalli, G.; Vzquez, R.

2014-01-01

29

Sinc-collocation method for solving the Blasius equation

Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic

K. Parand

2009-01-01

30

Sinc-collocation method for solving the Blasius equation

NASA Astrophysics Data System (ADS)

Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.

Parand, K.; Dehghan, Mehdi; Pirkhedri, A.

2009-10-01

31

Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation

The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.

Ismail, M. S. [Department of Mathematics, College of Science, P.O.Box 80203, King Abdulaziz University, Jeddah (Saudi Arabia)

2010-09-30

32

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

33

NASA Astrophysics Data System (ADS)

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

34

Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.

In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L? and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions. PMID:24427270

Abbas, Muhammad; Majid, Ahmad Abd; Md Ismail, Ahmad Izani; Rashid, Abdur

2014-01-01

35

Sinc-Collocation method for solving astrophysics equations

In this paper we propose Sinc-Collocation method for solving LaneEmden equation which is a nonlinear ordinary differential equation on a semi-infinite interval. It is found that Sinc procedure converges with the solution at an exponential rate. This method is utilized to reduce the computation of this problem to some algebraic equations. We also compare this solution with some well-known results

K. Parand; A. Pirkhedri

2010-01-01

36

Sinc-Collocation method for solving astrophysics equations

NASA Astrophysics Data System (ADS)

In this paper we propose Sinc-Collocation method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on a semi-infinite interval. It is found that Sinc procedure converges with the solution at an exponential rate. This method is utilized to reduce the computation of this problem to some algebraic equations. We also compare this solution with some well-known results and show that it is accurate.

Parand, K.; Pirkhedri, A.

2010-08-01

37

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

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

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

38

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

NASA Astrophysics Data System (ADS)

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical-cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.

Lee, Wei-Ming

2012-05-01

39

A B-spline Galerkin method for the Dirac equation

The B-spline methods Johnson and Sapirstein (1, 2) introduced into relativistic many-body perturbation the- ory have produced results of unprecedented accuracy (3). Essentially, the local non-orthogonal B-spline basis was transformed to an orthogonal orbital basis by the ap- plication of the Galerkin method to the Dirac equation over a finite interval (4). The resulting basis was fi- nite and effectively

Charlotte Froese Fischer; Oleg Zatsarinny

2009-01-01

40

Higher-order numerical solutions using cubic splines

NASA Technical Reports Server (NTRS)

A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.

Rubin, S. G.; Khosla, P. K.

1976-01-01

41

The chain collocation method: A spectrally accurate calculus of forms

NASA Astrophysics Data System (ADS)

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

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

2014-01-01

42

Rational scaled generalized Laguerre function collocation method for solving the Blasius equation

In this paper we propose, a collocation method for solving the Blasius equation. The Blasius equation is a third-order nonlinear ordinary differential equation. This approach is based on a rational scaled generalized Laguerre function collocation method. We also present the comparison of this work with some well-known results and show that the present solution is accurate.

K. Parand; A. Taghavi

2009-01-01

43

Rational scaled generalized Laguerre function collocation method for solving the Blasius equation

NASA Astrophysics Data System (ADS)

In this paper we propose, a collocation method for solving the Blasius equation. The Blasius equation is a third-order nonlinear ordinary differential equation. This approach is based on a rational scaled generalized Laguerre function collocation method. We also present the comparison of this work with some well-known results and show that the present solution is accurate.

Parand, K.; Taghavi, A.

2009-12-01

44

Dynamically Adaptive Wavelet Collocation Method for Shock Computations

NASA Astrophysics Data System (ADS)

Most explicit TVD schemes make use of artificial viscosity to reduce oscillations and avoid the stability requirements that an explicitly written dissipation term would require when solving hyperbolic conservation equations. In this talk an adaptive wavelet collocation method for shock computation is described. The method for determining a shock's location is similar to Harten's multiresolution algorithm, but its implementation is more continuous. The presence of wavelet coefficients on the finest level of resolution indicates that the maximum allowed resolution has been reached and localized artificial viscous terms should be added to smooth the solution. The localized viscosity is constructed by creating a mask of the wavelet coefficients on the finest level that are greater than a given threshold parameter. The mask is smoothed to reduce oscillations that can be induced due to spatial discontinuities in the second derivative. The main advantage of this technique are its generality and zero losses away from shocks. Since the viscosity is written explicitly, sonic points are no longer problematic and there is no need to track wind direction or introduce flux splitting. One- and two-dimensional examples are given and discussed.

Regele, Jonathan

2005-11-01

45

Generalized Laguerre Polynomials Collocation Method for Solving Lane-Emden Equation

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a general- ized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equa- tions.We also present the comparison of this

K. Parand; A. Taghavi

2008-01-01

46

NASA Astrophysics Data System (ADS)

A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach can be significantly less than that associated with the discrete-ordinates approach. A general diffusion equation treating both symmetric and asymmetric scattering is developed and used in a synthetic acceleration algorithm to accelerate the iterative convergence of collocation solutions. It is shown that a certain type of asymmetric scattering can radically alter the asymptotic behavior of the transport solution and is mathematically equivalent within the diffusion approximation to particle transport under the influence of an electric field.

Morel, J. E.

1981-01-01

47

A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

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

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

48

Efficient Interpolation-based Error Estimation for 1D Time-Dependent PDE Collocation Codes

based on B-spline collocation. BACOL generates the spatial error estimate by computing two global collocation solutions to the PDEs, one based on B-splines of degree p and the other on B-splines of degree p+1 equivalent to the error of the collocation solution. We implement these new schemes within a modified version

49

n this paper we show how stochastic collocation method (SCM) could fail to con- verge for nonlinear differential equations with random coefficients. First, we consider Navier-Stokes equation with uncertain viscosity and derive error estimates for stochastic collocation discretization. Our analysis gives some indicators on how the nonlinearity negatively affects the accuracy of the method. The stochastic collocation method is then applied to noisy Lorenz system. Simulation re- sults demonstrate that the solution of a nonlinear equation could be highly irregular on the random data and in such cases, stochastic collocation method cannot capture the correct solution.

Webster, Clayton G [ORNL; Tran, Hoang A [ORNL; Trenchea, Catalin S [ORNL

2013-01-01

50

NASA Technical Reports Server (NTRS)

In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.

Zhang, Zhimin; Tomlinson, John; Martin, Clyde

1994-01-01

51

In this paper we propose to apply the golden section search algorithm to determining a good shape parameter of multiquadrics (MQ) for the solution of partial differential equations. We use two radial basis function based meshless collocation methods, the method of approximate particular solutions (MAPS) and Kansa's method, to solve partial differential equations. Due to the severely ill-conditioned matrix system

C. H. Tsai; Joseph Kolibal; Ming Li

2010-01-01

52

In this paper we propose, a collocation method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi- infnite interval. This approach is based on generalized Laguerre poly- nomials and rational Chebyshev functions. This method reduces the solution of this problem to the solution of a system of algebraic equa- tions. We also present the comparison

K. Parand; M. Shahini; A. Taghavi

2009-01-01

53

Spacecraft Orbit Determination with The B-spline Approximation Method

NASA Astrophysics Data System (ADS)

It is known that the dynamical orbit determination is the most common way to get the precise orbits of spacecraft. However, it is hard to build up the precise dynamical model of spacecraft sometimes. In order to solve this problem, the technique of the orbit determination with the B-spline approximation method based on the theory of function approximation is presented in this article. In order to verify the effectiveness of this method, simulative orbit determinations in the cases of LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and HEO (Highly Eccentric Orbit) satellites are performed, and it is shown that this method has a reliable accuracy and stable solution. The approach can be performed in both the conventional celestial coordinate system and the conventional terrestrial coordinate system. The spacecraft's position and velocity can be calculated directly with the B-spline approximation method, it needs not to integrate the dynamical equations, nor to calculate the state transfer matrix, thus the burden of calculations in the orbit determination is reduced substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can serve as a conventional algorithm in the spacecraft orbit determination.

Song, Ye-zhi; Huang, Yong; Hu, Xiao-gong; Li, Pei-jia; Cao, Jian-feng

2014-04-01

54

A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach can be significantly less than that associated with the discrete-ordinates approach. A general diffusion equation treating both symmetric and asymmetric scattering is developed and used in a synthetic acceleration algorithm to accelerate the iterative convergence of collocation solutions. It is shown that a certain type of asymmetric scattering can radically alter the asymptotic behavior of the transport solution and is mathematically equivalent within the diffusion approximation to particle transport under the influence of an electric field. The method is easily extended to other geometries and higher dimensions. Applications exist in the areas of neutron transport with highly anisotropic scattering (such as that associated with hydrogenous media), charged-particle transport, and particle transport in controlled-fusion plasmas. 23 figures, 6 tables.

Morel, J.E.

1981-01-01

55

A tensor product b-spline method for 3D multi-block elliptic grid generation

We formulate a tensor product b-spline method for multi-block numerical grid generation. The Cartesian coordinate functions for a block are represented as a sum of tensor product b-spline basis functions defined on a parameter space for the block. The tensor product b-spline basis functions are constructed so that the basis functions and their first partials are continuous on the parameter

Manke

1988-01-01

56

An analytic reconstruction method for PET based on cubic splines

NASA Astrophysics Data System (ADS)

PET imaging is an important nuclear medicine modality that measures in vivo distribution of imaging agents labeled with positron-emitting radionuclides. Image reconstruction is an essential component in tomographic medical imaging. In this study, we present the mathematical formulation and an improved numerical implementation of an analytic, 2D, reconstruction method called SRT, Spline Reconstruction Technique. This technique is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of 'custom made' cubic splines. It also imposes sinogram thresholding which restricts reconstruction only within object pixels. Furthermore, by utilizing certain symmetries it achieves a reconstruction time similar to that of FBP. We have implemented SRT in the software library called STIR and have evaluated this method using simulated PET data. We present reconstructed images from several phantoms. Sinograms have been generated at various Poison noise levels and 20 realizations of noise have been created at each level. In addition to visual comparisons of the reconstructed images, the contrast has been determined as a function of noise level. Further analysis includes the creation of line profiles when necessary, to determine resolution. Numerical simulations suggest that the SRT algorithm produces fast and accurate reconstructions at realistic noise levels. The contrast is over 95% in all phantoms examined and is independent of noise level.

Kastis, George A.; Kyriakopoulou, Dimitra; Fokas, Athanasios S.

2014-03-01

57

The multiquadric radial basis function (MQ) method is a recent meshless collocation method with global basis functions. It was introduced for discretizing partial differential equations (PDEs) by Kansa in the early 1990s. The MQ method was originally used for interpolation of scattered data, and it was shown to have exponential convergence for interpolation problems.In [1], we have extended the Kansa-MQ

E. J. Kansa; M FRIEDMAN

2002-01-01

58

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Quarteroni, Alfio

1989-01-01

59

Collocation method using sinc and Rational Legendre functions for solving Volterras population model

This paper proposes two approximate methods to solve Volterras population model for population growth of a species in a closed system. Volterras model is a nonlinear integro-differential equation on a semi-infinite interval, where the integral term represents the effect of toxin. The proposed methods have been established based on collocation approach using Sinc functions and Rational Legendre functions. They are

K. Parand

2011-01-01

60

A non-polynomial collocation method for fractional terminal value problems

NASA Astrophysics Data System (ADS)

In this work we are concerned with the numerical approximation of terminal (or boundary) value problems for fractional differential equations. The approach used is based on the equivalence between this kind of problem and a Fredholm integral equation. Taking into account the potential non-smoothness of the solution of such problems at the origin, we propose a non-polynomial collocation method on a uniform mesh. Some numerical results are presented and we discuss briefly the convergence of the method.

Morgado, M. L.; Rebelo, M.; Ford, N. J.

2012-09-01

61

A method fortting regression splines with varying polynomial order in the linear mixed model

SUMMARY The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models oers the analyst additionalexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven conrmatory analyses. We propose a method fortting piecewise polynomial regression splines with varying polynomial order in the ?xed eects and =or

Lloyd J. Edwards; Paul W. Stewart; James E. MacDougall; Ronald W. Helms

2005-01-01

62

A novel stochastic collocation method for uncertainty propagation in complex mechanical systems

NASA Astrophysics Data System (ADS)

This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.

Qi, WuChao; Tian, SuMei; Qiu, ZhiPing

2015-02-01

63

A novel stochastic collocation method for uncertainty propagation in complex mechanical systems

NASA Astrophysics Data System (ADS)

This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions' statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it's a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.

Qi, WuChao; Tian, SuMei; Qiu, ZhiPing

2014-08-01

64

GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD

GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD BY DANDAN MIAO BS...............................................................................................39 2.2 Snake Method....................................................................................................................40 2.2.1 Snake Method Definition...............................................

New Hampshire, University of

65

An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orthogonal basis functions and

Chia-Chien Huang; Chia-Chih Huang; Jaw-Yen Yang

2003-01-01

66

A subdivision-based implementation of the hierarchical b-spline finite element method PPZ, U.K. Abstract A novel technique is presented to facilitate the implementation of hierarchical b-splines functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision

Cirak, Fehmi

67

The Chain Collocation Method: A Spectrally Accurate Calculus of Forms

, Patrick Mullen, Mathieu Desbrun Applied Geometry Lab, Caltech Abstract Preserving in the discrete realm, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces guarantees [6]. However, geometric discretizations of elasticity, electromagnetism, or fluid me- chanics have

Desbrun, Mathieu

68

Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.

Webster, Clayton G [ORNL; Zhang, Guannan [ORNL; Gunzburger, Max D [ORNL

2012-10-01

69

A collocation method for certain elliptic boundary-value problems

for linear boundary value problems, Bulletin of the Institute of Mathematics, Academia Sinica, 1 (1973) p 41-55. 43 l2. H. S. Price, J. C. Cavendish, and R. S. Varga, Numerical methods of higher order accuracy for diffusion ? convection equations, Soc...+S)GO '0 1 CONTINUE ITER=101 GO TO 5 C 0 NT I NUE I TER=K 5 RETURN END I M PL I CI 7 P F A L". 8 ( A ? H p 0- 2 ) DIMFNSION F(36&36) sX(36) sA(36~37) ~G(36) ~Y(36) vFG(36i36) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC...

Hord, Susan Kathleen

2012-06-07

70

Spline finite difference methods for singular two point boundary value problems

Summary In this paper we discuss the construction of a spline function for a class of singular two-point boundary value problemx-a(xau')=f (x, u),u(0)=A,u(1)=B, 0u'(0)=0,u(1)=B. Three point finite difference methods, using the above splines, are obtained for the solution of the boundary value problem. These methods are of second order and are illustrated by four numerical examples.

S. R. K. Iyengar; Pragya Jain

1986-01-01

71

Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs

The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. PMID:25485295

Javadi, H. H. S.; Navidi, H. R.

2014-01-01

72

Collocation method using sinc and Rational Legendre functions for solving Volterras population model

NASA Astrophysics Data System (ADS)

This paper proposes two approximate methods to solve Volterra's population model for population growth of a species in a closed system. Volterra's model is a nonlinear integro-differential equation on a semi-infinite interval, where the integral term represents the effect of toxin. The proposed methods have been established based on collocation approach using Sinc functions and Rational Legendre functions. They are utilized to reduce the computation of this problem to some algebraic equations. These solutions are also compared with some well-known results which show that they are accurate.

Parand, K.; Delafkar, Z.; Pakniat, N.; Pirkhedri, A.; Kazemnasab Haji, M.

2011-04-01

73

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

NASA Technical Reports Server (NTRS)

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

Kouatchou, Jules

1999-01-01

74

NASA Astrophysics Data System (ADS)

This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.

Blakely, Christopher D.

75

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

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

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

2014-01-01

76

A semi-implicit collocation method - Application to thermal convection in 2D compressible fluids

NASA Astrophysics Data System (ADS)

A semiimplicit pseudo-spectral collocation method using a third-order Runge-Kutta numerical scheme for the full Navier-Stokes equations is described. The Courant-Friedrichs-Lewy condition is overcome by the implicit handling of a diffusive term. All such terms are solved with an iterative scheme in the Fourier space. Simulation of thermal convection in 2D compressible fluids is made by expanding variables on a Fourier-Chebyshev basis. Examples of subsonic and supersonic steady solutions are given in the case where the heat flux at the upper boundary is governed by a black body.

Gauthier, Serge

1991-06-01

77

B-Spline Based Monotone Multigrid Methods, with an Application to the Pricing of American Options

We propose a monotone multigrid method based on a B-spline basis of arbitrary smooth- ness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi-optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B-spline expansion coefficients.

Markus Holtz; Angela Kunoth

78

Efficient implementation of B-spline modal method for lamellar gratings.

The B-spline modal method (BMM) as applied to lamellar gratings analysis is revisited, and a new implementation is presented. The main difference with our previous work is that we now take into account discontinuities by putting a spline with a degenerate knot on them. Our new approach is compared with other implementations of the BMM and is shown to be superior in terms of numerical convergence. PMID:24562032

Granet, Grard

2014-02-01

79

Methods of spline approximation in the problem of amplitude-time analysis of a pulse wave

We analyze the applicability of the methods for restoration of signal derivatives by cubic and B-splines in the problem of\\u000a amplitude-time analysis of a pulse wave. It is found that interpolating splines are sufficiently sensitive to the presence\\u000a of noises in the signal processed. We propose a pre-processing procedure that is based on the use of a specially constructed\\u000a low-frequency

V. V. Boronoyev; O. S. Rinchinov

1998-01-01

80

Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains

NASA Astrophysics Data System (ADS)

Powell-Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and Neumann conditions, and we show that a particular choice of the PS-triangles at the boundary can greatly simplify the corresponding constraints. Finally, we consider an application where the techniques developed in this paper are used: the numerical solution of a partial differential equation by the Galerkin and collocation method.

Speleers, Hendrik; Dierckx, Paul; Vandewalle, Stefan

2007-09-01

81

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

82

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

83

Interpolation of Superconducting Gravity Observations Using Least-Squares Collocation Method

NASA Astrophysics Data System (ADS)

A pre-processing of the gravity data measured by superconducting gravimeter involves removing of spikes, offsets and gaps. Their presence in observations can limit the data analysis and degrades the quality of obtained results. Short data gaps are filling by theoretical signal in order to get continuous records of gravity. It requires the accurate tidal model and eventually atmospheric pressure at the observed site. The poster presents a design of algorithm for interpolation of gravity observations with a sampling rate of 1 min. Novel approach is based on least-squares collocation which combines adjustment of trend parameters, filtering of noise and prediction. It allows the interpolation of missing data up to a few hours without necessity of any other information. Appropriate parameters for covariance function are found using a Bayes' theorem by modified optimization process. Accuracy of method is improved by the rejection of outliers before interpolation. For filling of longer gaps the collocation model is combined with theoretical tidal signal for the rigid Earth. Finally, the proposed method was tested on the superconducting gravity observations at several selected stations of Global Geodynamics Project. Testing demonstrates its reliability and offers results comparable with the standard approach implemented in ETERNA software package without necessity of an accurate tidal model.

Habel, Branislav; Janak, Juraj

2014-05-01

84

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

NASA Astrophysics Data System (ADS)

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

Ranjan, R.; Pantano, C.

2013-01-01

85

Fast Split-Step Wavelet Collocation Method for WDM System Parameter Optimization

NASA Astrophysics Data System (ADS)

To meet rapidly increasing bandwidth requirements, extensive numerical simulations are an important optimization step for optical networks. Using a basis of cardinal functions with compact support, a new split-step wavelet collocation method (SSWCM) was developed as a general solver for the nonlinear Schrdinger equation describing pulse propagation in nonlinear optical fibers. With N as the number of discretization points, this technique has the optimum complexity cal(N) for a fixed accuracy, which is superior to the complexity cal(N log2 N) of the standard split-step Fourier method (SSFM). For the simulation of a large 40-Gb/s dense-wavelength-division-multiplexing (DWDM) system with 64 channels, the SSWCM requires less than 40% of computation time compared with the SSFM. This improvement allows a systematic optimization of wavelength-division-multiplexing (WDM) system parameters to achieve a minimum bit-error rate.

Kremp, Tristan; Freude, Wolfgang

2005-03-01

86

Solving non-linear Lane-Emden type equations using Bessel orthogonal functions collocation method

NASA Astrophysics Data System (ADS)

The Lane-Emden type equations are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. These equations are categorized as non-linear singular ordinary differential equations on the semi-infinite domain [0,infty ). In this research we introduce the Bessel orthogonal functions as new basis for spectral methods and also, present an efficient numerical algorithm based on them and collocation method for solving these well-known equations. We compare the obtained results with other results to verify the accuracy and efficiency of the presented scheme. To obtain the orthogonal Bessel functions we need their roots. We use the algorithm presented by Glaser et al. (SIAM J Sci Comput 29:1420-1438, 2007) to obtain the N roots of Bessel functions.

Parand, Kourosh; Nikarya, Mehran; Rad, Jamal Amani

2013-05-01

87

NASA Astrophysics Data System (ADS)

A new meshfree method based on a discrete transformation of Green's basis functions is introduced to simulate Poisson problems with complex morphologies. The proposed Green's Discrete Transformation Method (GDTM) uses source points that are located along a virtual boundary outside the problem domain to construct the basis functions needed to approximate the field. The optimal number of Green's functions source points and their relative distances with respect to the problem boundaries are evaluated to obtain the best approximation of the partition of unity condition. A discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions. A comprehensive convergence study is presented to investigate the accuracy and convergence rate of the GDTM. We will also demonstrate the application of this meshfree method for simulating the conductive heat transfer in a heterogeneous materials system and the dissolved aluminum ions concentration in the electrolyte solution formed near a passive corrosion pit.

Soghrati, Soheil; Mai, Weijie; Liang, Bowen; Buchheit, Rudolph G.

2015-01-01

88

Analysis of defect in E.U.V. lithography mask using a Modal Method by Nodal B-Spline Expansion) The spline nodal basis function implemented in this paper is the first step toward a multiresolution scheme

Paris-Sud XI, Université de

89

This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.

Webster, Clayton; Tempone, Raul (Florida State University, Tallahassee, FL); Nobile, Fabio (Politecnico di Milano, Italy)

2007-12-01

90

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

NASA Astrophysics Data System (ADS)

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 convergence is achieved rather than polynomial rates. The solution methodology proposed, the CCSLBM, is also extended to three dimensions and a 3D regularized cavity is simulated; the corresponding results are presented and validated. Indications are that the CCSLBM developed and applied herein is robust, efficient, and accurate for computing 2D and 3D low-speed flows. Note also that high-accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the assessment of other LBM-based flow solvers.

Hejranfar, Kazem; Hajihassanpour, Mahya

2015-01-01

91

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

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 convergence is achieved rather than polynomial rates. The solution methodology proposed, the CCSLBM, is also extended to three dimensions and a 3D regularized cavity is simulated; the corresponding results are presented and validated. Indications are that the CCSLBM developed and applied herein is robust, efficient, and accurate for computing 2D and 3D low-speed flows. Note also that high-accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the assessment of other LBM-based flow solvers. PMID:25679733

Hejranfar, Kazem; Hajihassanpour, Mahya

2015-01-01

92

Triangulated spherical splines for geopotential reconstruction

NASA Astrophysics Data System (ADS)

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplaces equation on the Earths exterior to compute a spherical spline to approximate the geopotential at the Earths surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earths surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 ( n max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earths surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation.

Lai, M. J.; Shum, C. K.; Baramidze, V.; Wenston, P.

2009-08-01

93

NASA Astrophysics Data System (ADS)

This paper details to an electromagnetic modeling of an extreme ultraviolet (EUV) lithography mask. For that purpose, a modal method based on a spline nodal expansion (MMSNE) is presented. The results obtained using first, and second-order splines as basis functions are compared with those obtained using other modal methods, such as modal method by Fourier expansion (MMFE). The agreement between the results obtained using different methods is very good, and a convergence test is also performed. The spline nodal basis function implemented in this paper is the first step toward the realization of a multiresolution scheme that is expected to perform much more efficiently than conventional schemes.

Edee, Kofi; Schiavone, Patrick; Granet, Grard

2005-09-01

94

NASA Astrophysics Data System (ADS)

The correspondence principle is customarily used with the Laplace-Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mcanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599-1606) have shown the equivalence between the collocation method used to invert Laplace-Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.

Vu, Q. H.; Brenner, R.; Castelnau, O.; Moulinec, H.; Suquet, P.

2012-03-01

95

A spectral method of Chebyshev collocation with domain decomposition is introduced for linear interaction between sound and structure in a duct lined with flexible walls backed by cavities with or without a porous material. The spectral convergence is validated by a one-dimensional problem with a closed-form analytical solution, and is then extended to the two-dimensional configuration and compared favorably against a previous method based on the Fourier-Galerkin procedure and a finite element modeling. The nonlocal, exact Dirichlet-to-Neumann boundary condition is embedded in the domain decomposition scheme without imposing extra computational burden. The scheme is applied to the problem of high-frequency sound absorption by duct lining, which is normally ineffective when the wavelength is comparable with or shorter than the duct height. When a tensioned membrane covers the lining, however, it scatters the incident plane wave into higher-order modes, which then penetrate the duct lining more easily and get dissipated. For the frequency range of f=0.3-3 studied here, f=0.5 being the first cut-on frequency of the central duct, the membrane cover is found to offer an additional 0.9 dB attenuation per unit axial distance equal to half of the duct height. PMID:19045780

Huang, Lixi

2008-11-01

96

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations

K. Parand; Mehdi Dehghan; A. R. Rezaei; S. M. Ghaderi

2010-01-01

97

NASA Astrophysics Data System (ADS)

An efficient Legendre-Gauss-Lobatto collocation (L-GL-C) method is applied to solve the space-fractional advection diffusion equation with nonhomogeneous initial-boundary conditions. The Legendre-Gauss-Lobatto points are used as collocation nodes for spatial fractional derivatives as well as the Caputo fractional derivative. This approach is reducing the problem to the solution of a system of ordinary differential equations in time which can be solved by using any standard numerical techniques. The proposed numerical solutions when compared with the exact solutions reveal that the obtained solution produces highly accurate results. The results show that the proposed method has high accuracy and is efficient for solving the space-fractional advection diffusion equation.

Bhrawy, A. H.; Baleanu, D.

2013-10-01

98

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

NASA Technical Reports Server (NTRS)

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.

1997-01-01

99

NASA Astrophysics Data System (ADS)

The high-order purely frequency-based harmonic balance method (HBM) presented by Cochelin and Vergez (2009) [1] and extended by Karkar et al. (2013) [2] now allows to follow the periodic solutions of regularized non-smooth systems (stiff systems). This paper compares its convergence property to a reference method in applied mathematics: orthogonal collocation with piecewise polynomials. A first test is conducted on a nonlinear smooth 2 degree-of-freedom spring mass system, showing better convergence of the HBM. The second test is conducted on a one degree-of-freedom vibro-impact system with a very stiff regularization of the impact law. The HBM continuation of the nonlinear mode was found to be very robust, even with a very large number of harmonics. Surprisingly, the HBM was found to have a better convergence than the collocation method for this vibro-impact system. absolute threshold on the norm of the residue for the Newton-Raphson corrector: ?NR=10-9 (the residue norm is checked at the end of each step, and correction is carried out only if necessary), ANM series threshold used for step length estimation: ?ANM=10-12, ANM series order: Nseries=20. The choice of a small correction threshold ensures that the accuracy of a solution is mainly dependent on the accuracy of the discretization method, and not on that of the solver of the quadratic problem. Similarly, the choice of an even smaller ANM threshold ensures that the approximation at the end of each step is accurate enough so that no correction is usually needed at the beginning of the next step. Finally, the choice of the series order is arbitrary and mainly influences the step length.

Karkar, Sami; Cochelin, Bruno; Vergez, Christophe

2014-06-01

100

A force identification method using cubic B-spline scaling functions

NASA Astrophysics Data System (ADS)

For force identification, the solution may differ from the desired force seriously due to the unknown noise included in the measured data, as well as the ill-posedness of inverse problem. In this paper, an efficient basis function expansion method based on wavelet multi-resolution analysis using cubic B-spline scaling functions as basis functions is proposed for identifying force history with high accuracy, which can overcome the deficiency of the ill-posed problem. The unknown force is approximated by a set of translated cubic B-spline scaling functions at a certain level and thereby the original governing equation of force identification is reformulated to find the coefficients of scaling functions, which yields a well-posed problem. The proposed method based on wavelet multi-resolution analysis has inherent numerical regularization for inverse problem by changing the level of scaling functions. The number of basis functions employed to approximate the identified force depends on the level of scaling functions. A regularization method for selecting the optimal level of cubic B-spline scaling functions by virtue of condition number of matrix is proposed. In this paper, the validity and applicability of the proposed method are illustrated by two typical examples of Volterra-Fredholm integral equations that are both typical ill-posed problems. Force identification experiments including impact and harmonic forces are conducted on a cantilever beam to compare the accuracy and efficiency of the proposed method with that of the truncated singular value decomposition (TSVD) technique.

Qiao, Baijie; Zhang, Xingwu; Luo, Xinjie; Chen, Xuefeng

2015-02-01

101

Quantification of the spatial strain distribution of scoliosis using a thin-plate spline method.

The objective of this study was to quantify the three-dimensional spatial strain distribution of a scoliotic spine by nonhomogeneous transformation without using a statistically averaged reference spine. The shape of the scoliotic spine was determined from computed tomography images from a female patient with adolescent idiopathic scoliosis. The shape of the scoliotic spine was enclosed in a rectangular grid, and symmetrized using a thin-plate spline method according to the node positions of the grid. The node positions of the grid were determined by numerical optimization to satisfy symmetry. The obtained symmetric spinal shape was enclosed within a new rectangular grid and distorted back to the original scoliotic shape using a thin-plate spline method. The distorted grid was compared to the rectangular grid that surrounded the symmetrical spine. Cobb's angle was reduced from 35 in the scoliotic spine to 7 in the symmetrized spine, and the scoliotic shape was almost fully symmetrized. The scoliotic spine showed a complex Green-Lagrange strain distribution in three dimensions. The vertical and transverse compressive/tensile strains in the frontal plane were consistent with the major scoliotic deformation. The compressive, tensile and shear strains on the convex side of the apical vertebra were opposite to those on the concave side. These results indicate that the proposed method can be used to quantify the three-dimensional spatial strain distribution of a scoliotic spine, and may be useful in quantifying the deformity of scoliosis. PMID:24183547

Kiriyama, Yoshimori; Watanabe, Kota; Matsumoto, Morio; Toyama, Yoshiaki; Nagura, Takeo

2014-01-01

102

A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

NASA Astrophysics Data System (ADS)

The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the ? and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r??. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions.

Dufresne, L.; Dumas, G.

2003-03-01

103

A Stochastic Collocation Algorithm for Uncertainty Analysis

NASA Technical Reports Server (NTRS)

This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.

Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)

2003-01-01

104

NASA Astrophysics Data System (ADS)

A collocation spectral domain decomposition method (CSDDM) based on the influence matrix technique is developed to solve radiative transfer problems within a participating medium of 2D partitioned domains. In this numerical approach, the spatial domains of interest are decomposed into rectangular sub-domains. The radiative transfer equation (RTE) in each sub-domain is angularly discretized by the discrete ordinates method (DOM) with the SRAPN quadrature scheme and then is solved by the CSDDM directly. Three test geometries that include square enclosure and two enclosures with one baffle and one centered obstruction are used to validate the accuracy of the developed method and their numerical results are compared to the data obtained by other researchers. These comparisons indicate that the CSDDM has a good accuracy for all solutions. Therefore this method can be considered as a useful approach for the solution of radiative heat transfer problems in 2D partitioned domains.

Chen, Shang-Shang; Li, Ben-Wen

2014-12-01

105

Nonpolynomial sextic spline functions are used to approximate the solution of linear special case fifth-order boundary value problems. Since, presently, the convergence of spline solution of fifth-order boundary value problem is not found in the literature, therefore the convergence of the method is determined which is found to be of fifth order. The convergence of the method is the extension

Shahid S. Siddiqi; Ghazala Akram; Salman A. Malik

2007-01-01

106

NASA Astrophysics Data System (ADS)

Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions.

Gao, Wen-Wu; Wang, Zhi-Gang

2014-11-01

107

NASA Astrophysics Data System (ADS)

Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding the global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micrometeorological (MM) and dynamic flux chamber (DFC) measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and correlation with environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much more gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R>0.8, p<0.05), but the correlation between DFC and MM fluxes were from weak to moderate (R=0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (<10% difference). This suggests that incorporating an atmospheric turbulence property such as friction velocity for correcting the DFC-measured flux effectively bridged the gap between the Hg0 fluxes measured by enclosure and MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental factors have different degrees of impacts on the fluxes observed by different techniques, possibly caused by the underlying assumptions specific to each individual method. Recommendations regarding the application of flux quantification methods were made based on the data obtained in this study.

Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.

2015-01-01

108

The B-spline field approximation method is used to construct discrete models of straight Timoshenko beams. The traditional Timoshenko beam discretization treats deflection and rotation as the independent field variables and permits the use of C0 discretizations, but can sometimes exhibit unwanted shear locking behaviour. In this paper a new explanation of shear locking is presented and is used in selecting

A. H. Vermeulen; G. R. Heppler

1998-01-01

109

An efficient shape optimization scheme has been developed for designing axis symmetric structures. The sequential linear programming and Simplex method are coupled with finite element analysis. Selected sets of master nodes on design boundaries are employed as design variables and assigned to move towards their normal directions. By interpolating the repositioned master nodes, B-spline curves are constructed so that the

S Hyun; C Kim; J. H Son; S. H Shin; Y. S Kim

2004-01-01

110

A cubic non-polynomial spline technique is developed for the numerical solutions of a system of fourth order boundary value problems associated with obstacle, unilateral and contact problems. The end conditions consistent with the BVP are derived corresponding to the boundary conditions in terms of not only second derivatives but first derivatives as well. The present method has less computational cost

Shahid S. Siddiqi; Ghazala Akram

2007-01-01

111

The Schur-decomposition for three-dimensional matrix equations is developed and used to directly solve the radiative discrete ordinates equations which are discretized by Chebyshev collocation spectral method. Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented. The numerical results show the good accuracy of spectral method based on direct solvers. The CPU time cost comparisons against the resolutions between these three methods are made using MATLAB and FORTRAN 95 computer languages separately. The results show that the CPU time cost of Chebyshev collocation spectral method with 3D Schur-decomposition solver is the least, and almost only one thirtieth to one fiftieth CPU time is needed when using the spectral method with 3D Schur-decomposition solver compared with the standard discrete ordinates method.

Li Benwen [Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004 (China)], E-mail: heatli@hotmail.com; Tian Shuai; Sun Yasong; Hu, Zhang-Mao [Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, P.O. Box 314, Shenyang, Liaoning 110004 (China)

2010-02-20

112

A Critical Evaluation of the Resolution Properties of B-Spline and Compact Finite Difference Methods

Resolution properties of B-spline and compact finite difference schemes are compared using Fourier analysis in periodic domains, and tests based on solution of the wave and heat equations in finite domains, with uniform and nonuniform grids. Results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution. However, B-spline schemes have a more

Wai Yip Kwok; Robert D. Moser; Javier Jimnez

2001-01-01

113

NASA Astrophysics Data System (ADS)

Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier-Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal, the consistent projection methods (denoted as algorithms III and IV) obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces. Dependent on treatment of the continuous surface force, the pressure gradient in algorithm III or the sum of the pressure gradient and the surface force in algorithm IV at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method. A non-viscous 3D static drop with serials of density ratios is numerically simulated. Using the consistent projection methods, the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations. The developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution.

Ni, Ming-Jiu

2009-10-01

114

NASA Astrophysics Data System (ADS)

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrdinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

115

In this paper we propose a collocation method for solving some well-known\\u000aclasses of Lane-Emden type equations which are nonlinear ordinary differential\\u000aequations on the semi-infinite domain. They are categorized as singular initial\\u000avalue problems. The proposed approach is based on a Hermite function\\u000acollocation (HFC) method. To illustrate the reliability of the method, some\\u000aspecial cases of the equations

K. Parand; Mehdi Dehghan; A. R. Rezaei; S. M. Ghaderi

2010-01-01

116

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.

K. Parand; Mehdi Dehghan; A. R. Rezaei; S. M. Ghaderi

2010-08-12

117

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.

Parand, K; Rezaei, A R; Ghaderi, S M; 10.1016/j.cpc.2010.02.018

2010-01-01

118

NASA Astrophysics Data System (ADS)

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.

Parand, K.; Dehghan, Mehdi; Rezaei, A. R.; Ghaderi, S. M.

2010-06-01

119

Inverse B-spline interpolation

B-splines provide an accurate and ecient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined problems and a more accurate result in

Sergey Fomel

2000-01-01

120

NASA Astrophysics Data System (ADS)

In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.

Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Kumar, Jai

2014-11-01

121

A novel high-order panel method is developed for potential flows. These Uniform Bi-Cubic B-Spline (UBCBS) panels are intended for the simulation of unsteady, nonlinear, three-dimensional, free-surface waves. The integral-equation -based method is formulated using Green's theorem, with singular-kernel integrals which are evaluated numerically using a series of variable transformations to desingularize the kernels. The issue of edge conditions for surfaces

Philip Scott Coaxley

1995-01-01

122

B-spline approximation in boundary face method for three-dimensional linear elasticity

In this paper, basis functions generated from B-spline or Non-Uniform Rational B-spline (NURBS), are used for approximating the boundary variables to solve the 3D linear elasticity Boundary Integral Equations (BIEs). The implementation is based on the BFM framework in which both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces to keep the exact

Jinliang Gu; Jianming Zhang; Xiaomin Sheng; Guanyao Li

2011-01-01

123

Summary This paper is concerned with the problem of convexity-preservng (orc-preserving) interpolation by using Exponential Splines in Tension (or EST's). For this purpose the notion of ac-preserving interpolant, which is usually employed in spline-in-tension interpolation, is refined and the existence ofc-preserving EST's is established for the so-calledc-admissible data sets. The problem of constructing ac-preserving and visually pleasing EST is then

N. S. Sapidis; P. D. Kaklis; T. A. Loukakis

1989-01-01

124

NASA Astrophysics Data System (ADS)

A quantum spline is a smooth curve parametrized by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm of the time rate of change of the associated Hamiltonian is minimized. The solution to the quantum spline problem is obtained, and is applied in an example that illustrates quantum control of coherent states. An efficient numerical scheme for computing quantum splines is discussed and implemented in the examples.

Brody, Dorje C.; Holm, Darryl D.; Meier, David M.

2012-09-01

125

In this paper, we study a nonlinear two-point boundary value problem on semi-infinite interval that describes the unsteady gas equation. The solution of the mentioned ordinary differential equation (ODE) is investigated by means of the radial basis function (RBF) collocation method. The RBF reduces the solution of the above-mentioned problem to the solution of a system of algebraic equations and

S. Kazem; J. A. Rad; K. Parand; M. Shaban; H. Saberi

2012-01-01

126

Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional MCMC sim- ulations. The computational efficiency is expected to be more beneficial to more computational expensive groundwater problems.

Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL

2012-09-01

127

We have develop a fast method that can capture piecewise smooth functions in high dimensions with high order and low computational cost. This method can be used for both approximation and error estimation of stochastic simulations where the computations can either be guided or come from a legacy database.

Archibald, Richard K [ORNL] [ORNL; Deiterding, Ralf [ORNL] [ORNL; Hauck, Cory D [ORNL] [ORNL; Jakeman, John D [ORNL] [ORNL; Xiu, Dongbin [ORNL] [ORNL

2012-01-01

128

A least-squares preconditioner for radial basis functions collocation methods

Although meshless radial basis function (RBF) methods applied to partial differential equations (PDEs) are not only simple to implement and enjoy exponential convergence rates as compared to standard mesh-based schemes, the system of equations required to find the expansion coefficients are typically badly conditioned and expensive using the global Gaussian elimination (G-GE) method requiring \\u000a$\\\\mathcal{O}(N^{3})$ \\u000aflops. We present a simple

Leevan Ling; Edward J. Kansa

2005-01-01

129

A collocation reliability analysis method for probabilistic and fuzzy mixed variables

NASA Astrophysics Data System (ADS)

The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts. Existing methods are either computationally unaffordable or with limited application scope. Accordingly, a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed. The fuzziness propagation in the random reliability, which is the focus of the present study, is performed by the proposed method, in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation. First-Order, Second-Moment (FOSM) method which can be replaced by its counterparts is utilized to calculate the structural random reliability. Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.

Xu, MengHui; Qiu, ZhiPing

2014-07-01

130

Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

NASA Technical Reports Server (NTRS)

An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.

Yang, Jiann-Cherng; Soni, B. K.

1992-01-01

131

The Schwarz alternating method (SAM) coupled with various numerical discretization schemes has already been established as an efficient alternative for solving differential equations on various parallel machines. In this paper we consider an extension of SAM (generalized Schwarz splittingGSS) for solving elliptic boundary value problems with generalized interface conditions that depend on a parameter that might differ in each overlapping

Yu-Ling Lai; Apostolos Hadjidimos; Elias N. Houstis

1996-01-01

132

Multiresolution B-spline Radiosity Yizhou Yu and Qunsheng Peng

--- Multiresolution B-spline Radiosity Yizhou YuÝ and Qunsheng Peng State Key Laboratory of CAD radiosity method called multiresolution B-spline radiosity, which uses B-splines of different scales is rectilinear. Keywords: Computer graphics, Radiosity, Wavelet, B-spline. 1 Introduction In computer graphics

Yu, Yizhou

133

We present an overlapping domain decomposition technique for solving the hypersingular integral equation on the sphere with\\u000a spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O(H\\/?), where H is the size of the coarse mesh and ? is the overlap size, which is chosen to be proportional to the size of the

Duong Pham; Thanh Tran

134

Multivariate Adaptive Regression Splines

A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning

Jerome H. Friedman

1991-01-01

135

Interchangeable spline reference guide

The WX-Division Integrated Software Tools (WIST) Team evolved from two previous committees, First was the W78 Solid Modeling Pilot Project`s Spline Subcommittee, which later evolved into the Vv`X-Division Spline Committee. The mission of the WIST team is to investigate current CAE engineering processes relating to complex geometry and to develop methods for improving those processes. Specifically, the WIST team is developing technology that allows the Division to use multiple spline representations. We are also updating the contour system (CONSYS) data base to take full advantage of the Division`s expanding electronic engineering process. Both of these efforts involve developing interfaces to commercial CAE systems and writing new software. The WIST team is comprised of members from V;X-11, -12 and 13. This {open_quotes}cross-functional{close_quotes} approach to software development is somewhat new in the Division so an effort is being made to formalize our processes and assure quality at each phase of development. Chapter one represents a theory manual and is one phase of the formal process. The theory manual is followed by a software requirements document, specification document, software verification and validation documents. The purpose of this guide is to present the theory underlying the interchangeable spline technology and application. Verification and validation test results are also presented for proof of principal.

Dolin, R.M.

1994-05-01

136

Number systems, ?-splines and refinement

NASA Astrophysics Data System (ADS)

This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case ?=1+i, we prove better results. We introduce ?-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of ?-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of ?-splines to subdivision with several examples. It turns out that ?-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of ?-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of ?-splines: partition of unity and the refinement equation.

Zube, Severinas

2004-12-01

137

In this paper, we apply the B-spline and Shannon wavelets bases for approximation the solution of linear integral equations of the second kind, then by this wavelet bases we construct Galerkin system, which is important the expansion methods in solving linear integral equations. At the end, For showing efficiency of this method, we use numerical examples.

Khosrow Maleknejad; T. Lotfi

2006-01-01

138

NASA Astrophysics Data System (ADS)

The basic ideas of the B-spline R-matrix (BSR) approach are reviewed, and the use of the method is illustrated with a variety of applications to atomic structure, electron-atom collisions and photo-induced processes. Special emphasis is placed on complex, open-shell targets, for which the method has proven very successful in reproducing, for example, a wealth of near-threshold resonance structures. Recent extensions to a fully relativistic framework and intermediate energies have allowed for an accurate treatment of heavy targets as well as a fully nonperturbative scheme for electron-impact ionization. Finally, field-free BSR Hamiltonian and electric dipole matrices can be employed in the time-dependent treatment of intense short-pulse laser-atom interactions.

Zatsarinny, Oleg; Bartschat, Klaus

2013-06-01

139

Focusing light onto nanostructures thanks to spherical lenses is a first step in enhancing the field and is widely used in applications. Nonetheless, the electromagnetic response of such nanostructures, which have subwavelength patterns, to a focused beam cannot be described by the simple ray tracing formalism. Here, we present a method for computing the response to a focused beam, based on the B-spline modal method adapted to nanostructures in conical mounting. The eigenmodes are computed in each layer for both polarizations and are then combined for the computation of scattering matrices. The simulation of a Gaussian focused beam is obtained thanks to a truncated decomposition into plane waves computed on a single period, which limits the computation burden. PMID:25121523

Chevalier, Paul; Bouchon, Patrick; Pardo, Fabrice; Hadar, Riad

2014-08-01

140

NASA Astrophysics Data System (ADS)

This study develops a wavelet Galerkin method (WGM) that uses B-spline wavelet bases for application to solid mechanics problems. A fictitious domain is often adopted to treat general boundaries in WGMs. In the analysis, the body is extended to its exterior but very low stiffness is applied to the exterior region. The stiffness matrix in the WGM becomes singular without the use of a fictitious domain. The problem arises from the lack of linear independence of the basis functions. A technique to remove basis functions that can be represented by the superposition of the other basis functions is proposed. The basis functions are automatically eliminated in the pre conditioning step. An adaptive strategy is developed using the proposed technique. The solution is refined by superposing finer wavelet functions. Numerical examples of solid mechanics problems are presented to demonstrate the multiresolution properties of the WGM.

Tanaka, Satoyuki; Okada, Hiroshi; Okazawa, Shigenobu

2012-07-01

141

NASA Astrophysics Data System (ADS)

The aim of this paper is to describe the application of Quarter-Sweep Gauss-Seidel (QSGS) iterative method using quadratic spline scheme for solving fourth order two-point linear boundary value problems. In the line to derive approximation equations, firstly the fourth order problems need to be reduced onto a system of second-order two-point boundary value problems. Then two linear systems have been constructed via discretization process by using the corresponding quarter-sweep quadratic spline approximation equations. The generated linear systems have been solved using the proposed QSGS iterative method to show the superiority over Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods. Computational results are provided to illustrate that the effectiveness of the proposed QSGS method is more superior in terms of computational time and number of iterations as compared to other tested methods.

Mohd Fauzi, Norizyan Izzati; Sulaiman, Jumat

2013-04-01

142

NASA Astrophysics Data System (ADS)

Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micro-meteorological (MM) and enclosure measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen-ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and sensitivity to environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R > 0.8, p < 0.05), but the correlation between DFC and MM instantaneous fluxes were from weak to moderate (R = 0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM-techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (< 10% difference). This implicates that the NDFC technique, which accounts for internal friction velocity, effectively bridged the gap in measured Hg0 flux compared to MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental factors have different degrees of impacts on the fluxes observed by different techniques, possibly caused by the underlying assumptions specific to each individual method. Recommendations regarding the application of flux quantification methods were made based on the data obtained in this study.

Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.

2014-09-01

143

A Fully Relativistic B-Spline R-Matrix Method for Electron and Photon Collisions with Atoms and Ions

NASA Astrophysics Data System (ADS)

We have extended our B-spline R-matrix (close-coupling) method [1] to fully account for relativistic effects in a Dirac-Coulomb formulation. Our numerical implementation of the close-coupling method enables us to construct term-dependent, non-orthogonal sets of one-electron orbitals for the bound and continuum electrons. This is a critical aspect for complex targets, where individually optimized one-electron orbitals can significantly reduce the size of the multi-configuration expansions needed for an accurate target description. Core-valence correlation effets are treated fully ab initio, rather than through semi-empirical model potentials. The method is described in detail and will be illustrated by comparing our theoretical predictions for e-Cs collisions [2] with benchmark experiments for angle-integrated and angle-differential cross sections [3], various spin-dependent scattering asymmetries [4], and Stokes parameters measured in superelastic collisions with laser-excited atoms [5]. [1] O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006). [2] O. Zatsarinny and K. Bartschat, Phys. Rev. A 77, 062701 (2008). [3] W. Gehenn and E. Reichert, J. Phys. B 10, 3105 (1977). [4] G. Baum et al., Phys. Rev. A 66, 022705 (2002) and 70, 012707 (2004). [5] D.S. Slaughter et al., Phys. Rev. A 75, 062717 (2007).

Zatsarinny, Oleg; Bartschat, Klaus

2008-10-01

144

A Full-Relativistic B-Spline R-Matrix Method for Electron and Photon Collisions with Atoms and Ions

NASA Astrophysics Data System (ADS)

We have extended our B-spline R-matrix (close-coupling) method [1] to fully account for relativistic effects in a Dirac-Coulomb formulation. Our numerical implementation of the close-coupling method enables us to construct term-dependent, non-orthogonal sets of one-electron orbitals for the bound and continuum electrons. This is a critical aspect for complex targets, where individually optimized one-electron orbitals can significantly reduce the size of the multi-configuration expansions needed for an accurate target description. Furthermore, core-valence correlation effets are treated fully ab initio, rather than through semi-empirical, and usually local, model potentials. The method will be described in detail and illustrated by comparing our theoretical predictions for e-Cs collisions with benchmark experiments for angle-integrated and angle-differential cross sections [2], various spin-dependent scattering asymmetries [3], and Stokes parameters measured in superelastic collisions with laser-excited atoms [4]. [1] O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006). [2] W. Gehenn and E. Reichert, J. Phys. B 10, 3105 (1977). [3] G. Baum et al., Phys. Rev. A 66, 022705 (2002) and 70, 012707 (2004). [4] D.S. Slaughter et al., Phys. Rev. A 75, 062717 (2007).

Zatsarinny, Oleg; Bartschat, Klaus

2008-05-01

145

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. PMID:22376200

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

146

Parallel boxing in B-spline intersection

A modified formulation of oriented boxing called oriented slab boxing is presented. It almost doubles the speed of the oriented boxing component in B-spline intersection. The method used to accelerate B-spline intersection includes algorithmic improvements and parallelization of the algorithm at different levels of granularity to find an optimum solution on a network of parallel processors. The software testbed is

J. Yen; S. Spach; M. T. Smith; R. W. Pulleyblank

1991-01-01

147

The L2Polynomial Spline Pyramid

The authors are concerned with the derivation of general methods for the L2 approximation of signals by polynomial splines. The main result is that the expansion coefficients of the approximation are obtained by linear filtering and sampling. The authors apply those results to construct a L2 polynomial spline pyramid that is a parametric multiresolution representation of a signal. This hierarchical

Michael Unser; Akram Aldroubi; Murray Eden

1993-01-01

148

K-matrix method with B-splines: ?nell, ?n and resonances in He photoionization below N = 4 threshold

NASA Astrophysics Data System (ADS)

A B-spline based K-matrix method has been implemented to investigate the photoionization of atoms with simple valence shells. With a particular choice of knots, the present method is able to reproduce all the essential features of the continuum wavefunctions including up to 20-25 resonant multiplets below each ionization threshold. A detailed study of the interval between the N = 3 and N = 4 thresholds where the state labelled [031]+5 (parabolic quantum numbers: [N1N2m]An), the first of a series converging to the higher N = 5 threshold, is known to fall, is presented. According to propensity rules this state cannot decay directly in the underlying continuum, but interacts strongly with the [021]+n series and appreciably with the [030]-n series. As a result all parameters of the two series are strongly modulated and, between 75.5 eV and 75.57 eV, partial cross section and asymmetry parameter patterns change dramatically.

Argenti, Luca; Moccia, Roberto

2006-06-01

149

Collocation Mining: Exploiting Corpora for Collocation Identification and Representation

collocational from noncollocational word combinations. Finally, identifi cation results for German based on a newspaper and a newsgroup corpus are discussed. 2.1 Initial Candidate Selection Corpora used for collocation. For identification of German PPverb colloca tions such constraints are: preposition and noun must be constituents

150

Tridimensional image reconstruction method based on the modified algebraic reconstruction technique . This study presents an algorithm for three-dimensional reconstruction of tomographic images based of the method was first destined to image reconstruction of the minitomographer at the National Center

151

NASA Technical Reports Server (NTRS)

Smooth curves drawn among plotted data easily. Rational-Spline Approximation with Automatic Tension Adjustment algorithm leads to flexible, smooth representation of experimental data. "Tension" denotes mathematical analog of mechanical tension in spline or other mechanical curve-fitting tool, and "spline" as denotes mathematical generalization of tool. Program differs from usual spline under tension, allows user to specify different values of tension between adjacent pairs of knots rather than constant tension over entire range of data. Subroutines use automatic adjustment scheme that varies tension parameter for each interval until maximum deviation of spline from line joining knots less than or equal to amount specified by user. Procedure frees user from drudgery of adjusting individual tension parameters while still giving control over local behavior of spline.

Schiess, James R.; Kerr, Patricia A.; Smith, Olivia C.

1988-01-01

152

[abridged] The inspiral of a stellar compact object into a massive black hole is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be obtained from the regularization of the perturbations created by the stellar compact object on the massive black hole geometry. In this paper we extend a new time-domain technique for the computation of the self-force from the circular case to the case of eccentric orbits around a non-rotating black hole. The main idea behind our scheme is to use a multidomain framework in which the small compact object, described as a particle, is located at the interface between two subdomains. Then, the equations at each subdomain are homogeneous wave-type equations, without distributional sources. In this particle-without-particle formulation, the solution of the equations is smooth enough to provide good convergence properties for the numerical computations. This formulation is implemented by using a pseudospectral collocation method for the spatial discretization, combined with a Runge Kutta algorithm for the time evolution. We present results from several simulations of eccentric orbits in the case of a scalar charged particle around a Schwarzschild black hole. In particular, we show the convergence of the method and its ability to resolve the field and its derivatives across the particle location. Finally, we provide numerical values of the self-force for different orbital parameters.

P. Canizares; C. F. Sopuerta; J. L. Jaramillo

2010-06-16

153

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated polynomials, and that they retain most of the important properties of the classical ones: smoothness, recurrence, and two-scale relations, Riesz basis

Brigitte Forster; Thierry Blu; Michael Unser

2006-01-01

154

Clothoid spline transition spirals

NASA Astrophysics Data System (ADS)

Highway and railway designers use clothoid splines (planar {G^2} curves consisting of straight line segments, circular arcs, and clothoid segments) as center lines in route location. This paper considers the problem of finding a clothoid spline transition spiral which joins two given points and matches given curvatures and unit tangents at the two points. Conditions are given for the existence and uniqueness of the clothoid spline transition spirals, and algorithms for finding them are outlined.

Meek, D. S.; Walton, D. J.

1992-07-01

155

A common problem in signal processing is to estimate the structure of an object from noisy measurements linearly related to the desired image. These problems are broadly known as inverse problems. A key feature which complicates the solution to such problems is their ill-posedness. That is, small perturbations in the data arising e.g. from noise can and do lead to severe, non-physical artifacts in the recovered image. The process of stabilizing these problems is known as regularization of which Tikhonov regularization is one of the most common. While this approach leads to a simple linear least squares problem to solve for generating the reconstruction, it has the unfortunate side effect of producing smooth images thereby obscuring important features such as edges. Therefore, over the past decade there has been much work in the development of edge-preserving regularizers. This technique leads to image estimates in which the important features are retained, but computationally the y require the solution of a nonlinear least squares problem, a daunting task in many practical multi-dimensional applications. In this thesis we explore low-order models for reducing the complexity of the re-construction process. Specifically, B-Splines are used to approximate the object. If a ''proper'' collection B-Splines are chosen that the object can be efficiently represented using a few basis functions, the dimensionality of the underlying problem will be significantly decreased. Consequently, an optimum distribution of splines needs to be determined. Here, an adaptive refining and pruning algorithm is developed to solve the problem. The refining part is based on curvature information, in which the intuition is that a relatively dense set of fine scale basis elements should cluster near regions of high curvature while a spares collection of basis vectors are required to adequately represent the object over spatially smooth areas. The pruning part is a greedy search algorithm to find and delete redundant knots based on the estimation of a weight associated with each basis vector. The overall algorithm iterates by inserting and deleting knots and end up with much fewer knots than pixels to represent the object, while the estimation error is within a certain tolerance. Thus, an efficient reconstruction can be obtained which significantly reduces the complexity of the problem. In this thesis, the adaptive B-Spline method is applied to a cross-well tomography problem. The problem comes from the application of finding underground pollution plumes. Cross-well tomography method is applied by placing arrays of electromagnetic transmitters and receivers along the boundaries of the interested region. By utilizing inverse scattering method, a linear inverse model is set up and furthermore the adaptive B-Spline method described above is applied. The simulation results show that the B-Spline method reduces the dimensional complexity by 90%, compared with that o f a pixel-based method, and decreases time complexity by 50% without significantly degrading the estimation.

Li, Xin; Miller, Eric L.; Rappaport, Carey; Silevich, Michael

2000-04-11

156

Automated process planning method to machine A B-Spline free-form feature on a millturn center

In this paper, we present a methodology for automating the process planning and NC code generation for a widely encountered class of free-form features that can be machined on a 3-axis millturn center. The free-form feature family that is considered is that of extruded protrusions whose cross-section is a closed, periodic B-Spline curve. In this methodology, for machining a part

Nikhil Date; Prakash Krishnaswami; V. V. Satish K. Motipalli

2009-01-01

157

NSDL National Science Digital Library

The Cubic Spline Model displays a cubic spline and its derivatives. The model constructs N third-order piecewise continuous polynomialz (cubic splines) that connect N data points (nodes) with unit separation. Polynomial coefficients are chosen such that the resulting curve and its first derivative are smooth at the nodes. Users can drag the nodes and observe the resulting curve. Radio buttons display first and second derivative curves. Note that the second derivative curve consists of line segments because the second derivative of a piecewise cubic polynomial is a piecewise first order polynomial. The Cubic Spline Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double click the ejs_math_CubicSplineDemo.jar file to run the program if Java is installed.

Christian, Wolfgang

2011-09-17

158

The inspiral of a stellar compact object into a massive black hole, an extreme-mass-ratio inspiral, is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems, which makes them truly high-precision tools for gravitational-wave astronomy. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them, we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be obtained from the regularization of the perturbations created by the stellar compact object on the massive black hole geometry. In this paper we extend a new time-domain technique for the computation of the self-force from the circular case to the case of eccentric orbits around a nonrotating black hole. The main idea behind our scheme is to use a multidomain framework in which the small compact object, described as a particle, is located at the interface between two subdomains. Then, the equations at each subdomain are homogeneous wave-type equations, without distributional sources. In this particle-without-particle formulation, the solution of the equations is smooth enough to provide good convergence properties for the numerical computations. This formulation is implemented by using a pseudospectral collocation method for the spatial discretization, combined with a Runge-Kutta algorithm for the time evolution. We present results from several simulations of eccentric orbits in the case of a scalar charged particle around a Schwarzschild black hole, an excellent test bed model for testing the techniques for self-force computations. In particular, we show the convergence of the method and its ability to resolve the field and its derivatives across the particle location. Finally, we provide numerical values of the self-force for different orbital parameters.

Canizares, Priscilla; Sopuerta, Carlos F. [Institut de Ciencies de l'Espai (CSIC-IEEC), Facultat de Ciencies, Campus UAB, Torre C5 parells, E-08193 Bellaterra (Spain); Jaramillo, Jose Luis [Max Planck Institute fuer Gravitationsphysik, Albert-Einstein-Institute, 14476 Postdam (Germany); Laboratoire Univers et Theories (LUTH), Observatoire de Paris, CNRS, Universite Paris Diderot, 5 place Jules Janssen, 92190 Meudon (France)

2010-08-15

159

. Introduction Splines have their roots in the lofting technique used in the shipbuilding and aircraft industries throughout the first half of the 20th century. The first mathematical reference to the notion of splines is accredited to the work of Schoenberg [1... associated with control vectors have been raised to a power of 1, 2, . . . , 10 (coloured from red to blue). Note that this curve cannot be generated using quartic B-splines. (For interpretation of the references to colour in this figure legend, the reader...

Kosinka, Ji?i; Sabin, Malcolm A.; Dodgson, Neil A.

2014-09-03

160

NASA Astrophysics Data System (ADS)

The methods of Least-Squares Collocation (LSC) and the Reduced Point Mass method (RPM) both uses radial basis-functions for the representation of the anomalous gravity potential (T). LSC uses as many base-functions as the number of observations, while the RPM method uses as many as deemed necessary. Both methods have been evaluated and for some tests compared in the two areas (Central Europe and South-East Pacific). For both areas test data had been generated using EGM2008. As observational data (a) ground gravity disturbances, (b) airborne gravity disturbances, (c) GOCE like Second order radial derivatives and (d) GRACE along-track potential differences were available. The use of these data for the computation of values of (e) T in a grid was the target of the evaluation and comparison investigation. Due to the fact that T in principle can only be computed using global data, the remove-restore procedure was used, with EGM2008 subtracted (and later added to T) up to degree 240 using dataset (a) and (b) and up to degree 36 for datasets (c) and (d). The estimated coefficient error was accounted for when using LSC and in the calculation of error-estimates. The main result is that T was estimated with an error (computed minus control data, (e) from which EGM2008 to degree 240 or 36 had been subtracted ) as found in the table (LSC used): Area Europe Data-set (mgal) (e)-240(a) (b) (e)-36 (c) (d) Mean -0.0 0.0 -0.1 -0.1 -0.3 -1.8 Standard deviation4.1 0.8 2.7 32.6 6.0 19.2 Max. difference 19.9 10.4 16.9 69.9 31.3 47.0 Min.difference -16.2 -3.7 -15.5 -92.1 -27.8 -65.5 Area Pacific Data-set (mgal) (e)-240(a) (b) (e)-36 (c) (d) Mean -0.1 -0.1 -0.1 4.6 -0.2 0.2 Standard deviation4.8 0.2 1.9 49.1 6.7 18.6 Max.difference 22.2 1.8 13.4 115.5 26.9 26.5 Min.difference -28.7 -3.1 -15.7 -106.4 -33.6 22.1 The result using RPM with data-sets (a), (b), (c) gave comparable results. The use of (d) with the RPM method is being implemented. Tests were also done computing dataset (a) from the other datasets. The results here may serve as a bench-mark for other radial basis-function implementations for computing approximations to T. Improvements are certainly possible, e.g. by taking the topography and bathymetry into account.

Tscherning, Carl Christian; Herceg, Matija

2014-05-01

161

Collocations: A Neglected Variable in EFL.

ERIC Educational Resources Information Center

Addresses the issue of collocations as an important and neglected variable in English-as-a-Foreign-Language classes. Two questionnaires, in English and Arabic, involving common collocations relating to food, color, and weather were administered to English majors and English language teachers. Results show both groups deficient in collocations. (36

Farghal, Mohammed; Obiedat, Hussein

1995-01-01

162

NASA Astrophysics Data System (ADS)

The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m2 and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R2), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.

M Ali, M. K.; Ruslan, M. H.; Muthuvalu, M. S.; Wong, J.; Sulaiman, J.; Yasir, S. Md.

2014-06-01

163

Interpolation using surface splines.

NASA Technical Reports Server (NTRS)

A surface spline is a mathematical tool for interpolating a function of two variables. It is based upon the small deflection equation of an infinite plate. The surface spline depends upon the solution of a system of linear equations, and thus, will ordinarily require the use of a digital computer. The closed form solution involves no functions more complicated than logarithms, and is easily coded. Several modifications which can be incorporated are discussed.

Harder, R. L.; Desmarais, R. N.

1972-01-01

164

Particle Flow Simulation by Using Polyharmonic Splines

Summary. This contribution reports on novel concepts of adaptive particle methods for flow simulation, where scattered data reconstruction by polyharmonic splines plays a key role. Our discussion includes the construction of both Lagrangian and Eulerian particle methods, where two different prototypes are being presented: one semi-Lagrangian particle method (SLPM) and one finite volume particle method (FVPM). It is shown how

Armin Iske

165

PIECEWISE LINEAR WAVELET COLLOCATION, APPROXIMATION OF THE BOUNDARY MANIFOLD, AND QUADRATURE

In this paper we consider a piecewise linear wavelet collocation method for the solution of boundary integral equations of order r = 0; 1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the

S. EHRICHy

166

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces

K. Parand; A. R. Rezaei; A. Taghavi

2010-01-01

167

Interlanguage Development and Collocational Clash

ERIC Educational Resources Information Center

Background: Persian English learners committed mistakes and errors which were due to insufficient knowledge of different senses of the words and collocational structures they formed. Purpose: The study reported here was conducted for a thesis submitted in partial fulfillment of the requirements for The Master of Arts degree, School of Graduate

Shahheidaripour, Gholamabbass

2000-01-01

168

Analysis of chromatograph systems using orthogonal collocation

NASA Technical Reports Server (NTRS)

Research is generating fundamental engineering design techniques and concepts for the chromatographic separator of a chemical analysis system for an unmanned, Martian roving vehicle. A chromatograph model is developed which incorporates previously neglected transport mechanisms. The numerical technique of orthogonal collocation is studied. To establish the utility of the method, three models of increasing complexity are considered, the latter two being limiting cases of the derived model: (1) a simple, diffusion-convection model; (2) a rate of adsorption limited, inter-intraparticle model; and (3) an inter-intraparticle model with negligible mass transfer resistance.

Woodrow, P. T.

1974-01-01

169

Statistical Chromaticity Models for Lip Tracking with B-splines

A method for lip tracking intended to support personal verification is presented in this paper. Lip contours are represented by mea ns of quadratic B- splines. The lips are automatically localised in the origin al image and an ellip- tic B-spline is generated to start up tracking. Lip localisa tion exploits grey-level gradient projections as well as chromaticity models to

M U Ramos Sfinchez; Jiri Matas; Josef Kittler

1997-01-01

170

Construction of multiresolution triangular B-spline surfaces using hexagonal filters

We present multiresolution B-spline surfaces of arbitrary order defined over triangular domains. Unlike existing methods, the basic idea of our approach is to construct the triangular basis functions from their tensor product rela- tives in the spirit of box splines by projecting them onto the barycentric plane. The scheme works for splines of any order where the fundamental building blocks

A. Dreger; Markus H. Gross; J. Schlegel

2000-01-01

171

NASA Technical Reports Server (NTRS)

Scientific data often contains random errors that make plotting and curve-fitting difficult. The Rational-Spline Approximation with Automatic Tension Adjustment algorithm lead to a flexible, smooth representation of experimental data. The user sets the conditions for each consecutive pair of knots:(knots are user-defined divisions in the data set) to apply no tension; to apply fixed tension; or to determine tension with a tension adjustment algorithm. The user also selects the number of knots, the knot abscissas, and the allowed maximum deviations from line segments. The selection of these quantities depends on the actual data and on the requirements of a particular application. This program differs from the usual spline under tension in that it allows the user to specify different tension values between each adjacent pair of knots rather than a constant tension over the entire data range. The subroutines use an automatic adjustment scheme that varies the tension parameter for each interval until the maximum deviation of the spline from the line joining the knots is less than or equal to a user-specified amount. This procedure frees the user from the drudgery of adjusting individual tension parameters while still giving control over the local behavior of the spline The Rational Spline program was written completely in FORTRAN for implementation on a CYBER 850 operating under NOS. It has a central memory requirement of approximately 1500 words. The program was released in 1988.

Schiess, J. R.

1994-01-01

172

Spline Potential Eigenfunctions Model

NSDL National Science Digital Library

The Spline Potential Eigenfunctions Model computes the Schrödinger equation energy eigenvalues and eigenfunctions for a particle confined to a potential well with hard walls at -a/2 and a/2 and a smooth potential energy function between these walls. The potential energy function is a third-order piecewise continuous polynomial (cubic spline) that connects N draggable control points. Cubic-spline coefficients are chosen such that the resulting potential energy function and its first derivative is smooth throughout the interior and has zero curvature at the endpoints. Users can vary the number of control points and can drag the control points to study level splitting in multi-well systems. Additional windows show a table of energy eigenvalues and their corresponding energy eigenfunctions. The Spline Potential Eigenfunctions Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_SplinePotentialEigenfunctions.jar file will run the program if Java is installed.

Christian, Wolfgang

2012-01-09

173

Collocation analysis for UMLS knowledge-based word sense disambiguation

Background The effectiveness of knowledge-based word sense disambiguation (WSD) approaches depends in part on the information available in the reference knowledge resource. Off the shelf, these resources are not optimized for WSD and might lack terms to model the context properly. In addition, they might include noisy terms which contribute to false positives in the disambiguation results. Methods We analyzed some collocation types which could improve the performance of knowledge-based disambiguation methods. Collocations are obtained by extracting candidate collocations from MEDLINE and then assigning them to one of the senses of an ambiguous word. We performed this assignment either using semantic group profiles or a knowledge-based disambiguation method. In addition to collocations, we used second-order features from a previously implemented approach. Specifically, we measured the effect of these collocations in two knowledge-based WSD methods. The first method, AEC, uses the knowledge from the UMLS to collect examples from MEDLINE which are used to train a Nave Bayes approach. The second method, MRD, builds a profile for each candidate sense based on the UMLS and compares the profile to the context of the ambiguous word. We have used two WSD test sets which contain disambiguation cases which are mapped to UMLS concepts. The first one, the NLM WSD set, was developed manually by several domain experts and contains words with high frequency occurrence in MEDLINE. The second one, the MSH WSD set, was developed automatically using the MeSH indexing in MEDLINE. It contains a larger set of words and covers a larger number of UMLS semantic types. Results The results indicate an improvement after the use of collocations, although the approaches have different performance depending on the data set. In the NLM WSD set, the improvement is larger for the MRD disambiguation method using second-order features. Assignment of collocations to a candidate sense based on UMLS semantic group profiles is more effective in the AEC method. In the MSH WSD set, the increment in performance is modest for all the methods. Collocations combined with the MRD disambiguation method have the best performance. The MRD disambiguation method and second-order features provide an insignificant change in performance. The AEC disambiguation method gives a modest improvement in performance. Assignment of collocations to a candidate sense based on knowledge-based methods has better performance. Conclusions Collocations improve the performance of knowledge-based disambiguation methods, although results vary depending on the test set and method used. Generally, the AEC method is sensitive to query drift. Using AEC, just a few selected terms provide a large improvement in disambiguation performance. The MRD method handles noisy terms better but requires a larger set of terms to improve performance. PMID:21658291

2011-01-01

174

A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical ..beta../sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab.

Cheng, C.Z.

1988-12-01

175

Patient-specific models of the hearts mitral valve (MV) exhibit potential for surgical planning. While advances in 3D echocardiography (3DE) have provided adequate resolution to extract MV leaflet geometry, no study has quantitatively assessed the accuracy of their modeled leaflets versus a ground-truth standard for temporal frames beyond systolic closure or for differing valvular dysfunctions. The accuracy of a 3DE-based segmentation methodology based on J-splines was assessed for porcine MVs with known 4D leaflet coordinates within a pulsatile simulator during closure, peak closure, and opening for a control, prolapsed, and billowing MV model. For all time points, the mean distance error between the segmented models and ground-truth data were 0.400.32 mm, 0.520.51 mm, and 0.740.69 mm for the control, flail, and billowing models. For all models and temporal frames, 95% of the distance errors were below 1.64 mm. When applied to a patient data set, segmentation was able to confirm a regurgitant orifice and post-operative improvements in coaptation. This study provides an experimental platform for assessing the accuracy of an MV segmentation methodology at phases beyond systolic closure and for differing MV dysfunctions. Results demonstrate the accuracy of a MV segmentation methodology for the development of future surgical planning tools. PMID:23460042

Siefert, Andrew W.; Icenogle, David A.; Rabbah, Jean-Pierre; Saikrishnan, Neelakantan; Rossignac, Jarek; Lerakis, Stamatios; Yoganathan, Ajit P.

2013-01-01

176

A smoothing algorithm using cubic spline functions

NASA Technical Reports Server (NTRS)

Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

Smith, R. E., Jr.; Price, J. M.; Howser, L. M.

1974-01-01

177

SURVIVAL ESTIMATION USING SPLINES

A non parametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. t approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. pecial case is that proposed by...

178

ERIC Educational Resources Information Center

Although it is widely acknowledged that collocations play an important part in second language learning, especially at intermediate-advanced levels, learners' difficulties with collocations have not been investigated in much detail so far. The present study examines ESL learners' use of verb-noun collocations, such as "take notes," "place an

Miyakoshi, Tomoko

2009-01-01

179

NASA Technical Reports Server (NTRS)

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

180

Supporting Collocation Learning with a Digital Library

ERIC Educational Resources Information Center

Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on

Wu, Shaoqun; Franken, Margaret; Witten, Ian H.

2010-01-01

181

NASA Technical Reports Server (NTRS)

To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.

Fang, Ming; Bowin, Carl

1992-01-01

182

Mining visual collocation patterns via self-supervised subspace learning.

Traditional text data mining techniques are not directly applicable to image data which contain spatial information and are characterized by high-dimensional visual features. It is not a trivial task to discover meaningful visual patterns from images because the content variations and spatial dependence in visual data greatly challenge most existing data mining methods. This paper presents a novel approach to coping with these difficulties for mining visual collocation patterns. Specifically, the novelty of this work lies in the following new contributions: 1) a principled solution to the discovery of visual collocation patterns based on frequent itemset mining and 2) a self-supervised subspace learning method to refine the visual codebook by feeding back discovered patterns via subspace learning. The experimental results show that our method can discover semantically meaningful patterns efficiently and effectively. PMID:22156999

Yuan, Junsong; Wu, Ying

2012-04-01

183

C1 Hermite shape preserving polynomial splines in R3

NASA Astrophysics Data System (ADS)

The C 2 variable degree splines1-3 have been proven to be an efficient tool for solving the curve shape-preserving interpolation problem in two and three dimensions. Based on this representation, the current paper proposes a Hermite interpolation scheme, to construct C 1 shape-preserving splines of variable degree. After this, a slight modification of the method leads to a C 1 shape-preserving Hermite cubic spline. Both methods can easily be developed within a CAD system, since they compute directly (without iterations) the B-spline control polygon. They have been implemented and tested within the DNV Software CAD/CAE system GeniE. [Figure not available: see fulltext.

Gabrielides, Nikolaos C.

2012-06-01

184

Surface deformation over flexible joints using spline blending techniques

NASA Astrophysics Data System (ADS)

Skinning over a skeleton joint is the process of skin deformation based on joint transformation. Popular geometric skinning techniques include implicit linear blending and dual quaternions. Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended by Ck-smooth basis functions. A smooth skinning surface can be constructed over a transformable skeleton joint by combining various types of local surface constructions and applying local Hermite interpolation. Compared to traditional spline methods, increased flexibility and local control with respect to surface deformation can be achieved using the GERBS blending construction. We present a method using a blending-type spline surface for skinning over a flexible joint, where local geometry is individually adapted to achieve natural skin deformation based on skeleton transformations..

Haavardsholm, Birgitte; Bratlie, Jostein; Dalmo, Rune

2014-12-01

185

Theory, computation, and application of exponential splines

NASA Technical Reports Server (NTRS)

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

Mccartin, B. J.

1981-01-01

186

Active contour model(or'snake') is efficient in object contour extraction. It is widely applied in many fields, such as human facial feature extraction, segmenation of medical images, vedio object segmentation, 3D reconstruction, and so on. The implementation of GVF into the B Spline snake is specified, the resulting GVF B spline snake, retains the advantages of GVF snake. In this paper

Wang Xin; Tu Yunxia

2009-01-01

187

NASA Technical Reports Server (NTRS)

Ball-bearing carrier includes splined outer surface mating with slightly larger splined inner surface of housing and provides constant deadband, unaffected by movements of other components. Deadband needed to establish radial spring rate and provide for axial movement of bearing for thrust balance. Bearing carrier and bearing intended for use in high-pressure turbopump.

Moore, Jerry H.

1992-01-01

188

B-Spline Approximation Using an EKF for Signal Reconstruction of Nonlinear Multifunctional Sensors

In this paper, a novel method based on a B-spline approximation and the extended Kalman filter (EKF) is pro- posed for the signal reconstruction of nonlinear multifunctional sensors. The B-spline approximation is a very effective and con- ventional tool for nonlinear modeling. However, the computa- tion of the B-spline control array by the least square method is very complex for

Xin Wang; Guo Wei; Jin-Wei Sun

2011-01-01

189

B-spline solver for one-electron Schrdinger equation

A numerical algorithm for solving the one-electron Schrdinger equation is presented. The algorithm is based on the Finite Element method, and the basis functions are tensor products of univariate B-splines. The application of cubic or higher order B-splines guarantees that the searched solution belongs to a continuous and one time differentiable function space, which is a desirable property in the

Zbigniew Romanowski

2011-01-01

190

N-sided patches with B-spline boundaries

We present a method for constructing an n-sided patch of parametric surface, with n greater than 2. The main property of the resulting patch is that its boundary coincides with a B-spline. Thus, it can easily be connected to given B-spline surfaces with fixed continuity conditions.The patch is built from a star-shaped input mesh that outlines a generic n-hole and

Nria Pla Garcia; Marc Vigo Anglada; Josep Cotrina Navau

2006-01-01

191

In recent years, there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary/partial differential equations. To this end, the spectral stochastic finite element method (SSFEM) is the most popular method due to its fast convergence rate. Recently, the stochastic sparse grid collocation method has emerged as an attractive alternative to SSFEM. It approximates the solution in the stochastic space using Lagrange polynomial interpolation. The collocation method requires only repetitive calls to an existing deterministic solver, similar to the Monte Carlo method. However, both the SSFEM and current sparse grid collocation methods utilize global polynomials in the stochastic space. Thus when there are steep gradients or finite discontinuities in the stochastic space, these methods converge very slowly or even fail to converge. In this paper, we develop an adaptive sparse grid collocation strategy using piecewise multi-linear hierarchical basis functions. Hierarchical surplus is used as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptively refine the collocation points in this region. Numerical examples, especially for problems related to long-term integration and stochastic discontinuity, are presented. Comparisons with Monte Carlo and multi-element based random domain decomposition methods are also given to show the efficiency and accuracy of the proposed method.

Ma Xiang [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States); Zabaras, Nicholas [Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States)], E-mail: zabaras@cornell.edu

2009-05-01

192

Fragment-based Evaluation of Non-Uniform B-spline Surfaces on GPUs

In this paper, we propose a fragment-based evaluation method for non-uniform B-spline surfaces using recent programmable graphics hardware (GPU). A position on a non-uniform B-spline surface is evaluated by the linear combination of both control points and B-spline basis functions. Hence the computational costs can be reduced by pre-computing a knot interval of a parameter from a knot vector. We

Takashi Kanai

2007-01-01

193

Mars Mission Optimization Based on Collocation of Resources

NASA Technical Reports Server (NTRS)

This paper presents a powerful approach for analyzing Martian data and for optimizing mission site selection based on resource collocation. This approach is implemented in a program called PROMT (Planetary Resource Optimization and Mapping Tool), which provides a wide range of analysis and display functions that can be applied to raw data or imagery. Thresholds, contours, custom algorithms, and graphical editing are some of the various methods that can be used to process data. Output maps can be created to identify surface regions on Mars that meet any specific criteria. The use of this tool for analyzing data, generating maps, and collocating features is demonstrated using data from the Mars Global Surveyor and the Odyssey spacecraft. The overall mission design objective is to maximize a combination of scientific return and self-sufficiency based on utilization of local materials. Landing site optimization involves maximizing accessibility to collocated science and resource features within a given mission radius. Mission types are categorized according to duration, energy resources, and in-situ resource utilization. Optimization results are shown for a number of mission scenarios.

Chamitoff, G. E.; James, G. H.; Barker, D. C.; Dershowitz, A. L.

2003-01-01

194

Maternal MCG interference cancellation using splined independent component subtraction.

Signal distortion is commonly observed when using independent component analysis (ICA) to remove maternal cardiac interference from the fetal magnetocardiogram. This can be seen even in the most conservative case where only the independent components dominated by maternal interference are subtracted from the raw signal, a procedure we refer to as independent component subtraction (ICS). Distortion occurs when the subspaces of the fetal and maternal signals have appreciable overlap. To overcome this problem, we employed splining to remove the fetal signal from the maternal source component. The maternal source components were downsampled and then interpolated to their original sampling rate using a cubic spline. A key aspect of the splining procedure is that the maternal QRS complexes are downsampled much less than the rest of the maternal signal so that they are not distorted, despite their higher bandwidth. The splined maternal source components were projected back onto the magnetic field measurement space and then subtracted from the raw signal. The method was evaluated using data from 24 subjects. We compared the results of conventional, i.e., unsplined, ICS with our method, splined ICS, using matched filtering as a reference. Correlation and subjective assessment of the P-wave and QRS complex were used to assess the performance. Using ICS, we found that the P-wave was adversely affected in 7 of 24 (29%) subjects, all having correlations less than 0.8. Splined ICS showed negligible distortion and improved the signal fidelity to some extent in all subjects. We also demonstrated that maternal T-wave interference could be problematic when the fetal and maternal heartbeats were synchronous. In these instances, splined ICS was more effective than matched filtering. PMID:21712157

Yu, Suhong; Wakai, Ronald T

2011-10-01

195

Gauging the Effects of Exercises on Verb-Noun Collocations

ERIC Educational Resources Information Center

Many contemporary textbooks for English as a foreign language (EFL) and books for vocabulary study contain exercises with a focus on collocations, with verb-noun collocations (e.g. "make a mistake") being particularly popular as targets for collocation learning. Common exercise formats used in textbooks and other pedagogic materials

Boers, Frank; Demecheleer, Murielle; Coxhead, Averil; Webb, Stuart

2014-01-01

196

Circle and Sphere as rational splines Claudia Bangert and Hartmut Prautzsch1

Circle and Sphere as rational splines Claudia Bangert and Hartmut Prautzsch1 Universitat Karlsruhe A simple method is given to construct periodic spline representations for circles. These are n-times di erentiable and of minimal degree. Further, the extension to spheres is discussed. Keywords circle, sphere

Prautzsch, Hartmut

197

Parallel B-Spline Surface Interpolation on a Mesh-Connected Processor Array

A parallel implementation of Chebyshev method is presented for the B-spline surface interpolation problem. The algorithm finds the control points of a uniform bicubic B-spline surface that interpolates m n data points on an m n mesh-connected processor array in constant time. Hence it is optimal. Due to its numerical stability, the algorithm can successfully be used in

Fuhua Cheng; Grzegorz W. Wasilkowski; Jiaye Wang; Caiming Zhang; Wenping Wang

1995-01-01

198

Implementation of B-splines in a Conventional Finite Element Framework

The use of B-spline interpolation functions in the finite element method (FEM) is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B...

Owens, Brian C.

2010-01-16

199

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

NASA Technical Reports Server (NTRS)

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

Desai, Prasun N.; Conway, Bruce A.

2005-01-01

200

47 CFR 51.323 - Standards for physical collocation and virtual collocation.

Code of Federal Regulations, 2014 CFR

...the least expensive, effective security option that is viable for the physical...collocation space assigned. Reasonable security measures that the incumbent LEC may adopt include: (1) Installing security cameras or other monitoring systems;...

2014-10-01

201

47 CFR 51.323 - Standards for physical collocation and virtual collocation.

Code of Federal Regulations, 2013 CFR

...the least expensive, effective security option that is viable for the physical...collocation space assigned. Reasonable security measures that the incumbent LEC may adopt include: (1) Installing security cameras or other monitoring systems;...

2013-10-01

202

Collocations in Computer Assisted Language Gabriela Ferraro

professor was willing to sell them and he could buy two masks to amplify our collection. two masks to [extend] our collection two masks to [complete] our collection two masks to [increase] our collection 7 with a few training examples) - Test the collocation classification with out of domain data - Classification

Heiser, Gernot

203

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.

Parand, K; Taghavi, A; 10.1002/mma.1318

2010-01-01

204

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.

K. Parand; A. R. Rezaei; A. Taghavi

2010-08-16

205

NASA Astrophysics Data System (ADS)

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve the Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro-differential equations.

Parand, K.; Rezaei, A. R.; Taghavi, A.

2010-11-01

206

B-Spline Wavelet Paint Luiz Velho

implementation in two dimensions. RITA · Volume IX · N´umero 2 · Outubro 02 101 #12;B-Spline Wavelet Paint 2B-Spline Wavelet Paint Luiz Velho Ken Perlin Abstract This paper describes an unbounded of Mathematical Sciences #12;B-Spline Wavelet Paint 1. Introduction It is desirable and intuitively natural

207

Bounded optimal knots for regression splines

Using a B-spline representation for splines with knots seen as free variables, the approxima- tion to data by splines improves greatly. The main limitations are the presence of too many local optima in the univariate regression context, and it becomes even worse in multivariate additive modeling. When the number of knots is a priori 9xed, we present a simple algorithm

Nicolas Molinari; Robert Sabatier

208

Spline filter for target tracking

NASA Astrophysics Data System (ADS)

In this paper an efficient approach to nonlinear non-Gaussian state estimation based on spline filtering is presented. The estimation of the conditional probability density of the unknown state can be ideally achieved through Bayes rule. However, the associated computational requirements make it impossible to implement this online filter in practice. In the general particle filtering problem, estimation accuracy increases with the number of particles at the expense of increased computational load. In this paper, B-Spline interpolation is used to represent the density of the state pdf through a low order continuous polynomial. The motivation is to reduce the computational cost. The motion of spline control points and corresponding coefficients is achieved through implementation of the Fokker-Planck equation, which describes the propagation of state probability density function between measurement instants. This filter is applicable for a general state estimation problem as no assumptions are made about the underlying probability density.

Kocherry, Donna L.; Tharmarasa, R.; Lang, Tom; Kirubarajan, T.

2010-04-01

209

A simulation study of the overdetermined geodetic boundary value problem using collocation

This problem is defined in general by the Laplacian and at least two different boundary conditions holding on a spherical boundary, or overlapping parts of it. The least-squares collocation method is applied to estimate spherical harmonic coefficients for the disturbing potential. An algorithm was developed and the method was tested using simulated gravity anomaly and undulation signals. Point as well

Lucia Tsaoussi

1989-01-01

210

The ground state energies and expectation values of atoms are given by Hartree-Fock-Roothaan calculations with one B-spline set. For the neutral atoms He to Uuo, the total energies, kinetic energies, potential energies, and virial ratios are tabulated. Our total energies are in excellent agreement with the highly accurate 10-digit numerical Hartree-Fock energies given by Koga and Thakkar [T. Koga, A.J. Thakkar, J. Phys. B 29 (1996) 2973]. The virial ratios are in complete agreement to within 12-digits of the exact value -2. Orbital energies, electron densities at the nucleus, electron-nucleus cusp ratios, and radial expectation values

Saito, Shiro L. [School of International Liberal Studies, Chukyo University, Toyota 470-0393 (Japan)], E-mail: luna@trinity.lets.chukyo-u.ac.jp

2009-11-15

211

Bidirectional elastic image registration using B-spline affine transformation.

A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bidirectional instead of the traditional unidirectional objective/cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210

Gu, Suicheng; Meng, Xin; Sciurba, Frank C; Ma, Hongxia; Leader, Joseph; Kaminski, Naftali; Gur, David; Pu, Jiantao

2014-06-01

212

A cubic spline approximation for problems in fluid mechanics

NASA Technical Reports Server (NTRS)

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.; Graves, R. A., Jr.

1975-01-01

213

Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline

NASA Astrophysics Data System (ADS)

This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To construct a gap-free T-spline, templates are designed for each type of node and applied to elements in the input mesh. In the geometry stage, an efficient surface fitting technique is developed to improve the surface accuracy with sharp feature preservation. The constructed T-spline surface and solid T-spline interpolate every boundary node in the input mesh, with C 2-continuity everywhere except the local region around irregular nodes. Finally, a Bzier extraction technique is developed and linear independence of the constructed T-splines is studied to facilitate T-spline based isogeometric analysis.

Wang, Wenyan; Zhang, Yongjie; Xu, Guoliang; Hughes, Thomas J. R.

2012-07-01

214

Spline Approximation of Thin Shell Dynamics

NASA Technical Reports Server (NTRS)

A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.

delRosario, R. C. H.; Smith, R. C.

1996-01-01

215

Student Presentation Smoothing spline analysis and error assessment of Holocene

B-spline basis with 50 years knot spacing f(t) = N i=0 miBi,k(t) · Method for determination is implemented to produce models capturing the robust aspects of Holocene lake sediment records. This also allows

Finlay, Christopher

216

The orthogonal collocation method is applied to solve the mathematical model of a monolith catalytic converter, in which the reaction takes place in a porous catalytic layer deposited on the wall of a tube. A sequence of models is developed, with the most complicated one involving transient heat and mass transfer in three dimensions.

Larry C. Young; Bruce A. Finlayson

1976-01-01

217

Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation

Flight Testing a Real Time Implementation of a UAV Path Planner Using Direct Collocation Brian R by tracking a second UAV flying a predefined pattern. Finally, a method of commanding the observation vector ^s UAV sensor line of sight unit vector p Attraction point u UAV Control vector xt Target state

218

A collocation model for water-hammer dynamics with application to leak detection

This paper presents a new model for so-called water hammer equations based on a collocation method. This model is shown to fairly represent possible leak effects in a pipeline and thus to be useful in the purpose of leak detection. This is illustrated in simulation by an example of observer-based leak detector relying on this model.

Flor Lizeth Torres Ortiz; Gildas Besancon; Didier Georges

2008-01-01

219

of expansion in Chebyshev polynomials has been used for solving ordinary differential equations since at least. The new approach is also compared to the conventional Chebyshev collocation method. ? 2011 Elsevier B for solving differential equations. These equations can be ordin- ary differential equations (ODE), either

Butcher, Eric A.

220

An adaptive hierarchical sparse grid collocation algorithm for the solution of

the discontinuity region in the stochastic space and adaptively refine the col- location points in this regionAn adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic discontinuities in the stochastic space, these methods converge very slowly or even fail to converge

Zabaras, Nicholas J.

221

An adaptive three-dimensional RHT-splines formulation in linear elasto-statics and elasto-dynamics

NASA Astrophysics Data System (ADS)

An adaptive three-dimensional isogeometric formulation based on rational splines over hierarchical T-meshes (RHT-splines) for problems in elasto-statics and elasto-dynamics is presented. RHT-splines avoid some short-comings of NURBS-based formulations; in particular they allow for adaptive h-refinement with ease. In order to drive the adaptive refinement, we present a recovery-based error estimator for RHT-splines. The method is applied to several problems in elasto-statics and elasto-dynamics including three-dimensional modeling of thin structures. The results are compared to analytical solutions and results of NURBS based isogeometric formulations.

Nguyen-Thanh, N.; Muthu, J.; Zhuang, X.; Rabczuk, T.

2014-02-01

222

NASA Astrophysics Data System (ADS)

The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.

Kuczy?ski, Pawe?; Bia?ecki, Ryszard

2014-06-01

223

An introduction to multivariate adaptive regression splines.

Multivariate Adaptive Regression Splines (MARS) is a method for flexible modelling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by recursive partitioning (e.g. CART) and shares its ability to capture high order interactions. However, it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables, and produces continuous models with continuous derivatives. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with different multivariable interactions. This paper summarizes the basic MARS algorithm, as well as extensions for binary response, categorical predictors, nested variables and missing values. It presents tips on interpreting the output of the standard FORTRAN implementation of MARS, and provides an example of MARS applied to a set of clinical data. PMID:8548103

Friedman, J H; Roosen, C B

1995-09-01

224

NASA Astrophysics Data System (ADS)

We have developed the Savart-Plate Lateral-shearing Interferometric Nuller for Exoplanets (SPLINE), which is a kind of a nulling interferometer, for directly imaging exoplanets. The SPLINE consists of two polarizers and a Savart plate between them. The SPLINE can theoretically obtain fully achromatic and stable nulled output. However, a drawback of the SPLINE is its low system throughput due to the polarizers. For improving the system throughput, we propose a dualchannel SPLINE using polarization beam splitters instead of the polarizers. We have carried out laboratory demonstration of the dual-channel SPLINE. The achievable contrast of the SPLINE is limited by residual speckles caused by surface roughness of optical elements. For improving the achievable contrast, we propose a method of wavefront correction using a liquid-crystal spatial light modulator (LCSLM). We have carried out preliminary laboratory demonstration using a liquid-crystal variable retarder (LCVR), instead of the LCSLM, for simulating the proposed wavefront correction method. We report the laboratory demonstration in this paper.

Kitou, Hirofumi; Murakami, Naoshi; Kida, Manabu; Baba, Naoshi; Matsuo, Taro; Kotani, Takayuki; Kawahara, Hajime; Tamura, Motohide

2014-07-01

225

Deconvolution of variable rate reservoir performance data using B-splines

This work presents the development, validation and application of a novel deconvolution method based on B-splines for analyzing variable-rate reservoir performance data. Variable-rate deconvolution is a mathematically unstable problem which has been...

Ilk, Dilhan

2007-04-25

226

Code of Federal Regulations, 2014 CFR

...Agreement for the Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication...Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal...

2014-10-01

227

C 2 quartic spline surface interpolation

This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An\\u000a approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed,

Caiming Zhang; Jiaye Wang

2002-01-01

228

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The cen- tral idea is to base our design on the isotropic polyhar- monic B-splines, a new type of polyharmonic B-splines that do converge to a Gaussian as the order increases. We opt for the quincunx subsampling scheme which allows us to characterize the wavelet spaces with

Dimitri Van De Ville; Thierry Blu; Brigitte Forster; Michael Unser

229

Optimal spline regression utilizing steepest descent

OPTIMAL SPLINE REGRESSION UTILIZING STEEPEST DESCENT A Thesis ERIC SHIRLEY FLORA Submitted to the Graduate College of Texas A&M University in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE May l975 Major Sub...]ect: Mathematics OPTIMAL SPLINE REGRESSION UTILIZING STEEPEST DESCENT A Thesis ERIC SHIRLEY FLORA Approved as to style and content by; (Chai an of Committee) (Head of Department) ~' (Member) (Member ) May 1975 ABSTRACT Optimal Spline Regression Utilizing...

Flora, Eric Shirley

1975-01-01

230

Ten good reasons for using spline wavelets

NASA Astrophysics Data System (ADS)

The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: orthogonal (Battle-Lemarie), semi-orthogonal (e.g., B-spline), shift-orthogonal, and biorthogonal (Cohen-Daubechies-Feauveau). Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates their manipulation. They allow for a progressive transition between the two extreme cases of a multiresolution: Haar's piecewise constant representation (spline of degree zero) versus Shannon's bandlimited model (which corresponds to a spline of infinite order). Spline wavelets are extremely regular and usually symmetrical or anti-symmetric. They can be designed to have compact support and to achieve optimal time-frequency localization (B-spline wavelets). The underlying scaling functions are the B-splines, which are the shortest and most regular scaling functions of order L. Finally, splines have the best approximation properties among all known wavelets of a given order L. In other words, they are the best for approximating smooth functions.

Unser, Michael A.

1997-10-01

231

Two-dimensional B-spline finite elements and their application to the computation of solitons

Contents In this paper we investigate the interaction of localized solutions with stable shape and constant velocity, so called solitons, of the Kadomtsev-Petviashvili-equation by numberical methods. B-spline finite elements turn out to be well suited for this purpose. The concept of two-dimensional B-spline finite elements and their numerical implementation is presented. In order to test the method, a diffusion problem

S. Wendel; H. Maisch; H. Karl; G. Lehner

1993-01-01

232

NASA Astrophysics Data System (ADS)

B-spline methods are now well established as widely applicable tools for the evaluation of atomic and molecular continuum states. The mathematical technique of exterior complex scaling has been shown, in a variety of other implementations, to be a powerful method with which to solve atomic and molecular scattering problems, because it allows the correct imposition of continuum boundary conditions without their explicit analytic application. In this paper, an implementation of exterior complex scaling in B-splines is described that can bring the well-developed technology of B-splines to bear on new problems, including multiple ionization and breakup problems, in a straightforward way. The approach is demonstrated for examples involving the continuum motion of nuclei in diatomic molecules as well as electronic continua. For problems involving electrons, a method based on Poisson's equation is presented for computing two-electron integrals over B-splines under exterior complex scaling.

McCurdy, C. William; Martn, Fernando

2004-02-01

233

B-spline methods are now well established as widely applicable tools for the evaluation of atomic and molecular continuum states. The mathematical technique of exterior complex scaling has been shown, in a variety of other implementations, to be a powerful method with which to solve atomic and molecular scattering problems, because it allows the correct imposition of continuum boundary conditions without their explicit analytic application. In this paper, an implementation of exterior complex scaling in B-splines is described that can bring the well-developed technology of B-splines to bear on new problems, including multiple ionization and breakup problems, in a straightforward way. The approach is demonstrated for examples involving the continuum motion of nuclei in diatomic molecules as well as electronic continua. For problems involving electrons, a method based on Poisson's equation is presented for computing two-electron integrals over B-splines under exterior complex scaling.

McCurdy, C. William; Martin, Fernando

2003-11-18

234

Modelling Childhood Growth Using Fractional Polynomials and Linear Splines

Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651

Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.

2014-01-01

235

Implicit B-Spline Surface Reconstruction.

This paper presents a fast and flexible curve, and surface reconstruction technique based on implicit B-spline. This representation does not require any parameterization and it is locally supported. This fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations. This method is further accelerated to reduce the dimension to the active control lattice. Moreover, the surface smoothness and user interaction are allowed for controlling the surface. Finally, a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions. The whole framework is very fast and efficient and can handle large cloud of points with very low computational cost. The experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies. Comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data. PMID:25373084

Rouhani, Mohammad; Sappa, Angel D; Boyer, Edmond

2015-01-01

236

Evaluation on Second Language Collocational Congruency with Computational Semantic Similarity

Evaluation on Second Language Collocational Congruency with Computational Semantic Similarity Ching of the important building blocks for the development of language competence. Remarkably, it is influenced by L1 in lexical components which underpin the foundation of language competence. The notion of collocational

237

Collocation and its impacts on central office backup power systems

The 1996 Telecommunications Act led to a huge expansion in the number and size of collocators (CLECs or Collocated Local Exchange Carriers). Due to maintenance, weight, and environmental issues associated with DC plants; CLECs usually want the incumbent (ILEC) to provide power to their equipment. The incumbents can recoup their costs if they take the proper steps; however there are

Curtis Ashton

1998-01-01

238

Registration of sliding objects using direction dependent B-splines decomposition

NASA Astrophysics Data System (ADS)

Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. This work was presented in part at the 4th International Workshop on Pulmonary Image Analysis during the Medical Image Computing and Computer Assisted Intervention (MICCAI) in Toronto, Canada (2011).

Delmon, V.; Rit, S.; Pinho, R.; Sarrut, D.

2013-03-01

239

of these estimates, and of the related histosplines, allows the use of the finite element method as an approximation to the fundamental solution we seek. This extends to many of the usual finite element variations, including to the many others who have influenced me and who are far too numerous to name; without them, I could

Keinan, Alon

240

Systolic architecture for B-spline surfaces

B-spline surfaces are among the most commonly used types of surfaces for modeling objects in computer graphics and CAD applications. One of the time consuming operations in B-spline surface generation is that of inversion. An efficient algorithm is proposed for solving this problem. This algorithm is implemented on a systolic architecture in order to facilitate fast interactive surface design.

Ajjanagadde, V.G.; Patnaik, L.M.

1986-12-01

241

FOVEATED SPLINES AND WAVELETS GAO XIAOJIE

FOVEATED SPLINES AND WAVELETS GAO XIAOJIE , T. N. T. GOODMAN AND S. L. LEE Abstract. Spline regions of interest. 1. Introduction A foveated image is a nonuniform resolution image in which the resolution is highest at a point, called a fovea, or a region (foveation region), but falls off away from

Martin, Ralph R.

242

Triangular bubble spline surfaces

We present a new method for generating a Gn-surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple Gn-condition between two neighboring bubble patches, which are used to construct surface patches, connected with Gn-continuity. For n?2, we describe the obtained Gn-condition in detail. It can be generalized to anyn?3. The construction of a single surface patch is based on GordonCoons interpolation for triangles. Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of G0, G1 and G2-surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness. PMID:22267872

Kapl, Mario; Byrtus, Marek; Jttler, Bert

2011-01-01

243

Triangular bubble spline surfaces.

We present a new method for generating a [Formula: see text]-surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple [Formula: see text]-condition between two neighboring bubble patches, which are used to construct surface patches, connected with [Formula: see text]-continuity. For [Formula: see text], we describe the obtained [Formula: see text]-condition in detail. It can be generalized to any[Formula: see text]. The construction of a single surface patch is based on Gordon-Coons interpolation for triangles.Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of [Formula: see text], [Formula: see text] and [Formula: see text]-surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness. PMID:22267872

Kapl, Mario; Byrtus, Marek; Jttler, Bert

2011-11-01

244

On developing B-spline registration algorithms for multi-core processors

Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on

J. A. Shackleford; N. Kandasamy; G. C. Sharp

2010-01-01

245

Restoration of Micro-Ct Images Using Locally Adaptive B-Spline Smoothing

We present a novel adaptive B-spline based smoothing filter for the restoration of micro-CT images of mice lung. Our algorithm implements the filter as the convolution of the input image with a B-spline kernel whose size matches the underlying image local characteristics. We show that our method outperforms other traditional adaptive or anisotropic filters in terms of noise reduction, while

Xabier Artaechevarria; Arrate Muoz-barrutia; Carlos Ortiz-de-solorzano

2007-01-01

246

Generalized non-uniform B-spline functions for discrete signal interpolation

This paper is concerned with the problem of recovering a discrete signal from a set of irregular spaced samples at known locations. We propose a local interpolation method based on non-uniform B-spline functions. Under specific constraints (multiplicity order imposed on each knot), we generalize the non-uniform B-spline functions for any degree of the interpolation function. We show that whatever the

N. Chihab; A. Zergainoh; J.-P. Astruc

2003-01-01

247

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Capilla, M.; Talavera, C. F.; Ginestar, D. [Dept. of Nuclear Engineering, Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)

2012-07-01

248

A Penalized spline approach to functional mixed effects model analysis

Summary In this work, we propose penalized spline based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects and residual measurement error processes. Using penalized splines, we propose nonparametric estimation of the population mean function, varying-coefficient, random subject-specific curves and the associated covariance function which represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Proposed methods offer flexible estimation of both the population-level and subject-level curves. In addition, decomposing variability of the outcomes as a between-subject and a within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood based method to select multiple smoothing parameters. Furthermore, we study the asymptotics of the baseline P-spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between- and within-subject covariance decomposition is illustrated through an analysis of Berkeley growth data where we identified clearly distinct patterns of the between- and within-subject covariance functions of children's heights. We also apply the proposed methods to estimate the effect of anti-hypertensive treatment from the Framingham Heart Study data. PMID:18047528

Chen, Huaihou; Wang, Yuanjia

2010-01-01

249

Translational Covering of Closed Planar Cubic B-Spline Curves

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines. Inner and outer polygonal approximations to

Cristina Neacsu; Karen Daniels

2006-01-01

250

Using 3D Spline Differentiation to Compute Quantitative Optical Flow

,jlmari}@esil.univ-mrs.fr Abstract We show that differentiation via fitting B-splines to the spatio-temporal intensity data flow than that computed via Simoncelli's balanced/matched filters. Keywords: B-Splines, Filters's matched/balanced filters [16] and via B-spline dif- ferentiation. As Unser [21] points out, splines

Barron, John

251

Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers

ERIC Educational Resources Information Center

The development of adequate collocational knowledge is important for foreign language learners; nonetheless, learners often have difficulties in producing proper collocations in the target language. Among the various ways of learning collocations, the DDL (data-driven learning) approach encourages independent learning of collocations and allows

Chen, Hao-Jan Howard

2011-01-01

252

Rational-spline approximation with automatic tension adjustment

NASA Technical Reports Server (NTRS)

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.

Schiess, J. R.; Kerr, P. A.

1984-01-01

253

Spline-based procedures for dose-finding studies with active control

In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the doseresponse relationship and to find the smallest target dose concentration d*, which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean doseresponse function with the expected efficacy of the active control has to be estimated. The focus of this paper is a cubic spline-based method for deriving an estimator of the target dose without assuming a specific doseresponse function. Furthermore, the construction of a spline-based bootstrap CI is described. Estimator and CI are compared with other flexible and parametric methods such as linear spline interpolation as well as maximum likelihood regression in simulation studies motivated by a real clinical trial. Also, design considerations for the cubic spline approach with focus on bias minimization are presented. Although the spline-based point estimator can be biased, designs can be chosen to minimize and reasonably limit the maximum absolute bias. Furthermore, the coverage probability of the cubic spline approach is satisfactory, especially for bias minimal designs. 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. PMID:25319931

Helms, Hans-Joachim; Benda, Norbert; Zinserling, Jrg; Kneib, Thomas; Friede, Tim

2015-01-01

254

Spline-based procedures for dose-finding studies with active control.

In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the dose-response relationship and to find the smallest target dose concentration d(*) , which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean dose-response function with the expected efficacy of the active control has to be estimated. The focus of this paper is a cubic spline-based method for deriving an estimator of the target dose without assuming a specific dose-response function. Furthermore, the construction of a spline-based bootstrap CI is described. Estimator and CI are compared with other flexible and parametric methods such as linear spline interpolation as well as maximum likelihood regression in simulation studies motivated by a real clinical trial. Also, design considerations for the cubic spline approach with focus on bias minimization are presented. Although the spline-based point estimator can be biased, designs can be chosen to minimize and reasonably limit the maximum absolute bias. Furthermore, the coverage probability of the cubic spline approach is satisfactory, especially for bias minimal designs. 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. PMID:25319931

Helms, Hans-Joachim; Benda, Norbert; Zinserling, Jrg; Kneib, Thomas; Friede, Tim

2015-01-30

255

BSR: B-spline atomic R-matrix codes

BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electronatom and electronion scattering, and radiative processes such as boundbound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the BreitPauli Hamiltonian.

Oleg Zatsarinny

2006-01-01

256

Using spline-enhanced ordinary differential equations for PK/PD model development.

A spline-enhanced ordinary differential equation (ODE) method is proposed for developing a proper parametric kinetic ODE model and is shown to be a useful approach to PK/PD model development. The new method differs substantially from a previously proposed model development approach using a stochastic differential equation (SDE)-based method. In the SDE-based method, a Gaussian diffusion term is introduced into an ODE to quantify the system noise. In our proposed method, we assume an ODE system with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function vector that is estimated using penalized splines. B(t) is used to construct a quantitative measure of model uncertainty useful for finding the proper model structure for a given data set. By means of two examples with simulated data, we demonstrate that the spline-enhanced ODE method can provide model diagnostics and serve as a basis for systematic model development similar to the SDE-based method. We compare and highlight the differences between the SDE-based and the spline-enhanced ODE methods of model development. We conclude that the spline-enhanced ODE method can be useful for PK/PD modeling since it is based on a relatively uncomplicated estimation algorithm which can be implemented with readily available software, provides numerically stable, robust estimation for many models, is distribution-free and allows for identification and accommodation of model deficiencies due to model misspecification. PMID:18989761

Wang, Yi; Eskridge, Kent; Zhang, Shunpu; Wang, Dong

2008-10-01

257

A B-spline approach for empirical mode decompositions

We propose an alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals. Motivated\\u000a by this new approach, we derive recursive formulas of the Hilbert transform of B-splines and discuss Euler splines as spline\\u000a intrinsic mode functions in the decomposition. We also develop the Bedrosian identity for signals having vanishing moments.\\u000a We present numerical implementations of the B-spline

Qiuhui Chen; Norden Huang; Sherman D. Riemenschneider; Yuesheng Xu

2006-01-01

258

An Algorithm for Direct Multiplication of B-Splines

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using

Xianming Chen; Richard F. Riesenfeld; Elaine Cohen

2009-01-01

259

Sliding windows algorithm for B-spline multiplication

B-spline multiplication, that is, finding the coefficients of the prod- uct B-spline of two given B-splines, is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of poly- nomial

Xianming Chen; Richard F. Riesenfeld; Elaine Cohen

2007-01-01

260

An arc spline approximation to a clothoid

NASA Astrophysics Data System (ADS)

The clothoid is a spiral used in highway and railway route design. Clothoids are transcendental functions and so have been approximated by polynomials, by power series and continued fractions, and by rational functions. Here the clothoid is approximated by an arc spline. The chief advantage in doing so is that arc splines are very easy to lay out and to offset. Examples show that the approximation is of extremely high accuracy. It is proved that if the arc spline has n arcs, then the error in the approximation is of order O(1/n2).

Meek, D. S.; Walton, D. J.

2004-09-01

261

NASA Astrophysics Data System (ADS)

Wavelet expansion has been demonstrated to be suitable for the representation of spatial functions. Here we propose the so-called B-spline wavelets to represent spatial time-series of GPS-derived global ionosphere maps (GIMs) of the vertical total electron content (TEC) from the Earths surface to the mean altitudes of GPS satellites, over Japan. The scalar-valued B-spline wavelets can be defined in a two-dimensional, but not necessarily planar, domain. Generated by a sequence of knots, different degrees of B-splines can be implemented: degree 1 represents the Haar wavelet; degree 2, the linear B-spline wavelet, or degree 4, the cubic B-spline wavelet. A non-uniform version of these wavelets allows us to handle data on a bounded domain without any edge effects. B-splines are easily extended with great computational efficiency to domains of arbitrary dimensions, while preserving their properties. This generalization employs tensor products of B-splines, defined as linear superposition of products of univariate B-splines in different directions. The data and model may be identical at the locations of the data points if the number of wavelet coefficients is equal to the number of grid points. In addition, data compression is made efficient by eliminating the wavelet coefficients with negligible magnitudes, thereby reducing the observational noise. We applied the developed methodology to the representation of the spatial and temporal variations of GIM from an extremely dense GPS network, the GPS Earth Observation Network (GEONET) in Japan. Since the sampling of the TEC is registered regularly in time, we use a two-dimensional B-spline wavelet representation in space and a one-dimensional spline interpolation in time. Over the Japan region, the B-spline wavelet method can overcome the problem of bias for the spherical harmonic model at the boundary, caused by the non-compact support. The hierarchical decomposition not only allows an inexpensive calculation, but also separates visualisation at different levels of detail. Each level corresponds to a certain spatial frequency band, leading to a detection of structures and enhancement in the ionosphere at different resolutions.

Mautz, R.; Ping, J.; Heki, K.; Schaffrin, B.; Shum, C.; Potts, L.

2005-05-01

262

Single-grid spectral collocation for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

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.

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

1988-01-01

263

Data reduction using cubic rational B-splines

NASA Technical Reports Server (NTRS)

A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.

Chou, Jin J.; Piegl, Les A.

1992-01-01

264

Usability Study of Two Collocated Prototype System Displays

NASA Technical Reports Server (NTRS)

Currently, most of the displays in control rooms can be categorized as status screens, alerts/procedures screens (or paper), or control screens (where the state of a component is changed by the operator). The primary focus of this line of research is to determine which pieces of information (status, alerts/procedures, and control) should be collocated. Two collocated displays were tested for ease of understanding in an automated desktop survey. This usability study was conducted as a prelude to a larger human-in-the-loop experiment in order to verify that the 2 new collocated displays were easy to learn and usable. The results indicate that while the DC display was preferred and yielded better performance than the MDO display, both collocated displays can be easily learned and used.

Trujillo, Anna C.

2007-01-01

265

Translating Collocations for Bilingual Lexicons: A Statistical Approach

Collocations are notoriously difficult for non-native speakers to translate, primarily because they are opaque and cannot be translated on a word-by-word basis. We describe a program named Champollion which, given a pair of parallel corpora in two different languages and a list of collocations in one of them, automatically produces their translations. Our goal is to provide a tool for

Frank A. Smadja; Kathleen R. Mckeown; Vasileios Hatzivassiloglou

1996-01-01

266

Subcell resolution in simplex stochastic collocation for spatial discontinuities

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSCSR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSCSR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.

Witteveen, Jeroen A.S., E-mail: jeroen.witteveen@cwi.nl [Center for Turbulence Research, Stanford University, Building 500, Stanford, CA 94305-3035 (United States); Center for Mathematics and Computer Science (CWI), Science Park 123, 1098XG Amsterdam (Netherlands); Iaccarino, Gianluca, E-mail: jops@stanford.edu [Center for Turbulence Research, Stanford University, Building 500, Stanford, CA 94305-3035 (United States)] [Center for Turbulence Research, Stanford University, Building 500, Stanford, CA 94305-3035 (United States)

2013-10-15

267

Subcell resolution in simplex stochastic collocation for spatial discontinuities

NASA Astrophysics Data System (ADS)

Subcell resolution has been used in the Finite Volume Method (FVM) to obtain accurate approximations of discontinuities in the physical space. Stochastic methods are usually based on local adaptivity for resolving discontinuities in the stochastic dimensions. However, the adaptive refinement in the probability space is ineffective in the non-intrusive uncertainty quantification framework, if the stochastic discontinuity is caused by a discontinuity in the physical space with a random location. The dependence of the discontinuity location in the probability space on the spatial coordinates then results in a staircase approximation of the statistics, which leads to first-order error convergence and an underprediction of the maximum standard deviation. To avoid these problems, we introduce subcell resolution into the Simplex Stochastic Collocation (SSC) method for obtaining a truly discontinuous representation of random spatial discontinuities in the interior of the cells discretizing the probability space. The presented SSC-SR method is based on resolving the discontinuity location in the probability space explicitly as function of the spatial coordinates and extending the stochastic response surface approximations up to the predicted discontinuity location. The applications to a linear advection problem, the inviscid Burgers' equation, a shock tube problem, and the transonic flow over the RAE 2822 airfoil show that SSC-SR resolves random spatial discontinuities with multiple stochastic and spatial dimensions accurately using a minimal number of samples.

Witteveen, Jeroen A. S.; Iaccarino, Gianluca

2013-10-01

268

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

NASA Technical Reports Server (NTRS)

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.

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

1995-01-01

269

Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles

NASA Astrophysics Data System (ADS)

The quantification of measurement uncertainty of atmospheric parameters is a key factor in assessing the uncertainty of global change estimates given by numerical prediction models. One of the critical contributions to the uncertainty budget is related to the collocation mismatch in space and time among observations made at different locations. This is particularly important for vertical atmospheric profiles obtained by radiosondes or lidar. In this paper we propose a statistical modelling approach capable of explaining the relationship between collocation uncertainty and a set of environmental factors, height and distance between imperfectly collocated trajectories. The new statistical approach is based on the heteroskedastic functional regression (HFR) model which extends the standard functional regression approach and allows a natural definition of uncertainty profiles. Along this line, a five-fold decomposition of the total collocation uncertainty is proposed, giving both a profile budget and an integrated column budget. HFR is a data-driven approach valid for any atmospheric parameter, which can be assumed smooth. It is illustrated here by means of the collocation uncertainty analysis of relative humidity from two stations involved in the GCOS reference upper-air network (GRUAN). In this case, 85% of the total collocation uncertainty is ascribed to reducible environmental error, 11% to irreducible environmental error, 3.4% to adjustable bias, 0.1% to sampling error and 0.2% to measurement error.

Fass, A.; Ignaccolo, R.; Madonna, F.; Demoz, B. B.; Franco-Villoria, M.

2014-06-01

270

Hypothesis testing in b-spline regression

Linea0r combinations of B-spline coefficients which provide statistically meaningful hypothesis tests are identified. These tests include the importance of breakpoints, continuity constraints, and higher order terms.The important linear combinations turn out to be contrasts whose coefficients are determined by differencing the left- and right-hand limits of the B-splines or their derivatives at certain knots. A FORTRAN program for testing single

Patricia L. Smith

1982-01-01

271

Beta-splines used in visualization techniques differ from b-splines in that they are constructed using geometric continuity constraints instead of parametric derivative constraints. They are piecewise polynomial interpolating functions. We show how to exactly compute the samples of these functions from a sparse set of points. This computation uses only summations, and no multiplications after initial setup, and the summations can

John P. Refling; Leonard A. Ferrari

1993-01-01

272

An Hermitian Approach for Multiresolution Splines Laurent Grisoni, Christophe Schlick, Carole Blanc

is presented through the use of HBsplines, a specific subset of particular Bsplines that include some. This multiresolution scheme is presented through the use of HBsplines, a specific subset of particular Bsplines approach, that associates the HBspline model [5] (a special case of Bsplines that presents some specific

Grisoni, Laurent

273

Continuous Groundwater Monitoring Collocated at USGS Streamgages

NASA Astrophysics Data System (ADS)

USGS Office of Groundwater funded a 2-year pilot study collocating groundwater wells for monitoring water level and temperature at several existing continuous streamgages in Montana and Wyoming, while U.S. Army Corps of Engineers funded enhancement to streamgages in Mississippi. To increase spatial relevance with in a given watershed, study sites were selected where near-stream groundwater was in connection with an appreciable aquifer, and where logistics and cost of well installations were considered representative. After each well installation and surveying, groundwater level and temperature were easily either radio-transmitted or hardwired to existing data acquisition system located in streamgaging shelter. Since USGS field personnel regularly visit streamgages during routine streamflow measurements and streamgage maintenance, the close proximity of observation wells resulted in minimum extra time to verify electronically transmitted measurements. After field protocol was tuned, stream and nearby groundwater information were concurrently acquired at streamgages and transmitted to satellite from seven pilot-study sites extending over nearly 2,000 miles (3,200 km) of the central US from October 2009 until October 2011, for evaluating the scientific and engineering add-on value of the enhanced streamgage design. Examination of the four-parameter transmission from the seven pilot study groundwater gaging stations reveals an internally consistent, dynamic data suite of continuous groundwater elevation and temperature in tandem with ongoing stream stage and temperature data. Qualitatively, the graphical information provides appreciation of seasonal trends in stream exchanges with shallow groundwater, as well as thermal issues of concern for topics ranging from ice hazards to suitability of fish refusia, while quantitatively this information provides a means for estimating flux exchanges through the streambed via heat-based inverse-type groundwater modeling. In June USGS Fact Sheet 2012-3054 was released online, summarizing the results of the pilot project.

Constantz, J. E.; Eddy-Miller, C.; Caldwell, R.; Wheeer, J.; Barlow, J.

2012-12-01

274

Collocation and Pattern Recognition Effects on System Failure Remediation

NASA Technical Reports Server (NTRS)

Previous research found that operators prefer to have status, alerts, and controls located on the same screen. Unfortunately, that research was done with displays that were not designed specifically for collocation. In this experiment, twelve subjects evaluated two displays specifically designed for collocating system information against a baseline that consisted of dial status displays, a separate alert area, and a controls panel. These displays differed in the amount of collocation, pattern matching, and parameter movement compared to display size. During the data runs, subjects kept a randomly moving target centered on a display using a left-handed joystick and they scanned system displays to find a problem in order to correct it using the provided checklist. Results indicate that large parameter movement aided detection and then pattern recognition is needed for diagnosis but the collocated displays centralized all the information subjects needed, which reduced workload. Therefore, the collocated display with large parameter movement may be an acceptable display after familiarization because of the possible pattern recognition developed with training and its use.

Trujillo, Anna C.; Press, Hayes N.

2007-01-01

275

Beyond triple collocation: Applications to soil moisture monitoring

NASA Astrophysics Data System (ADS)

collocation (TC) is routinely used to resolve approximated linear relationships between different measurements (or representations) of a geophysical variable that are subject to errors. It has been utilized in the context of calibration, validation, bias correction, and error characterization to allow comparisons of diverse data records from various direct and indirect measurement techniques including in situ remote sensing and model-based approaches. However, successful applications of TC require sufficiently large numbers of coincident data points from three independent time series and, within the analysis period, homogeneity of their linear relationships and error structures. These conditions are difficult to realize in practice due to infrequent spatiotemporal sampling of satellite and ground-based sensors. TC can, however, be generalized within the framework of instrumental variable (IV) regression theory to address some of the conceptual constraints of TC. We review the theoretics of IV and consider one possible strategy to circumvent the three-data constraint by use of lagged variables (LV) as instruments. This particular implementation of IV is suitable for circumstances where multiple data records are limited and the geophysical variable of interest is sampled at time intervals shorter than its temporal correlation length. As a demonstration of utility, the LV method is applied to microwave satellite soil moisture data sets to recover their errors over Australia and to estimate temporal properties of their relationships with in situ and model data. These results are compared against standard two-data linear estimators and the TC estimator as benchmark.

Su, Chun-Hsu; Ryu, Dongryeol; Crow, Wade T.; Western, Andrew W.

2014-06-01

276

Spatially Variant Convolution With Scaled B-Splines

We present an efficient algorithm to compute multidimensional spatially variant convolutions-or inner products-between N-dimensional signals and B-splines-or their derivatives-of any order and arbitrary sizes. The multidimensional B-splines are computed as tensor products of 1-D B-splines, and the input signal is expressed in a B-spline basis. The convolution is then computed by using an adequate combination of integration and scaled finite

Arrate Muoz-Barrutia; Xabier Artaechevarria; Carlos Ortiz-de-Solorzano

2010-01-01

277

An approximation for discrete B-splines in time domain

A simple discrete version of B-splines defined as a multifold discrete convolution of sampled rectangles is proposed in the analogy of B-splines being multifold convolution integrals of rectangular functions. Then it is proven that its staircase interpolation tends to the B-spline when the sampling interval goes to zero. This version can be regarded as an approximation for the discrete B-splines

Koichi Ichige; Masaru Kamada

1997-01-01

278

In this paper we are going to discuss and analyze the different methods which are developed to detect the Lung nodules which cause the lung cancer. At the end of analyzing different methods, the new methodology of detecting the lung nodules using Spline Wavelet technique has been proposed in this paper. Continuous modeling of data often required in medical imaging, Polynomial Splines are especially useful to consider image data as continuum rather than discrete array of pixels. The multi resolution property of Splines makes them prime candidates for constructing wavelet bases. Wavelet tool also let us to compress the original CT image to greater factor without any sacrifice in accuracy of nodule detection. Different Algorithms for segmentation/ detection of lung nodules from CT image is discussed in this paper. PMID:23675284

Senthil Kumar, T. K.; Ganesh, E. N.

2013-01-01

279

Error Estimates Derived from the Data for Least-Squares Spline Fitting

The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.

Jerome Blair

2007-06-25

280

NASA Technical Reports Server (NTRS)

A partial spline model is a model for a response as a function of several variables, which is the sum of a smooth function of several variables and a parametric function of the same plus possibly some other variables. Partial spline models in one and several variables, with direct and indirect data, with Gaussian errors and as an extension of GLIM to partially penalized GLIM models are described. Application to the modeling of change of regime in several variables is described. Interaction splines are introduced and described and their potential use for modeling non-linear interactions between variables by semiparametric methods is noted. Reference is made to recent work in efficient computational methods.

Wahba, Grace

1987-01-01

281

Restricted trivariate polycube splines for volumetric data modeling.

This paper presents a volumetric modeling framework to construct a novel spline scheme called restricted trivariate polycube splines (RTP-splines). The RTP-spline aims to generalize both trivariate T-splines and tensor-product B-splines; it uses solid polycube structure as underlying parametric domains and strictly bounds blending functions within such domains. We construct volumetric RTP-splines in a top-down fashion in four steps: 1) Extending the polycube domain to its bounding volume via space filling; 2) building the B-spline volume over the extended domain with restricted boundaries; 3) inserting duplicate knots by adding anchor points and performing local refinement; and 4) removing exterior cells and anchors. Besides local refinement inherited from general T-splines, the RTP-splines have a few attractive properties as follows: 1) They naturally model solid objects with complicated topologies/bifurcations using a one-piece continuous representation without domain trimming/patching/merging. 2) They have guaranteed semistandardness so that the functions and derivatives evaluation is very efficient. 3) Their restricted support regions of blending functions prevent control points from influencing other nearby domain regions that stay opposite to the immediate boundaries. These features are highly desirable for certain applications such as isogeometric analysis. We conduct extensive experiments on converting complicated solid models into RTP-splines, and demonstrate the proposed spline to be a powerful and promising tool for volumetric modeling and other scientific/engineering applications where data sets with multiattributes are prevalent. PMID:22442125

Wang, Kexiang; Li, Xin; Li, Bo; Xu, Huanhuan; Qin, Hong

2012-05-01

282

Development of adaptive B-splines using CMAC neural networks

Summary form only given. Adaptive splines can be used to construct smooth approximations to unknown functions as data are received online. When the adaptive spline is multidimensional with a large number of knot points, the computational requirements of conventional implementations can limit the utility of an adaptive spline approach. Artificial neural networks have shown that multidimensional nonlinear functions can be

D. A. Handelman; J. J. Gelfand

1989-01-01

283

Efficient one-sided linearization of spline geometry Jorg Peters

, such as b-splines, B´ezier patches and subdivision surfaces, offer improved compression (if the target shape, and for the majority of finite element codes. No wonder then that b-spline, B´ezier and subdivision control nets look curved object. Consequently, despite their geometrically indicative control structure, objects in b-spline

Peters, Jörg

284

Spectral domain B-spline identification in acoustic echo cancellation

Spectral domain B-spline identification is proposed for acoustic echo cancellation. Two approaches are considered. The first is based on the solution of normal equations; we describe an efficient technique for such a solution, which benefits from the sparseness of the system matrix due to B-splines. The second approach is based on using local splines, enabling further simplification. We also show

Y. Zakharov; T. Tozer

2005-01-01

285

B-spline methods are now well established as widely applicable tools for the evaluation of atomic and molecular continuum states. The mathematical technique of exterior complex scaling has been shown, in a variety of other implementations, to be a powerful method with which to solve atomic and molecular scattering problems, because it allows the correct imposition of continuum boundary conditions without

C. William McCurdy; Fernando Martin

2003-01-01

286

B-spline methods are now well established as widely applicable tools for the evaluation of atomic and molecular continuum states. The mathematical technique of exterior complex scaling has been shown, in a variety of other implementations, to be a powerful method with which to solve atomic and molecular scattering problems, because it allows the correct imposition of continuum boundary conditions without

C. William McCurdy; Fernando Martn

2004-01-01

287

FRACTIONAL ORDER NUMERICAL DIFFERENTIATION WITH B-SPLINE FUNCTIONS , T.M. Laleg-Kirati1

FRACTIONAL ORDER NUMERICAL DIFFERENTIATION WITH B-SPLINE FUNCTIONS D.Y. Liu1 , T.M. Laleg-Kirati1 the Tikhonov regularization problem. Then, we propose a fractional order differentiator by calculating of the proposed method in comparison with some existing methods. Keywords: Fractional order numerical

Paris-Sud XI, Université de

288

Uniform Powell-Sabin spline wavelets

NASA Astrophysics Data System (ADS)

This paper discusses how the subdivision scheme for uniform Powell-Sabin spline surfaces makes it possible to place those surfaces in a multiresolution context. We first show that the basis functions are translates and dilates of one vector of scaling functions. This defines a sequence of nested spaces. We then use the subdivision scheme as the prediction step in the lifting scheme and add an update step to construct wavelets that describe a sequence of complement spaces. Finally, as an example application, we use the new wavelet transform to reduce noise on a uniform Powell-Sabin spline surface.

Windmolders, Joris; Vanraes, Evelyne; Dierckx, Paul; Bultheel, Adhemar

2003-05-01

289

C^1 spline wavelets on triangulations

NASA Astrophysics Data System (ADS)

In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in C^1 wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of C^1 quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct C^1 wavelet bases on general triangulations and give explicit expressions for the wavelets on the three-direction mesh. A general theory is developed so as to verify the global stability of these wavelets in Besov spaces. The wavelet bases constructed in this paper will be useful for numerical solutions of partial differential equations.

Jia, Rong-Qing; Liu, Song-Tao

2008-03-01

290

L2 Learner Production and Processing of Collocation: A Multi-Study Perspective

ERIC Educational Resources Information Center

This article presents a series of studies focusing on L2 production and processing of adjective-noun collocations (e.g., "social services"). In Study 1, 810 adjective-noun collocations were extracted from 31 essays written by Russian learners of English. About half of these collocations appeared frequently in the British National Corpus (BNC);

Siyanova, Anna; Schmitt, Norbert

2008-01-01

291

An algorithm for surface smoothing with rational splines

NASA Technical Reports Server (NTRS)

Discussed is an algorithm for smoothing surfaces with spline functions containing tension parameters. The bivariate spline functions used are tensor products of univariate rational-spline functions. A distinct tension parameter corresponds to each rectangular strip defined by a pair of consecutive spline knots along either axis. Equations are derived for writing the bivariate rational spline in terms of functions and derivatives at the knots. Estimates of these values are obtained via weighted least squares subject to continuity constraints at the knots. The algorithm is illustrated on a set of terrain elevation data.

Schiess, James R.

1987-01-01

292

Real-time image rotation using B-spline interpolation on FPGA's board

NASA Astrophysics Data System (ADS)

The aim of our work is to realize the implementation of a real-time high-quality image rotation on FPGA's board. The method we used is based on M. Unser's work and consists in applying a B-spline interpolator. The difficulty of this problem is due to the relatively weak integration capacity of FPGAs. To solve this problem we have searched for determining the minimum number of bits to code the filter while keeping a good accuracy of filtering output. In this article, we remind a few definitions about B-spline functions and we present how we use B- spline interpolation for the image rotation problem. Then, we describe the way we calculate probability density function of the output error in order to determine the filter data coding.

Berthaud, Cyril; Bourennane, El-Bay; Paindavoine, Michel; Milan, Claude

1998-10-01

293

Smoothing two-dimensional Malaysian mortality data using P-splines indexed by age and year

NASA Astrophysics Data System (ADS)

Nonparametric regression implements data to derive the best coefficient of a model from a large class of flexible functions. Eilers and Marx (1996) introduced P-splines as a method of smoothing in generalized linear models, GLMs, in which the ordinary B-splines with a difference roughness penalty on coefficients is being used in a single dimensional mortality data. Modeling and forecasting mortality rate is a problem of fundamental importance in insurance company calculation in which accuracy of models and forecasts are the main concern of the industry. The original idea of P-splines is extended to two dimensional mortality data. The data indexed by age of death and year of death, in which the large set of data will be supplied by Department of Statistics Malaysia. The extension of this idea constructs the best fitted surface and provides sensible prediction of the underlying mortality rate in Malaysia mortality case.

Kamaruddin, Halim Shukri; Ismail, Noriszura

2014-06-01

294

Local Filters of B-spline Wavelets

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the local- ity of their decomposition and reconstruction filters. How- ever, Haar wavelets are not satisfactory for some applica- tions due to their non-continuous behaviour. Having a par- ticular level of smoothness is important for many applica- tions. B-spline wavelets are capable of

Faramarz F. Samavati; Richard H. Bartels

2004-01-01

295

Pseudolinearization of the acrobot using spline functions

The authors present an algorithm for the construction of approximation to both the nonlinear control and coordinate transformation under which a single-input nonlinear system has a linear tangent model independent of its operating point. Substituting spline approximations for functions that can be difficult to compute yields a stable closed-loop system with an arbitrarily small deterioration in performance. The approximate pseudolinearization

S. A. Bortoff; M. W. Spong

1992-01-01

296

Higher-order numerical methods derived from three-point polynomial interpolation

NASA Technical Reports Server (NTRS)

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.; Khosla, P. K.

1976-01-01

297

NASA/CR2003212153 A Stochastic Collocation Algorithm

NASA/CR2003212153 A Stochastic Collocation Algorithm for Uncertainty Analysis Lionel Mathelin and M. Yousuff Hussaini Florida State University, Tallahassee, Florida February 2003 #12;The NASA STI Program Office . . . in Profile Since its founding, NASA has been dedicated to the advancement

Mathelin, Lionel

298

Collocation Software for Boundary Value DifferentialAlgebraic Equations

and engineers to solve practical problems that can be formulated as systems of ordinary differential equationsCollocation Software for Boundary Value DifferentialAlgebraic Equations Uri M. Ascher \\Lambdaexplicit differentialalgebraic equations (DAEs) of index at most 2. Fully implicit index1 boundary value DAE problems

Spiteri, Raymond J.

299

Validation of ocean wind and wave data using triple collocation

Significant wave height and wind speed fields from ERA-40 are validated against buoy, ERS-1, and Topex altimeter measurements. To do so, we propose and apply a triple collocation statistical model. The model takes into account the random errors in observations and model results and allows the estimation of the variances of the errors. We first examine the case where the

S. Caires; A. Sterl

2003-01-01

300

A Collocation Database for German Verbs and Nouns

The paper presents a database of collocations for German verbs and nouns. The colloca- tions are induced from a statistical grammar model, whose parameters have been trained on 35 million words of German newspaper corpora. Concerning verbs, the database con- centrates on subcategorisation properties and verb-noun c ollocations with regard to their specific subcategorisation relation (i.e. the representat ion of

SABINE SCHULTE

301

A Self-Sensing Piezoelectric Actuator for Collocated Control

A technique has been developed which allows a single piece of piezoelec tric material to concurrently sense and actuate in a closed loop system. The motivation behind the technique is that such a self-sensing actuator will be truly collocated and has applications in active and intelligent structures, such as vibration suppression. A theoreti cal basis for the self-sensing actuator is

Jeffrey J. Dosch; Daniel J. Inman; Ephrahim Garcia

1992-01-01

302

Semisupervised Feature Selection via Spline Regression for Video Semantic Recognition.

To improve both the efficiency and accuracy of video semantic recognition, we can perform feature selection on the extracted video features to select a subset of features from the high-dimensional feature set for a compact and accurate video data representation. Provided the number of labeled videos is small, supervised feature selection could fail to identify the relevant features that are discriminative to target classes. In many applications, abundant unlabeled videos are easily accessible. This motivates us to develop semisupervised feature selection algorithms to better identify the relevant video features, which are discriminative to target classes by effectively exploiting the information underlying the huge amount of unlabeled video data. In this paper, we propose a framework of video semantic recognition by semisupervised feature selection via spline regression (S(2)FS(2)R) . Two scatter matrices are combined to capture both the discriminative information and the local geometry structure of labeled and unlabeled training videos: A within-class scatter matrix encoding discriminative information of labeled training videos and a spline scatter output from a local spline regression encoding data distribution. An l2,1 -norm is imposed as a regularization term on the transformation matrix to ensure it is sparse in rows, making it particularly suitable for feature selection. To efficiently solve S(2)FS(2)R , we develop an iterative algorithm and prove its convergency. In the experiments, three typical tasks of video semantic recognition, such as video concept detection, video classification, and human action recognition, are used to demonstrate that the proposed S(2)FS(2)R achieves better performance compared with the state-of-the-art methods. PMID:25608288

Han, Yahong; Yang, Yi; Yan, Yan; Ma, Zhigang; Sebe, Nicu; Zhou, Xiaofang

2015-02-01

303

B-Spline Free-Form Deformation of Polygonal Objects through Fast Functional Composition

Free-form deformation, abbreviated to FFD, plays an important role in both computer animation and geometric modeling. When polygonal objects are deformed by the traditional FFD scheme, however aliasing will appear since the deformation only acts on the sample points of the objects. To eliminate this problem, a new method of accurate B-spline FFD was proposed by authors previously, which is

Jieqing Feng; Qunsheng Peng

2000-01-01

304

. In this paper we consider a certain class of geodetic linear inverse problems in a reproducing kernel Hilbert space setting to obtain a bounded inverse operator . For a numerical realization we assume to be given at a finite number of discrete points to which we employ a spherical spline interpolation method adapted to the\\u000a Hilbert spaces. By applying

F. Schneider

1996-01-01

305

To solve the inverse gravimetric problem, i.e. to reconstruct the Earth's mass density distribution by using the gravitational potential, we introduce a spline interpolation method for the ellipsoidal Earth model, where the ellipsoid has a rotational symmetry. This problem is ill-posed in the sense of Hadamard as the solution may not exist, it is not unique and it is not

Nahid Akhtar; Volker Michel

2011-01-01

306

The objective of this work was to develop a segmentation technique for thickness measurements of the articular cartilage in MR images and to assess the interobserver reproducibility of the method in comparison with manual segmentation. The algorithm is based on a B-spline snakes approach and is able to delineate the cartilage boundaries in real time and with minimal user interaction.

Tobias Stammberger; Felix Eckstein; Markus Michaelis; Karl-Hans Englmeier; Maximilian Reiser

1999-01-01

307

We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters. PMID:25362291

Ruberti, M; Averbukh, V; Decleva, P

2014-10-28

308

Translational Covering of Closed Planar Cubic B-Spline Curves Cristina Neacsu, Karen Daniels

Translational Covering of Closed Planar Cubic B-Spline Curves Cristina Neacsu, Karen Daniels in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines recent results on B-spline curve envelopes, we bound the distance from the spline curve to its

Daniels, Karen M.

309

Using spline-enhanced ordinary differential equations for PK\\/PD model development

A spline-enhanced ordinary differential equation (ODE) method is proposed for developing a proper parametric kinetic ODE model\\u000a and is shown to be a useful approach to PK\\/PD model development. The new method differs substantially from a previously proposed\\u000a model development approach using a stochastic differential equation (SDE)-based method. In the SDE-based method, a Gaussian\\u000a diffusion term is introduced into an

Yi Wang; Kent Eskridge; Shunpu Zhang; Dong Wang

2008-01-01

310

Trajectory control of an articulated robot with a parallel drive arm based on splines under tension

NASA Astrophysics Data System (ADS)

Today's industrial robots controlled by mini/micro computers are basically simple positioning devices. The positioning accuracy depends on the mathematical description of the robot configuration to place the end-effector at the desired position and orientation within the workspace and on following the specified path which requires the trajectory planner. In addition, the consideration of joint velocity, acceleration, and jerk trajectories are essential for trajectory planning of industrial robots to obtain smooth operation. The newly designed 6 DOF articulated robot with a parallel drive arm mechanism which permits the joint actuators to be placed in the same horizontal line to reduce the arm inertia and to increase load capacity and stiffness is selected. First, the forward kinematic and inverse kinematic problems are examined. The forward kinematic equations are successfully derived based on Denavit-Hartenberg notation with independent joint angle constraints. The inverse kinematic problems are solved using the arm-wrist partitioned approach with independent joint angle constraints. Three types of curve fitting methods used in trajectory planning, i.e., certain degree polynomial functions, cubic spline functions, and cubic spline functions under tension, are compared to select the best possible method to satisfy both smooth joint trajectories and positioning accuracy for a robot trajectory planner. Cubic spline functions under tension is the method selected for the new trajectory planner. This method is implemented for a 6 DOF articulated robot with a parallel drive arm mechanism to improve the smoothness of the joint trajectories and the positioning accuracy of the manipulator. Also, this approach is compared with existing trajectory planners, 4-3-4 polynomials and cubic spline functions, via circular arc motion simulations. The new trajectory planner using cubic spline functions under tension is implemented into the microprocessor based robot controller and motors to produce combined arc and straight-line motion. The simulation and experiment show interesting results by demonstrating smooth motion in both acceleration and jerk and significant improvements of positioning accuracy in trajectory planning.

Yi, Seung-Jong

311

ERIC Educational Resources Information Center

In this article I examine the collocational behaviour of groups of semantically related verbs (e.g., "head, run, manage") and nouns (e.g., "issue, factor, aspect") from the domain of business English. The results of this corpus-based study show that much of the collocational behaviour exhibited by these lexical items can be explained by examining

Walker, Crayton Phillip

2011-01-01

312

Control point adjustment for B-spline curve approximation

Pottmann et al propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards

Huaiping Yang; Wenping Wang; Jia-guang Sun

2004-01-01

313

Scattered Data Interpolation with Multilevel B-Splines

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines areintroduced to compute a C2-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofinehierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desiredinterpolation function. Large performance gains are realized by using B-spline refinement

Seungyong Lee; George Wolberg; Sung Yong Shin

1997-01-01

314

Isotropic polyharmonic B-splines: scaling functions and wavelets

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of ra- dial basis functions. We show that Rabut's elementary polyhar- monic B-splines do not converge to a Gaussian as the order param- eter increases, as opposed to their separable B-spline counterparts. Therefore, we introduce a more

Dimitri Van De Ville; Thierry Blu; Michael Unser

2005-01-01

315

Fast on-line B-spline interpolation

A computationally inexpensive algorithm for signal interpolation using B-spline functionsis presented in this work. Specifically, the convolution between the B-spline coefficientsand the B-spline function itself, widely acknowledged as the most costly aspect of B-splineinterpolation, is reformulated such that it is directly amenable to implementation at a muchlower computational cost (16.25% of the cost of direct evaluation).1 IntroductionInterpolation of a discrete

Saul R. Dooley; Robert W. Stewart; T. S. Durrani

1999-01-01

316

Control point adjustment for B-spline curve approximation

Pottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards

Huaiping Yang; Wenping Wang; Jiaguang Sun

317

B-spline signal processing. II. Efficiency design and applications

For pt.I see ibid., vol.41, no.2, p.821-33 (1993). A class of recursive filtering algorithms for the efficient implementation of B-spline interpolation and approximation techniques is described. In terms of simplicity of realization and reduction of computational complexity, these algorithms compare favorably with conventional matrix approaches. A filtering interpretation (low-pass filter followed by an exact polynomial spline interpolator) of smoothing spline

Michael Unser; Akram Aldroubi; Murray Eden

1993-01-01

318

Isotropic-polyharmonic B-splines and wavelets

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on isotropic-polyharmonic B-splines, a new type of polyharmonic B-splines that converge to a Gaussian as the order increases. We opt for the quincunx subsampling scheme which allows us to characterize the wavelet spaces with a single wavelet, the isotropic-polyharmonic

Dimitri Van De Ville; Thierry Blu; Brigitte Forster; Michael Unser

2004-01-01

319

On the spline-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Jameson, Leland

1993-01-01

320

PARALLEL SMAC ALGORITHMS TO SOLVE SHALLOW WATER EQUATION WITH UNSTRUCTURED COLLOCATED GRID SYSTEM

NASA Astrophysics Data System (ADS)

A computational method to solve shallow water equations has been investigated with an SMAC method which is usually employed in the simulation for incompressible fluids. In particular, this numerical method is implemented in the unstructured collocated grid system with the distributed memory system to increase the parallel efficiency. The developed computational method was applied to the 1D dam-break problem and the free-surface flows in a meandering open channel. As a result of the 1D dam-break simulations, it was confirmed that this method improve the numerical stability. While, in the case of the meandering open channel, it was confirmed that the predicted water depth and depth-averaged velocity distributions are qualitatively in good agreement with the experimental results and that the reasonable parallel efficiencies are attained by parallel computations.

Yamashita, Haruka; Ushijima, Satoru

321

Nonnegative surface fitting with Powell-Sabin splines

NASA Astrophysics Data System (ADS)

Algorithms are presented for fitting a nonnegative Powell-Sabin spline to a set of scattered data. Existing necessary and sufficient nonnegativity conditions for a quadratic polynomial on a triangle are used to compose a set of necessary and sufficient nonnegativity constraints for the PS-spline. The PS-spline is expressed as a linear combination of locally supported basis functions, of which the Bernstein-Bzier representation is considered to improve the efficiency. Numerical examples illustrate the profit of nonnegative surface fitting with Powell-Sabin splines.

Willemans, Karin; Dierckx, Paul

1995-09-01

322

NASA Astrophysics Data System (ADS)

Two numerical techniques are presented for solving the solution of Riccati differential equation. These methods use the cubic B-spline scaling functions and Chebyshev cardinal functions. The methods consist of expanding the required approximate solution as the elements of cubic B-spline scaling function or Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the new techniques. The methods are easy to implement and produce very accurate results.

Lakestani, Mehrdad; Dehghan, Mehdi

2010-05-01

323

A Mixed Basis Density Functional Approach for Low Dimensional Systems with B-splines

A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction. B-splines have the following advantages:(1) the associated matrix elements are sparse, (2) B-splines possess a superior treatment of derivatives, (3) B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With this mixed basis set we can directly calculate the total energy of the system instead of using the conventional supercell model with a slab sandwiched between vacuum regions. A generalized Lanczos-Krylov iterative method is implemented for the diagonalization of the Hamiltonian matrix. To demonstrate the present approach, we apply it to study the C(001)-(2x1) surface with the norm-conserving pseudopotential, the n-type delta-doped graphene, and graphene nanoribbon with Vanderbilt...

Ren, Chung-Yuan; Chang, Yia-Chung

2014-01-01

324

NASA Technical Reports Server (NTRS)

A method based on the use of constrained spline fits is used to overcome the difficulties arising when body-wave data in the form of T-delta are reduced to the tau-p form in the presence of cusps. In comparison with unconstrained spline fits, the method proposed here tends to produce much smoother models which lie approximately in the middle of the bounds produced by the extremal method. The method is noniterative and, therefore, computationally efficient. The method is applied to the lunar seismic data, where at least one triplication is presumed to occur in the P-wave travel-time curve. It is shown, however, that because of an insufficient number of data points for events close to the antipode of the center of the lunar network, the present analysis is not accurate enough to resolve the problem of a possible lunar core.

Jarosch, H. S.

1982-01-01

325

Fast Selection of Spectral Variables with B-Spline Compression

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual infor...

Rossi, Fabrice; Wertz, Vincent; Meurens, Marc; Verleysen, Michel

2007-01-01

326

We propose a multi-element stochastic collocation method that can be applied in high-dimensional parameter space for functions with discontinuities lying along manifolds of general geometries. The key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized. On each of the resulting elements the function is smooth and can be approximated using high-order methods with fast convergence properties. The decomposition strategy is in direct contrast to the traditional multi-element approaches which define the sub-domains by repeated splitting of the axes in the parameter space. Such methods are more prone to the curse-of-dimensionality because of the fast growth of the number of elements caused by the axis based splitting. The present method is a two-step approach. Firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth. The detector uses an efficient combination of the high-order polynomial annihilation technique along with adaptive sparse grids, and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low-dimensional. After partitioning, an adaptive technique based on the least orthogonal interpolant is used to construct a generalized Polynomial Chaos surrogate on each element. The adaptive technique reuses all information from the partitioning and is variance-suppressing. We present numerous numerical examples that illustrate the accuracy, efficiency, and generality of the method. When compared against standard locally-adaptive sparse grid methods, the present method uses many fewer number of collocation samples and is more accurate.

Jakeman, John D., E-mail: jdjakem@sandia.gov [Sandia National Laboratories, Albuquerque, NM 87185 (United States); Narayan, Akil, E-mail: akil.narayan@umassd.edu [Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747 (United States)] [Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747 (United States); Xiu, Dongbin, E-mail: dxiu@purdue.edu [Department of Mathematics, Purdue University, West Lafayette, IN 47907 (United States)] [Department of Mathematics, Purdue University, West Lafayette, IN 47907 (United States)

2013-06-01

327

Cubic B-spline calibration for 3D super-resolution measurements using astigmatic imaging.

In recent years three-dimensional (3D) super-resolution fluorescence imaging by single-molecule localization (localization microscopy) has gained considerable interest because of its simple implementation and high optical resolution. Astigmatic and biplane imaging are experimentally simple methods to engineer a 3D-specific point spread function (PSF), but existing evaluation methods have proven problematic in practical application. Here we introduce the use of cubic B-splines to model the relationship of axial position and PSF width in the above mentioned approaches and compare the performance with existing methods. We show that cubic B-splines are the first method that can combine precision, accuracy and simplicity. PMID:24921733

Proppert, Sven; Wolter, Steve; Holm, Thorge; Klein, Teresa; van de Linde, Sebastian; Sauer, Markus

2014-05-01

328

Collocations and Cultural Connotations of Common Words.

ERIC Educational Resources Information Center

In a response to Halliday (1993), Gee (1994) discussed the analogies between learning a language and learning in general. The article presents two of his proposals and discusses an empirical method for studying them. The article focuses on identifying the units acquired during language learning and the relevance of the concept of an innate

Stubbs, Michael

1995-01-01

329

Rational spectral collocation method for a coupled system of ...

Jun 27, 2011 ... Under Assumptions 2.12.2, v and w defined as (2.1) and (2.2) satisfy v(j) ..... In order to find how the selection of sinh-transform parameter ? affects ..... The support from the National Natural Science Foundation of China.

2011-06-21

330

Fast Safe Spline Surrogates for Large Point Clouds Ashish Myles

a trimmed uni- form tensor-product spline function from one direction. The graph of this spline serves, 3]. -shapes [7] can be used to associate a a smooth skin or accessible surface with a point set [4 and structurally sim- ple functions whose graphs serve as surrogate surfaces with the ability to trade tightness

Peters, Jörg

331

Bivariate B-splines in generalised linear models

The bivariate B-splines are considered for estimating regression surfaces in generalized linear models. They are useful for describing the surface caused by the joint effect of two continuous covariates. For implementation a simple adaptive knot-selection algorithm is introduced. The performance of bivariate B-splines is investigated by numerical studies.

Ja-Yong Koo; Youngjo Lee

1994-01-01

332

DIGITAL IMAGE RESAMPLING BY MODIFIED B-SPLINE FUNCTIONS

We investigate the applicability of modified B-spline functions in digital image resampling tasks. We con- sider a modification that is based on the use of a linear combination of shifted B-splines of different degrees. By optimizing the weighting coefficients, we get interpolat- ing functions with improved frequency responses - flat- ter characteristics in the passband and a higher attenua- tion

Atanas Gotchev; Jussi Vesma; Tapio Saramki; Karen Egiazarian

1964-01-01

333

Planar Spline Trajectory Following for an Autonomous Helicopter

trajectory is specified by a cubic B-spline. This spline format is desirable be- cause it can be easily stabilizes the robot and enforces trajectory fol- lowing, has been implemented and tested on an autonomous been implemented in simulation 9) . Circular trajectory following has also been implemented on real

Sukhatme, Gaurav S.

334

Multiresolution Analysis of UTAT B-spline Curves

NASA Astrophysics Data System (ADS)

In this paper, we describe a multiresolution curve representation based on periodic uniform tension algebraic trigonometric (UTAT) spline wavelets of class ??? and order four. Then we determine the decomposition and the reconstruction vectors corresponding to UTAT-spline spaces. Finally, we give some applications in order to illustrate the efficiency of the proposed approach.

Lamnii, A.; Mraoui, H.; Sbibih, D.; Zidna, A.

2011-09-01

335

Color management with a hammer: the B-spline fitter

NASA Astrophysics Data System (ADS)

To paraphrase Abraham Maslow: If the only tool you have is a hammer, every problem looks like a nail. We have a B-spline fitter customized for 3D color data, and many problems in color management can be solved with this tool. Whereas color devices were once modeled with extensive measurement, look-up tables and trilinear interpolation, recent improvements in hardware have made B-spline models an affordable alternative. Such device characterizations require fewer color measurements than piecewise linear models, and have uses beyond simple interpolation. A B-spline fitter, for example, can act as a filter to remove noise from measurements, leaving a model with guaranteed smoothness. Inversion of the device model can then be carried out consistently and efficiently, as the spline model is well behaved and its derivatives easily computed. Spline-based algorithms also exist for gamut mapping, the composition of maps, and the extrapolation of a gamut. Trilinear interpolation---a degree-one spline---can still be used after nonlinear spline smoothing for high-speed evaluation with robust convergence. Using data from several color devices, this paper examines the use of B-splines as a generic tool for modeling devices and mapping one gamut to another, and concludes with applications to high-dimensional and spectral data.

Bell, Ian E.; Liu, Bonny H. P.

2003-01-01

336

Monotone spline regression for accurate MTF measurement at low frequencies.

The modulation transfer function (MTF) of radiographic systems is frequently evaluated by the system's line spread function (LSF) using narrow slits. The conventional slit method requires LSF tail approximation, which is achieved by exponentially extrapolating the LSF tails beyond 1% of peak value. However, the estimated MTF at low frequencies from extrapolation may not reflect the true performance of the system. In this study, a monotone spline regression technique for LSF tail approximation is developed to improve the accuracy of MTF estimation at low frequencies. This technique is based on the underlying physical principles of the system response. The advantages of this technique are demonstrated with simulated examples of which the true MTFs are known. The application of this measurement technique is also demonstrated. PMID:25321715

Zhou, Zhongxing; Gao, Feng; Zhao, Huijuan; Zhang, Lixin; Ren, Liqiang; Li, Zheng; Ghani, Muhammad U; Liu, Hong

2014-09-22

337

Maxentropic interpolation by cubic splines with possibly noisy data

NASA Astrophysics Data System (ADS)

The gist of this note is to present a procedure for obtaining numerical solutions of Fredholm equations of the first kind of the type ?01K(s,t)x(t)dt+?(s)=y(s), where K:V-->W is a linear operator mapping V=C([0,1]), the continuous functions on [0, 1], into some other Banach space of functions W, and ? is a W-valued random process. The procedure followed consists of partitioning [0, 1] and leaving the values of x(t) at the points of the partitions as unknowns to be found by the method of maximum entropy in the mean. The data vector is also approximated by a finitely dimensional vector, and at the end we obtain an algebraic problem Ax+?=ywhere the matrix A is obtained from the kernel K applied to the cubic spline that approximates x. .

Gzyl, H.; Velasquez, Y.

2001-05-01

338

Image registration using hierarchical B-splines.

Hierarchical B-splines have been widely used for shape modeling since their discovery by Forsey and Bartels. In this paper, we present an application of this concept, in the form of free-form deformation, to image registration by matching two images at increasing levels of detail. Results using MRI brain data are presented that demonstrate high degrees of matching while unnecessary distortions are avoided. We compare our results with the nonlinear ICP (Iterative Closest Point) algorithm (used for landmark-based registration) and optical flow (used for intensity-based registration). PMID:15382700

Xie, Zhiyong; Farin, Gerald E

2004-01-01

339

This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems.

Alwan, Aravind; Aluru, N.R.

2013-12-15

340

NASA Astrophysics Data System (ADS)

This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems.

Alwan, Aravind; Aluru, N. R.

2013-12-01

341

To develop an effective curve-fitting algorithm with a regularization term for measuring the modulation transfer function (MTF) of digital radiographic imaging systems, in comparison with representative prior methods, a C-spline regression technique based upon the monotonicity and convex/concave shape restrictions of the edge spread function (ESF) was proposed for ESF estimation in this study. Two types of oversampling techniques and following four curve-fitting algorithms including the C-spline regression technique were considered for ESF estimation. A simulated edge image with a known MTF was used for accuracy determination of algorithms. Experimental edge images from two digital radiography systems were used for statistical evaluation of each curve-fitting algorithm on MTF measurements uncertainties. The simulation results show that the C-spline regression algorithm obtained a minimum MTF measurement error (an average error of 0.12% 0.11% and 0.18% 0.17% corresponding to two types of oversampling techniques, respectively, up to the cutoff frequency) among all curve-fitting algorithms. In the case of experimental edge images, the C-spline regression algorithm obtained the best uncertainty performance of MTF measurement among four curve-fitting algorithms for both the Pixarray-100 digital specimen radiography system and Hologic full-field digital mammography system. Comparisons among MTF estimates using four curve-fitting algorithms revealed that the proposed C-spline regression technique outperformed other algorithms on MTF measurements accuracy and uncertainty performance. PMID:24658257

Zhou, Zhongxing; Zhu, Qingzhen; Zhao, Huijuan; Zhang, Lixin; Ma, Wenjuan; Gao, Feng

2014-04-01

342

Volume xx (200y), Number z, pp. 110 Anti-aliasing with Stratified B-spline Filters

-aliasing in ray traced images. The method uses stratified sampling to reduce the occurrence of artifacts of Newton-Raphson iterations, to obtain the optimal sample positions in screen space. The proposed method: Anti-aliasing, B-spline filter, ray tracing, stratified sampling Categories and Subject Descriptors

Maddock, Steve

343

Metal flowing of involute spline cold roll-beating forming

NASA Astrophysics Data System (ADS)

The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating, the theory of roller design, and the stress and strain field analysis of cold roll-beating, etc. However, the research on law of metal flow in the forming process of involute spline cold roll-beating is rare. According to the principle of involute spline cold roll-beating, the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established, and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded. A finite element model of the spline cold roll-beating process is established, the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied, and the node flow tracks of the deformation area are analyzed. The experimental research on the metal flow of cold roll-beating spline is conducted, and the metallographic structure variation, grain characteristics and metal flow line of the different tooth profile area are analyzed. The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance. There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming. The characteristics of involute spline cold roll-beating forming are given, and the forming mechanism of involute spline cold roll-beating is revealed. This paper researches the law of metal flow in the forming process of involute spline cold roll-beating, which provides theoretical supports for solving the tooth profile forming quality problem.

Cui, Fengkui; Wang, Xiaoqiang; Zhang, Fengshou; Xu, Hongyu; Quan, Jianhui; Li, Yan

2013-09-01

344

Retrospective Evaluation of a Topology Preserving Non-Rigid Registration Method

proposes a comprehensive evaluation of a monomodal B-spline-based non-rigid registration algorithm allowing methods [Hellier et al., 2003]. The topology preserving B-spline-based method proved to outperform-based registration methods are also highlighted through this work. Key words: non-rigid image registration, B-spline

Genaud, Stéphane

345

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Deville, Michel O.; Mund, Ernest H.

1990-01-01

346

CSC6870 Computer Graphics II B-Spline Curves and NURBS

CSC6870 Computer Graphics II B-Spline Curves and NURBS CSC6870 Computer Graphics II Motivation continuity CSC6870 Computer Graphics II B-spline Curve CSC6870 Computer Graphics II B-Splines · Curve CSC6870 Computer Graphics II B-Splines Basis Functions: Cox- deBoor recursion · The basis function

Hua, Jing

347

Symmetric Box-splines on the A School of Computer Science,

. Introduction Box-splines shifted on the Cartesian lattice are a useful generalization of uniform B-splines aliasing of level sets than the standard C1 tri-quadratic B-spline for the same number of samples on the Cartesian grid. Entezari et al. [16] show that the quality of reconstruction of the C2 tri-cubic B-spline

Peters, Jörg

348

A modal filter approach to non-collocated vibration control of structures

NASA Astrophysics Data System (ADS)

This paper employs modal filters for simultaneous and independent control of multiple vibration modes of a flexible structure embedded with a non-collocated pair of sensor and actuator. Each modal filter of second order is designed to be sensitive to the target mode for control while insensitive to the others. Based on the fact that there are only in- and out-of-phase modes in lightly and proportionally damped finite structures, those in-phase modes are controlled in the same way as that for collocated control using negative feedback, while those out-of-phase modes are controlled exactly in the opposite way using positive feedback. These two are equivalent as far as single mode control is concerned and are electrical realizations of a mechanical dynamic vibration absorber. Feedback control experiments were conducted on a cantilever beam embedded with a piezoelectric actuator at the root and an accelerometer at the end tip. The results reveal a number of peculiar advantages of using non-collocated control over collocated control. Non-collocated plants generally exhibit better high-frequency roll-off characteristics because there are weaker mechanical and electrical feedthrough couplings between non-collocated transducers. Furthermore, the high frequency control spillover can be greatly eliminated by appropriately adjusting the gains of modal filters. It is thus often possible to make the performance and robustness of non-collocated control as well as or even better than those using collocated control.

Kim, Sang-Myeong; Oh, Jae-Eung

2013-04-01

349

English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information

ERIC Educational Resources Information Center

We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic

Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji

2012-01-01

350

STABILIZATION OF A CLAMPED-FREE BEAM WITH COLLOCATED PIEZOELECTRIC SENSOR/ACTUATOR

STABILIZATION OF A CLAMPED-FREE BEAM WITH COLLOCATED PIEZOELECTRIC SENSOR/ACTUATOR Pierre Le Gall at the other, and to which are attached a piezoelectric actuator and a collocated sensor. We provide an output feedback law and characterize the sensor/actuator location for which the strong stabilization holds

Rosier, Lionel - Institut de Mathématiques ?lie Cartan, Université Henri Poincaré

351

ShadowPuppets: supporting collocated interaction with mobile projector phones using hand shadows

Pico projectors attached to mobile phones allow users to view phone content using a large display. However, to provide input to projector phones, users have to look at the device, diverting their attention from the projected image. Additionally, other collocated users have no way of interacting with the device. We present ShadowPuppets, a system that supports collocated interaction with mobile

Lisa G. Cowan; Kevin A. Li

2011-01-01

352

Real-time image rotation using B-spline interpolation on FPGA's board

The aim of our work is to realize the implementation of a real-time high-quality image rotation on FPGA's board. The method we used is based on M. Unser's work and consists in applying a B-spline interpolator. The difficulty of this problem is due to the relatively weak integration capacity of FPGAs. To solve this problem we have searched for determining

Cyril Berthaud; El-Bay Bourennane; Michel Paindavoine; Claude Milan

1998-01-01

353

Robot Skill Transfer Based on B-Spline Fuzzy Controllers for Force-Control Tasks

Human-beings can easily describe their behaviour by IF-THEN rules, which can be transferred from one task to another with slight local changes. However, standard tech- niques for function approximation like neuronal networks or associative memories are unable to work with rules. We introduce a method for extracting and importing human readable rules from and to a B-spline fuzzy controller. Rule

Markus Ferch; Jianwei Zhang; Alois Knoll

1999-01-01

354

Implementation of a Real Time Image Rotation using B-Spline Interpolation on FPGA's Board

The aim of our work is to realize the implementation of a real-time high-quality image rotation on FPGA's board. The method we used is based on M. Unser's work (1993) and consists in applying a B-spline interpolator. The difficulty of this problem is due to the relatively weak integration capacity of FPGAs. To solve this problem, we have searched for

Cyril Berthaud; El-bay Bourennane; Michel Paindavoine; Claude Milan

1998-01-01

355

Non-rigid Groupwise Registration using B-Spline Deformation Model

In this work, we extend a previously demonstrated entropy based groupwise registration method to in- clude a non-rigid deformation model based on B-splines. We describe an open source implementation of the groupwise registration algorithm using the Insight Toolkit ITK www.itk.org. We provide the source code, parameters, input and output data that we used for validation. We describe an efficient implementation

Serdar K. Balci; Polina Golland; William M. Wells

356

ERIC Educational Resources Information Center

Previous work in the literature reveals that EFL learners were deficient in collocations that are a hallmark of near native fluency in learner's writing. Among different types of collocations, the verb-noun (V-N) one was found to be particularly difficult to master, and learners' first language was also found to heavily influence their collocation

Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin

2008-01-01

357

Isotropic polyharmonic B-splines: scaling functions and wavelets.

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-splines do not converge to a Gaussian as the order parameter increases, as opposed to their separable B-spline counterparts. Therefore, we introduce a more isotropic localization operator that guarantees this convergence, resulting into the isotropic polyharmonic B-splines. Next, we focus on the two-dimensional quincunx subsampling scheme. This configuration is of particular interest for image processing because it yields a finer scale progression than the standard dyadic approach. However, up until now, the design of appropriate filters for the quincunx scheme has mainly been done using the McClellan transform. In our approach, we start from the scaling functions, which are the polyharmonic B-splines and, as such, explicitly known, and we derive a family of polyharmonic spline wavelets corresponding to different flavors of the semi-orthogonal wavelet transform; e.g., orthonormal, B-spline, and dual. The filters are automatically specified by the scaling relations satisfied by these functions. We prove that the isotropic polyharmonic B-spline wavelet converges to a combination of four Gabor atoms, which are well separated in the frequency domain. We also show that these wavelets are nearly isotropic and that they behave as an iterated Laplacian operator at low frequencies. We describe an efficient fast Fourier transform-based implementation of the discrete wavelet transform based on polyharmonic B-splines. PMID:16279181

Van De Ville, Dimitri; Blu, Thierry; Unser, Michael

2005-11-01

358

Modified B-spline interpolators and filters: synthesis and efficient implementation

Interpolation techniques are widely used in many applications of signal processing. This paper is devoted to synthesizing and efficiently implementing a class of generalized spline-interpolators. A new parametric class of generalized B-splines is introduced. It contains as special cases B-splines and alternative B-splines. In the most general case, the proposed spline functions can be represented as a linear combination of

Karen Egiazarian; Tapio Saramaki; Hegine Chugurian; J. Astola

1996-01-01

359

Multimodal image registration by edge attraction and regularization using a B-spline grid

NASA Astrophysics Data System (ADS)

Multi modal image registration enables images from different modalities to be analyzed in the same coordinate system. The class of B-spline-based methods that maximize the Mutual Information between images produce satisfactory result in general, but are often complex and can converge slowly. The popular Demons algorithm, while being fast and easy to implement, produces unrealistic deformation fields and is sensitive to illumination differences between the two images, which makes it unsuitable for multi-modal registration in its original form. We propose a registration algorithm that combines a B-spline grid with deformations driven by image forces. The algorithm is easy to implement and is robust against large differences in the appearance between the images to register. The deformation is driven by attraction-forces between the edges in both images, and a B-spline grid is used to regularize the sparse deformation field. The grid is updated using an original approach by weighting the deformation forces for each pixel individually with the edge strengths. This approach makes the algorithm perform well even if not all corresponding edges are present. We report preliminary results by applying the proposed algorithm to a set of (multi-modal) test images. The results show that the proposed method performs well, but is less accurate than state of the art registration methods based on Mutual Information. In addition, the algorithm is used to register test images to manually drawn line images in order to demonstrate the algorithm's robustness.

Klein, Almar; Kroon, Dirk-Jan; Hoogeveen, Yvonne; Schultze Kool, Leo J.; Renema, W. Klaas Jan; Slump, Cornelis H.

2011-03-01

360

The algorithms for rational spline interpolation of surfaces

NASA Technical Reports Server (NTRS)

Two algorithms for interpolating surfaces with spline functions containing tension parameters are discussed. Both algorithms are based on the tensor products of univariate rational spline functions. The simpler algorithm uses a single tension parameter for the entire surface. This algorithm is generalized to use separate tension parameters for each rectangular subregion. The new algorithm allows for local control of tension on the interpolating surface. Both algorithms are illustrated and the results are compared with the results of bicubic spline and bilinear interpolation of terrain elevation data.

Schiess, J. R.

1986-01-01

361

The spline probability hypothesis density filter

NASA Astrophysics Data System (ADS)

The Probability Hypothesis Density Filter (PHD) is a multitarget tracker for recursively estimating the number of targets and their state vectors from a set of observations. The PHD filter is capable of working well in scenarios with false alarms and missed detections. Two distinct PHD filter implementations are available in the literature: the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters. The SMC-PHD filter uses particles to provide target state estimates, which can lead to a high computational load, whereas the GM-PHD filter does not use particles, but restricts to linear Gaussian mixture models. The SMC-PHD filter technique provides only weighted samples at discrete points in the state space instead of a continuous estimate of the probability density function of the system state and thus suffers from the well-known degeneracy problem. This paper proposes a B-Spline based Probability Hypothesis Density (S-PHD) filter, which has the capability to model any arbitrary probability density function. The resulting algorithm can handle linear, non-linear, Gaussian, and non-Gaussian models and the S-PHD filter can also provide continuous estimates of the probability density function of the system state. In addition, by moving the knots dynamically, the S-PHD filter ensures that the splines cover only the region where the probability of the system state is significant, hence the high efficiency of the S-PHD filter is maintained at all times. Also, unlike the SMC-PHD filter, the S-PHD filter is immune to the degeneracy problem due to its continuous nature. The S-PHD filter derivations and simulations are provided in this paper.

Sithiravel, Rajiv; Tharmarasa, Ratnasingham; McDonald, Mike; Pelletier, Michel; Kirubarajan, Thiagalingam

2012-06-01

362

On developing B-spline registration algorithms for multi-core processors.

Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields. PMID:20938071

Shackleford, J A; Kandasamy, N; Sharp, G C

2010-11-01

363

On developing B-spline registration algorithms for multi-core processors

NASA Astrophysics Data System (ADS)

Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields.

Shackleford, J. A.; Kandasamy, N.; Sharp, G. C.

2010-11-01

364

Noise correction on LANDSAT images using a spline-like algorithm

NASA Technical Reports Server (NTRS)

Many applications using LANDSAT images face a dilemma: the user needs a certain scene (for example, a flooded region), but that particular image may present interference or noise in form of horizontal stripes. During automatic analysis, this interference or noise may cause false readings of the region of interest. In order to minimize this interference or noise, many solutions are used, for instane, that of using the average (simple or weighted) values of the neighboring vertical points. In the case of high interference (more than one adjacent line lost) the method of averages may not suit the desired purpose. The solution proposed is to use a spline-like algorithm (weighted splines). This type of interpolation is simple to be computer implemented, fast, uses only four points in each interval, and eliminates the necessity of solving a linear equation system. In the normal mode of operation, the first and second derivatives of the solution function are continuous and determined by data points, as in cubic splines. It is possible, however, to impose the values of the first derivatives, in order to account for shapr boundaries, without increasing the computational effort. Some examples using the proposed method are also shown.

Vijaykumar, N. L. (principal investigator); Dias, L. A. V.

1985-01-01

365

Toward the true near-surface wind speed: Error modeling and calibration using triple collocation

NASA Astrophysics Data System (ADS)

Wind is a very important geophysical variable to accurately measure. However, a statistical phenomenon important for the validation or calibration of winds is the small dynamic range relative to the typical measurement uncertainty, i.e., the generally small signal-to-noise ratio. In such cases, pseudobiases may occur when standard validation or calibration methods are applied, such as regression or bin-average analyses. Moreover, nonlinear transformation of random error, for instance, between wind components and speed and direction, may give rise to substantial pseudobiases. In fact, validation or calibration can only be done properly when the full error characteristics of the data are known. In practice, the problem is that prior knowledge on the error characteristics is seldom available. In this paper we show that simultaneous error modeling and calibration can be achieved by using triple collocations. This is a fundamental finding that is generally relevant to all geophysical validation. To illustrate the statistical analysis using triple collocations, in situ, ERS scatterometer, and forecast model winds are used. Wind component error analysis is shown to be more convenient than wind speed and direction error analysis. The anemometer winds from the National Oceanic and Atmospheric Administration (NOAA) buoys are shown to have the largest error variance, followed by the scatterometer and the National Centers for Environmental Prediction (NCEP) forecast model winds proved the most accurate. When using the in situ winds as a reference, the scatterometer wind components are biased low by -4%. The NCEP forecast model winds are found to be biased high by -6%, After applying a higher-order calibration procedure an improved ERS scatterometer wind retrieval is proposed. The systematic and random error analysis is relevant for the use of nearsurface winds to compute fluxes of momentum, humidity, or heat or to drive ocean wave or circulation models.

Stoffelen, Ad

1998-04-01

366

Construction of spline functions in spreadsheets to smooth experimental data

Technology Transfer Automated Retrieval System (TEKTRAN)

A previous manuscript detailed how spreadsheet software can be programmed to smooth experimental data via cubic splines. This addendum corrects a few errors in the previous manuscript and provides additional necessary programming steps. ...

367

The effects of spline interpolation on power spectral density

NASA Technical Reports Server (NTRS)

This paper discusses the power spectral effects of spline interpolators. A general technique is given for finding the steady-state spectral effects of splines of all orders, when applied following uniform sampling of the input function. The following observations are made: (1) the even order splines that were examined (second and fourth order) possessed divergent steady-state frequency transfer functions, (2) the degree of preservation of the power spectral density of the input process increased with the order of the (odd order) spline used for interpolation, and (3) the reconstruction of a stationary random process over a finite record length will, on the average, have less power than indicated by the steady-state transfer function.

Horowitz, L. L.

1974-01-01

368

Modeling terminal ballistics using blending-type spline surfaces

NASA Astrophysics Data System (ADS)

We explore using GERBS, a blending-type spline construction, to represent deform able thin-plates and model terminal ballistics. Strategies to construct geometry for different scenarios of terminal ballistics are proposed.

Pedersen, Aleksander; Bratlie, Jostein; Dalmo, Rune

2014-12-01

369

Simple Algorithms and Architectures for B-spline Interpolation

It is proved that the Toeplitz binary value matrix inversion associated with mth-order B-spline interpolation can be implemented using only 2(m+1) additions. Pipelined architectures are developed for real-time B-spline interpolation based on simple running average filters. It is shown that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can be implemented using

P. V. Sankar; Leonard A. Ferrari

1988-01-01

370

Scale-Space Derived From B-Splines

It is well-known that the linear scale-space theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scale-space theory based on B-spline kernels. Our aim is twofold. On one hand, we present a general framework and show how B-splines provide a flexible tool to design various scale-space representations: continuous scale-

Yu-ping Wang; Seng Luan Lee

1998-01-01

371

Beta-function B-spline smoothing on triangulations

NASA Astrophysics Data System (ADS)

In this work we investigate a novel family of Ck-smooth rational basis functions on triangulations for fitting, smoothing, and denoising geometric data. The introduced basis function is closely related to a recently introduced general method introduced in utilizing generalized expo-rational B-splines, which provides Ck-smooth convex resolutions of unity on very general disjoint partitions and overlapping covers of multidimensional domains with complex geometry. One of the major advantages of this new triangular construction is its locality with respect to the star-1 neighborhood of the vertex on which the said base is providing Hermite interpolation. This locality of the basis functions can be in turn utilized in adaptive methods, where, for instance a local refinement of the underlying triangular mesh affects only the refined domain, whereas, in other method one needs to investigate what changes are occurring outside of the refined domain. Both the triangular and the general smooth constructions have the potential to become a new versatile tool of Computer Aided Geometric Design (CAGD), Finite and Boundary Element Analysis (FEA/BEA) and Iso-geometric Analysis (IGA).

Dechevsky, Lubomir T.; Zanaty, Peter

2013-03-01

372

Algebraic grid generation using tensor product B-splines. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.

Saunders, B. V.

1985-01-01

373

User's guide for Wilson-Fowler spline software: SPLPKG, WFCMPR, WFAPPX - CADCAM-010

The Wilson-Fowler spline is widely used in computer aided manufacturing, but is not available in all commercial CAD/CAM systems. These three programs provide a capability for generating, comparing, and approximating Wilson-Fowler splines. SPLPKG generates a spline passing through given nodes, and computes a piecewise linear approximation to the spline. WFCMPR computes the difference between two splines with common nodes. WFAPPX computes the difference between a spline and a piecewise linear curve. The programs are in Fortran 77 and are machine independent.

Fletcher, S.K.

1985-02-01

374

Fast parallel MRI reconstruction using B-spline approximation (PROBER)

NASA Astrophysics Data System (ADS)

Parallel MRI (pMRI) is a way to increase the speed of the MRI acquisition by combining data obtained simultaneously from several receiver coils with distinct spatial sensitivities. The measured data contains additional information about the position of the signal with respect to data obtained by a standard, uniform sensitivity coil. The idea is to speed up the acquisition by sampling more sparsely in the k-space and to compensate the data loss using the additional information obtained by a higher number of receiver coils. Most parallel reconstruction methods work in image domain and estimate the reconstruction transformation independently in each pixel. We propose an algorithm that uses B-spline functions to approximate the reconstruction map which reduces the number of parameters to estimate and makes the reconstruction faster and less sensitive to noise. The proposed method is tested on both phantom and in vivo images. The results are compared with commercial implementation of GRAPPA and SENSE algorithms in terms of time complexity and quality of the reconstruction.

Petr, Jan; Kybic, Jan; Hlav?, Vclav; Mller, Sven; Bock, Michael

2006-03-01

375

Smoothing spline ANOVA frailty model for recurrent event data.

Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data. PMID:21457192

Du, Pang; Jiang, Yihua; Wang, Yuedong

2011-12-01

376

NASA Technical Reports Server (NTRS)

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Rummel, R.; Sjoeberg, L.; Rapp, R. H.

1978-01-01

377

words: sensitivity analysis, singular boundary integral equations, hypersingular integrals, boundaryTangential derivative of singular boundary integrals with respect to the position of collocation perturbations of the singular point, of boundary integrals having either weak or strong singularity. Both scalar

Paris-Sud XI, Université de

378

The effects of multimedia communication technology on non-collocate d teams: a case study

Collaborative teams are becoming increasing important for industry, both within and across companies. There is a need for communication technology to support teams because many teams are non-collocated, or \\

Jean Carletta; Anne H. Anderson; Rachel McEwan

379

Stable Local Volatility Calibration Using Kernel Splines

NASA Astrophysics Data System (ADS)

We propose an optimization formulation using L1 norm to ensure accuracy and stability in calibrating a local volatility function for option pricing. Using a regularization parameter, the proposed objective function balances the calibration accuracy with the model complexity. Motivated by the support vector machine learning, the unknown local volatility function is represented by a kernel function generating splines and the model complexity is controlled by minimizing the 1-norm of the kernel coefficient vector. In the context of the support vector regression for function estimation based on a finite set of observations, this corresponds to minimizing the number of support vectors for predictability. We illustrate the ability of the proposed approach to reconstruct the local volatility function in a synthetic market. In addition, based on S&P 500 market index option data, we demonstrate that the calibrated local volatility surface is simple and resembles the observed implied volatility surface in shape. Stability is illustrated by calibrating local volatility functions using market option data from different dates.

Coleman, Thomas F.; Li, Yuying; Wang, Cheng

2010-09-01

380

Growth curve analysis for plasma profiles using smoothing splines

We are developing a profile analysis code for the statistical estimation of the parametric dependencies of the temperature and density profiles in tokamaks. Our code uses advanced statistical techniques to determine the optimal fit, i.e. the fit which minimized the predictive error. For a forty TFTR Ohmic profile dataset, our preliminary results indicate that the profile shape depends almost exclusively on q[sub a][prime] but that the shape dependencies are not Gaussian. We are now comparing various shape models on the TFTR data. In the first six months, we have completed the core modules of the code, including a B-spline package for variable knot locations, a data-based method to determine the optimal smoothing parameters, self-consistent estimation of the bias errors, and adaptive fitting near the plasma edge. Visualization graphics already include three dimensional surface plots, and discharge by discharge plots of the predicted curves with error bars together with the actual measurements values, and plots of the basis functions with errors.

Imre, K.

1993-05-01

381

Spline-based models for predictiveness curves and surfaces

A biomarker is defined to be a biological characteristic that is objectively measured and evaluated as an indicator of normal biologic processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention. The use of biomarkers in cancer has been advocated for a variety of purposes, which include use as surrogate endpoints, early detection of disease, proxies for environmental exposure and risk prediction. We deal with the latter issue in this paper. Several authors have proposed use of the predictiveness curve for assessing the capacity of a biomarker for risk prediction. For most situations, it is reasonable to assume monotonicity of the biomarker effects on disease risk. In this article, we propose the use of flexible modelling of the predictiveness curve and its bivariate analogue, the predictiveness surface, through the use of spline algorithms that incorporate the appropriate monotonicity constraints. Estimation proceeds through use of a two-step algorithm that represents the smooth, then monotonize approach. Subsampling procedures are used for inference. The methods are illustrated to data from a melanoma study. PMID:22003414

Ghosh, Debashis; Sabel, Michael

2010-01-01

382

Free-Form B-spline Deformation Model for Groupwise Registration.

In this work, we extend a previously demonstrated entropy based groupwise registration method to include a free-form deformation model based on B-splines. We provide an efficient implementation using stochastic gradient descents in a multi-resolution setting. We demonstrate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation labels to evaluate the quality of alignment. Our results indicate that increasing the complexity of the deformation model improves registration accuracy significantly, especially at cortical regions. PMID:20224762

Balci, Serdar K; Golland, Polina; Shenton, Martha; Wells, William M

2007-01-01

383

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

1990-01-01

384

Fast B-spline Transforms for Continuous Image Representation and Interpolation

Efficient algorithms for the continuous representation of a discrete signal in terms of B-splines (direct B-spline transform) and for interpolative signal reconstruction (indirect B-spline transform) with an expansion factor m are described. Expressions for the z-transforms of the sampled B-spline functions are determined and a convolution property of these kernels is established. It is shown that both the direct and

Michael Unser; Akram Aldroubi; Murray Eden

1991-01-01

385

Solar absorption over Europe from collocated surface and satellite observations

NASA Astrophysics Data System (ADS)

Solar radiation is the primary source of energy for the Earth's climate system. Although the incoming and outgoing solar fluxes at the top of atmosphere can be quantified with high accuracy, large uncertainties still exist in the partitioning of solar absorption between surface and atmosphere. To compute best estimates of absorbed solar radiation at the surface and within the atmosphere representative for Europe during 2000-2010, we combine temporally homogeneous and spatially representative ground-based observations of surface downwelling solar radiation with collocated satellite-retrieved surface albedo and top-of-atmosphere net irradiance. We find best estimates of Europe land annual mean surface and atmospheric absorption of 117.3 6 W m-2 (41.6 2% of top-of-atmosphere incident irradiance) and 65.0 3 W m-2 (23.0 1%). The fractional atmospheric absorption of 23% represents a robust estimate largely unaffected by variations in latitude and season, thus, making it a potentially useful quantity for first-order validation of regional climate models. Uncertainties of the individual absorption estimates arise mostly from the measurements themselves. In this context, the surface albedo and the ground-based solar radiation data are the most critical variables. Other sources of uncertainty, like the multiplicative combination of spatially averaged surface solar radiation and surface albedo estimates, and the spatial representativeness of the point observations, are either negligibly small or can be corrected for.

Hakuba, M. Z.; Folini, D.; Schaepman-Strub, G.; Wild, M.

2014-03-01

386

Ecient Evaluation of Triangular B-splines Michael Franssen z Remco C. Veltkamp Wieger Wesselink z

E?cient Evaluation of Triangular B-splines Michael Franssen z Remco C. Veltkamp #3; Wieger are essential for any application that uses triangular B-splines. This paper describes an algorithm to e?ciently evaluate triangular B-splines. The novelty of the algorithm is its generality: there is no restriction

Utrecht, Universiteit

387

B-Spline Neural Network Based Single-Carrier Frequency Domain Equalisation for Hammerstein Channels

B-Spline Neural Network Based Single-Carrier Frequency Domain Equalisation for Hammerstein Channels, the standard SC-FDE scheme no longer works. We propose a novel B- spline neural network based nonlinear SC-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one

388

Anti-aliasing with Stratified B-spline Filters of Arbitrary Order

Anti-aliasing with Stratified B-spline Filters of Arbitrary Order MANUEL N. GAMITO and STEVE C to reduce the occurrence of artifacts in the image and features a B-spline filter, of some desired order of the filter order. A B-spline filter of order one amounts to a simple anti-aliasing scheme with box filtering

Maddock, Steve

389

Comparison of Lifting and B-spline DWT Implementations for Implantable Neuroprosthetics.

Comparison of Lifting and B-spline DWT Implementations for Implantable Neuroprosthetics. Awais M, this paper identifies and compares optimal implementations of the lifting and B- spline architectures where of the lifting and B-spline DWT schemes for multi-level, multi-channel DWT and analyzes their performance

Mason, Andrew

390

B-spline active rays segmentation of microcalcifications in mammography

Accurate segmentation of microcalcifications in mammography is crucial for the quantification of morphologic properties by features incorporated in computer-aided diagnosis schemes. A novel segmentation method is proposed implementing active rays (polar-transformed active contours) on B-spline wavelet representation to identify microcalcification contour point estimates in a coarse-to-fine strategy at two levels of analysis. An iterative region growing method is used to delineate the final microcalcification contour curve, with pixel aggregation constrained by the microcalcification contour point estimates. A radial gradient-based method was also implemented for comparative purposes. The methods were tested on a dataset consisting of 149 mainly pleomorphic microcalcification clusters originating from 130 mammograms of the DDSM database. Segmentation accuracy of both methods was evaluated by three radiologists, based on a five-point rating scale. The radiologists' average accuracy ratings were 3.96{+-}0.77, 3.97{+-}0.80, and 3.83{+-}0.89 for the proposed method, and 2.91{+-}0.86, 2.10{+-}0.94, and 2.56{+-}0.76 for the radial gradient-based method, respectively, while the differences in accuracy ratings between the two segmentation methods were statistically significant (Wilcoxon signed-ranks test, p<0.05). The effect of the two segmentation methods in the classification of benign from malignant microcalcification clusters was also investigated. A least square minimum distance classifier was employed based on cluster features reflecting three morphological properties of individual microcalcifications (area, length, and relative contrast). Classification performance was evaluated by means of the area under ROC curve (A{sub z}). The area and length morphologic features demonstrated a statistically significant (Mann-Whitney U-test, p<0.05) higher patient-based classification performance when extracted from microcalcifications segmented by the proposed method (0.82{+-}0.06 and 0.86{+-}0.05, respectively), as compared to segmentation by the radial gradient-based method (0.71{+-}0.08 and 0.75{+-}0.08). The proposed method demonstrates improved segmentation accuracy, fulfilling human visual criteria, and enhances the ability of morphologic features to characterize microcalcification clusters.

Arikidis, Nikolaos S.; Skiadopoulos, Spyros; Karahaliou, Anna; Likaki, Eleni; Panayiotakis, George; Costaridou, Lena [Department of Medical Physics, School of Medicine, University of Patras, 265 00 Patras (Greece); Department of Radiology, School of Medicine, University of Patras, 265 00 Patras (Greece); Department of Medical Physics, School of Medicine, University of Patras, 265 00 Patras (Greece)

2008-11-15

391

A high-order conservative collocation scheme and its application to global shallow water equations

NASA Astrophysics Data System (ADS)

An efficient and conservative collocation method is proposed and used to develop a global shallow water model in this paper. Being a nodal type high-order scheme, the present method solves the point-wise values of dependent variables as the unknowns within each control volume. The solution points are arranged as Gauss-Legendre points to achieve the high-order accuracy. The time evolution equations to update the unknowns are derived under the flux-reconstruction (FR) framework (Huynh, 2007). Constraint conditions used to build the spatial reconstruction for the flux function include the point-wise values of flux function at the solution points, which are computed directly from the dependent variables, as well as the numerical fluxes at the boundaries of the control volume which are obtained as the Riemann solutions between the adjacent cells. Given the reconstructed flux function, the time tendencies of the unknowns can be obtained directly from the governing equations of differential form. The resulting schemes have super convergence and rigorous numerical conservativeness. A three-point scheme of fifth-order accuracy is presented and analyzed in this paper. The proposed scheme is adopted to develop the global shallow-water model on the cubed-sphere grid where the local high-order reconstruction is very beneficial for the data communications between adjacent patches. We have used the standard benchmark tests to verify the numerical model, which reveals its great potential as a candidate formulation for developing high-performance general circulation models.

Chen, C.; Li, X.; Shen, X.; Xiao, F.

2014-07-01

392

Parallel iterative solution of the Hermite Collocation equations on GPUs II

NASA Astrophysics Data System (ADS)

Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation.

Vilanakis, N.; Mathioudakis, E.

2014-03-01

393

Normal type-2 fuzzy interpolating B-spline curve

NASA Astrophysics Data System (ADS)

This paper discusses about the construction of a normal type-2 fuzzy interpolating B-spline curves. The construction of this model is based on type-2 fuzzy sets theory. This theory defines complex uncertainty data sets which form the type-2 fuzzy control and data points. In addition, the definition of normal type-2 fuzzy control and data points are also explained in this paper. The processes such as the fuzzification, reduction and defuzzification of interpolating B-spline curves and surfaces are explained. The final section illustrates a numerical example on the practicalities of the proposed model.

Zakaria, Rozaimi; Wahab, Abd Fatah; Gobithaasan, R. U.

2014-07-01

394

Comparison of various drag coefficient expansions using polynomials and splines

NASA Technical Reports Server (NTRS)

The longitudinal differential equation of motion has been used to investigate various aerodynamic expansion techniques. The total drag coefficient was expanded using conventional polynomials and splines with and without floating knot locations. This paper discusses the various techniques and approaches, compares results obtained from simultaneously fitting four separate flights (time vs distance measurements) and outlines the potential advantages and/or disadvantages of the various aerodynamic expansion techniques. It is believed that this is the first time splines have been used in the aerodynamic coefficient estimation process and that these results and techniques are germane to other applications.

Sabot, S. M.; Winchenbach, G. L.; Chapman, G. T.

1984-01-01

395

How to fly an aircraft with control theory and splines

NASA Technical Reports Server (NTRS)

When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations.

Karlsson, Anders

1994-01-01

396

Yarowsky, David. ``One Sense Per Collocation.'' In Proceedings, ARPA Human Language Technology Linguistics; revised version published in Computational Linguistics, 16(1), 1990. Reprinted in T. Fontenelle

Palmer, Martha

397

Application of the convergence of the control net of box splines to scale-space filtering.

In this correspondence, we propose a new approach to scale-space filtering using a box spline representation of multidimensional signals. The use of box splines is motivated by their ability to handle complex geometries better than tensor-product B-splines. The box spline we use is defined by a set of vectors invariant under the multiplication by a sampling matrix. We show that such a box spline satisfies a dilation equation which is the basis for the scale-space filtering we propose. Several numerical applications in 2-D conclude the correspondence. PMID:17990760

Meignen, Sylvain

2007-11-01

398

and shares the continuity and approximation order of the triquadratic B-spline. We observe less aliasing by the lower degree and smaller stencil-size of the C1 6-direction box spline over the triquadratic B-spline it to the triquadratic B-spline reconstruction of the Cartesian data. This is a fair · CISE Department, University

Peters, Jörg

399

Data assimilation using Bayesian filters and B-spline geological models

NASA Astrophysics Data System (ADS)

This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir.

Duan, Lian; Farmer, Chris; Hoteit, Ibrahim; Luo, Xiaodong; Moroz, Irene

2011-04-01

400

The machining process is very important in many engineering applications. In high precision machining, surface finish is strongly correlated with vibrations and the dynamic interactions between the part and the cutting tool. Parameters affecting these vibrations and dynamic interactions, such as spindle speed, cut depth, feed rate, and the part's material properties can vary in real-time, resulting in unexpected or undesirable effects on the surface finish of the machining product. The focus of this research is the development of an improved machining process through the use of active vibration damping. The tool holder employs a high bandwidth piezoelectric actuator with an adaptive positive position feedback control algorithm for vibration and chatter suppression. In addition, instead of using external sensors, the proposed approach investigates the use of a collocated piezoelectric sensor for measuring the dynamic responses from machining processes. The performance of this method is evaluated by comparing the surface finishes obtained with active vibration control versus baseline uncontrolled cuts. Considerable improvement in surface finish (up to 50%) was observed for applications in modern day machining.

Radecki, Peter P [Los Alamos National Laboratory; Farinholt, Kevin M [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory; Bement, Matthew T [Los Alamos National Laboratory

2008-01-01

401

Fair and Robust Circle Splines Carlo H. Squin*

Fair and Robust Circle Splines Carlo H. Séquin* CS Division, U.C. Berkeley Kiha Lee ME Department above, and several such schemes have been published, e.g. [Szilvasi-Nagy and Vendel 2000]. But even these end conditions at points Pi, Pi+1 and that it is well-behaved in between, i.e., has no cusps

O'Brien, James F.

402

Radial Splines Would Prevent Rotation Of Bearing Race

NASA Technical Reports Server (NTRS)

Interlocking fine-pitch ribs and grooves formed on otherwise flat mating end faces of housing and outer race of rolling-element bearing to be mounted in housing, according to proposal. Splines bear large torque loads and impose minimal distortion on raceway.

Kaplan, Ronald M.; Chokshi, Jaisukhlal V.

1993-01-01

403

Image interpolation using adaptive fast B-spline filtering

An adaptive version of a B-spline interpolation algorithm is proposed. Adaptivity is used in two different phases: (1) adaptive zero order interpolation is realized by considering directional edge information, and (2) adaptive length of the moving average filter in four directions is obtained by computing the local image statistics. The proposed algorithm exhibits significant improvements in image quality compared with

Seong Won Lee; Joon Ki Paik

1993-01-01

404

Adaptive parametrization of multivariate B-splines for image registration

We present an adaptive parametrization scheme for dynamic mesh refinement in the application of parametric image registration. The scheme is based on a refinement measure ensuring that the control points give an efficient representation of the warp fields, in terms of minimizing the registration cost function. In the current work we introduce multivariate B-splines as a novel alternative to the

Michael Sass Hansen; Rasmus Larsen; Ben Glocker; Nassir Navab

2008-01-01

405

Modeling with multivariate B-spline surfaces over arbitrary triangulations

This paper describes the first results of a test implementation of the new multivariate B-splines as recently developed for quadratics and cubics. The surface scheme is based on blending functions and control points and allows us to model Ck-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations of the parameter plane. The surface scheme exhibits both affine invariance and

Philip Fong; Hans-Peter Seidel

1992-01-01

406

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization.

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization. Houman) minimizing the L2 norm of the source terms; its (pre-)computation involves minimizing O(H-d ) quadratic (cell) problems on (super-)localized sub-domains of size O(H ln(1/H)). The result- ing localized linear systems

Berlyand, Leonid

407

Odds Ratio Estimation in Bernoulli Smoothing Spline ANOVA Models

Odds Ratio Estimation in Bernoulli Smoothing Spline ANOVA Models Yuedong Wang \\Lambda Department the odds ratios based on a SS ANOVA model for binary data and construct Bayesian confidence in tervals. We intervals. Our simulations suggest that the odds ratio estimates are quite reasonable in general but may

Wang, Yuedong

408

Some Algorithms for Linear Spline and Piecewise Multiple Linear Regression

This paper develops some efficient algorithms for linear spline and piecewise multiple linear regression. A plotting procedure that shows the existence and location of changes in linear regression models is developed as an adjunct to one of the algorithms. The algorithms are compared with other presently available algorithms both in terms of efficiency and in terms of performance on sets

James E. Ertel; Edward B. Fowlkes

1976-01-01

409

Inference in generalized additive mixed models by using smoothing splines

Summary. Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and

Xihong Lin

1999-01-01

410

Cubic spline approximation techniques for parameter estimation in distributed systems

NASA Technical Reports Server (NTRS)

Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.

Banks, H. T.; Crowley, J. M.; Kunisch, K.

1983-01-01

411

High order interpolation and differentiation using B-splines

We present a methodology of high order accuracy that constructs in a systematic way functions which can be used for the accurate interpolation and differentiation of scattered data. The functions are based on linear combination of polynomials (herein B-splines are used). The technique is applied to one-dimensional datasets but can be extended as needed for multidimensional interpolation and differentiation. The

A. K. Chaniotis; D. Poulikakos

2004-01-01

412

NASA Astrophysics Data System (ADS)

We show the numerical applicability of a multiresolution method based on harmonic splines on the 3-D ball which allows the regularized recovery of the harmonic part of the Earth's mass density distribution out of different types of gravity data, for example, different radial derivatives of the potential, at various positions which need not be located on a common sphere. This approximated harmonic density can be combined with its orthogonal anharmonic complement, for example, determined out of the splitting function of free oscillations, to an approximation of the whole mass density function. The applicability of the presented tool is demonstrated by several test calculations based on simulated gravity values derived from EGM96. The method yields a multiresolution in the sense that the localization of the constructed spline basis functions can be increased which yields in combination with more data a higher resolution of the resulting spline. Moreover, we show that a locally improved data situation allows a highly resolved recovery in this particular area in combination with a coarse approximation elsewhere which is an essential advantage of this method, for example, compared to polynomial approximation.

Michel, Volker; Wolf, Kerstin

2008-04-01

413

Fast Simulation of X-ray Projections of Spline-based Surfaces using an Append Buffer

Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector, and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically. Source code is available at http://conrad.stanford.edu/ PMID:22975431

Maier, Andreas; Hofmann, Hannes G.; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca

2012-01-01

414

Temporal gravity field modeling based on least square collocation with short-arc approach

NASA Astrophysics Data System (ADS)

After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.

ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet

2014-05-01

415

1 Abstract-In this paper, collocated antennas for MIMO systems are presented. The structure that the proposed antenna system can replace a classical system based on space diversity. Index Terms-collocated antennas, radiation pattern diversity, MIMO system, channel capacity measurements I. INTRODUCTION ULTIPLE

Paris-Sud XI, Université de

416

New basis functions are obtained by satisfying the static homogeneous governing differential equation of a rotating beam at one and two collocation points within the beam element. These new basis functions depend on rotation speed, position of element in the beam and the position of collocation point. They show faster convergence for lower modes at high rotating speeds, compared to

D. Sasha; Ranjan Ganguli

2012-01-01

417

Evaluation of the spline reconstruction technique for PET

Purpose: The spline reconstruction technique (SRT), based on the analytic formula for the inverse Radon transform, has been presented earlier in the literature. In this study, the authors present an improved formulation and numerical implementation of this algorithm and evaluate it in comparison to filtered backprojection (FBP). Methods: The SRT is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of custom made cubic splines. By restricting reconstruction only within object pixels and by utilizing certain mathematical symmetries, the authors achieve a reconstruction time comparable to that of FBP. The authors have implemented SRT in STIR and have evaluated this technique using simulated data from a clinical positron emission tomography (PET) system, as well as real data obtained from clinical and preclinical PET scanners. For the simulation studies, the authors have simulated sinograms of a point-source and three digital phantoms. Using these sinograms, the authors have created realizations of Poisson noise at five noise levels. In addition to visual comparisons of the reconstructed images, the authors have determined contrast and bias for different regions of the phantoms as a function of noise level. For the real-data studies, sinograms of an{sup 18}F-FDG injected mouse, a NEMA NU 4-2008 image quality phantom, and a Derenzo phantom have been acquired from a commercial PET system. The authors have determined: (a) coefficient of variations (COV) and contrast from the NEMA phantom, (b) contrast for the various sections of the Derenzo phantom, and (c) line profiles for the Derenzo phantom. Furthermore, the authors have acquired sinograms from a whole-body PET scan of an {sup 18}F-FDG injected cancer patient, using the GE Discovery ST PET/CT system. SRT and FBP reconstructions of the thorax have been visually evaluated. Results: The results indicate an improvement in FWHM and FWTM in both simulated and real point-source studies. In all simulated phantoms, the SRT exhibits higher contrast and lower bias than FBP at all noise levels, by increasing the COV in the reconstructed images. Finally, in real studies, whereas the contrast of the cold chambers are similar for both algorithms, the SRT reconstructed images of the NEMA phantom exhibit slightly higher COV values than those of FBP. In the Derenzo phantom, SRT resolves the 2-mm separated holes slightly better than FBP. The small-animal and human reconstructions via SRT exhibit slightly higher resolution and contrast than the FBP reconstructions. Conclusions: The SRT provides images of higher resolution, higher contrast, and lower bias than FBP, by increasing slightly the noise in the reconstructed images. Furthermore, it eliminates streak artifacts outside the object boundary. Unlike other analytic algorithms, the reconstruction time of SRT is comparable with that of FBP. The source code for SRT will become available in a future release of STIR.

Kastis, George A., E-mail: gkastis@academyofathens.gr; Kyriakopoulou, Dimitra [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece)] [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece); Gaitanis, Anastasios [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece)] [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece); Fernndez, Yolanda [Centre dImatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain)] [Centre dImatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain); Hutton, Brian F. [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom)] [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom); Fokas, Athanasios S. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)] [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)

2014-04-15

418

The objective of this study was to examine the feasibility of using random regression-spline (RR-spline) models for fitting growth traits in a multibreed beef cattle population. To meet the objective, the results from the RR-spline model were compared with the widely used multitrait (MT) model when both were fit to a data set (1.8 million records and 1.1 million animals) provided by the American Gelbvieh Association. The effect of prior information on the EBV of sires was also investigated. In both RR-spline and MT models, the following effects were considered: individual direct and maternal additive genetic effects, contemporary group, age of the animal at measurement, direct and maternal heterosis, and direct and maternal additive genetic mean effect of the breed. Additionally, the RR-spline model included an individual direct permanent environmental effect. When both MT and RR-spline models were applied to a data set containing records for weaning weight (WWT) and yearling weight (YWT) within specified age ranges, the rankings of bulls' direct EBV (as measured via Pearson correlations) provided by both models were comparable, with slightly greater differences in the reranking of bulls observed for YWT evaluations (>or=0.99 for BWT and WWT and >or=0.98 for YWT); also, some bulls dropped from the top 100 list when these lists were compared across methods. For maternal effects, the estimated correlations were slightly smaller, particularly for YWT; again, some drops from the top 100 animals were observed. As in regular MT multibreed genetic evaluations, the heterosis effects and the additive genetic effects of the breed could not be estimated from field data, because there were not enough contemporary groups with the proper composition of purebred and crossbred animals; thus, prior information based on literature values had to be included. The inclusion of prior information had a negligible effect in the overall ranking for bulls with greater than 20 birth weight progeny records; however, the effect of prior information for breeds or groups poorly represented in the data was important. The Pearson correlations for direct and maternal WWT and YWT ranged from 0.95 to 0.98 when comparing evaluations of data sets for which the out-of-range age records were removed or retained. Random regression allows for avoiding the discarding of records that are outside the usual age ranges of measurement; thus, greater accuracies are achieved, and greater genetic progress could be expected. PMID:17965329

Snchez, J P; Misztal, I; Aguilar, I; Bertrand, J K

2008-02-01

419

Miniaturized Multi-Band Antenna via Element Collocation

The resonant frequency of a microstrip patch antenna may be reduced through the addition of slots in the radiating element. Expanding upon this concept in favor of a significant reduction in the tuned width of the radiator, nearly 60% of the antenna metallization is removed, as seen in the top view of the antennas radiating element (shown in red, below, left). To facilitate an increase in the gain of the antenna, the radiator is suspended over the ground plane (green) by an air substrate at a height of 0.250? while being mechanically supported by 0.030? thick Rogers RO4003 laminate in the same profile as the element. Although the entire surface of the antenna (red) provides 2.45 GHz operation with insignificant negative effects on performance after material removal, the smaller square microstrip in the middle must be isolated from the additional aperture in order to afford higher frequency operation. A low insertion loss path centered at 2.45 GHz may simultaneously provide considerable attenuation at additional frequencies through the implementation of a series-parallel, resonant reactive path. However, an inductive reactance alone will not permit lower frequency energy to propagate across the intended discontinuity. To mitigate this, a capacitance is introduced in series with the inductor, generating a resonance at 2.45 GHz with minimum forward transmission loss. Four of these reactive pairs are placed between the coplanar elements as shown. Therefore, the aperture of the lower-frequency outer segment includes the smaller radiator while the higher frequency section is isolated from the additional material. In order to avoid cross-polarization losses due to the orientation of a transmitter or receiver in reference to the antenna, circular polarization is realized by a quadrature coupler for each collocated antenna as seen in the bottom view of the antenna (right). To generate electromagnetic radiation concentrically rotating about the direction of propagation, ideally one-half of the power must be delivered to the output of each branch with a phase shift of 90 degrees and identical amplitude. Due to this, each arm of the coupler is spaced ?/4 wavelength apart.

Martin, R. P.

2012-06-01

420

Change detection of lung cancer using image registration and thin-plate spline warping

NASA Astrophysics Data System (ADS)

Lung cancer has the lowest survival rate comparing to other types of cancer and determination of the patient's cancer stage is the most vital issue regarding the cancer treatment process. In most cases accurate estimation of the cancer stage is not easy to achieve. The changes in the size of the primary tumor can be detected using image registration techniques. The registration method proposed in this paper uses Normalized Mutual Information metric and Thin-Plate Spline transformation function for the accurate determination of the correspondence between series of the lung cancer Computed Tomography images. The Normalized Mutual Information is used as a metric for the rigid registration of the images to better estimate the global motion of the tissues and the Thin Plate Spline is used to deform the image in a locally supported manner. The Control Points needed for the transformation are extracted semiautomatically. This new approach in change detection of the lung cancer is implemented using the Insight Toolkit. The results from implementing this method on the CT images of 8 patients provided a satisfactory quality for change detection of the lung cancer.

Almasslawi, Dawood M. S.; Kabir, Ehsanollah

2011-06-01

421

Railroad inspection based on ACFM employing a non-uniform B-spline approach

NASA Astrophysics Data System (ADS)

The stresses sustained by rails have increased in recent years due to the use of higher train speeds and heavier axle loads. For this reason surface and near-surface defects generate by Rolling Contact Fatigue (RCF) have become particularly significant as they can cause unexpected structural failure of the rail, resulting in severe derailments. The accident that took place in Hatfield, UK (2000), is an example of a derailment caused by the structural failure of a rail section due to RCF. Early detection of RCF rail defects is therefore of paramount importance to the rail industry. The performance of existing ultrasonic and magnetic flux leakage techniques in detecting rail surface-breaking defects, such as head checks and gauge corner cracking, is inadequate during high-speed inspection, while eddy current sensors suffer from lift-off effects. The results obtained through rail inspection experiments under simulated conditions using Alternating Current Field Measurement (ACFM) probes, suggest that this technique can be applied for the accurate and reliable detection of surface-breaking defects at high inspection speeds. This paper presents the B-Spline approach used for the accurate filtering the noise of the raw ACFM signal obtained during high speed tests to improve the reliability of the measurements. A non-uniform B-spline approximation is employed to calculate the exact positions and the dimensions of the defects. This method generates a smooth approximation similar to the ACFM dataset points related to the rail surface-breaking defect.

Chacn Muoz, J. M.; Garca Mrquez, F. P.; Papaelias, M.

2013-11-01

422

An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel. PMID:24124265

Ahn, W.; Anderson, K.S.; De, S.

2013-01-01

423

Your Participation Is "Greatly/Highly" Appreciated: Amplifier Collocations in L2 English

ERIC Educational Resources Information Center

The current study sets out to investigate collocational knowledge for a set of 13 English amplifiers among native and nonnative speakers of English, by providing a partial replication of one of the projects reported on in Granger (1998). The project combines both phraseological and distributional approaches to research into formulaic language to

Edmonds, Amanda; Gudmestad, Aarnes

2014-01-01

424

Raman lidar is a leading candidate for providing the detailed space - and time-resolved measurements of water vapor needed by a variety of atmospheric studies. Simultaneous measurements of atmospheric water vapor are described using two collocated Raman lidar systems. These lidar systems, developed at the NASA\\/Goddard Space Flight Center and Sandia National Laboratories, acquired approximately 12 hours of simultaneous water

J. E. M. Goldsmith; Scott E. Bisson; Richard A. Ferrare; Keith D. Evans; David N. Whiteman; S. H. Melfi

1994-01-01

425

Code of Federal Regulations, 2010 CFR

...or more than the width of the tower structure at the level of the appurtenance...Antennas on Buildings and Non-Tower Structures Outside of Historic Districts...mounted on a building or non-tower structure without such collocation...

2010-10-01

426

Collocational Differences between L1 and L2: Implications for EFL Learners and Teachers

ERIC Educational Resources Information Center

Collocations are one of the areas that produce problems for learners of English as a foreign language. Iranian learners of English are by no means an exception. Teaching experience at schools, private language centers, and universities in Iran suggests that a significant part of EFL learners' problems with producing the language, especially at

Sadeghi, Karim

2009-01-01

427

Lexical Collocation and Topic Occurrence in Well-Written Editorials: A Study in Form.

ERIC Educational Resources Information Center

To explore the concept of lexical collocation, or relationships between words, a study was conducted based on three assumptions: (1) that a text structure for a unit of discourse was analogous to that existing at the level of the sentence, (2) that such a text form could be discovered if a large enough sample of generically similar texts was

Addison, James C., Jr.

428

Strategies in Translating Collocations in Religious Texts from Arabic into English

ERIC Educational Resources Information Center

The present study investigated the strategies adopted by students in translating specific lexical and semantic collocations in three religious texts namely, the Holy Quran, the Hadith and the Bible. For this purpose, the researchers selected a purposive sample of 35 MA translation students enrolled in three different public and private Jordanian

Dweik, Bader S.; Shakra, Mariam M. Abu

2010-01-01

429

A Comparison of Collocation-Based Similarity Measures in Query Expansion.

ERIC Educational Resources Information Center

Presents a comparison of collocation-based similarity measures for the proper selection of additional search terms in query expansion. Highlights include evaluating retrieval effectiveness in a vector space model, thesauri, document ranking, and experiments on two Korean test collections. (Author/LRW)

Kim, Myoung-Cheol; Choi, Key-Sun

1999-01-01

430

Experimental validation of a collocated PVDF volume velocity sensor\\/actuator pair

The active control of sound transmission through a rectangular panel is experimentally verified. The control system is based on a collocated volume velocity sensor\\/actuator pair which measures and excites the first radiation mode of the panel. Suppression of the first radiation mode is an efficient strategy to control the low frequency sound radiation from the panel. This configuration leads to

K. Henrioulle; P. Sas

2003-01-01

431

prediction of Aerosol Optical Density (AOD) which is defined as the amount of loss a beam of light incurs of solar radiation. An important metric of aerosol's concentration in the atmosphere is Aerosol OpticalReducing Need for Collocated Ground and Satellite based Observations in Statistical Aerosol Optical

Vucetic, Slobodan

432

as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptivelyAn adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic in the stochastic space. Thus when there are steep gradients or finite discontinuities in the stochastic space

Zabaras, Nicholas J.

433

Frequent Collocates and Major Senses of Two Prepositions in ESL and ENL Corpora

ERIC Educational Resources Information Center

This contribution assesses in quantitative terms frequent collocates and major senses of "between" and "through" in the corpus of Cameroonian English (CCE), the corpus of East-African (Kenya and Tanzania) English which is part of the International Corpus of English (ICE) project (ICE-EA), and the London Oslo/Bergen (LOB) corpus of British English.

Nkemleke, Daniel

2009-01-01

434

Verb-Noun Collocations in Second Language Writing: A Corpus Analysis of Learners' English

ERIC Educational Resources Information Center

The present study investigates the use of English verb-noun collocations in the writing of native speakers of Hebrew at three proficiency levels. For this purpose, we compiled a learner corpus that consists of about 300,000 words of argumentative and descriptive essays. For comparison purposes, we selected LOCNESS, a corpus of young adult native

Laufer, Batia; Waldman, Tina

2011-01-01

435

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors

NASA Technical Reports Server (NTRS)

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Balakrishnan, A. V.

1994-01-01

436

aircraft measurements Robert D. Cess,1 Minghua Zhang,1 Francisco P. J. Valero,2 Shelly K. Pope,2 Anthony the interpretations made in two prior studies of the aircraft shortwave radiation measurements that were obtained from two collocated aircraft, an upper aircraft flying above the clouds at an altitude of roughly 14 km

Zender, Charles

437

Spline function approximation for velocimeter Doppler frequency measurement

NASA Technical Reports Server (NTRS)

A spline function approximation approach for measuring the Doppler spectral peak frequency in a laser Doppler velocimeter system is presented. The processor is designed for signal bursts with mean Doppler shift frequencies up to 100 MHz, input turbulence up to 20 percent, and photon counts as low as 300. The frequency-domain processor uses a bank of digital bandpass filters for the capture of the energy spectrum of each signal burst. The average values of the filter output energies, as a function of normalized frequency, are modeled as deterministic spline functions which are linearly weighted to evaluate the spectral peak location associated with the Doppler shift. The weighting coefficients are chosen to minimize the mean square error. Performance evaluation by simulation yields average errors in estimating mean Doppler frequencies within 0.5 percent for poor signal-to-noise conditions associated with a low photon count of 300 photons/burst.

Savakis, Andreas E.; Stoughton, John W.; Kanetkar, Sharad V.

1989-01-01

438

FSP Workshop on Computational Methods for Algebraic Spline Surfaces

:50 Wenping Wang On Free-form Mesh Surfaces with Planar Hexagonal Faces 15:50 - 16:15 Huaiping Yang Shape Parameterization via Aligning Optimal Local Flattening 15:50 - 16:15 Hans-Peter Schröcker Kinematics and Algebraic:00 Brian Moore Determination of the complete set of statically balanced planar four- bar mechanisms Friday

Jüttler, Bert

439

Application of B-splines in digital filtering

Summary form only given, as follows. In many digital signal processing applications, the input signal rate is higher than the output signal Nyquist rate. In the case of an FIR (finite-impulse-response) digital filter, it has been found that a B-spline representation of the filter response leads to minimal time and circuit complexities. The number of filter coefficients required in this

L. Ferrari

1989-01-01

440

Control theory and splines, applied to signature storage

NASA Technical Reports Server (NTRS)

In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.

Enqvist, Per

1994-01-01

441

Bivariate C^1 quadratic finite elements and vertex splines

NASA Astrophysics Data System (ADS)

Following work of Heindl and of Powell and Sabin, each triangle of an arbitrary (regular) triangulation ? of a polygonal region ? in {R^2} is subdivided into twelve triangles, using the three medians, yielding the refinement hat ? of ? , so that {C^1} quadratic finite elements can be constructed. In this paper, we derive the Bezier nets of these elements in terms of the parameters that describe function and first partial derivative values at the vertices and values of the normal derivatives at the midpoints of the edges of ? . Consequently, bivariate {C^1} quadratic (generalized) vertex splines on ? have an explicit formulation. Here, a generalized vertex spline is one which is a piecewise polynomial on the refined grid partition hat ? and has support that contains at most one vertex of the original partition ? in its interior. The collection of all {C^1} quadratic generalized vertex splines on ? so constructed is shown to form a basis of S_2^1(hat ? ) , the vector space of all functions on {C^1}(? ) whose restrictions to each triangular cell of the partition hat ? are quadratic polynomials. A subspace with the basis given by appropriately chosen generalized vertex splines with exactly one vertex of ? in the interior of their supports, that reproduces all quadratic polynomials, is identified, and hence, has approximation order three. Quasi-interpolation formulas using this subspace are obtained. In addition, a constructive procedure that yields a locally supported basis of yet another subspace with dimension given by the number of vertices of ? , that has approximation order three, is given.

Chui, Charles K.; He, Tian Xiao

1990-01-01

442

Application of integrodifferential splines to solving an interpolation problem

NASA Astrophysics Data System (ADS)

This paper deals with cases when the values of derivatives of a function are given at grid nodes or the values of integrals of a function over grid intervals are known. Polynomial and trigonometric integrodifferential splines for computing the value of a function from given values of its nodal derivatives and/or from its integrals over grid intervals are constructed. Error estimates are obtained, and numerical results are presented.

Burova, I. G.; Rodnikova, O. V.

2014-12-01

443

NASA Technical Reports Server (NTRS)

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Phillips, J. R.

1996-01-01

444

VLSI architecture for discrete wavelet transform based on B-spline factorization

Based on B-spline factorization, a new category of architectures for the discrete wavelet transform (DWT) is proposed. The B-spline factorization mainly consists of the B-spline part and the distributed part. The former is proposed to be constructed by use of a Pascal implementation. The latter is the only part requiring multipliers and can be implemented with type-I or type-II polyphase

Chao-Tsung Huang; Po-Chih Tseng; Liang-Gee Chen

2003-01-01

445

Cubic B-spline approximation in scalers: Efficient design and implementation

Scaling is a very important process in digital image\\/video processing. This paper studies the application of cubic B-spline in image\\/video scaling. Cubic B-spline is very popular in image\\/video scaling, but in most cases it is not applied properly. We explain why a pre-filtering process is necessary when cubic B-spline kernel is applied to interpolate the image or video, and we

Yinping Huang; Yong Ding

2008-01-01

446

ECS 178 Course Notes THE GEOMETRIC DEFINITION OF A B-SPLINE CURVE

ECS 178 Course Notes THE GEOMETRIC DEFINITION OF A B-SPLINE CURVE Kenneth I. Joy Institute for Data the knot sequence that tells us something about the parameterization. The B-Spline Curve Geometric+k} the B-Spline curve of order k is defined to be P(t) = P (k-1) l (t) if t [tl, tl+1) (1) where P (j) i

California at Davis, University of

447

Multiscale curvature-based shape representation using B-spline wavelets

This paper presents a new multiscale curvature-based shape representation technique withapplication to curve data compression using B-spline wavelets. The properties and behavior ofevolving curves in B-spline scale-space are investigated. They are shown to be similar to thatin Gaussian scale-space, but B-spline representation enjoys a number of advantages over Gaussiankernels, for instance, the availability of fast algorithms. As an application of

Yu-Ping Wang; Seng Luan Lee; Kazuo Toraichi

1999-01-01

448

Transformation of a Dynamic B-Spline Curve into Piecewise Power Basis Representation

In the fields of computer aided geometric design and computer graphics, B-spline curves and surfaces are often adopted as\\u000a a geometric modelling tool and their evaluation is frequently required for a various geometric processing. In this paper,\\u000a we present a new algorithm to convert B-spline curves into piecewise polynomials in power form. The proposed algorithm considers\\u000a recursive B-spline basis function

Joonghyun Ryul; Youngsong Chol; Deok-soo Kim

2002-01-01

449

B-spline snakes: a flexible tool for parametric contour detection

Abstract, We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the tra-ditional formulation by showing that the optimal, curvature-con-strained snake is a cubic spline, irrespective of the form of the ex-ternal energy field. Unfortunately, such regularized snakes

Patrick Brigger; Jeff Hoeg; Michael Unser

2000-01-01

450

Explicit B-spline regularization in diffeomorphic image registration.

Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline "flavored" diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools. PMID:24409140

Tustison, Nicholas J; Avants, Brian B

2013-01-01

451

Explicit B-spline regularization in diffeomorphic image registration

Diffeomorphic mappings are central to image registration due largely to their topological properties and success in providing biologically plausible solutions to deformation and morphological estimation problems. Popular diffeomorphic image registration algorithms include those characterized by time-varying and constant velocity fields, and symmetrical considerations. Prior information in the form of regularization is used to enforce transform plausibility taking the form of physics-based constraints or through some approximation thereof, e.g., Gaussian smoothing of the vector fields [a la Thirion's Demons (Thirion, 1998)]. In the context of the original Demons' framework, the so-called directly manipulated free-form deformation (DMFFD) (Tustison et al., 2009) can be viewed as a smoothing alternative in which explicit regularization is achieved through fast B-spline approximation. This characterization can be used to provide B-spline flavored diffeomorphic image registration solutions with several advantages. Implementation is open source and available through the Insight Toolkit and our Advanced Normalization Tools (ANTs) repository. A thorough comparative evaluation with the well-known SyN algorithm (Avants et al., 2008), implemented within the same framework, and its B-spline analog is performed using open labeled brain data and open source evaluation tools. PMID:24409140

Tustison, Nicholas J.; Avants, Brian B.

2013-01-01

452

Application of a polynomial spline in higher-order accurate viscous-flow computations

NASA Technical Reports Server (NTRS)

A quartic spline, S(4,2), is proposed which overcomes some of the difficulties associated with the use of splines S(5,3) and S(3,1) and provides fourth-order accurate results with relatively few grid points. The accuracy of spline S(4,2) is comparable to or better than that of the fourth-order box scheme and the compact differencing scheme. The use of spline S(4,2) is suggested as a possible way of obtaining fourth-order accurate solutions to Navier-Stokes equations.

Turner, M. G.; Keith, J. S.; Ghia, K. N.; Ghia, U.

1982-01-01

453

Orthogonal polynomials and numerical methods for integral equations

Orthogonal polynomials and numerical methods for integral equations The topics of this series polynomials (c) Mapping properties (described by orthogonal polynomials) of sin- gular and hypersingular integral operators 2. Stability of collocation methods for singular integral equations (a) Basics from

Potts, Daniel

454

Explosion Source Location Study Using Collocated Acoustic and Seismic Networks in Israel

NASA Astrophysics Data System (ADS)

We explore a joined analysis of seismic and infrasonic signals for improvement in automatic monitoring of small local/regional events, such as construction and quarry blasts, military chemical explosions, sonic booms, etc. using collocated seismic and infrasonic networks recently build in Israel (ISIN) in the frame of the project sponsored by the Bi-national USA-Israel Science Foundation (BSF). The general target is to create an automatic system, which will provide detection, location and identification of explosions in real-time or close-to-real time manner. At the moment the network comprises 15 stations hosting a microphone and seismometer (or accelerometer), operated by the Geophysical Institute of Israel (GII), plus two infrasonic arrays, operated by the National Data Center, Soreq: IOB in the South (Negev desert) and IMA in the North of Israel (Upper Galilee),collocated with the IMS seismic array MMAI. The study utilizes a ground-truth data-base of numerous Rotem phosphate quarry blasts, a number of controlled explosions for demolition of outdated ammunitions and experimental surface explosions for a structure protection research, at the Sayarim Military Range. A special event, comprising four military explosions in a neighboring country, that provided both strong seismic (up to 400 km) and infrasound waves (up to 300 km), is also analyzed. For all of these events the ground-truth coordinates and/or the results of seismic location by the Israel Seismic Network (ISN) have been provided. For automatic event detection and phase picking we tested the new recursive picker, based on Statistically optimal detector. The results were compared to the manual picks. Several location techniques have been tested using the ground-truth event recordings and the preliminary results obtained have been compared to the ground-truth locations: 1) a number of events have been located as intersection of azimuths estimated using the wide-band F-K analysis technique applied to the infrasonic phases of the two distant arrays; 2) a standard robust grid-search location procedure based on phase picks and a constant celerity for a phase (tropospheric or stratospheric) was applied; 3) a joint coordinate grid-search procedure using array waveforms and phase picks was tested, 4) the Bayesian Infrasonic Source Localization (BISL) method, incorporating semi-empirical model-based prior information, was modified for array+network configuration and applied to the ground-truth events. For this purpose we accumulated data of the former observations of the air-to-ground infrasonic phases to compute station specific ground-truth Celerity-Range Histograms (ssgtCRH) and/or model-based CRH (mbCRH), which allow to essentially improve the location results. For building the mbCRH the local meteo-data and the ray-tracing modeling in 3 available azimuth ranges, accounting seasonal variations of winds directivity (quadrants North:315-45, South: 135-225, East 45-135) have been used.

Pinsky, V.; Gitterman, Y.; Arrowsmith, S.; Ben-Horin, Y.

2013-12-01

455

NUMERICAL METHODS FOR BOUNDARY VALUE PROBLEMS WITH APPLICATION TO BIFURCATION PROBLEMS

of orthogonal collocation for solving boundary value problems in ordinary differential equation is described the capabilities of software based on orthogonal collocation for analyzing nonlinear differential equations. A new discretiza tion method for the solution of elliptic partial differential equations is described

Doedel, Eusebius

456

History matching by spline approximation and regularization in single-phase areal reservoirs

NASA Technical Reports Server (NTRS)

An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity distributions and on the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional real reservoir from well pressure data. The regularization feature of the algorithm is used to convert the ill-posed history matching problem into a well-posed problem. The algorithm employs the conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (non-regularized) automatic history matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.

Lee, T. Y.; Kravaris, C.; Seinfeld, J.

1986-01-01

457

Full-turn symplectic map from a generator in a Fourier-spline basis

Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton`s method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been appliedto a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10{sup 7} turns on an IBM RS6000 model 320 workstation, in a run of about one day.

Berg, J.S.; Warnock, R.L.; Ruth, R.D. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Forest, E. [Lawrence Berkeley Lab., CA (United States)

1993-04-01

458

Objective We previously developed a flexible specification of the UNAIDS Estimation and Projection Package (EPP) that relied on splines to generate time-varying values for the force of infection parameter. Here, we test the feasibility of this approach for concentrated HIV/AIDS epidemics with very sparse data and compare two methods for making short-term future projections with the spline-based model. Methods Penalised B-splines are used to model the average infection risk over time within the EPP 2011 modelling framework, which includes antiretroviral treatment effects and CD4 cell count progression, and is fit to sentinel surveillance prevalence data with a Bayesian algorithm. We compare two approaches for future projections: (1) an informative prior related to equilibrium prevalence and (2) a random walk formulation. Results The spline-based model produced plausible fits across a range of epidemics, which included 87 subpopulations from 14 countries with concentrated epidemics and 75 subpopulations from 33 countries with generalised epidemics. The equilibrium prior and random walk approaches to future projections yielded similar prevalence estimates, and both performed well in tests of out-of-sample predictive validity for prevalence. In contrast, in some cases the two approaches varied substantially in estimates of incidence, with the random walk formulation avoiding extreme changes in incidence. Conclusions A spline-based approach to allowing the force of infection parameter to vary over time within EPP 2011 is robust across a diverse array of epidemics, including concentrated ones with limited surveillance data. Future work on the EPP model should consider the impact that different modelling approaches have on estimates of HIV incidence. PMID:23172346

Hogan, Daniel R; Salomon, Joshua A

2012-01-01

459

PurposeA fast and robust algorithm was developed for automatic segmentation of the left ventricular endocardial boundary in echocardiographic\\u000a images. The method was applied to calculate left ventricular volume and ejection fraction estimation.\\u000a \\u000a \\u000a \\u000a \\u000a MethodsA fast adaptive B-spline snake algorithm that resolves the computational concerns of conventional active contours and avoids\\u000a computationally expensive optimizations was developed. A combination of external forces, adaptive

Mahdi Marsousi; Armin Eftekhari; Armen Kocharian; Javad Alirezaie

2010-01-01

460

NASA Technical Reports Server (NTRS)

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

461

Time Varying Compensator Design for Reconfigurable Structures Using Non-Collocated Feedback

NASA Technical Reports Server (NTRS)

Analysis and synthesis tools are developed to improved the dynamic performance of reconfigurable nonminimum phase, nonstrictly positive real-time variant systems. A novel Spline Varying Optimal (SVO) controller is developed for the kinematic nonlinear system. There are several advantages to using the SVO controller, in which the spline function approximates the system model, observer, and controller gain. They are: The spline function approximation is simply connected, thus the SVO controller is more continuous than traditional gain scheduled controllers when implemented on a time varying plant; ft is easier for real-time implementations in storage and computational effort; where system identification is required, the spline function requires fewer experiments, namely four experiments; and initial startup estimator transients are eliminated. The SVO compensator was evaluated on a high fidelity simulation of the Shuttle Remote Manipulator System. The SVO controller demonstrated significant improvement over the present arm performance: (1) Damping level was improved by a factor of 3; and (2) Peak joint torque was reduced by a factor of 2 following Shuttle thruster firings.

Scott, Michael A.

1996-01-01

462

Particular solutions of Helmholtz-type operators using higher order polyhrmonic splines

We obtain explicit analytical particular solutions for Helmholtz-type operators, using higher order splines. These results\\u000a generalize those in Golberg, Chen and Rashed (1998) and Chen and Rashed (1998) for thin plate splines. This enables one to\\u000a substantially improve the accuracy of algorithms for solving boundary value problems for Helmholtz-type equations.

A. S. Muleshkov; M. A. Golberg; C. S. Chen

1999-01-01

463

Splines and Linear Control Theory Zhimin Zhang, John Tomlinson and Clyde Martin

Splines and Linear Control Theory Zhimin Zhang, John Tomlinson and Clyde Martin Department and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic

Zhang, Zhimin

464

In the speech processing field, stylization of fundamental frequency F 0 has been subjected to numerous works. Models proposed in the literature rely on knowledge stemming from phonology and linguistics. We propose an approach that deals with the issue of F 0 curve stylization requiring as few linguistic assumptions as possible and in the framework of B-spline models. A B-spline

Damien Lolive; Nelly Barbot; Olivier Boeffard

2010-01-01

465

Calculations of absolute triple-differential and single-differential cross sections for helium double photoionization are performed using an implementation of exterior complex scaling in B -splines. Results for cross sections, well converged in partial waves, are presented and compared with both experiment and earlier theoretical calculations. These calculations establish the practicality and effectiveness of the complex B -spline approach to calculations of

C. W. McCurdy; D. A. Horner; T. N. Rescigno; F. Martn

2004-01-01

466

Random regression analyses using B-splines to model growth of Australian Angus cattle

Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. Data comprised 84 533 records on 20 731 animals in 43

Karin Meyer

2005-01-01

467

B-spline Snakes and a JAVA Interface: An Intuitive Tool for General Contour Outlining

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. The theory is implemented in a platform independent JAVA interface, which allows real time computation of the snake curve. In this paper, our main focus is on two points. First, we propose a novel B-spline snake formulation, where the

Patrick Brigger; Robert Engel; Michael Unser

1998-01-01

468

Reconstruction of three-dimensional curve by discrete curvature based on B-spline

Three dimensional curve reconstruction of a fiber Bragg grating (FBG) intelligent smart rod is implemented using B-spline interpolated orthogonal curvatures. By introducing the sketch of curvature detection principle of the orthogonal distributed fiber Bragg grating, this paper proposed the detailed algorithm processes and implementation steps of the B-spline curve fitting algorithm for curvature continuity as well as the recursive algorithm

Jiang Lina; Sun Bing; Yi Jincong; Zhu Xiaojin

2010-01-01

469

B-spline factorization-based architecture for inverse discrete wavelet transform

In this paper, the VLSI architecture for the inverse discrete wavelet transform (IDWT) is proposed on the basis of B-spline factorization that is the intrinsic property of DWT and comprises two parts: B-spline part and distributed part. After the polyphase decomposition, the former can be constructed by Pascal or direct implementation. And the latter one can be implemented by serial

Chao-tsung Huang; Po-chih Tseng; Liang-gee Chen

2004-01-01

470

In this paper. we design a new family of biorthogonal wavelet transforms and describe their applications to still image compression. The wavelet transforms are constructed from various types of interpolatory and quasiinterpolatory splines. The trans- forms use finite impulse response and infinite impulse response fil- ters that are implemented in a fast lifting mode. Index TermsImage compression, lifting scheme, spline,

Amir Z. Averbuch; Valery A. Zheludev

2004-01-01

471

Multi Focus Image Fusion Based on Spline Pyramidal Direction Filter Banks

Contourlet transform is a powerful analysis tool of image which has lines and hyper-plane singularity. It uses Laplacian pyramid transform to decompose source images. But the loss of information of Laplacian pyramid is large than that of the difference pyramid constructed from spline pyramid. In this paper, we use spline pyramid transform to get a multi scale decomposition tree, construct

Yong Chai; Wen Wang; You He

2009-01-01

472

Smoothing scattered data with a monotone Powell-Sabin spline surface

NASA Astrophysics Data System (ADS)

An algorithm is presented for smoothing arbitrarily distributed noisy measurement data with a Powell-Sabin spline surface that satisfies necessary and sufficient monotonicity conditions. The Powell-Sabin spline is expressed as a linear combination of locally supported basis functions used in their Bernstein-Bzier representation. Numerical examples are given to illustrate the performance of the algorithm.

Willemans, Karin; Dierckx, Paul

1996-03-01

473

With many predictors, choosing an appropriate subset of the covariates is a crucial, and difficult, step in nonparametric regression. We propose a Bayesian nonparametric regression model for curve-fitting and variable selection. We use the smoothing spline ANOVA framework to decompose the regression function into interpretable main effect and interaction functions. Stochastic search variable selection via MCMC sampling is used to search for models that fit the data well. Also, we show that variable selection is highly-sensitive to hyperparameter choice and develop a technique to select hyperparameters that control the long-run false positive rate. The method is used to build an emulator for a complex computer model for two-phase fluid flow. PMID:19789732

Reich, Brian J; Storlie, Curtis B; Bondell, Howard D

2009-05-01

474

TWO-LEVEL TIME MARCHING SCHEME USING SPLINES FOR SOLVING THE ADVECTION EQUATION. (R826371C004)

A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian flux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme...

475

Recovering coseismic point ground tilts from collocated high-rate GPS and accelerometers

NASA Astrophysics Data System (ADS)

Rotational along with translational and strain measurements are essential for a complete description of the motion of a deformable body in a seismic event. We propose a new seismogeodetic approach where collocated high-rate GPS and accelerometer measurements are combined to estimate permanent and dynamic coseismic ground tilts at a point, whereas at present, only dynamic tilts are measured with either a dense seismic array or an expensive ring laser gyroscope. We estimate point tilts for a five-story structure on a shake table subjected to 13 earthquake strong motion records of increasing intensity. For the most intense record from the 2002 M7.9 Denali earthquake, we observe a peak-to-peak dynamic tilt of 0.12 and a permanent tilt of 0.16 for the structure's roof. Point tilts derived from networks of collocated GPS and accelerometers can be used to estimate the rotational component of the seismic wavefield for improved earthquake source characterization.

Geng, Jianghui; Melgar, Diego; Bock, Yehuda; Pantoli, Elide; Restrepo, Jos

2013-10-01

476

The convergence problem of collocation solutions in the framework of the stochastic interpretation

NASA Astrophysics Data System (ADS)

The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221-252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225-240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true. "Democrito che 'l mondo a caso pone" "Democritus who made the world stochastic" Dante Alighieri, La Divina Commedia, Inferno, IV - 136

Sans, F.; Venuti, G.

2011-01-01

477

NASA Technical Reports Server (NTRS)

Raman lidar is a leading candidate for providing the detailed space- and time-resolved measurements of water vapor needed by a variety of atmospheric studies. Simultaneous measurements of atmospheric water vapor are described using two collocated Raman lidar systems. These lidar systems, developed at the NASA/Goddard Space Flight Center and Sandia National Laboratories, acquired approximately 12 hours of simultaneous water vapor data during three nights in November 1992 while the systems were collocated at the Goddard Space Flight Center. Although these lidar systems differ substantially in their design, measured water vapor profiles agreeed within 0.15 g/kg between altitudes of 1 and 5 km. Comparisons with coincident radiosondes showed all instruments agreed within 0.2 g/kg in this same altitude range. Both lidars also clearly showed the advection of water vapor in the middle troposphere and the pronounced increase in water vapor in the nocturnal boundary layer that occurred during one night.

Goldsmith, J. E. M.; Bisson, Scott E.; Ferrare, Richard A.; Evans, Keith D.; Whiteman, David N.; Melfi, S. H.

1994-01-01

478

Determination of loose spline coupling coefficients of rotor bearing systems in turbomachinery

NASA Astrophysics Data System (ADS)

Analytical and experimental studies have been carried out to determine the stiffness and damping coefficients of loose spline couplings used in high speed rotating machinery from which a realistic assessment of rotor stability can be made at the turbomachinery design stage. This is believed to be the first attempt ever to determine these coefficients experimentally. Experimental modal parameters of the rotor bearing system with a spline coupling are found using modal testing for given spline geometry, misalignment, lubrication condition, torque, and rotational speeds. A dual rotor computer algorithm which contains a spline coupling model is developed in order to calculate the analytical modal parameters. Support bearing coefficients are obtained using a pressure dam bearing computer code which employs lubrication theory. Spline coupling coefficients are determined by adjusting the model until the analytical modal parameters match the experimental modal parameters. Both computer simulations and impact testing show that shaft speed and torque are the most important parameters which affect the system natural frequency and logarithmic decrement. However, the modal parameters are not very sensitive to the spine coupling coefficients. Only the second natural frequency shows any sensitivity to the spline angular stiffness. The lateral stiffness coefficient of the spline coupling decreases as rotational speed increases. Lateral and angular damping do not influence the modal parameter until unreasonably large values are considered. This is due to the large value of damping in the pressure dam bearings. Since the modal parameters are insensitive to the spline coefficients, a set of error bounds for the experimental values are chosen to determine the ranges of the loose spline coupling coefficients. The results show that the value of the spline lateral stiffness is between 2.0 x10(exp 7) and 8.0 x 10(exp 8) N/m and the spline angular stiffness is between 2.0 x 10(exp 5) and 8.0 x 10(exp 8) N/m, and the spline angular stiffness is between 2.0 x 10(exp 6) Nm/rad. However, it is impossible to identify the spline damping coefficients because the effect of the support bearing damping coefficients suppress the nonsynchronous whirling motion due to the spline friction even at speeds above the first critical speed.

Park, Sang Kyu

479

Spline-Based Smoothing of Airfoil Curvatures

NASA Technical Reports Server (NTRS)

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.; Krist, S.

2008-01-01

480

Use of tensor product splines in magnet optimization

Variational Metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated.

Davey, K.R. (American Maglev, Inc., New Smyrna Beach, FL (United States))

1999-05-01