Note: This page contains sample records for the topic spline collocation method from Science.gov.
While these samples are representative of the content of Science.gov,
they are not comprehensive nor are they the most current set.
We encourage you to perform a real-time search of Science.gov
to obtain the most current and comprehensive results.
Last update: August 15, 2014.
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

VIBRATION ANALYSIS OF PRE-TWISTED BEAMS USING THE SPLINE COLLOCATION METHOD  

Microsoft Academic Search

The variation in the accuracy of the calculated natural fre- quencies of pre-twisted beams solved with spline collocation method is investigated in this study. The spline collocation method is used to formulate the eigenvalue problems of pre-twisted beams. Three types of boundary conditions are considered. Numerical results indicate that the accuracy of the calculated natural frequencies is significantly dependent upon

Ming-Hung Hsu

2009-01-01

3

A CUBIC B-SPLINE COLLOCATION METHOD FOR THE EW EQUATION  

Microsoft Academic Search

A numerical solution of the Equal Width (EW) equation based on a collocation method incorporated cubic B-splines is investigated. Accuracy of the proposed method is shown numerically by calculating conservation laws, L2 and L? norms on studying migration of a single solitary wave. It is shown that the collocation scheme for solutions of the EW equation gives rise to smaller

Bülent Saka

2004-01-01

4

Extrapolation with Spline-Collocation Methods for Two-Point Boundary Value Problems. I. Justification and Proposals.  

National Technical Information Service (NTIS)

Asymptotic expansions for the error in some spline interpolation schemes are used to derive asymptotic expansions for the truncation errors in some spline collocation methods for two-point boundary-value problems. This raises the possibility of using Rich...

J. W. Daniel

1974-01-01

5

Parameter estimation technique for boundary value problems by spline collocation method  

NASA Technical Reports Server (NTRS)

A parameter-estimation technique for boundary-integral equations of the second kind is developed. The output least-squares identification technique using the spline collocation method is considered. The convergence analysis for the numerical method is discussed. The results are applied to boundary parameter estimations for two-dimensional Laplace and Helmholtz equations.

Kojima, Fumio

1988-01-01

6

Taylor-Galerkin and Taylor-collocation methods for the numerical solutions of Burgers’ equation using B-splines  

NASA Astrophysics Data System (ADS)

In this paper, for the numerical solution of Burgers' equation, we give two B-spline finite element algorithms which involve a collocation method with cubic B-splines and a Galerkin method with quadratic B-splines. In time discretization of the equation, Taylor series expansion is used. In order to verify the stabilities of the purposed methods, von-Neumann stability analysis is employed. To see the accuracy of the methods, L2 and L? error norms are calculated and obtained results are compared with some earlier studies.

Da?, ?dris; Can?var, Aynur; ?ahin, Ali

2011-07-01

7

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems  

NASA Astrophysics Data System (ADS)

An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only O(N) operations where N is the number of unknowns. Moreover, it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.

Fernandes, Ryan I.; Fairweather, Graeme

2012-08-01

8

Splines. Their Equivalence to Collocation.  

National Technical Information Service (NTIS)

The application of splines in geodesy was mainly restricted to the solution of one-dimensional problems like interpolation, differentiation, approximation, solution of differential equations, etc. Two-dimensional splines turned out to be an adequate tool ...

H. Sonkel

1984-01-01

9

Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions  

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

10

Numerical methods based on polynomial spline interpolation  

Microsoft Academic Search

Polynomial spline interpolation is used to develop various higher-order collocation methods for numerical solutions of the equations of fluid mechanics. The Hermite formulation is shown to be a hybrid method resulting from two different polynomial splines, and by extending this formulation a sixth-order block-tridiagonal procedure is developed. The analyses show that, for equal accuracy, the Spline 4 procedure requires one-fourth

S. G. Rubin; P. K. Khosla

1976-01-01

11

Spectral collocation methods  

NASA Technical Reports Server (NTRS)

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

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

1987-01-01

12

Numerical methods based on polynomial spline interpolation  

Microsoft Academic Search

Polynomial spline interpolation has been used to develop a variety of higher-order collocation methods. Only those polynomials\\u000a resulting in tridiagonal, or at worst 3×3 block- tridiagonal, matrix systems have been evaluated.It is- shown that the Padé\\u000a or Hermite formulation is a hybrid method resulting from two different poly nomial splines.An extension to sixth-order is\\u000a presented in this paper. Of the

S. Rubin; P. Khosla

13

The Parabolic Spline Method  

NASA Astrophysics Data System (ADS)

A new and efficient parabolic spline based remapping algorithm is developed and tested herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed parabolic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A grid and sub-grid based monotonic filter is also incorporated into the overall scheme. A truncation error analysis of the scheme is presented and discussed in terms of results from test cases. The analysis shows that although it has a similar truncation error in the converged limit as that of the widely used Piecewise Parabolic Method (PPM) for infinitely differentiable functions, PSM is more accurate than PPM for problems with slow spectral decay. Additionally, an operation count of the scheme is given which demonstrates the computational advantage of PSM compare

Zerroukat, M.; Wood, N.; Staniforth, A.

2006-08-01

14

Optimal order spline methods for nonlinear differential and integro-differential equations  

Microsoft Academic Search

In this work, we analyze new robust spline approximation methods for mth order boundary value problems described by nonlinear ordinary differential and integro-differential equations with m linear boundary conditions. Our main aim is to introduce a cost-effective alternative to the highly successful orthogonal collocation method, and to prove stability and convergence properties similar to the orthogonal collocation method. Our method

M. Ganesh; I. H. Sloan

1999-01-01

15

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

16

Collocation Methods for Singular Boundary Value Problems.  

National Technical Information Service (NTIS)

The application of collocation methods based on piecewise polynomials to the numerical solution of boundary value problems for systems of ordinary differential equations with a singularity of the first kind is examined. The schemes are shown to be stable ...

F. R. de Hoog R. Weiss

1975-01-01

17

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's  

NASA Technical Reports Server (NTRS)

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Cai, Wei; Wang, Jian-Zhong

1993-01-01

18

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

19

An enhanced splined saddle method.  

PubMed

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

20

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.; Vázquez, R.

2014-01-01

21

Spline-based tomographic reconstruction method  

NASA Astrophysics Data System (ADS)

In this paper, a new approach to the Filtered BackProjection (FBP) algorithm is presented. The method is based on the reconstruction stability in Sobolev spaces and B-spline functions which define a Pixel Intensity Distribution Model (PIDM-n) according to the spline degree n of the desired reconstruction. It is shown that PIDM-n reconstructions can be efficiently obtained. Angular sampling is studied and comparison with standard FBP shows the superiority of the algorithm presented. Moreover, simulation studies of noise degradation and blur in the projections show the algorithm to be superior to FBP in this more realistic case.

Guedon, Jean-Pierre; Bizais, Yves J.

1991-07-01

22

Collocation method for fractional quantum mechanics  

SciTech Connect

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.

Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)

2010-12-15

23

Brill wave initial data: Using the Galerkin-collocation method  

NASA Astrophysics Data System (ADS)

In this paper, we have implemented the Galerkin-collocation method to determine the initial data in two cases of interest for numerical relativity: vacuum axisymmetric Brill waves, and the interaction of axisymmetric Brill waves with a nonrotating black hole, or a distorted black hole. The numerical method combines the main features of the Galerkin and collocation methods which produce very accurate initial data. We have also calculated the Arnowitt-Deser-Misner masses and the location of the apparent horizons of the initial data sets under consideration.

de Oliveira, H. P.; Rodrigues, E. L.

2012-09-01

24

Numerical Method Using Cubic B-Spline for a Strongly Coupled Reaction-Diffusion System  

PubMed Central

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 and error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.

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

2014-01-01

25

Aerodynamic influence coefficient method using singularity splines  

NASA Technical Reports Server (NTRS)

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Mercer, J. E.; Weber, J. A.; Lesferd, E. P.

1974-01-01

26

Transient heat flow analysis using the fundamental collocation method  

Microsoft Academic Search

The fundamental collocation method for general two dimensional transient heat flow problems in solids is presented. The numerical procedure is applied directly to heat conduction in the time domain and is illustrated using several example problems. The method is capable of handling problems of arbitrary shapes subjected to arbitrary initial conditions and mixed time-dependent boundary conditions. Its simplicity and minimal

Gary Burgess; Enayat Mahajerin

2003-01-01

27

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

28

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media  

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

29

Radial point interpolation collocation method (RPICM) for the solution of nonlinear poisson problems  

NASA Astrophysics Data System (ADS)

This paper applies radial point interpolation collocation method (RPICM) for solving nonlinear Poisson equations arising in computational chemistry and physics. Thin plate spline (TPS) Radial basis functions are used in the work. A series of test examples are numerically analysed using the present method, including 2D Liouville equation, Bratu problem and Poisson-Boltzmann equation, in order to test the accuracy and efficiency of the proposed schemes. Several aspects have been numerically investigated, namely the enforcement of additional polynomial terms; and the application of the Hermite-type interpolation which makes use of the normal gradient on Neumann boundary for the solution of PDEs with Neumann boundary conditions. Particular emphasis was on an efficient scheme, namely Hermite-type interpolation for dealing with Neumann boundary conditions. The numerical results demonstrate that a good accuracy can be obtained. The h-convergence rates are also studied for RPICM with coarse and fine discretization models.

Liu, Xin; Liu, G. R.; Tai, Kang; Lam, K. Y.

2005-09-01

30

Adaptive wavelet collocation method on the shallow water model  

NASA Astrophysics Data System (ADS)

This paper presents an integrated approach for modeling several ocean test problems on adaptive grids using novel boundary techniques. The adaptive wavelet collocation method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. It is a general method for the solving a large class of partial differential equations, but is applied to the shallow water equations here. In addition to developing wavelet-based computational models, this work also uses an extension of the Brinkman penalization method to represent irregular and non-uniform continental boundaries. This technique is used to enforce no slip boundary conditions through the addition of a term to the field equations. When coupled with the adaptive wavelet collocation method, the flow near the boundary can be well resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow and the boundary is important, thus, those are the test cases presented here.

Reckinger, Shanon M.; Vasilyev, Oleg V.; Fox-Kemper, Baylor

2014-08-01

31

Domain decomposition preconditioners for the spectral collocation method  

NASA Technical Reports Server (NTRS)

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

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

32

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

33

Spectral collocation methods for polymer brushes  

NASA Astrophysics Data System (ADS)

We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework of self-consistent field theory (SCFT). SCFT of molten polymer brushes has proved numerically challenging in the past because of sharp features that arise in the self-consistent pressure field at the grafting surface due to the chain end tethering constraint. We show that this pressure anomaly can be reduced by smearing the grafting points over a narrow zone normal to the surface in an incompressible model, and/or by switching to a compressible model for the molten brush. In both cases, we use results obtained from a source (delta function) distribution of grafting points as a reference. At the grafting surface, we consider both Neumann and Dirichlet conditions, where the latter is paired with a masking method to mimic a confining surface. When only the density profiles and relative free energies of two comparison phases are of interest, either source or smeared distributions of grafting points can be used, but a smeared distribution of grafting points exhibits faster convergence with respect to the number of chain contour steps. Absolute free energies converge only within the smeared model. In addition, when a sine basis is used with the masking method and a smeared distribution, fewer iterations are necessary to converge the SCFT fields for the compressible model. The numerical methods described here and investigated in one-dimension will provide an enabling platform for computationally more demanding three-dimensional SCFT studies of a broad range of mixed polymer brush systems.

Chantawansri, Tanya L.; Hur, Su-Mi; García-Cervera, Carlos J.; Ceniceros, Hector D.; Fredrickson, Glenn H.

2011-06-01

34

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

35

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

36

Lunar soft landing rapid trajectory optimization using direct collocation method and nonlinear programming  

Microsoft Academic Search

Direct collocation method has been widely used for trajectory optimization. In this paper, the application of direct optimization method (direct collocation method & nonlinear programming (NLP)) to lunar probe soft-landing trajectory optimization is introduced. Firstly, the model of trajectory optimization control problem to lunar probe soft landing trajectory is established and the equations of motion are simplified respectively based on

Lianghui Tu; Jianping Yuan; Jianjun Luo; Xin Ning; Ruiwu Zhou

2007-01-01

37

Simulation of Gravity Waves by Spectral Collocation Methods.  

National Technical Information Service (NTIS)

Gravity waves propagating in a stratified environment with a vertically shared horizontal wind are treated by aid of spectral collocation. Wave breaking caused by nonlinear wave-wind interaction, forming a critical layer, is shown to form instabilities wh...

O. Andreassen

1994-01-01

38

Bethe-logarithm calculation using the B-spline method  

NASA Astrophysics Data System (ADS)

A method based on the B-spline basis set is developed that significantly simplifies the Bethe-logarithm calculations for the atomic hydrogen. Without any auxiliary optimization and extrapolation, this method not only can calculate the Bethe logarithms of low-lying states to high precision using relatively small basis sets, but can also calculate high-lying Rydberg states efficiently. For the ground state, the Bethe logarithm is calculated to 24 significant figures using 450 B-spline functions. For high-lying Rydberg states, we can reproduce all the results of Jentschura and Mohr [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.72.012110 72, 012110 (2005)].

Tang, Yongbo; Zhong, Zhenxiang; Li, Chengbin; Qiao, Haoxue; Shi, Tingyun

2013-02-01

39

Spurious Modes in Spectral Collocation Methods with Two Non-Periodic Directions.  

National Technical Information Service (NTIS)

Collocation implementation of the Kleiser-Schumann's method in geometries with two non-periodic directions is shown to suffer from three spurious modes -- line, column and checkerboard -- contaminating the computed pressure field. The corner spurious mode...

S. Balachandar R. K. Madabhushi

1992-01-01

40

Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method  

ERIC Educational Resources Information Center

This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

Cui, Zhongmin; Kolen, Michael J.

2009-01-01

41

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

42

Computing bivariate splines in scattered data fitting and the finite-element method  

NASA Astrophysics Data System (ADS)

A number of useful bivariate spline methods are global in nature, i.e., all of the coefficients of an approximating spline must be computed at one time. Typically this involves solving a system of linear equations. Examples include several well-known methods for fitting scattered data, such as the minimal energy, least-squares, and penalized least-squares methods. Finite-element methods for solving boundary-value problems are also of this type. It is shown here that these types of globally-defined splines can be efficiently computed, provided we work with spline spaces with stable local minimal determining sets.

Schumaker, Larry

2008-07-01

43

Spline methods for approximating quantile functions and generating random samples  

NASA Technical Reports Server (NTRS)

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

Schiess, J. R.; Matthews, C. G.

1985-01-01

44

B-Spline Method for Solving Boundary Value Problems of Linear Ordinary Differential Equations  

Microsoft Academic Search

\\u000a B-spline functions play important roles in both mathematics and engineering. In this paper, we develop a numerical method\\u000a for solving the boundary value problem of linear ODE with second-order by using B-spline. First, the cubic B-spline basis\\u000a functions are introduced, and then we use the linear combination of cubic B-spline basis to approximate the solution. Finally,\\u000a we obtain the numerical

Jincai Chang; Qianli Yang; Chunfeng Liu

45

THE LOSS OF ACCURACY OF STOCHASTIC COLLOCATION METHOD IN SOLVING NONLINEAR DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA  

SciTech Connect

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

46

A meshless collocation method based on the differential reproducing kernel interpolation  

NASA Astrophysics Data System (ADS)

A differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving partial differential equations governing a certain physical problem. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the DRK interpolation function, without directly differentiating the DRK interpolation function. In addition, the shape function of the DRK interpolation function at each sampling node is separated into a primitive function processing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied. A point collocation method based on the present DRK interpolation is developed for the analysis of one-dimensional bar problems, two-dimensional potential problems, and plane problems of elastic solids. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach, with excellent accuracy and fast convergence rate.

Wang, Yung-Ming; Chen, Syuan-Mu; Wu, Chih-Ping

2010-05-01

47

A Laplace transform-based fundamental collocation method for two-dimensional transient heat flow  

Microsoft Academic Search

The fundamental collocation method (FCM) is extended to handle two dimensional transient heat conduction problems in solids. The method is applied in the Laplace transform domain, after which an inversion technique is used to retrieve the time-domain solution. Examples are used to illustrate the method and a technique for evaluating accuracy is discussed. The performance was found to be very

Enayat Mahajerin; Gary Burgess

2003-01-01

48

A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations  

NASA Astrophysics Data System (ADS)

In this paper, a shifted Jacobi-Gauss collocation spectral method is proposed for solving the nonlinear Lane-Emden type equation. The spatial approximation is based on shifted Jacobi polynomials PT,n(?,?)(x) with ?, ? ? (-1, ?), T > 0, and n is the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and yields very accurate results.

Bhrawy, A. H.; Alofi, A. S.

2012-01-01

49

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

Microsoft Academic Search

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

50

Active image: A shape and topology preserving segmentation method using B-spline free form deformations  

Microsoft Academic Search

Unlike most conventional active contour models that drive the initial contours to match the object boundaries, we propose an “active image” segmentation method that deforms the image to match the initial contours, and hence can simultaneously segment multiple objects. The deformation field is modeled by B-spline free form deformations (FFD). Penalizing the bending energy of B-spline FFD enables us to

Chao Li; Ying Sun

2010-01-01

51

Meshless Local Petrov-Galerkin(MLPG) Mixed Collocation Method For Elasticity Problems  

Microsoft Academic Search

The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to inter- polate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is establishedat the nodal points, for the stresses, by using

S. N. Atluri; H. T. Liu; Z. D. Han

52

NOKIN1D: one-dimensional neutron kinetics based on a nodal collocation method  

NASA Astrophysics Data System (ADS)

The TRAC-BF1 one-dimensional kinetic model is a formulation of the neutron diffusion equation in the two energy groups' approximation, based on the analytical nodal method (ANM). The advantage compared with a zero-dimensional kinetic model is that the axial power profile may vary with time due to thermal-hydraulic parameter changes and/or actions of the control systems but at has the disadvantages that in unusual situations it fails to converge. The nodal collocation method developed for the neutron diffusion equation and applied to the kinetics resolution of TRAC-BF1 thermal-hydraulics, is an adaptation of the traditional collocation methods for the discretization of partial differential equations, based on the development of the solution as a linear combination of analytical functions. It has chosen to use a nodal collocation method based on a development of Legendre polynomials of neutron fluxes in each cell. The qualification is carried out by the analysis of the turbine trip transient from the NEA benchmark in Peach Bottom NPP using both the original 1D kinetics implemented in TRAC-BF1 and the 1D nodal collocation method.

Verdú, G.; Ginestar, D.; Miró, R.; Jambrina, A.; Barrachina, T.; Soler, Amparo; Concejal, Alberto

2014-06-01

53

Collocation method for the solution of the neutron transport equation with both symmetric and asymmetric scattering  

SciTech Connect

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

54

Weighted extended B-spline method for the approximation of the stationary Stokes problem  

NASA Astrophysics Data System (ADS)

A new stabilized, mesh-free method for the approximation of the Stokes problem, using weighted extended B-splines (WEB-splines) as shape functions has been proposed. The web-spline based bilinear velocity-constant pressure element satisfies the so called inf-sup condition or Ladyshenskaya-Babus[breve]ka-Brezzi (LBB) condition. The main advantage of this method over standard finite element methods is that it uses regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre-processing step. Convergence and Condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions.

Kumar, V. V. K. Srinivas; Kumar, B. V. Rathish; Das, P. C.

2006-02-01

55

Bicubic B-spline interpolation method for two-dimensional Laplace's equations  

NASA Astrophysics Data System (ADS)

Two-dimensional Laplace's equation is solved using bicubic B-spline interpolation method. An arbitrary surface with some unknown coefficients is generated using bicubic B-spline surface's formula. This surface is presumed to be the solution for the equation. The values of the coefficients are calculated by spline interpolation technique using the corresponding differential equations and boundary conditions. This method produces approximated analytical solution for the equation. A numerical example will be presented along with a comparison of the results with finite element and isogeometrical methods.

Abd Hamid, Nur Nadiah; Abd. Majid, Ahmad; Md. Ismail, Ahmad Izani

2013-04-01

56

Improved collocation methods with application to six-degree-of-freedom trajectory optimization  

NASA Astrophysics Data System (ADS)

An improved collocation method is developed for a class of problems that is intractable, or nearly so, by conventional collocation. These are problems in which there are two distinct timescales of the system states, that is, where a subset of the states have high-frequency variations while the remaining states vary comparatively slowly. In conventional collocation, the timescale for the discretization would be set by the need to capture the high-frequency dynamics. The problem then becomes very large and the solution of the corresponding nonlinear programming problem becomes geometrically more time consuming and difficult. A new two-timescale discretization method is developed for the solution of such problems using collocation. This improved collocation method allows the use of a larger time discretization for the low-frequency dynamics of the motion, and a second finer time discretization scheme for the higher-frequency dynamics of the motion. The accuracy of the new method is demonstrated first on an example problem, an optimal lunar ascent. The method is then applied to the type of challenging problem for which it is designed, the optimization of the approach to landing trajectory for a winged vehicle returning from space, the HL-20 lifting body vehicle. The converged solution shows a realistic landing profile and fully captures the higher-frequency rotational dynamics. A source code using the sparse optimizer SNOPT is developed for the use of this method which generates constraint equations, gradients, and the system Jacobian for problems of arbitrary size. This code constitutes a much-improved tool for aerospace vehicle design but has application to all two-timescale optimization problems.

Desai, Prasun N.

57

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation  

NASA Technical Reports Server (NTRS)

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

58

Higher-Order Numerical Solutions Using Cubic Splines.  

National Technical Information Service (NTIS)

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 ob...

S. G. Rubin, P. K. Khosla

1976-01-01

59

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

60

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

NASA Technical Reports Server (NTRS)

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

Solomonoff, A.; Turkel, E.

1986-01-01

61

A numerical method for KdV equation using collocation and radial basis functions  

Microsoft Academic Search

Recently, there has been an increasing interest in the study of initial boundary value problems for Korteweg–de Vries (KdV)\\u000a equations. In this paper, we propose a numerical scheme to solve the third-order nonlinear KdV equation using collocation\\u000a points and approximating the solution using multiquadric (MQ) radial basis function (RBF). The scheme works in a similar fashion\\u000a as finite-difference methods. Numerical

Mehdi Dehghan; Ali Shokri

2007-01-01

62

Spurious Modes in Spectral Collocation Methods with Two Non-Periodic Directions  

NASA Technical Reports Server (NTRS)

Collocation implementation of the Kleiser-Schumann's method in geometries with two non-periodic directions is shown to suffer from three spurious modes - line, column and checkerboard - contaminating the computed pressure field. The corner spurious modes are also present but they do not affect evaluation of pressure related quantities. A simple methodology in the inversion of the influence matrix will efficiently filter out these spurious modes.

Balachandar, S.; Madabhushi, Ravi K.

1992-01-01

63

A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids  

Microsoft Academic Search

An accurate Fourier-Chebyshev spectral collocation method has been developed for simulating flow past prolate spheroids. The incompressible Navier-Stokes equations are transformed to the prolate spheroidal co-ordinate system and discretized on an orthogonal body fitted mesh. The infinite flow domain is truncated to a finite extent and a Chebyshev discretization is used in the wall-normal direction. The azimuthal direction is periodic

Rajat Mittal

1999-01-01

64

Analysis of skewed plates by a Trefftz collocation method  

Microsoft Academic Search

A boundary technique, based on the Trefftz method, is applied to the analysis of skewed thin plates. The formulation uses a superposition of the approximating functions of the displacements (and its derivatives) followed by the approximate satisfaction of the boundary conditions (bc) at suitably chosen boundary points. The least squares criterion is used to obtain the unknowns of the problem,

V. M. A. Leitão; C. M. T. Fernandes

65

A Fourier collocation time domain method for numerically solving Maxwell's equations  

NASA Technical Reports Server (NTRS)

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Shebalin, John V.

1991-01-01

66

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation  

NASA Technical Reports Server (NTRS)

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

67

A time domain collocation method for studying the aeroelasticity of a two dimensional airfoil with a structural nonlinearity  

NASA Astrophysics Data System (ADS)

A time domain collocation method for the study of the motion of a two dimensional aeroelastic airfoil with a cubic structural nonlinearity is presented. This method first transforms the governing ordinary differential equations into a system of nonlinear algebraic equations (NAEs), which are then solved by a Jacobian-inverse-free NAE solver. Using the aeroelastic airfoil as a prototypical system, the time domain collocation method is shown here to be mathematically equivalent to the well known high dimensional harmonic balance method. Based on the fact that the high dimensional harmonic balance method is essentially a collocation method in disguise, we clearly explain the aliasing phenomenon of the high dimensional harmonic balance method. On the other hand, the conventional harmonic balance method is also applied. Previous studies show that the harmonic balance method does not produce aliasing in the framework of solving the Duffing equation. However, we demonstrate that a mathematical type of aliasing occurs in the harmonic balance method for the present self-excited nonlinear dynamical system. Besides, a parameter marching procedure is used to sufficiently eliminate the effects of aliasing pertaining to the time domain collocation method. Moreover, the accuracy of the time domain collocation method is compared with the harmonic balance method.

Dai, Honghua; Yue, Xiaokui; Yuan, Jianping; Atluri, Satya N.

2014-08-01

68

Temporal registration of 2D x-ray mammogram using triangular B-splines finite element method (TBFEM)  

Microsoft Academic Search

In this paper we develop a novel image processing technique to register two dimensional temporal mammograms for effective diagnosis and therapy. Our registration framework is founded upon triangular B-spline finite element method (TBFEM). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B-splines are much more powerful, associated with many desirable advantages for image registration, such

Kexiang Wang; Ying He; Hong Qin; Paul R. Fisher; Wei Zhao

2006-01-01

69

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

PubMed Central

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.

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

2014-01-01

70

Estimation of the subdiurnal UT1-UTC variations by the least squares collocation method  

NASA Astrophysics Data System (ADS)

The result of the two-week VLBI experiment CONT'94 has been processed by the least squares collocation method to calculate the UT1-UTC time series with high temporal resolution (one value every few minutes). It allows us to estimate the influence of tidal variations arising from the world's oceans on the EOP. Time series of UT1-UTC with high temporal resolution is demonstrated. Estimates of the four main tides (M2, S2, K1, O1) are in a good agreement with results of other authors.

Titov, O. A.

71

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method  

NASA Astrophysics Data System (ADS)

The Element free Galerkin method, which is based on the Moving Least Squares approximation, requires only nodal data and no element connectivity, and therefore is more flexible than the conventional finite element method. Direct imposition of essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from the Moving Least Squares approximation do not have the delta function property. In the prior literature, a direct collocation of the fictitious nodal values û used as undetermined coefficients in the MLS approximation, uh(x) [uh(x)=?.û], was used to enforce the essential boundary conditions. A modified collocation method using the actual nodal values of the trial function uh(x) is presented here, to enforce the essential boundary conditions. This modified collocation method is more consistent with the variational basis of the EFG method. Alternatively, a penalty formulation for easily imposing the essential boundary conditions in the EFG method with the MLS approximation is also presented. The present penalty formulation yields a symmetric positive definite system stiffness matrix. Numerical examples show that the present penalty method does not exhibit any volumetric locking and retains high rates of convergence for both displacements and strain energy. The penalty method is easy to implement as compared to the Lagrange multiplier method, which increases the number of degrees of freedom and yields a non-positive definite system matrix.

Zhu, T.; Atluri, S. N.

72

MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA  

SciTech Connect

Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.

Webster, Clayton G [ORNL; Jantsch, Peter A [ORNL; Teckentrup, Aretha L [ORNL; Gunzburger, Max D [ORNL

2013-01-01

73

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

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

74

B-spline method for solving linear system of second-order boundary value problems  

Microsoft Academic Search

The B-spline method is used for the numerical solution of a linear system of second-order boundary value problems. Two examples are considered for the numerical illustration and the method is also compared with the method proposed by J. Lu [J. Lu, Variational iteration method for solving a nonlinear system of second-order boundary value problems, Comput. Math. Appl. 54 (2007) 1133–1138].

Nazan Caglar; Hikmet Caglar

2009-01-01

75

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

76

Variability on the Propagation of a Plane Wave Using Stochastic Collocation Methods in a Bio Electromagnetic Application  

Microsoft Academic Search

In this letter, the uncertainties on the angles of propagation of a plane wave in a bio electromagnetic application are studied using two non intrusive stochastic collocation methods. The proposed techniques are used in this application, which employs a finite-difference time-domain scheme, but they can be used when applying other kinds of methods without modifying programs. The results obtained using

J. Silly-Carette; D. Lautru; M.-F. Wong; A. Gati; J. Wiart; V. Fouad Hanna

2009-01-01

77

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

78

B-spline modal method: a polynomial approach compared to the Fourier modal method.  

PubMed

A detailed analysis of the B-spline Modal Method (BMM) for one- and two-dimensional diffraction gratings and a comparison to the Fourier Modal Method (FMM) is presented. Owing to its intrinsic capability to accurately resolve discontinuities, BMM avoids the notorious problems of FMM that are associated with the Gibbs phenomenon. As a result, BMM facilitates significantly more efficient eigenmode computations. With regard to BMM-based transmission and reflection computations, it is demonstrated that a novel Galerkin approach (in conjunction with a scattering-matrix algorithm) allows for an improved field matching between different layers. This approach is superior relative to the traditional point-wise field matching. Moreover, only this novel Galerkin approach allows for an competitive extension of BMM to the case of two-dimensional diffraction gratings. These improvements will be very useful for high-accuracy grating computations in general and for the analysis of associated electromagnetic field profiles in particular. PMID:23787657

Walz, Michael; Zebrowski, Thomas; Küchenmeister, Jens; Busch, Kurt

2013-06-17

79

Two-dimensional mesh embedding for Galerkin B-spline methods  

NASA Technical Reports Server (NTRS)

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Shariff, Karim; Moser, Robert D.

1995-01-01

80

Collocation Methods for the Boltzmann Equation; Hot Atom Relaxation and Ion Transport in Gases  

Microsoft Academic Search

We present a preliminary investigation of the use of a B-spline basis for solving the Boltzmann equation with the intent of extending the methodology to treat the mobility of tracer ions moving in electric fields with arbitrary temporal and spatial dependence. The current study examines a simplified one-dimensional model using the smooth hard sphere Wigner Wilkins kernel and cubic B-splines.

Saheba Khurana; Mark Thachuk

2011-01-01

81

The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data.  

SciTech Connect

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

82

Membrane covered duct lining for high-frequency noise attenuation: prediction using a Chebyshev collocation method.  

PubMed

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

83

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method  

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 Mécanique 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

84

B-spline soliton solution of the fifth order KdV type equations  

NASA Astrophysics Data System (ADS)

In this paper, we develop a numerical solution based on sextic B-spline collocation method for solving the generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The numerical results are found to be in good agreement with the exact solution.

Zahra, W. K.; Ouf, W. A.; El-Azab, M. S.

2013-10-01

85

Spline-approximation solution of stress–strain problems for beveled cylindrical shells  

Microsoft Academic Search

The problem of bending of beveled circular cylindrical shells is solved by parametrizing the shell and reducing the two-dimensional\\u000a boundary-value problem to a one-dimensional one by the spline-collocation method. This problem is solved by the stable discrete-orthogonalization\\u000a method. The effect of the variability of the geometrical parameters on the displacement fields of circular cylinders is analyzed

Ya. M. Grigorenko; N. N. Kryukov; N. S. Kholkina

2009-01-01

86

Estimation of CRF and TRF from VLBI observations by the Least Square Collocation method  

NASA Astrophysics Data System (ADS)

The aim of this work is to obtain the Terrestrial Reference Frame (TRF), Celestial Reference Frame (CRF) and Earth Orientation Parameters (EOP) series from processing Very Long Baseline Interferometry (VLBI) data by the Least Square Collocation (LSC) method. The observations from 1979 to 2006 were processed with the QUASAR software. More than 4.5 millions delays were used. Coordinates and velocities of 126 VLBI stations and coordinates of 707 radio-sources were estimated. The 12 stations which have more than 200000 observations were used for no-net-translation/no-net-rotation tie to the VTRF2003 catalogue. The 212 defining radio-sources of ICRF-ext.2 were used for no-net-rotation tie to the CRF. The wet component of tropospheric delay and station clock offsets were estimated as sum of polynomial trend and stochastic signal with a-priori defined covariance function. The catalogues with and without stations antenna axis offset estimation were obtained and compared. The obtained solution were compared with other TRF/CRF VLBI solutions and there are showed that the QUASAR LSC solution have the same precision than others.

Kurdubov, S. L.

2006-08-01

87

A sequential method for spline approximation with variable knots. [recursive piecewise polynomial signal processing  

NASA Technical Reports Server (NTRS)

In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.

Mier Muth, A. M.; Willsky, A. S.

1978-01-01

88

Using the Stochastic Collocation Method for the Uncertainty Quantification of Drug Concentration Due to Depot Shape Variability  

PubMed Central

Numerical simulations entail modeling assumptions that impact outcomes. Therefore, characterizing, in a probabilistic sense, the relationship between the variability of model selection and the variability of outcomes is important. Under certain assumptions, the stochastic collocation method offers a computationally feasible alternative to traditional Monte Carlo approaches for assessing the impact of model and parameter variability. We propose a framework that combines component shape parameterization with the stochastic collocation method to study the effect of drug depot shape variability on the outcome of drug diffusion simulations in a porcine model. We use realistic geometries segmented from MR images and employ level-set techniques to create two alternative univariate shape parameterizations. We demonstrate that once the underlying stochastic process is characterized, quantification of the introduced variability is quite straightforward and provides an important step in the validation and verification process.

Preston, J. Samuel; Tasdizen, Tolga; Terry, Christi M.; Cheung, Alfred K.

2010-01-01

89

Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification  

Microsoft Academic Search

Non-intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) meth- ods are attractive techniques for uncertainty quantification (UQ) due to their strong math- ematical basis and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampling, linear regression, tensor-product quadra- ture, or Smolyak

M. S. Eldred

2009-01-01

90

A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems  

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

91

Temporal registration of 2D x-ray mammogram using triangular B-splines finite element method (TBFEM)  

NASA Astrophysics Data System (ADS)

In this paper we develop a novel image processing technique to register two dimensional temporal mammograms for effective diagnosis and therapy. Our registration framework is founded upon triangular B-spline finite element method (TBFEM). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B-splines are much more powerful, associated with many desirable advantages for image registration, such as flexible triangular domain, local control, space-varying smoothness, and sharp feature modeling. Empowered by the rigorous theory of triangular B-splines, our method can explicitly model the transformation between temporal mammogram pairs over irregular region of interest(ROI), using a collection of triangular B-splines. In addition, it is also capable of describing C0 continuous deformation at the interfaces between different elastic tissues, while the overall displacement field is smooth. Our registration process consists of two steps: 1) The template image is first nonlinearly deformed using TBFEM model, subject to pre-segmented feature constraints; 2) The deformed template image is further perturbed by applying pseudo image forces, aiming to reducing intensity-based discrepancies. The proposed registration framework has been tested extensively on practical clinical data, and the experimental results demonstrates that the registration accuracy is improved comparing to using conventional FEMs. Besides, the modeling of local C0 continuities of the displacement field helps to further increase the registration quality considerably.

Wang, Kexiang; He, Ying; Qin, Hong; Fisher, Paul R.; Zhao, Wei

2006-03-01

92

Free vibration of generally-laminated, shear-deformable, composite rectangular plates using a spline Rayleigh-Ritz method  

NASA Astrophysics Data System (ADS)

A Rayleigh-Ritz method is presented for predicting the natural frequencies of flat rectangular laminates which can have arbitrary lay-up. The effects of through-thickness shear deformation are included in the analysis. The displacement field utilizes B-spline functions in what has been referred to in earlier work as a B(k,k-1)-spline Rayleigh-Ritz method and the approach is versatile in the specification of boundary conditions. The results of a number of applications are presented in the form of studies showing the convergence of frequency values with increase in the number of spline sections used. The analysis procedure is seen to have good convergence characteristics when dealing with laminates of thin and thick geometry.

Dawe, D. J.; Wang, S.

93

Wave-front reconstruction with a shack-hartmann sensor with an iterative spline fitting method.  

PubMed

One limitation of the conventional Shack-Hartmann sensor is that the spots of each microlens have to remain in their respective subapertures. We present an algorithm that assigns the spots to their reference points unequivocally even if they are situated far outside their subaperture. For this assignment a spline function is extrapolated in successive steps of the iterative algorithm. The proposed method works in a single-shot technique and does not need any aid from mechanical devices. The reconstruction of a simulated steep aspherical wave front (approximately 100 lambda/mm slope) is described as well as experimental results of the measurement of a spherical wave front with a huge peak-to-valley value (approximately 400 lambda). The performance of the method is compared with the unwrapping method, which has been published before. PMID:18337926

Groening, S; Sick, B; Donner, K; Pfund, J; Lindlein, N; Schwider, J

2000-02-01

94

High-order numerical solutions using cubic splines  

NASA Technical Reports Server (NTRS)

The cubic spline collocation procedure for the numerical solution of partial differential equations was 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 for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

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

1975-01-01

95

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions  

NASA Astrophysics Data System (ADS)

In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 105) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov-Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ?, the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.

Loukopoulos, V. C.; Bourantas, G. C.; Skouras, E. D.; Nikiforidis, G. C.

2011-02-01

96

Study on spline wavelet finite-element method in multi-scale analysis for foundation  

NASA Astrophysics Data System (ADS)

A new finite element method (FEM) of B-spline wavelet on the interval (BSWI) is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the proposed finite elements have higher precision than the traditional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundationmodel excited by external or internal dynamic load. The proposed finite elements can be also used to connect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Xu, Qiang; Chen, Jian-Yun; Li, Jing; Xu, Gang; Yue, Hong-Yuan

2013-10-01

97

Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation.  

PubMed

The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images. PMID:17605385

Gelas, Amaud; Bernard, Olivier; Friboulet, Denis; Prost, Rémy

2007-07-01

98

An approximation algorithm for the solution of astrophysics equations using rational scaled generalized Laguerre function collocation method based on transformed Hermite-Gauss nodes  

NASA Astrophysics Data System (ADS)

In this paper we propose a collocation method for solving Lane-Emden type equation which is nonlinear or-dinary differential equation on the semi-infinite domain. This equation is categorized as singular initial value problems. We solve this equation by the generalized Laguerre polynomial collocation method based on Her-mite-Gauss nodes. This method solves the problem on the semi-infinite domain without truncating it to a fi-nite domain and transforming domain of the problem to a finite domain. In addition, this method reduces so-lution of the problem to solution of a system of algebraic equations.

Pirkhedri, Ali; Daneshjoo, P.; Javadi, H. H. S.; Navidi, H. R.; Khodamoradi, S.; Ghaderi, K.

2011-06-01

99

Spline Histogram Method for Reconstruction of Probability Density Functions of Clusters of Galaxies  

NASA Astrophysics Data System (ADS)

We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from www.virac.lv/en/soft.html.

Docenko, Dmitrijs; Berzins, Karlis

100

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

101

Examination of the circle spline routine  

NASA Technical Reports Server (NTRS)

The Circle Spline routine is currently being used for generating both two and three dimensional spline curves. It was developed for use in ESCHER, a mesh generating routine written to provide a computationally simple and efficient method for building meshes along curved surfaces. Circle Spline is a parametric linear blending spline. Because many computerized machining operations involve circular shapes, the Circle Spline is well suited for both the design and manufacturing processes and shows promise as an alternative to the spline methods currently supported by the Initial Graphics Specification (IGES).

Dolin, R. M.; Jaeger, D. L.

1985-01-01

102

Watermarking T-Spline surfaces  

Microsoft Academic Search

This paper proposes two data embedding algorithms for T-spline surfaces, one is suitable for steganography, and the other for robust shape-preserving watermarking. For steganography, we embed data into the points on T-spline surfaces by using constrained optimization method. For robust shape-preserving watermarking, we use the local knot insertion of T-spline surfaces. The experiment results and their analyses are also presented.

Weng Bin; Pan Ri-jing; Yao Zhi-qiang; Yang Shan-chao; Feng Xiao-qing; Pan Zhi-geng

2008-01-01

103

Capacitance matrix technique for avoiding spurious eigenmodes in the solution of hydrodynamic stability problems by Chebyshev collocation method  

NASA Astrophysics Data System (ADS)

We present a simple technique for avoiding physically spurious eigenmodes that often occur in the solution of hydrodynamic stability problems by the Chebyshev collocation method. The method is demonstrated on the solution of the Orr-Sommerfeld equation for plane Poiseuille flow. Following the standard approach, the original fourth-order differential equation is factorised into two second-order equations using a vorticity-type auxiliary variable with unknown boundary values which are then eliminated by a capacitance matrix approach. However the elimination is constrained by the conservation of the structure of matrix eigenvalue problem, it can be done in two basically different ways. A straightforward application of the method results in a couple of physically spurious eigenvalues which are either huge or close to zero depending on the way the vorticity boundary conditions are eliminated. The zero eigenvalues can be shifted to any prescribed value and thus removed by a slight modification of the second approach.

Hagan, Jonathan; Priede, J?nis

2013-04-01

104

a High-Order B-Spline Based Panel Method for Unsteady, Nonlinear, Three-Dimensional FreeSurface Flows  

Microsoft Academic Search

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

105

Sub-band denoising and spline curve fitting method for hemodynamic measurement in perfusion MRI  

NASA Astrophysics Data System (ADS)

In clinical research, non-invasive MR perfusion imaging is capable of investigating brain perfusion phenomenon via various hemodynamic measurements, such as cerebral blood volume (CBV), cerebral blood flow (CBF), and mean trasnit time (MTT). These hemodynamic parameters are useful in diagnosing brain disorders such as stroke, infarction and periinfarct ischemia by further semi-quantitative analysis. However, the accuracy of quantitative analysis is usually affected by poor signal-to-noise ratio image quality. In this paper, we propose a hemodynamic measurement method based upon sub-band denoising and spline curve fitting processes to improve image quality for better hemodynamic quantitative analysis results. Ten sets of perfusion MRI data and corresponding PET images were used to validate the performance. For quantitative comparison, we evaluate gray/white matter CBF ratio. As a result, the hemodynamic semi-quantitative analysis result of mean gray to white matter CBF ratio is 2.10 +/- 0.34. The evaluated ratio of brain tissues in perfusion MRI is comparable to PET technique is less than 1-% difference in average. Furthermore, the method features excellent noise reduction and boundary preserving in image processing, and short hemodynamic measurement time.

Lin, Hong-Dun; Huang, Hsiao-Ling; Hsu, Yuan-Yu; Chen, Chi-Chen; Chen, Ing-Yi; Wu, Liang-Chi; Liu, Ren-Shyan; Lin, Kang-Ping

2003-05-01

106

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies  

NASA Technical Reports Server (NTRS)

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.

1985-01-01

107

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

PubMed

The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE. PMID:12159927

Nielsen, S A; Hesthaven, J S

2002-05-01

108

One sense per collocation  

Microsoft Academic Search

Previous work [Gale, Church and Yarowsky, 1992] showed that with high probability a polysemous word has one sense per discourse. In this paper we show that for certain definitions of collocation, a polysemous word exhibits essentially only one sense per collocation. We test this empirical hypothesis for several definitions of sense and collocation, and discover that it holds with 90--99%

David Yarowsky

1993-01-01

109

Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method  

SciTech Connect

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

110

Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces.  

PubMed

An accurate creeping ray-tracing algorithm is presented in this paper to determine the tracks of creeping waves (or creeping rays) on arbitrarily shaped free-form parametric surfaces [nonuniform rational B-splines (NURBS) surfaces]. The main challenge in calculating the surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths along which the creeping rays propagate. On one single parametric surface patch, the geodesic paths need to be computed by solving the geodesic equations numerically. Furthermore, realistic objects are generally modeled as the union of several connected NURBS patches. Due to the discontinuity of the parameter between the patches, it is more complicated to compute geodesic paths on several connected patches than on one single patch. Thus, a creeping ray-tracing algorithm is presented in this paper to compute the geodesic paths of creeping rays on the complex objects that are modeled as the combination of several NURBS surface patches. In the algorithm, the creeping ray tracing on each surface patch is performed by solving the geodesic equations with a Runge-Kutta method. When the creeping ray propagates from one patch to another, a transition method is developed to handle the transition of the creeping ray tracing across the border between the patches. This creeping ray-tracing algorithm can meet practical requirements because it can be applied to the objects with complex shapes. The algorithm can also extend the applicability of NURBS for electromagnetic and optical applications. The validity and usefulness of the algorithm can be verified from the numerical results. PMID:23595326

Chen, Xi; He, Si-Yuan; Yu, Ding-Feng; Yin, Hong-Cheng; Hu, Wei-Dong; Zhu, Guo-Qiang

2013-04-01

111

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

112

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

NASA Astrophysics Data System (ADS)

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

Wang, Chunqi; Huang, Lixi

2012-09-01

113

Adaptive subdivision method with crack prevention for rendering Beta-spline objects. Technical report, 7 August 1984-6 August 1987  

SciTech Connect

Adaptive subdivision is a method of creating polygonal approximations to spline surfaces. An adaptive subdivision algorithm takes an input a spline surface and a tolerance epsilon, and outputs a piecewise planar approximation to the surface that is guaranteed to differ from the actual surface by a distance no greater than epsilon. These algorithms proceed by recursively splitting the surface into smaller subsurfaces, ultimately approximating subsurfaces with planar polyhedra. These algorithms are therefore characterized by the mathematics behind the splitting of a surface, the test that is used to determine when to stop the recursion, and the method by which a subsurface is approximated by polyhedra. Algorithms of this type are currently known for spline techniques such as Bezier and B-splines. This paper describes the Beta-spline curve and surface technique and derive the equations governing the splitting of Beta-spline curves and surfaces. It presents a very general adaptive subdivision algorithm that can be used with a variety of surface techniques. It incorporates splitting criteria based on flatness and prevents cracks from occuring between approximating polyhedra. The tolerance controlling the splitting process may itself be adaptive, so that as an object moves farther away, the tolerance is automatically increased.

Barsky, B.A.; DeRose, T.D.; Dippe, M.D.

1987-08-06

114

A Comparison of Some Model Order Reduction Methods for Fast Simulation of Soft Tissue Response using the Point Collocation-based Method of Finite Spheres (PCMFS)  

PubMed Central

In this paper we develop the Point Collocation-based Method of Finite Spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation, Hankel optimal model and truncated balanced realization techniques for PCMFS. The PCMFS was developed in [1] as a physics-based technique for real time simulation of surgical procedures. It is a meshfree numerical method in which discretization is performed using a set of nodal points with approximation functions compactly supported on spherical subdomains centered at the nodes. The point collocation method is used as the weighted residual technique where the governing differential equations are directly applied at the nodal points. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, truncated balanced realization results in the highest accuracy while modal truncation results in the highest efficiency.

BaniHani, Suleiman; De, Suvranu

2009-01-01

115

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method  

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

116

Three-dimensional anisotropic seismic wave modelling in spherical coordinates by a collocated-grid finite-difference method  

NASA Astrophysics Data System (ADS)

To simulate seismic wave propagation in the spherical Earth, the Earth's curvature has to be taken into account. This can be done by solving the seismic wave equation in spherical coordinates by numerical methods. In this paper, we use an optimized, collocated-grid finite-difference scheme to solve the anisotropic velocity-stress equation in spherical coordinates. To increase the efficiency of the finite-difference algorithm, we use a non-uniform grid to discretize the computational domain. The grid varies continuously with smaller spacing in low velocity layers and thin layer regions and with larger spacing otherwise. We use stress-image setting to implement the free surface boundary condition on the stress components. To implement the free surface boundary condition on the velocity components, we use a compact scheme near the surface. If strong velocity gradient exists near the surface, a lower-order scheme is used to calculate velocity difference to stabilize the calculation. The computational domain is surrounded by complex-frequency shifted perfectly matched layers implemented through auxiliary differential equations (ADE CFS-PML) in a local Cartesian coordinate. We compare the simulation results with the results from the normal mode method in the isotropic and anisotropic models and verify the accuracy of the finite-difference method.

Zhang, Wei; Shen, Yang; Zhao, Li

2012-03-01

117

Multivariate Adaptive Regression Splines  

Microsoft Academic Search

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

118

A Hermite DRK interpolation-based collocation method for the analyses of Bernoulli-Euler beams and Kirchhoff-Love plates  

NASA Astrophysics Data System (ADS)

A Hermite differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the Hermite DRK interpolation, without directly differentiating it. In addition, the shape function of this interpolation at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. A weighted least-squares collocation method based on this interpolation is developed for the static analyses of classical beams and plates with fully simple and clamped supports, in which its accuracy and convergence rate are examined, and some guidance for using this method is suggested.

Chen, Syuan-Mu; Wu, Chih-Ping; Wang, Yung-Ming

2011-04-01

119

Variational B-spline level-set method for fast image segmentation  

Microsoft Academic Search

In the field of image segmentation, most of level-set-based active contour approaches are based on a discrete represen- tation of the associated implicit function. We present in this paper a different formulation where the level-set is modelled as a continuous parametric function expressed on a B-spline basis. Starting from the Mumford-Shah energy functional, we show that this formulation allows computing

Olivier Bernard; Denis Friboulet; Philippe Thévenaz; Michael Unser

2008-01-01

120

Analysis of three-dimensional splines and their application to the initial graphics exchange specification  

SciTech Connect

This research develops the fundamental theories associated with three-dimensional splines and the philosophies underlying the Initial Graphics Exchange Specification (IGES). Splines have been classified into three main categories: polynomial splines, splines-in-tension, and blending splines. The importance of a three-dimensional spline standard is given. It is shown that no single spline routine can adequately define a curve for every possible application. A possible three-dimensional spline standard should therefore contain a spline routine from each of the three categories. The B-spline, Cline's spline-in-tension, and Circle Spline were the three spline routines selected. The properties and characteristics that these splines should possess are defined. Two methods for extending a two-dimensional spline into three dimensions are given. The B-spline is extended parametrically and the Spline-in-Tension is extended explicitly. It will be shown that the parametric form is the more powerful and computationally efficient method. An alternative method for representing splines in IGES is presented. This alternate method uses the IGES Copious Data Entity. It has a smaller file size than the traditionally used Parametric Spline Curve Entity. The use of this method is geared toward the application of splines in design and analysis work. The data stored within the file by each spline routine represents the minimum amount of information required to uniquely define the spline curve. The alternative method for storing and transferring spline data is structured in a manner that allows each spline routine to read and write files efficiently. Using this data file, a spline routine can generate a curve by reading the output of another spline routine. It will be demonstrated that spline transfer between both similar and dissimilar spline routines can be done accurately and efficiently. 72 refs., 16 figs.

Dolin, R.M.

1985-08-01

121

Interchangeable spline reference guide  

SciTech Connect

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

122

Incidental Learning of Collocation  

ERIC Educational Resources Information Center

This study investigated the effects of repetition on the learning of collocation. Taiwanese university students learning English as a foreign language simultaneously read and listened to one of four versions of a modified graded reader that included different numbers of encounters (1, 5, 10, and 15 encounters) with a set of 18 target collocations.…

Webb, Stuart; Newton, Jonathan; Chang, Anna

2013-01-01

123

Split spline screw  

NASA Technical Reports Server (NTRS)

A split spline screw type payload fastener assembly, including three identical male and female type split spline sections, is discussed. The male spline sections are formed on the head of a male type spline driver. Each of the split male type spline sections has an outwardly projecting load baring segment including a convex upper surface which is adapted to engage a complementary concave surface of a female spline receptor in the form of a hollow bolt head. Additionally, the male spline section also includes a horizontal spline releasing segment and a spline tightening segment below each load bearing segment. The spline tightening segment consists of a vertical web of constant thickness. The web has at least one flat vertical wall surface which is designed to contact a generally flat vertically extending wall surface tab of the bolt head. Mutual interlocking and unlocking of the male and female splines results upon clockwise and counter clockwise turning of the driver element.

Vranish, John M. (inventor)

1993-01-01

124

Approximation and error estimation in high dimensional space for stochastic collocation methods on arbitrary sparse samples  

SciTech Connect

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; Deiterding, Ralf [ORNL; Hauck, Cory D [ORNL; Jakeman, John D [ORNL; Xiu, Dongbin [ORNL

2012-01-01

125

An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers  

Microsoft Academic Search

Two mathematical approaches are combined to calculate high Reynolds number in- compressible fluid-structure interaction: a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion, and Brinkman penalization to enforce solid bound- aries of arbitrary complexity. We also implement a wavelet-based multilevel solver for the Poisson problem for the pressure at each time step. The method

Nicholas K.-R. Kevlahan; Oleg V. Vasilyev

2005-01-01

126

Spectral collocation methods for solution of Einstein's equations in null quasi-spherical coordinates  

Microsoft Academic Search

The spectral methods which are being used to solve Einstein's equations innull quasi-spherical coordinates are described. They include Fast Fourier methodsfor evaluating derivatives in a uniform grid representation and methods for transformingto and from spin-weighted spherical harmonic representations. In theory,expressions involving spherical harmonics up to any fixed maximum angular momentum L can be routinely manipulated with accuracy depending only on

Andrew H. Norton

127

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling  

SciTech Connect

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

128

Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids  

NASA Astrophysics Data System (ADS)

Surface topography has been considered a difficult task for seismic wave numerical modelling by the finite-difference method (FDM) because the most popular staggered finite-difference scheme requires a rectilinear grid. Even though there are numerous collocated grid schemes in other computational fields that could be used to solve the first-order hyperbolic equations, the lack of a stable free-surface boundary condition implementation for curvilinear grids also obstructs the adoption of curvilinear grids in seismic wave FDM modelling. In this study, we use generalized curvilinear grids that can fit the surface topography to discretize the computational domain and describe the implementation of a collocated grid finite-difference scheme, a higher order MacCormack scheme, to solve the first-order hyperbolic velocity-stress equations on the curvilinear grid. To achieve a sufficiently accurate and stable free-surface boundary condition implementation on the curvilinear grids, we propose the traction image method that antisymmetrically images the traction components instead of the stress components to the ghost points above the free surface. Since the velocity derivatives at the free surface are provided by the free-surface condition, we use a compact scheme to compute the velocity derivatives near the free surface and avoid the use of velocity values on the ghost points. Numerical tests verify that using the curvilinear grid, the collocated finite-difference scheme and the traction image technique can simulate seismic wave propagation in the presence of surface topography with sufficient accuracy.

Zhang, Wei; Zhang, Zhenguo; Chen, Xiaofei

2012-07-01

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

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

NASA Technical Reports Server (NTRS)

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

Karageorghis, Andreas; Phillips, Timothy N.

1990-01-01

131

Numerical method for shape optimization using T-spline based isogeometric method  

Microsoft Academic Search

Numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. However,\\u000a the finite-element-based shape design sensitivity analysis and optimization have experienced some bottleneck problems such\\u000a as design parameterization and design remodeling during optimization. In this paper, as a remedy for these problems, an isogeometric-based\\u000a shape design sensitivity analysis and optimization methods are developed incorporating with

Seung-Hyun Ha; K. K. Choi; Seonho Cho

2010-01-01

132

A constructive approach to nodal splines  

NASA Astrophysics Data System (ADS)

In the context of local spline interpolation methods, nodal splines have been introduced as possible fundamental functions by de Villiers and Rohwer in 1988. The corresponding local spline interpolation operator possesses the desirable property of reproducing a large class of polynomials. However, it was remarked that their definition is rather intricate so that it seems desirable to reveal the actual origin of these splines. The real source can be found in the Martensenoperator which can be obtained by two-point Hermite spline interpolation problem posed and proved by Martensen [Darstellung und Entwicklung des Restgliedes der Gregoryschen Quadraturformel mit Hilfe von Spline-Funktionen, Numer. Math. 21(1973)70-80]. On the one hand, we will show how to represent the Hermite Martensen spline recursively and, on the other hand, explicitly in terms of the B-spline by using the famous Marsden identity. Having introduced the Martensenoperator, we will show that the nodal spline interpolation operator can be obtained by a special discretization of the occurring derivatives. We will consider symmetric nodal splines of odd degree that can be obtained by our methods in a natural way.

Siewer, Ralf

2007-06-01

133

Monotone and convex quadratic spline interpolation  

NASA Technical Reports Server (NTRS)

A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.

Lam, Maria H.

1990-01-01

134

Regularization of B-Spline Objects*  

PubMed Central

By a d-dimensional B-spline object (denoted as ), we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object we mean the process of relocating the control points of such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for , d = 1, 2, 3 based on solving weak form L2-gradient flows constructed from the minimization of certain regularizing energy functionals. These flows are integrated via the finite element method using B-spline basis functions. Our experimental results demonstrate that our new regularization method is very effective.

Xu, Guoliang; Bajaj, Chandrajit

2010-01-01

135

B-spline interpolation compared with finite difference, finite element and finite volume methods which applied to two-point boundary value problems  

Microsoft Academic Search

This paper considers the B-spline interpolation and compares this method with finite difference, finite element and finite volume methods which applied to the two-point boundary value problem.-ddxp(x)dudx=f(x),axb,u(a)=u(b)=0.

Hikmet Caglar; Nazan Caglar; Khaled Elfaituri

2006-01-01

136

Application of the parabolic spline method (PSM) to a multi-dimensional conservative semi-Lagrangian transport scheme (SLICE)  

NASA Astrophysics Data System (ADS)

The recently devised one-dimensional parabolic spline method (PSM) for efficient, conservative, and monotonic remapping is introduced into the semi-Lagrangian inherently-conserving and efficient (SLICE) scheme for transport problems in multi-dimensions. To ensure mass conservation, an integral form of the transport equation is used rather than the differential form of classical semi-Lagrangian schemes. Integrals within the SLICE scheme are computed using multiple sweeps of PSM along flow-dependent cascade directions to avoid the large timestep-dependent splitting errors associated with traditional fixed-direction splitting. Accuracy of the overall scheme, including at large timestep, is demonstrated using two-dimensional test problems in both Cartesian and spherical geometries and compared with that of the piecewise parabolic method (PPM) applied within the same SLICE framework.

Zerroukat, M.; Wood, N.; Staniforth, A.

2007-07-01

137

A wavelet Galerkin method employing B-spline bases for solid mechanics problems without the use of a fictitious domain  

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

138

Shape identification technique for a two-dimensional elliptic system by boundary integral equation method  

NASA Technical Reports Server (NTRS)

The geometrical structure of the boundary shape for a two-dimensional boundary value problem is identified. The output least square identification method is considered for estimating partially unknown boundary shapes. A numerical parameter estimation technique using the spline collocation method is proposed.

Kojima, Fumio

1989-01-01

139

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

Code of Federal Regulations, 2011 CFR

...2011-10-01 false Standards for physical collocation and virtual collocation...Carriers § 51.323 Standards for physical collocation and virtual collocation...An incumbent LEC shall provide physical collocation and virtual...

2011-10-01

140

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

Code of Federal Regulations, 2012 CFR

...2012-10-01 false Standards for physical collocation and virtual collocation...Carriers § 51.323 Standards for physical collocation and virtual collocation...An incumbent LEC shall provide physical collocation and virtual...

2012-10-01

141

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

Code of Federal Regulations, 2010 CFR

...2010-10-01 false Standards for physical collocation and virtual collocation...Carriers § 51.323 Standards for physical collocation and virtual collocation...An incumbent LEC shall provide physical collocation and virtual...

2010-10-01

142

Shape preserving spline interpolation  

NASA Technical Reports Server (NTRS)

A rational spline solution to the problem of shape preserving interpolation is discussed. The rational spline is represented in terms of first derivative values at the knots and provides an alternative to the spline-under-tension. The idea of making the shape control parameters dependent on the first derivative unknowns is then explored. The monotonic or convex shape of the interpolation data can then be preserved automatically through the solution of the resulting non-linear consistency equations of the spline.

Gregory, J. A.

1985-01-01

143

Estimation of divergence and vorticity using multidimensional smoothing splines  

NASA Technical Reports Server (NTRS)

Laplacian smoothing splines, smoothing splines on the sphere, and smoothing pseudo splines on the sphere are presented. The method of generalized cross validation to choose the smoothing parameter is described. These methods are applied to estimate divergence and vorticity of the atmosphere from wind speed and wind direction.

Wendelberger, J. G.

1982-01-01

144

Application of a shock-fitted spectral collocation method for computing transient high-speed inviscid flows over a blunt nose  

NASA Astrophysics Data System (ADS)

Interaction of freestream disturbances with high-speed inviscid flow over a blunt nose is simulated utilizing a shock-fitted spectral collocation method. The unsteady flow computations are made through solving the 2D Euler equations by virtue of such a dissipation-free numerical algorithm for precise unsteady flow simulations. A shock-fitting technique is employed to accurately compute the unsteady shock motions and its interaction with monochromatic freestream disturbances of different conditions. A symmetry condition is proposed to accurately model the both steady and unsteady characters of the symmetry boundary, which allows the use of halved geometries and avoids the extra computational cost. The computational results for a cylinder at Mach 8.03 are presented and verified through comparisons with other numerical and promising analytical solutions. The stagnation line where the most energetic interactions take place is inspected carefully. The study shows the significant influence of the shock on its subsequent flow field in unsteady simulations and notable ability of the shock-fitted spectral collocation method implemented for the study of such problems.

Najafi, Mehdi; Hejranfar, Kazem; Esfahanian, Vahid

2014-01-01

145

The L2Polynomial Spline Pyramid  

Microsoft Academic Search

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

146

Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method  

NASA Astrophysics Data System (ADS)

The Finite Cell Method (FCM) is an embedded domain method, which combines the fictitious domain approach with high-order finite elements, adaptive integration, and weak imposition of unfitted Dirichlet boundary conditions. For smooth problems, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. The present contribution first unhinges the FCM concept from a special high-order basis. Several benchmarks of linear elasticity and a complex proximal femur bone with inhomogeneous material demonstrate that for small deformation analysis, FCM works equally well with basis functions of the p-version of the finite element method or high-order B-splines. Turning to large deformation analysis, it is then illustrated that a straightforward geometrically nonlinear FCM formulation leads to the loss of uniqueness of the deformation map in the fictitious domain. Therefore, a modified FCM formulation is introduced, based on repeated deformation resetting, which assumes for the fictitious domain the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis, preserving the full range of advantages of linear elastic FCM, in particular exponential rates of convergence. Finally, the weak imposition of unfitted Dirichlet boundary conditions via the penalty method, the robustness of FCM under severe mesh distortion, and the large deformation analysis of a complex voxel-based metal foam are addressed.

Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Düster, Alexander; Rank, Ernst

2012-10-01

147

Image Denoising Using Orthogonal Spline  

NASA Astrophysics Data System (ADS)

We apply new multiresolution theory based on orthogonal spline to image denoising. Just like spline interpolation, the new theory can well approximate any function. It also integrates symmetry, therefore there is no loss or getting and no phase derivation when one reconstruct signal after decomposition. The new method is applied to image denoising via soft-thresholding. Comparing with commonly used wavelets, the new method can well separate noise and image and shows potential application in improving vision quality and preserving edge information for denoised image.

Zhou, Kaiting; Zheng, Lixin; Lin, Fuyong

148

Spline approximation of quantile functions  

NASA Technical Reports Server (NTRS)

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.

Schiess, J. R.; Matthews, C. G.

1983-01-01

149

An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media  

SciTech Connect

In this study, a probabilistic collocation method (PCM) on sparse grids was used to solve stochastic equations describing flow and transport in three-dimensional in saturated, randomly heterogeneous porous media. Karhunen-Lo\\`{e}ve (KL) decomposition was used to represent the three-dimensional log hydraulic conductivity $Y=\\ln K_s$. The hydraulic head $h$ and average pore-velocity $\\bf v$ were obtained by solving the three-dimensional continuity equation coupled with Darcy's law with random hydraulic conductivity field. The concentration was computed by solving a three-dimensional stochastic advection-dispersion equation with stochastic average pore-velocity $\\bf v$ computed from Darcy's law. PCM is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using the sparse grid points, PCM can handle a random process with large number of random dimensions, with relatively lower computational cost, compared to full tensor products. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM. By comparing the MC and PCM results for mean and standard deviation of concentration, it is evident that the PCM approach is computational more efficient than Monte Carlo simulations. Unlike the conventional moment-equation approach, there is no limitation on the amplitude of random perturbation in PCM. Furthermore, PCM on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.

Lin, Guang; Tartakovsky, Alexandre M.

2009-05-01

150

Cubic splines for image interpolation and digital filtering  

Microsoft Academic Search

This paper presents the use of B-splines as a tool in various digital signal processing applications. The theory of B-splines is briefly reviewed, followed by discussions on B-spline interpolation and B-spline filtering. Computer implementation using both an efficient software viewpoint and a hardware method are discussed. Finally, experimental results are presented for illustrative purposes in two-dimensional image format. Applications to

Hsieh Hou; H. C. Andrews

1978-01-01

151

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method  

Microsoft Academic Search

The Element free Galerkin method, which is based on the Moving Least Squares approximation, re- quires only nodal data and no element connectivity, and therefore is more flexible than the conventional finite el- ement method. Direct imposition of essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from the Moving Least Squares

T. Zhu; S. N. Atluri

2007-01-01

152

Inelastic initial local buckling of skew thin thickness-tapered plates with and without intermediate supports using the isoparametric spline finite strip method  

Microsoft Academic Search

In this paper, skew isotropic plates subjected to in-plane loadings are analyzed using a stability analysis based on the isoparametric spline finite strip method, which includes inelasticity. Using this method, the initial inelastic local buckling of skew plates with or without intermediate line supports is studied based on Ramberg–Osgood representation of the stress–strain curve using the deformation theory of plasticity.

S. Lotfi; M. Azhari; A. Heidarpour

2011-01-01

153

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method  

Microsoft Academic Search

The Element free Galerkin method, which is based on the Moving Least Squares approximation, requires only nodal data and\\u000a no element connectivity, and therefore is more flexible than the conventional finite element method. Direct imposition of\\u000a essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from\\u000a the Moving Least Squares approximation do

T. Zhu; S. N. Atluri

1998-01-01

154

Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research  

PubMed Central

Summary 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 paper, 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 (DBE) 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 to an HIV study to further illustrate the usefulness of the proposed approaches.

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-01-01

155

Modeling and Design of All-Optical Integrated Logic Devices Using the Novel Local Interpolatory Cardinal Spline Method.  

NASA Astrophysics Data System (ADS)

A novel numerical method, hereafter called the Local Interpolatory Cardinal Spline (LICS) method, is developed to model and simulate the behavior of optical wave propagation in a nonlinear medium. The architecture of this method is as simple as the finite differences scheme, and it has higher efficiency and accuracy than the widely used Beam Propagation Method. Numerical comparisons between the LICS method and BPM are investigated in the context of solving the Nonlinear Schrodinger Equation. The LICS method is then used to study the phenomena of soliton fusion and steering in a Kerr-type nonlinear medium. In certain particularly simple cases, an analytical approach based on the perturbation method is used for analysis to give a fundamental understanding of the fusion and steering processes for solitons in both the temporal and spatial domains. The analytical expression of a two-soliton fusion and steering system is obtained and the relationships between the fusion process and other factors are determined. For more complicated cases, the LICS method is used to simulate the soliton dynamics. Analysis of this fusion and steering process resulted in the design of an all-optical 1 x 2 switching device. The performance of this switch is analyzed based on power transmission efficiency and control power. The compactness of size, the simple structure, and the switching speed of this device are evident from the design flexibility and the efficient use of fusion phenomena. Furthermore, the design of a one-stage 1 x 4 all-optical switch for time-division demultiplexing application is also presented in the dissertation. Simulations of the device performance are evaluated with the device operating in power-controlled mode. Optimal design parameters and flexibilities of the control-power setting are also demonstrated. In addition, the basic equation governing the fusion and steering for two different-colored solitons in nonlinear planar structures is derived. Possible applications for this phenomenon are discussed.

Zha, Jun

156

A note on bimodality in the log-likelihood function for penalized spline mixed models  

Microsoft Academic Search

For a smoothing spline or general penalized spline model, the smoothing parameter can be estimated using residual maximum likelihood (REML) methods by expressing the spline in the form of a mixed model. The possibility of bimodality in the profile log-likelihood function for the smoothing parameter of these penalized spline mixed models is demonstrated. A canonical transformation into independent observations is

Sue Welham; Robin Thompson

2009-01-01

157

Loops, polytopes and splines  

NASA Astrophysics Data System (ADS)

We uncover an unexpected connection between the physics of loop integrals and the mathematics of spline functions. One loop integrands are Laplace transforms of splines. This clarifies the geometry of the associated loop integrals, since a n-node spline has support on a n-vertex polyhedral cone. One-loop integrals are integrals of splines on a hyperbolic slice of the cone, yielding polytopes in AdS space. Splines thus give a geometrical counterpart to the rational function identities at the level of the integrand. Spline technology also allows for a clear, simple, algebraic decomposition of higher point loop integrals in lower dimensional kinematics in terms of lower point integrals — e.g. an hexagon integral in 2d kinematics can be written as a sum of scalar boxes. Higher loops can also be understood directly in terms of splines — they map onto spline convolutions, leading to an intriguing representation in terms of hyperbolic simplices integrated over other hyperbolic simplices. We finish with speculations on the interpretation of one-loop integrals as partition functions, inspired by the use of splines in counting points in polytopes.

Paulos, Miguel F.

2013-06-01

158

Spherical Splines  

Microsoft Academic Search

The idea of replacing line segments by geodesics in Riemannian manifolds to generalize classical constructions of Bezier polynomials has been around at least since 1985 (Shoemake, 1985), (Duff, 1985). However rather little is known about generalized Bezier curves in spheres. The practical use of generalized Bezier curves for interpolating spherical data is limited by a lack of systematic methods for

LYLE NOAKES

159

A New Modeling Method for Objects with Branching Problem Using Non-uniform B-Spline  

Microsoft Academic Search

In many applications, objects are reconstructed from cross-sections for visualization, finite element and dynamic analysis. Although cross-section of an object may contain multiple contours, a few papers have dealt with branching problem. Moreover ends of branches are described flatly. In this paper, as a basic study for dynamic analysis of a human knee joint, we present a new modeling method

Hyo Shin Kim; Yoon Hyuk Kim; Yeon Hyeon Choe; Sung-min Kim; Taeg-sang Cho; Joung Hwan Mun

2004-01-01

160

Computer program for fitting low-order polynomial splines by method of least squares  

NASA Technical Reports Server (NTRS)

FITLOS is computer program which implements new curve fitting technique. Main program reads input data, calls appropriate subroutines for curve fitting, calculates statistical analysis, and writes output data. Method was devised as result of need to suppress noise in calibration of multiplier phototube capacitors.

Smith, P. J.

1972-01-01

161

Interchangeable spline reference guide.  

National Technical Information Service (NTIS)

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 ...

R. M. Dolin

1994-01-01

162

Cubic Spline Model  

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

163

Detection of defects on apple using B-spline lighting correction method  

NASA Astrophysics Data System (ADS)

To effectively extract defective areas in fruits, the uneven intensity distribution that was produced by the lighting system or by part of the vision system in the image must be corrected. A methodology was used to convert non-uniform intensity distribution on spherical objects into a uniform intensity distribution. A basically plane image with the defective area having a lower gray level than this plane was obtained by using proposed algorithms. Then, the defective areas can be easily extracted by a global threshold value. The experimental results with a 94.0% classification rate based on 100 apple images showed that the proposed algorithm was simple and effective. This proposed method can be applied to other spherical fruits.

Li, Jiangbo; Huang, Wenqian; Guo, Zhiming

164

Accelerating the performance of a novel meshless method based on collocation with radial basis functions by employing a graphical processing unit as a parallel coprocessor  

NASA Astrophysics Data System (ADS)

In recent times, a variety of industries, applications and numerical methods including the meshless method have enjoyed a great deal of success by utilizing the graphical processing unit (GPU) as a parallel coprocessor. These benefits often include performance improvement over the previous implementations. Furthermore, applications running on graphics processors enjoy superior performance per dollar and performance per watt than implementations built exclusively on traditional central processing technologies. The GPU was originally designed for graphics acceleration but the modern GPU, known as the General Purpose Graphical Processing Unit (GPGPU) can be used for scientific and engineering calculations. The GPGPU consists of massively parallel array of integer and floating point processors. There are typically hundreds of processors per graphics card with dedicated high-speed memory. This work describes an application written by the author, titled GaussianRBF to show the implementation and results of a novel meshless method that in-cooperates the collocation of the Gaussian radial basis function by utilizing the GPU as a parallel co-processor. Key phases of the proposed meshless method have been executed on the GPU using the NVIDIA CUDA software development kit. Especially, the matrix fill and solution phases have been carried out on the GPU, along with some post processing. This approach resulted in a decreased processing time compared to similar algorithm implemented on the CPU while maintaining the same accuracy.

Owusu-Banson, Derek

165

An Adaptive B-Spline Method for Low-order Image Reconstruction Problems - Final Report - 09/24/1997 - 09/24/2000  

SciTech Connect

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

166

Retrieving Collocations from Text: Xtract  

Microsoft Academic Search

Natural languages are full of collocations, recurrent combinations of words that co-occur more often than expected by chance and that correspond to arbitrary word usages. Recent work in lexicography indicates that collocations are pervasive in English; apparently, they are common in all types of writing, including both technical and nontechnical genres. Several approaches have been proposed to retrieve various types

Frank A. Smadja

1993-01-01

167

Fast spline smoothing via spectral factorization concepts  

Microsoft Academic Search

When tuning the smoothness parameter of nonparametric regression splines, the evaluation of the so-called degrees of freedom is one of the most computer-intensive tasks. In the paper, a closed-form expression of the degrees of freedom is obtained for the case of cubic splines and equally spaced data when the number of data tends to infinity. State-space methods, Kalman filtering and

Giuseppe De Nicolao; Giancarlo Ferrari-Trecate; Giovanni Sparacino

2000-01-01

168

Modeling elastic beams using dynamic splines  

Microsoft Academic Search

In this paper, the authors present the description and an application of the theory of dynamic splines for the modeling of\\u000a very flexible beams in multibody systems. The use of spline formalism reveals an alternative method for the description of\\u000a continuum flexibility by using discrete parameters. The proposed approach is discussed in general terms and a specific example\\u000a is presented

Pier Paolo Valentini; Ettore Pennestrì

2011-01-01

169

A Proposal of a Visual Inspection Method for Detecting Low Contrast Defects of an IC Lead Frame by Using a Spline Function  

NASA Astrophysics Data System (ADS)

An automatic visual inspection method for an IC lead frame, which is effective to detect low contrast defects called stains and irregular luster, is desired. Low contrast defects are usually difficult to be distinguished clearly from the normal area by the difference of intensity level. Therefore, a simple subtraction technique using a good product as a reference image is not effective for detecting low contrast defects. This paper proposes a novel automatic visual inspection method effective to detect low contrast defects by using a spline function. In our method, a virtual good-product image is created for each product under the visual inspection by using a spline function. And the intensity subtraction technique is applied between a target image and a virtual good-product image. The intensity deviation of the virtual good-product image from the normal one can be made small enough to distinguish low contrast defects. Thus, the proposed method realizes an effective detection of low contrast defects and the reduction of false detection for the good product.

Shigemori, Kiyoshi; Kikuno, Toshihiro; Inoue, Takahiro

170

Nonlinear Spline Functions.  

National Technical Information Service (NTIS)

A mathematical characterization of nonlinear interpolating spline curves is developed through a variational calculus approach, based on the Euler-Bernoulli large-deflection theory for the bending of thin beams or elastica. Algorithms previously used for c...

M. A. Malcolm

1973-01-01

171

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

172

Multivariate splines and polynomial interpolation  

Microsoft Academic Search

CONTENTSIntroductionChapter I. Multivariate B-splines and spline-functions1.1. Geometrical interpretation of one-variable B-splines and truncated powers1.2. Multivariate B-splines and truncated powers1.3. Recursive relations for B-splines1.4. Multivariate spline-functions1.5. Polyhedral splinesChapter II. Box splines2.1. The definition and basic properties2.2. Integer translates of a box spline2.3. The system of differential equations related to \\\\mathcal D(X)2.4. Further properties of \\\\mathcal D(X) and \\\\mathcal P(X)2.5. Linear independence

A. A. Akopyan; A. A. Saakyan

1993-01-01

173

Learning Collocations: Do the Number of Collocates, Position of the Node Word, and Synonymy Affect Learning?  

ERIC Educational Resources Information Center

This study investigated the effects of three factors (the number of collocates per node word, the position of the node word, synonymy) on learning collocations. Japanese students studying English as a foreign language learned five sets of 12 target collocations. Each collocation was presented in a single glossed sentence. The number of collocates

Webb, Stuart; Kagimoto, Eve

2011-01-01

174

Examination of Absorbing Boundary Condition Using Perfectly Matched Layer for Collocated Orthogonal Grid in Method of Characteristics  

NASA Astrophysics Data System (ADS)

The time domain numerical analysis of sound wave propagation has been performed widely as a result of computer development. The method of characteristics (MOC) is used as a time domain numerical analysis method. In multidimensional MOC sound wave analysis, the so-called automatically absorbing boundary (without additional outer boundary treatment) does not have excellent absorbing performance. To overcome this problem, we introduce the perfectly matched layer (PML) technique into MOC simulation. Through this study, it is clarified that the PML (L = 16) reflection at a vertical incidence is approximately 22 dB lower than the automatically absorbing boundary (without PML) in the simulation by the QUICKEST method.

Adachi, Junpei; Okubo, Kan; Tagawa, Norio; Tsuchiya, Takao; Ishizuka, Takashi

2013-07-01

175

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

176

RATIONAL SPLINE SUBROUTINES  

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

177

Particle Flow Simulation by Using Polyharmonic Splines  

Microsoft Academic Search

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

178

Mathematical modelling for the drying method and smoothing drying rate using cubic spline for seaweed Kappaphycus Striatum variety Durian in a solar dryer  

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

179

Spline Approximation and Difference Schemes for the Heat Equation.  

National Technical Information Service (NTIS)

It is proved that the spline approximation by Galerkin's method of the solution of the initial-value problem for the heat equation can be considered as the successive application of an associated finite difference operator and a spline interpolation opera...

V. Thomee

1972-01-01

180

Parameter Estimation for Dynamic Volume Spline Based Facial Skin Model  

Microsoft Academic Search

There are various methods proposed for soft tissue modeling such as spring-mass models, finite element based models and spline based models. Each model type has its own problems. In this study, we propose a dynamic volume spline based facial skin model which is both realistic and computationally efficient. Some of the very important problems of realistic soft tissue modeling are

Murat Durmaz; Gerhard Wilhelm Weber

181

Capturing Anatomical Shape Variability Using B-Spline Registration  

Microsoft Academic Search

Registration based on B-spline transformations has attracted much attention in medical image processing recently. Non-rigid registra- tion provides the basis for many important techniques, such as statistical shape modeling. Validating the results, however, remains difficult - es- pecially in intersubject registration. This work explores the ability of B- spline registration methods to capture intersubject shape deformations. We study the effect

Thomas H. Wenckebach; Hans Lamecker; Hans-christian Hege

2005-01-01

182

Statistical Chromaticity Models for Lip Tracking with B-splines  

Microsoft Academic Search

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

183

Task-space trajectories via cubic spline optimization  

Microsoft Academic Search

We consider the task of planning smooth trajecto- ries for robot motion. In this paper we make two contributions. First we present a method for cubic spline optimization; this technique lets us simultaneously plan optimal task-space tra- jectories and fit cubic splines to the trajectories, while obeying many of the same constraints imposed by a typical motion planning algorithm. The

J. Zico Kolter; Andrew Y. Ng

2009-01-01

184

On optimizing knot positions for multidimensional B-spline models  

NASA Astrophysics Data System (ADS)

In this paper, we present a new method for optimizing knot positions for a multi-dimensional B-spline model. Using the results from from univariate polynomial approximation theory, spline approximation theory and multivariate tensor product theory, we develop the algorithm in three steps. First, we derive a local upper bound for the L? error in a multivariate B-spline tensor product approximation over a span. Second, we use this result to bound the approximation error for a multi-dimensional B-spline tensor product approximation. Third, we developed two knot position optimization methods based on the minimization of two global approximation errors: L? global error and L2 global error. We test our method with 2D surface fitting experiments using B-spline models defined in both 2D Cartesian and polar coordinates. Simulation results demonstrate that the optimized knots can fit a surface more accurately than fixed uniformly spaced knots.

Deng, Xiang; Denney, Thomas S., Jr.

2004-05-01

185

Multivariate splines and polynomial interpolation  

NASA Astrophysics Data System (ADS)

CONTENTSIntroductionChapter I. Multivariate B-splines and spline-functions1.1. Geometrical interpretation of one-variable B-splines and truncated powers1.2. Multivariate B-splines and truncated powers1.3. Recursive relations for B-splines1.4. Multivariate spline-functions1.5. Polyhedral splinesChapter II. Box splines2.1. The definition and basic properties2.2. Integer translates of a box spline2.3. The system of differential equations related to \\mathcal D(X)2.4. Further properties of \\mathcal D(X) and \\mathcal P(X)2.5. Linear independence of translates of a box spline2.6. Interpolation by translates of a box splineChapter III. Multivariate mean-value and dual pointwise interpolations3.1. Mean-value Lagrange interpolation3.2. Kergin interpolation and the scale of mean-value interpolations3.3. Multivariate interpolation generated by hyperplanesChapter IV. Multivariate pointwise interpolation4.1. Birkhoff interpolation4.2. Shifts of sets and differentiation of the Vandermonde determinant d_{\\mathcal H}(\\mathcal Z)4.3. Hermite interpolation4.4. Diagonal Birkhoff interpolation4.5. Uniform Hermite interpolationReferences

Akopyan, A. A.; Saakyan, A. A.

1993-10-01

186

Pseudospectral collocation methods for the computation of the self-force on a charged particle: Generic orbits around a Schwarzschild black hole  

NASA Astrophysics Data System (ADS)

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.; Jaramillo, José Luis

2010-08-01

187

Pseudospectral collocation methods for the computation of the self-force on a charged particle: Generic orbits around a Schwarzschild black hole  

SciTech Connect

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

188

Scalar and planar-valued curve fitting using splines under tension  

Microsoft Academic Search

The spline under tension was introduced by Schweikert in an attempt to imitate cubic splines but avoid the spurious critical points they induce. The defining equations are presented here, together with an efficient method for determining the necessary parameters and computing the resultant spline. The standard scalar-valued curve fitting problem is discussed, as well as the fitting of open and

A. K. Cline

1974-01-01

189

Accuracy of a mitral valve segmentation method using J-splines for real-time 3D echocardiography data.  

PubMed

Patient-specific models of the heart's 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 vs. 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 0.40 ± 0.32 mm, 0.52 ± 0.51 mm, and 0.74 ± 0.69 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 M; Saikrishnan, Neelakantan; Rossignac, Jarek; Lerakis, Stamatios; Yoganathan, Ajit P

2013-06-01

190

Accuracy of a Mitral Valve Segmentation Method Using J-Splines for Real-Time 3D Echocardiography Data  

PubMed Central

Patient-specific models of the heart’s 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 0.40±0.32 mm, 0.52±0.51 mm, and 0.74±0.69 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.

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

2013-01-01

191

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

192

Mr. Stockdale's Dictionary of Collocations.  

ERIC Educational Resources Information Center

This dictionary of collocations was compiled by an English-as-a-Second-Language (ESL) teacher in Saudi Arabia who teaches adult, native speakers of Arabic. The dictionary is practical in teaching English because it helps to focus on everyday events and situations. The dictionary works as follows: the teacher looks up a word, such as "talk"; next…

Stockdale, Joseph Gagen, III

193

Curve fitting and fairing using conic splines  

Microsoft Academic Search

We present an ecient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bezier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic

Xunnian Yang

2004-01-01

194

Spline screw payload fastening system  

NASA Astrophysics Data System (ADS)

A system for coupling an orbital replacement unit (ORU) to a space station structure via the actions of a robot and/or astronaut is described. This system provides mechanical and electrical connections both between the ORU and the space station structure and between the ORU and the ORU and the robot/astronaut hand tool. Alignment and timing features ensure safe, sure handling and precision coupling. This includes a first female type spline connector selectively located on the space station structure, a male type spline connector positioned on the orbital replacement unit so as to mate with and connect to the first female type spline connector, and a second female type spline connector located on the orbital replacement unit. A compliant drive rod interconnects the second female type spline connector and the male type spline connector. A robotic special end effector is used for mating with and driving the second female type spline connector. Also included are alignment tabs exteriorally located on the orbital replacement unit for berthing with the space station structure. The first and second female type spline connectors each include a threaded bolt member having a captured nut member located thereon which can translate up and down the bolt but are constrained from rotation thereabout, the nut member having a mounting surface with at least one first type electrical connector located on the mounting surface for translating with the nut member. At least one complementary second type electrical connector on the orbital replacement unit mates with at least one first type electrical connector on the mounting surface of the nut member. When the driver on the robotic end effector mates with the second female type spline connector and rotates, the male type spline connector and the first female type spline connector lock together, the driver and the second female type spline connector lock together, and the nut members translate up the threaded bolt members carrying the first type electrical connector up to the complementary second type connector for interconnection therewith.

Vranish, John M.

1993-09-01

195

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

196

Bootstrap re-sampling technique to evaluate the optimal formulation of theophylline tablets predicted by non-linear response surface method incorporating multivariate spline interpolation.  

PubMed

Optimal solutions of theophylline tablet formulations were derived from three types of experimental datasets, composed of different numbers of data-points using the response surface method incorporating multivariate spline interpolation (RSM(S)). The reliability of these optimal solutions was evaluated by a bootstrap re-sampling technique. Different levels of three causal factors were used as factors of response surface analysis: the lactose/cornstarch ratio (X(1)), the amount of carmellose calcium (X(2)), and the amount of hydroxypropylcellulose (X(3)). The target responses were the dissolution ratio of theophylline for the first 15 min (Y(1)) and the hardness (Y(2)) of each of the prepared tablets. Similar optimal solutions were estimated in three different sizes of datasets. A bootstrap re-sampling with replacements from the original dataset was applied, and optimal solutions for each bootstrap dataset were estimated. The frequency of the distribution of the optimal solution generated by the bootstrap re-sampling technique demonstrated almost normal distribution. The average and standard deviation of the optimal solution distribution were calculated as evaluation indices reflecting the accuracy and reproducibility of the optimal solution. It was confirmed that the accuracy was sufficiently high, irrespective of the dataset size; however, the reproducibility worsened with a decrease in the number of the experimental datasets. Consequently, it was considered that the novel evaluation method based on the bootstrap re-sampling technique was suitable for evaluating the reliability of the optimal solution. PMID:17409553

Arai, Hiroaki; Suzuki, Tatsuya; Kaseda, Chosei; Ohyama, Koichi; Takayama, Kozo

2007-04-01

197

Bayesian B-spline mapping for dynamic quantitative traits.  

PubMed

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located. PMID:22624568

Xing, Jun; Li, Jiahan; Yang, Runqing; Zhou, Xiaojing; Xu, Shizhong

2012-04-01

198

Collocating satellite-based radar and radiometer measurements - methodology and usage examples  

NASA Astrophysics Data System (ADS)

Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) on-board NOAA-18 and the Cloud Profiling Radar (CPR) on-board CloudSat. First, a simple method is presented to obtain those collocations and this method is compared with a more complicated approach found in literature. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to their centrepoints. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relation between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 ?m) and 11 (8.33 ?m). This shows a small improvement in the retrieval quality. The collocations described in the article are available for public use.

Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.

2010-06-01

199

Collocating satellite-based radar and radiometer measurements - methodology and usage examples  

NASA Astrophysics Data System (ADS)

Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) onboard NOAA-18 and the Cloud Profiling Radar (CPR) onboard the CloudSat CPR. First, a simple method is presented to obtain those collocations and this method is compared with a more complicated approach found in literature. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to their centrepoints. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relation between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 ?m) and 11 (8.33 ?m). This shows a small improvement in the retrieval quality. The collocations described in the article are available for public use.

Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.

2010-02-01

200

Chordlength Texturing of Spline Surfaces  

Microsoft Academic Search

This paper presents an inexpensive way to provide (s, t) texture coordinates of a spline surface, which mitigates texture compression and stretching artifacts. The approach employs a chordlength approximation based on the original spline-surface parameterization. Its success can be seen in existing Alias | Wavefront renderers since 1991.

Andrew Woo

1998-01-01

201

Fitting multidimensional splines using statistical variable selection techniques  

NASA Technical Reports Server (NTRS)

This report demonstrates the successful application of statistical variable selection techniques to fit splines. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs using the B-spline basis were developed, and the one for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.

Smith, P. L.

1982-01-01

202

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

203

Collocating satellite-based radar and radiometer measurements - methodology and usage examples.  

NASA Astrophysics Data System (ADS)

Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) onboard NOAA-18 and the Cloud Profiling Radar (CPR) onboard the CloudSat. First, a simple method is presented to obtain those collocations. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to its centrepoint. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relationship between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 ?m) and 11 (8.33 ?m). This shows a small improvement in the retrieval quality. The collocations are available for public use.

Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.

2010-05-01

204

Analysis of crustal structure of Venus utilizing residual Line-of-Sight (LOS) gravity acceleration and surface topography data. A trial of global modeling of Venus gravity field using harmonic spline method  

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

205

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

Code of Federal Regulations, 2010 CFR

...approved by the state commission; and (4) Permit physical collocation...or because of space limitations...the extent a state sets its own...demonstrated to the state commission that physical collocation...or because of space...

2009-10-01

206

Polynomial Interpolation Methods for Viscous Flow Calculations.  

National Technical Information Service (NTIS)

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different develo...

S. G. Rubin P. K. Khosla

1976-01-01

207

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

208

Polynominal Interpolation Methods for Viscous Flow Calculations  

NASA Technical Reports Server (NTRS)

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

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

1976-01-01

209

Investigating ESL Learners' Lexical Collocations: The Acquisition of Verb + Noun Collocations by Japanese Learners of English  

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

210

Optimisation of cam-follower motion using B-splines  

Microsoft Academic Search

This paper proposes design of cam-follower velocity curve by using B-spline polynomials. B-spline polynomials are smooth curves defined by control points. Curve shape can be modified by changing the control points. The traditional design method for improving the motion characteristics of the follower is to find an optimum displacement curve for which follower velocity, acceleration curves to be continuous and

N. Sateesh; C. S. P. Rao; T. A. Janardhan Reddy

2009-01-01

211

Collocation points distributions for optimal spacecraft trajectories  

NASA Astrophysics Data System (ADS)

The method of direct collocation with nonlinear programming (DCNLP) is a powerful tool to solve optimal control problems (OCP). In this method the solution time history is approximated with piecewise polynomials, which are constructed using interpolation points deriving from the Jacobi polynomials. Among the Jacobi polynomials family, Legendre and Chebyshev polynomials are the most used, but there is no evidence that they offer the best performance with respect to other family members. By solving different OCPs with interpolation points not only taken within the Jacoby family, the behavior of the Jacobi polynomials in the optimization problems is discussed. This paper focuses on spacecraft trajectories optimization problems. In particular orbit transfers, interplanetary transfers and station keepings are considered.

Fumenti, Federico; Circi, Christian; Romagnoli, Daniele

2013-03-01

212

Covariance modeling in geodetic applications of collocation  

NASA Astrophysics Data System (ADS)

Collocation method is widely applied in geodesy for estimating/interpolating gravity related functionals. The crucial problem of this approach is the correct modeling of the empirical covariance functions of the observations. Different methods for getting reliable covariance models have been proposed in the past by many authors. However, there are still problems in fitting the empirical values, particularly when different functionals of T are used and combined. Through suitable linear combinations of positive degree variances a model function that properly fits the empirical values can be obtained. This kind of condition is commonly handled by solver algorithms in linear programming problems. In this work the problem of modeling covariance functions has been dealt with an innovative method based on the simplex algorithm. This requires the definition of an objective function to be minimized (or maximized) where the unknown variables or their linear combinations are subject to some constraints. The non-standard use of the simplex method consists in defining constraints on model covariance function in order to obtain the best fit on the corresponding empirical values. Further constraints are applied so to have coherence with model degree variances to prevent possible solutions with no physical meaning. The fitting procedure is iterative and, in each iteration, constraints are strengthened until the best possible fit between model and empirical functions is reached. The results obtained during the test phase of this new methodology show remarkable improvements with respect to the software packages available until now. Numerical tests are also presented to check for the impact that improved covariance modeling has on the collocation estimate.

Barzaghi, Riccardo; Cazzaniga, Noemi; De Gaetani, Carlo; Reguzzoni, Mirko

2014-05-01

213

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

214

Orthogonal collocation of the nonlinear Boltzman equation  

NASA Astrophysics Data System (ADS)

A numerical solution to the nonlinear Boltzmann equation for Maxwell molecules, including the momentum conserving kernel by the method of orthogonal collocation, is presented and compared with the similarity solution of Krupp (1967), Bobylev (1975), Krook and Wu (1976) (KBKW). Excellent agreement is found between the two for KBKW initial values. The calculations of the evolution of a distribution function from nonKBKW initial conditions are examined. The correlation of the nonKBKW trajectories to the presence of a robust unstable manifold in the eigenspace of the linearized Boltzmann equation is considered. The results of a linear analysis are compared with the work of Wang Chang and Uhlenbeck (1952). The implications of the results for the relaxation of nonequilibrium distribution functions are discussed.

Morin, T. J.; Hawley, M. C.

1985-07-01

215

A Localized Tau Method PDE Solver  

NASA Technical Reports Server (NTRS)

In this paper we present a new form of the collocation method that allows one to find very accurate solutions to time marching problems without the unwelcome appearance of Gibb's phenomenon oscillations. The basic method is applicable to any partial differential equation whose solution is a continuous, albeit possibly rapidly varying function. Discontinuous functions are dealt with by replacing the function in a small neighborhood of the discontinuity with a spline that smoothly connects the function segments on either side of the discontinuity. This will be demonstrated when the solution to the inviscid Burgers equation is discussed.

Cottam, Russell

2002-01-01

216

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces  

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

217

Permanent and Collocated Randomm Number Sampling and the Coverage of Births and Deaths.  

National Technical Information Service (NTIS)

Permanent random number (PRN) and collocated random number (CRN) sampling are practical methods of controlling overlap between different samples. The techniques can be used for overlap control between samples for the same survey selected at different time...

L. R. Ernst R. Valliant R. J. Casady

1998-01-01

218

Discrimination of bed form scales using robust spline filters and wavelet transforms: Methods and application to synthetic signals and bed forms of the Río Paraná, Argentina  

NASA Astrophysics Data System (ADS)

There is no standard nomenclature and procedure to systematically identify the scale and magnitude of bed forms such as bars, dunes, and ripples that are commonly present in many sedimentary environments. This paper proposes a standardization of the nomenclature and symbolic representation of bed forms and details the combined application of robust spline filters and continuous wavelet transforms to discriminate these morphodynamic features, allowing the quantitative recognition of bed form hierarchies. Herein the proposed methodology for bed form discrimination is first applied to synthetic bed form profiles, which are sampled at a Nyquist ratio interval of 2.5-50 and a signal-to-noise ratio interval of 1-20 and subsequently applied to a detailed 3-D bed topography from the Río Paraná, Argentina, which exhibits large-scale dunes with superimposed, smaller bed forms. After discriminating the synthetic bed form signals into three-bed form hierarchies that represent bars, dunes, and ripples, the accuracy of the methodology is quantified by estimating the reproducibility, the cross correlation, and the standard deviation ratio of the actual and retrieved signals. For the case of the field measurements, the proposed method is used to discriminate small and large dunes and subsequently obtain and statistically analyze the common morphological descriptors such as wavelength, slope, and amplitude of both stoss and lee sides of these different size bed forms. Analysis of the synthetic signals demonstrates that the Morlet wavelet function is the most efficient in retrieving smaller periodicities such as ripples and smaller dunes and that the proposed methodology effectively discriminates waves of different periods for Nyquist ratios higher than 25 and signal-to-noise ratios higher than 5. The analysis of bed forms in the Río Paraná reveals that, in most cases, a Gamma probability distribution, with a positive skewness, best describes the dimensionless wavelength and amplitude for both the lee and stoss sides of large dunes. For the case of smaller superimposed dunes, the dimensionless wavelength shows a discrete behavior that is governed by the sampling frequency of the data, and the dimensionless amplitude better fits the Gamma probability distribution, again with a positive skewness. This paper thus provides a robust methodology for systematically identifying the scales and magnitudes of bed forms in a range of environments.

Gutierrez, Ronald R.; Abad, Jorge D.; Parsons, Daniel R.; Best, James L.

2013-09-01

219

Recurrence relations for Tchebycheffian B-splines  

Microsoft Academic Search

Four-term recurrence relations with constant coefficients are derived for a wide class of T chebycheffian B-splines, LB-splines\\u000a and complex B-splines. Such a relation exists whenever the differential operator defining the underlying “polynomial” space\\u000a can be factored in two essentially different ways. The four lower order B-splines in the recurrence relation appear in two\\u000a pairs, each pair corresponding to one of

Nira Dyn; Amos Ron

1988-01-01

220

Analytical research on intellectual control of yarning characteristics for cotton collocation and rotor spinning  

Microsoft Academic Search

This research deals with the analysis of the characteristics of cotton collocation and the quality characteristics of rotor\\u000a spinning. To achieve appropriate cotton collocation, the Taguchi method was employed in the experimental design in which the\\u000a cotton characteristics which were measured with a high volume instrument were used to design the experiment plan according\\u000a to the relevant orthogonal array. To

Chung-Feng Jeffrey Kuo; Ching-Pei Tien; Chin-Hsun Chiu

2007-01-01

221

Landmark and Intensity-Based Images Elastic Registration Using Hierarchical B-Splines  

Microsoft Academic Search

We present an elastic registration algorithm for the alignment of biological images. Our method combines and extends some of best techniques available in the context of medical imaging. We express the deformation field as a hierarchical B-splines model basing on the information of landmarks. The hierarchical B-splines model allows us to deal with a rich variety of deformations and match

Tiantian Bian; Zheng Qin; Yu Liu

2007-01-01

222

A spline-regularized minimal residual algorithm for iterative attenuation correction in SPECT  

Microsoft Academic Search

In SPECT, regularization is necessary to avoid divergence of the iterative algorithms used for non-uniform attenuation compensation. In this paper, we propose a spline-based regularization method for the minimal residual algorithm. First, the acquisition noise is filtered using a statistical model involving spline smoothing so that the filtered projections belong to a Sobolev space with specific continuity and derivability properties.

M. Pélégrini; I. Buvat; H. Benali; G. El Fakhri; P. Grangeat; R. Di Paola

1999-01-01

223

On using smoothing spline and residual correction to fuse rain gauge observations and remote sensing data  

NASA Astrophysics Data System (ADS)

Partial thin-plate smoothing spline model is used to construct the trend surface.Correction of the spline estimated trend surface is often necessary in practice.Cressman weight is modified and applied in residual correction.The modified Cressman weight performs better than Cressman weight.A method for estimating the error covariance matrix of gridded field is provided.

Huang, Chengcheng; Zheng, Xiaogu; Tait, Andrew; Dai, Yongjiu; Yang, Chi; Chen, Zhuoqi; Li, Tao; Wang, Zhonglei

2014-01-01

224

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities  

ERIC Educational Resources Information Center

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the…

Woods, Carol M.; Thissen, David

2006-01-01

225

Locating CVBEM collocation points for steady state heat transfer problems  

USGS Publications Warehouse

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

Hromadka, II, T. V.

1985-01-01

226

Interpolation in numerical optimization. [by cubic spline generation  

NASA Technical Reports Server (NTRS)

The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.

Hall, K. R.; Hull, D. G.

1975-01-01

227

B(asic)-Spline Basics.  

National Technical Information Service (NTIS)

This report contains the lecture notes for the first of four lectures which comprise the course entitled The extension of B-spline curve algorithms to surfaces given at SIGRAPH'86. It is an elaboration and extension of the MRC report 2896 by de Boor and H...

C. de Boor

1986-01-01

228

Bidirectional elastic image registration using B-spline affine transformation.  

PubMed

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

229

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

230

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

231

A new algorithm of B-Spline FEM for solving 2-D electromagnetic field problem of rectangular regions  

Microsoft Academic Search

The B-Spline FEM is an effective numerical computation method for solving 2-D electromagnetic field problem of rectangular regions. This method has high computational accuracy without destroying the continuity of adjacent field value. In this paper, a transferable gauss integral matrix algorithm (TGIMA) which can perform fleetly the B-spline FEM was proposed. By the algorithm, the B-spline function value of every

Wusheng Ji; Tinggang Zhao; Bin You; Xuedong Wang; Ying Li; Binying Li

2002-01-01

232

An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations  

SciTech Connect

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

233

The computation of Laplacian smoothing splines with examples  

NASA Technical Reports Server (NTRS)

Laplacian smoothing splines (LSS) are presented as generalizations of graduation, cubic and thin plate splines. The method of generalized cross validation (GCV) to choose the smoothing parameter is described. The GCV is used in the algorithm for the computation of LSS's. An outline of a computer program which implements this algorithm is presented along with a description of the use of the program. Examples in one, two and three dimensions demonstrate how to obtain estimates of function values with confidence intervals and estimates of first and second derivatives. Probability plots are used as a diagnostic tool to check for model inadequacy.

Wendelberger, J. G.

1982-01-01

234

Hartree-Fock-Roothaan energies and expectation values for the neutral atoms He to Uuo: The B-spline expansion method  

SciTech Connect

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 (n = 2, 1, -1, -2, -3) are also given.

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

235

B-LUT: Fast and low memory B-spline image interpolation.  

PubMed

We propose a fast alternative to B-splines in image processing based on an approximate calculation using precomputed B-spline weights. During B-spline indirect transformation, these weights are efficiently retrieved in a nearest-neighbor fashion from a look-up table, greatly reducing overall computation time. Depending on the application, calculating a B-spline using a look-up table, called B-LUT, will result in an exact or approximate B-spline calculation. In case of the latter the obtained accuracy can be controlled by the user. The method is applicable to a wide range of B-spline applications and has very low memory requirements compared to other proposed accelerations. The performance of the proposed B-LUTs was compared to conventional B-splines as implemented in the popular ITK toolkit for the general case of image intensity interpolation. Experiments illustrated that highly accurate B-spline approximation can be obtained all while computation time is reduced with a factor of 5-6. The B-LUT source code, compatible with the ITK toolkit, has been made freely available to the community. PMID:20034697

Sarrut, David; Vandemeulebroucke, Jef

2010-08-01

236

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

237

Least-Squares Fitting of Algebraic Spline Surfaces  

Microsoft Academic Search

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of

Bert Jüttler; Alf Felis

2002-01-01

238

Dynamic path planning and execution using B-Splines  

Microsoft Academic Search

This paper presents a technique for generating a continuous trajectory from a series of waypoints which represent a static path. Furthermore, a method is described for efficiently altering this trajectory in response to a dynamic environment. This is achieved by applying an interpolated B- spline to the waypoints which is only altered in the area local to the obstacle.

Timothy Arney

2007-01-01

239

Elastic Registration of Biological Images Using Vector-Spline Regularization  

Microsoft Academic Search

We present an elastic registration algorithm for the alignment of biological images. Our method combines and extends some of the best techniques available in the context of medical imaging. We express the deformation field as a B-spline model, which allows us to deal with a rich variety of deformations. We solve the registration problem by minimizing a pixelwise mean-square distance

Carlos Ó; S. Sorzano; Philippe Thévenaz; Michael Unser

2005-01-01

240

Elastic registration of biological images using vector-spline regularization  

Microsoft Academic Search

We present an elastic registration algorithm for the alignment of biological images. Our method combines and extends some of the best techniques available in the context of medical imaging. We express the deformation field as a B-spline model, which allows us to deal with a rich variety of deformations. We solve the registration problem by minimizing a pixelwise mean-square distance

C. O. S. Sorzano; P. Thevenaz; M. Unser

2005-01-01

241

Hermite spline interpolation on patches for parallel Vlasov beam simulations  

NASA Astrophysics Data System (ADS)

In this paper we present a novel interpolation technique for Vlasov simulations of intense space charge dominated beams. This new technique enables to localize the cubic spline interpolation generally performed in semi-Lagrangian Vlasov codes and thus to improve the scalability of the parallel version. This new method is applied to the propagation of a potassium beam in a periodic focusing channel.

Crouseilles, N.; Latu, G.; Sonnendrücker, E.

2007-07-01

242

Spline screw multiple rotations mechanism  

NASA Astrophysics Data System (ADS)

A system for coupling two bodies together and for transmitting torque from one body to another with mechanical timing and sequencing is reported. The mechanical timing and sequencing is handled so that the following criteria are met: (1) the bodies are handled in a safe manner and nothing floats loose in space, (2) electrical connectors are engaged as long as possible so that the internal processes can be monitored throughout by sensors, and (3) electrical and mechanical power and signals are coupled. The first body has a splined driver for providing the input torque. The second body has a threaded drive member capable of rotation and limited translation. The embedded drive member will mate with and fasten to the splined driver. The second body has an embedded bevel gear member capable of rotation and limited translation. This bevel gear member is coaxial with the threaded drive member. A compression spring provides a preload on the rotating threaded member, and a thrust bearing is used for limiting the translation of the bevel gear member so that when the bevel gear member reaches the upward limit of its translation the two bodies are fully coupled and the bevel gear member then rotates due to the input torque transmitted from the splined driver through the threaded drive member to the bevel gear member. An output bevel gear with an attached output drive shaft is embedded in the second body and meshes with the threaded rotating bevel gear member to transmit the input torque to the output drive shaft.

Vranish, John M.

1993-12-01

243

Spline screw multiple rotations mechanism  

NASA Technical Reports Server (NTRS)

A system for coupling two bodies together and for transmitting torque from one body to another with mechanical timing and sequencing is reported. The mechanical timing and sequencing is handled so that the following criteria are met: (1) the bodies are handled in a safe manner and nothing floats loose in space, (2) electrical connectors are engaged as long as possible so that the internal processes can be monitored throughout by sensors, and (3) electrical and mechanical power and signals are coupled. The first body has a splined driver for providing the input torque. The second body has a threaded drive member capable of rotation and limited translation. The embedded drive member will mate with and fasten to the splined driver. The second body has an embedded bevel gear member capable of rotation and limited translation. This bevel gear member is coaxial with the threaded drive member. A compression spring provides a preload on the rotating threaded member, and a thrust bearing is used for limiting the translation of the bevel gear member so that when the bevel gear member reaches the upward limit of its translation the two bodies are fully coupled and the bevel gear member then rotates due to the input torque transmitted from the splined driver through the threaded drive member to the bevel gear member. An output bevel gear with an attached output drive shaft is embedded in the second body and meshes with the threaded rotating bevel gear member to transmit the input torque to the output drive shaft.

Vranish, John M. (inventor)

1993-01-01

244

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

245

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

246

Cubic Spline Data Reduction Choosing the Knots from a Third Derivative Criterion  

NASA Astrophysics Data System (ADS)

This paper presents a data reduction method for functional data. Starting with noisy or not noisy data, we first define a function f, called the "reference function", as a cubic smoothing spline which is supposed to have the global form of the data. This reference function is then used to locate the knots of the final approximating spline by using a criterion based on the third derivative of f. Then, the least-squares spline approximating all the data is derived with these knots. Numerical results show the effectiveness of the method.

Conti, C.; Morandi, R.; Rabut, C.; Sestini, A.

2001-12-01

247

A weighted collocation on the strong form with mixed radial basis approximations for incompressible linear elasticity  

NASA Astrophysics Data System (ADS)

A weighted strong form collocation framework with mixed radial basis approximations for the pressure and displacement fields is proposed for incompressible and nearly incompressible linear elasticity. It is shown that with the proper choice of independent source points and collocation points for the radial basis approximations in the pressure and displacement fields, together with the analytically derived weights associated with the incompressibility constraint and boundary condition collocation equations, optimal convergence can be achieved. The optimal weights associated with the collocation equations are derived based on achieving balanced errors resulting from domain, boundaries, and constraint equations. Since in the proposed method the overdetermined system of the collocation equations is solved by a least squares method, independent pressure and displacement approximations can be selected without suffering from instability due to violation of the LBB stability condition. The numerical solutions verify that the solution of the proposed method does not exhibit volumetric locking and pressure oscillation, and that the solution converges exponentially in both L norm and H semi-norm, consistent with the error analysis results presented in this paper.

Chi, Sheng-Wei; Chen, Jiun-Shyan; Hu, Hsin-Yun

2014-02-01

248

A comparison of thin-plate splines with automatic correspondences and B-splines with uniform grids for multimodal prostate registration  

NASA Astrophysics Data System (ADS)

This paper provides a comparison of spline-based registration methods applied to register interventional Trans Rectal Ultrasound (TRUS) and pre-acquired Magnetic Resonance (MR) prostate images for needle guided prostate biopsy. B-splines and Thin-plate Splines (TPS) are the most prevalent spline-based approaches to achieve deformable registration. Pertaining to the strategic selection of correspondences for the TPS registration, we use an automatic method already proposed in our previous work to generate correspondences in the MR and US prostate images. The method exploits the prostate geometry with the principal components of the segmented prostate as the underlying framework and involves a triangulation approach. The correspondences are generated with successive refinements and Normalized Mutual Information (NMI) is employed to determine the optimal number of correspondences required to achieve TPS registration. B-spline registration with successive grid refinements are consecutively applied for a significant comparison of the impact of the strategically chosen correspondences on the TPS registration against the uniform B-spline control grids. The experimental results are validated on 4 patient datasets. Dice Similarity Coefficient (DSC) is used as a measure of the registration accuracy. Average DSC values of 0.97+/-0.01 and 0.95+/-0.03 are achieved for the TPS and B-spline registrations respectively. B-spline registration is observed to be more computationally expensive than the TPS registration with average execution times of 128.09 +/- 21.7 seconds and 62.83 +/- 32.77 seconds respectively for images with maximum width of 264 pixels and a maximum height of 211 pixels.

Mitra, Jhimli; Marti, Robert; Oliver, Arnau; Llado, Xavier; Vilanova, Joan C.; Meriaudeau, Fabrice

2011-03-01

249

Triangular bubble spline surfaces  

PubMed Central

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 any n?3. 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 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.

Kapl, Mario; Byrtus, Marek; Juttler, Bert

2011-01-01

250

Triangular bubble spline surfaces.  

PubMed

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; Jüttler, Bert

2011-11-01

251

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

252

Cubic hermite and cubic spline fractal interpolation functions  

NASA Astrophysics Data System (ADS)

Despite that the spline theory is a well studied topic, its relationship with the fractal theory is novel. Fractal approach offers a single specification for a large class of interpolants of which the classical spline is a particular member, and hence possesses considerable flexibility in the choice of an interpolant. The explicit construction of a C1-cubic Hermite fractal interpolation function (FIF) is introduced in the present work. If slopes at knot points are not known, then they are calculated through solution of a suitable linear system of equations so as to have C2 global smoothness for the resulting cubic FIF. Thus, the present method generalizes the classical C1-cubic Hermite and C2-cubic spline interpolants simultaneously, and offers a new approach to the development of cubic spline FIF in contrast to the construction through moments by Chand and Kapoor [SIAM J. Numer. Anal., 44(2), (2006), pp. 655-676]. It is shown that, for appropriate values of vertical scaling factors involved in the definition, developed C1-cubic Hermite FIF converges uniformly to the data generating function ? ? C4 at least as rapidly as fourth power of the mesh norm approaches zero.

Chand, A. K. B.; Viswanathan, P.

2012-09-01

253

A vehicle license plate recognition system based on fixed color collocation  

Microsoft Academic Search

Locating the region of license plate is the key of the vehicle plate recognition system. A new method is adopted in this paper instead of the traditional method based on gray image. The method that sufficiently utilizes the color characteristics of the colored image is based on the color collocation of the plate's background and characters combined with the plate's

Yao-Quan Yang; Jie Bai; Rui-Li Tian; Na Liu

2005-01-01

254

Brain Image Analysis Using Spherical Splines  

Microsoft Academic Search

We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspire d by the fact that, for brain surfaces, it is both necessary and natural to employ sph eres as their natural domains. We develop an automatic and efficient algorithm, wh ich transforms a brain surface to a single spherical spline

Ying He; Xin Li; Xianfeng Gu; Hong Qin

2005-01-01

255

Smoothing splines: Regression, derivatives and deconvolution  

NASA Technical Reports Server (NTRS)

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel intergral equation. These results are derived by developing a Fourier representation for a smoothing spline.

Rice, J.; Rosenblatt, M.

1982-01-01

256

B-spline FBP reconstructions for SPECT  

Microsoft Academic Search

The authors describe a generalization of the filtered backprojection (FBP) algorithm based on a pixel intensity distribution (PIDM) chosen in spline spaces. A set of reconstructions is obtained according to the degree of spline. The single photon emission computed tomography (SPECT) implementation is discussed in order to provide efficient algorithms and take into account the limitations induced by the ?-camera.

J.-P. Guedon; C. Barker; Y. Bizais

1991-01-01

257

Curve fitting and modeling with splines using statistical variable selection techniques  

NASA Technical Reports Server (NTRS)

The successful application of statistical variable selection techniques to fit splines is demonstrated. Major emphasis is given to knot selection, but order determination is also discussed. Two FORTRAN backward elimination programs, using the B-spline basis, were developed. The program for knot elimination is compared in detail with two other spline-fitting methods and several statistical software packages. An example is also given for the two-variable case using a tensor product basis, with a theoretical discussion of the difficulties of their use.

Smith, P. L.

1982-01-01

258

Pose invariant affect analysis using thin-plate splines  

Microsoft Academic Search

This paper introduces a method for pose-invariant facial affect analysis and a real-time system for facial affect analysis using this method. The method is centered on developing a feature vector that is more robust to rigid body movements while retaining information important to facial affect analysis. This feature vector is produced using thin-plate splines to extract affine transformations independently from

Joel C. McCall; Mohan M. Trivedi

2004-01-01

259

Combined Spline and B-spline for an Improved Automatic Skin Lesion Segmentation in Dermoscopic Images Using Optimal Color Channel.  

PubMed

In a computerized image analysis environment, the irregularity of a lesion border has been used to differentiate between malignant melanoma and other pigmented skin lesions. The accuracy of the automated lesion border detection is a significant step towards accurate classification at a later stage. In this paper, we propose the use of a combined Spline and B-spline in order to enhance the quality of dermoscopic images before segmentation. In this paper, morphological operations and median filter were used first to remove noise from the original image during pre-processing. Then we proceeded to adjust image RGB values to the optimal color channel (green channel). The combined Spline and B-spline method was subsequently adopted to enhance the image before segmentation. The lesion segmentation was completed based on threshold value empirically obtained using the optimal color channel. Finally, morphological operations were utilized to merge the smaller regions with the main lesion region. Improvement on the average segmentation accuracy was observed in the experimental results conducted on 70 dermoscopic images. The average accuracy of segmentation achieved in this paper was 97.21 % (where, the average sensitivity and specificity were 94 % and 98.05 % respectively). PMID:24957396

Abbas, A A; Guo, X; Tan, W H; Jalab, H A

2014-08-01

260

Accuracy and speed in computing the Chebyshev collocation derivative  

NASA Technical Reports Server (NTRS)

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

Don, Wai-Sun; Solomonoff, Alex

1991-01-01

261

A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities  

NASA Astrophysics Data System (ADS)

This paper investigates the stability of periodic delay systems with non-smooth coefficients using a multi-interval Chebyshev collocation approach (MIC). In this approach, each piecewise continuous interval is expanded in a Chebyshev basis of the first order. The boundaries of these intervals are placed at the points of discontinuity to recover the fast convergence properties of spectral methods. Stability is examined for a set of case studies that contain the complexities of periodic coefficients, delays and discontinuities. The new approach is also compared to the conventional Chebyshev collocation method.

Khasawneh, Firas A.; Mann, Brian P.; Butcher, Eric A.

2011-11-01

262

Implementation of exterior complex scaling in B-splines to solve atomic and molecular collision problems  

SciTech Connect

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

263

Stochastic Collocation and Lagrangian Sampling for Passive Tracer Transport in an Aquifer with Random Permeability  

NASA Astrophysics Data System (ADS)

To a large extent, the flow and transport behavior within an aquifer is governed by its permeability. Typically, permeability measurements of an aquifer are affordable at few spatial locations only. Due to this lack of information, permeability fields are preferably described by stochastic models rather than deterministically. A stochastic method is needed to asses the transition of the input uncertainty in permeability through the system of partial differential equations describing flow and transport to the output quantity of interest. The stochastic collocation method is an elegant and efficient tool for uncertainty quantification in subsurface problems. Several contributions (e.g., Li and Zhang, WRR, 2007) have successfully applied stochastic collocation-based frameworks for the flow problem. For the transport problem, however, Lin and Tartakovsky (AWR, 2009) have shown that an accurate solution via stochastic collocation is more challenging. We propose a hybrid approach that utilizes stochastic collocation to solve the flow problem only and Monte Carlo-type sampling for transport: By means of stochastic collocation, we approximate the random flow field with a polynomial chaos expansion. Subsequently, a conventional Monte Carlo sampling technique is used for passive tracer transport. Here, the computational costs per flow field sample are very low thanks to the polynomial chaos expansion. In case of negligible pore-scale dispersion, the same holds true for a passive tracer transport sample, since a Lagrangian transport formulation can be employed. Our approach avoids problems related to the accurate collocation-based solution of the transport problem, while being significantly faster than full Monte Carlo. (Full Monte Carlo does not rely on a polynomial chaos expansion of the random flow field). The proposed method is applied for passive tracer transport within a two-dimensional aquifer. A multi-point Gaussian logarithmic permeability field is assumed.

Meyer, Daniel W.; Müller, Florian; Jenny, Patrick

2014-05-01

264

Coupled anharmonic oscillators: the Rayleigh-Ritz approach versus the collocation approach  

NASA Astrophysics Data System (ADS)

For a system of coupled anharmonic oscillators we compare the convergence rate of the variational collocation approach presented recently by Amore and Fernández (2010 Phys. Scr. 81 045011) with the one obtained using the optimized Rayleigh-Ritz (RR) method. The monotonic convergence of the RR method allows us to obtain more accurate results at a lower computational cost.

Kuro?, Arkadiusz; Okopi?ska, Anna

2011-01-01

265

Parametrization of Level-Sets with B-Splines  

Microsoft Academic Search

Level-sets are powerful techniques to segment images because they can accommodate any contour topologies. We used B-splines to model level-set functions using fewer knots\\/coefficients than pixels. This forces the contours to be smooth without the need to minimize smoothing terms. We implemented a standard variational method where objects were segmented based on their edges. We also developed a method to

Olivier Salvado

2007-01-01

266

High-Quality Rendering of Quartic Spline Surfaces on the GPU  

Microsoft Academic Search

We present a novel GPU-based algorithm for high-quality rendering of bivariate spline surfaces. An essential difference to the known methods for rendering graph surfaces is that we use quartic smooth splines on triangulations rather than triangular meshes. Our rendering approach is direct since we do not use an intermediate tessellation but rather compute ray-surface intersections (by solving quartic equations numerically)

Gerd Reis; Frank Zeilfelder; Martin Hering-bertram; Gerald E. Farin; Hans Hagen

2008-01-01

267

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

268

B-Spline Signal Processing: Part I-Theory  

Microsoft Academic Search

This paper describes a set of efficient filtering techniques for the processing and representation of signals in terms of continuous B-spline basis functions. We first consider the problem of determining the spline coefficients for an exact signal interpolation (direct B-spline transform). The reverse operation is the signal reconstruction from its spline coefficients with an optional zooming factor rn (indirect B-spline

Michael Unser; Akram Aldroubi; Murray Eden

1993-01-01

269

Polynomial interpolation methods for viscous flow calculations  

Microsoft Academic Search

Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal

S. G. Rubin; P. K. Khosla

1977-01-01

270

IMPLEMENTATION OF CLEAR ALGORITHM ON COLLOCATED GRID SYSTEM AND APPLICATION EXAMPLES  

Microsoft Academic Search

Implementation of the CLEAR algorithm on a collocated grid system is conducted. Detailed discussion of the previous momentum interoperation method (MIM) is given to analyze the condition to get a unique converged solution that is independent of relaxation factor for steady flow. Six numerical examples on nonstaggered grids of forced-convective fluid flow and natural convection are provided to compare the

Z. G. Qu; W. Q. Tao; Y. L. He

2004-01-01

271

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation  

NASA Astrophysics Data System (ADS)

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

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

2014-02-01

272

Thin-plate spline quadrature of geodetic integrals  

NASA Astrophysics Data System (ADS)

Thin-plate splines — well known for their flexibility and fidelity in representing experimental data — are especially suited for the numerical evaluation of geodetic integrals in the area where these are most sensitive to the data, i.e. in the immediate vicinity of the computation point. Quadrature rules that are exact for thin-plate splines interpolating randomly spaced data are derived for the inner zone contribution (to a planar approximation) to Stokes's formula, to the formulae of Vening Meinesz and to the L 1 gradient operator in the analytical continuation solution of Molodensky's problem. The quadrature method is demonstrated by calculating the inner zone contribution to height anomalies in a mountainous area of Lesotho and carrying out a comparison with GPS-derived heights. Height anomalies are recovered with an accuracy of 6 cm.

van Gysen, Herman

1994-09-01

273

Capturing anatomical shape variability using B-spline registration.  

PubMed

Registration based on B-spline transformations has attracted much attention in medical image processing recently. Non-rigid registration provides the basis for many important techniques, such as statistical shape modeling. Validating the results, however, remains difficult--especially in intersubject registration. This work explores the ability of B-spline registration methods to capture intersubject shape deformations. We study the effect of different established and new shape representations, similarity measures and optimization strategies on the matching quality. To this end we conduct experiments on synthetic shapes representing deformations which typically may arise in intersubject registration, as well as on real patient data of the liver and pelvic bone. The experiments clearly reveal the influence of each component on the registration performance. The results may serve as a guideline for assessing intensity based registration. PMID:17354727

Wenckebach, Thomas H; Lamecker, Hans; Hege, Hans-Christian

2005-01-01

274

White matter fiber tracking directed by interpolating splines and a methodological framework for evaluation  

PubMed Central

Image-based tractography of white matter (WM) fiber bundles in the brain using diffusion weighted MRI (DW-MRI) has become a useful tool in basic and clinical neuroscience. However, proper tracking is challenging due to the anatomical complexity of fiber pathways, the coarse resolution of clinically applicable whole-brain in vivo imaging techniques, and the difficulties associated with verification. In this study we introduce a new tractography algorithm using splines (denoted Spline). Spline reconstructs smooth fiber trajectories iteratively, in contrast to most other tractography algorithms that create piecewise linear fiber tract segments, followed by spline fitting. Using DW-MRI recordings from eight healthy elderly people participating in a longitudinal study of cognitive aging, we compare our Spline algorithm to two state-of-the-art tracking methods from the TrackVis software suite. The comparison is done quantitatively using diffusion metrics (fractional anisotropy, FA), with both (1) tract averaging, (2) longitudinal linear mixed-effects model fitting, and (3) detailed along-tract analysis. Further validation is done on recordings from a diffusion hardware phantom, mimicking a coronal brain slice, with a known ground truth. Results from the longitudinal aging study showed high sensitivity of Spline tracking to individual aging patterns of mean FA when combined with linear mixed-effects modeling, moderately strong differences in the along-tract analysis of specific tracts, whereas the tract-averaged comparison using simple linear OLS regression revealed less differences between Spline and the two other tractography algorithms. In the brain phantom experiments with a ground truth, we demonstrated improved tracking ability of Spline compared to the two reference tractography algorithms being tested.

Losnegard, Are; Lundervold, Arvid; Hodneland, Erlend

2013-01-01

275

Optimization of Low-Thrust Spiral Trajectories by Collocation  

NASA Technical Reports Server (NTRS)

As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.

Falck, Robert D.; Dankanich, John W.

2012-01-01

276

Relative orbit control of collocated geostationary spacecraft  

NASA Astrophysics Data System (ADS)

A relative orbit control concept for collocated geostationary spacecraft is presented. One chief spacecraft, controlled from the ground, is responsible for the orbit determination and control of the remaining vehicles. Any orbit relative to the chief is described in terms of equinoctial orbit element differences and a linear mapping is employed for quick transformation from relative orbit measurements to orbit element differences. It is demonstrated that the concept is well-suited for spacecraft that are collocated using eccentricity-inclination vector separation and this formulation still allows for the continued use of well established and currently employed stationkeeping schemes, such as the Sun-pointing-perigee strategy. The relative approach allows to take determinisitc thruster cross-coupling effects in the computation of stationkeeping corrections into account. The control cost for the proposed concept is comparable to ground-based stationkeeping. A relative line-of-sight constraint between spacecraft separated in longitude is also considered and an algorithm is developed to provide enforcement options. The proposed on-board control approach maintains the deputy spacecraft relative orbit, is competitive in terms of propellant consumption, allows enforcement of a relative line-of-sight constraint and offers increased autonomy and flexibility for future missions.

Rausch, Raoul R.

277

Probabilistic collocation for period-1 limit cycle oscillations  

Microsoft Academic Search

In this paper probabilistic collocation for limit cycle oscillations (PCLCO) is proposed. Probabilistic collocation (PC) is a non-intrusive approach to compute the polynomial chaos description of uncertainty numerically. Polynomial chaos can require impractical high orders to approximate long-term time integration problems, due to the fast increase of required polynomial chaos order with time. PCLCO is a PC formulation for modeling

Jeroen A. S. Witteveen; Alex Loeven; Sunetra Sarkar; Hester Bijl

2008-01-01

278

Surface modeling of complicated geometries with incomplete erroneous data points-an extension to B-spline approach.  

PubMed

Based on the analogy between the B-spline curve modeling and the force-deflection behavior of a beam subjected to lateral point loads, an extension to the B-spline surface modeling method was introduced. The proposed method has strong extrapolating capability and can develop accurate surface models over an incomplete net of data points without affecting the original data. Extrapolation of the incomplete part of the data net is conducted simultaneously with interpolation of the existing part, with no need to recalculation. Approximation or data smoothing is a natural extension of the method, however, the smoothing intensity can be controlled continuously without reducing the number of spline intervals. The performance of the method was evaluated on some known analytical surfaces and produced more accurate results in comparison with the regular B-spline approach. The results indicate that the proposed method can also filter erroneous data points and reconstruct the original surface successfully. PMID:17282521

Jafari, Ali; Farahmand, Farzam; Meghdari, Ali

2005-01-01

279

Achieving high data reduction with integral cubic B-splines  

NASA Technical Reports Server (NTRS)

During geometry processing, tangent directions at the data points are frequently readily available from the computation process that generates the points. It is desirable to utilize this information to improve the accuracy of curve fitting and to improve data reduction. This paper presents a curve fitting method which utilizes both position and tangent direction data. This method produces G(exp 1) non-rational B-spline curves. From the examples, the method demonstrates very good data reduction rates while maintaining high accuracy in both position and tangent direction.

Chou, Jin J.

1993-01-01

280

Solution of problems of the theory of plates and shells with spline functions (survey)  

SciTech Connect

The study of the stress-strain state of plates and shells subjected to various types of loads with different support conditions entails the formulation of boundary-value problems that generally involve systems of partial differential equations with variable coefficients. The complexity of solving these problems stems not only from the high order of the system and the variability of the coefficients, but also from the need to exactly satisfy prescribed boundary conditions. The use of a given method to obtains a solution with a satisfactorily high degree of accuracy depends to a significant extent on the geometric and mechanical parameters characterizing certain aspects of the problem and the type of boundary conditions. These factors sometimes limit the possibilities of solving problems in the important (in a practical sense) cases in which the stiffness of the shell or plate supports is also variable. In addition, problems of the shell theory entail local and edge effects, which imposes certain stiffness conditions on boundary-value problems related to the phenomenon of instability in the computation. Spline functions have recently come into wide use to solve such problems in the areas of computational mathematics, mathematical physics, and mechanics. The popularity of this approach stems from the advantages offered by spline functions compared to other methods. Among these advantages: the stability of splines in relation to local perturbations, i.e. the behavior of the spline in the neighborhood of a point has no effect on the behavior of the spline as a whole (which is not the case in a polynomial approximation); good convergence of a spline-interpolation, in contrast to a polynomial interpolation; simplicity and ease of use of algorithms that construct and calculate splines on computers. 65 refs., 5 figs., 7 tabs.

Grogorenko, Ya.M.; Kryukov, N.N. [National Academy of Sciences of Ukraine, Kiev (Russian Federation)

1995-12-01

281

Multiple products of B-splines used in CAD system  

Microsoft Academic Search

The function upgrade of computer aided design (CAD) system requested that the multiple product of B- spline functions should be represented as a linear combination of some suitable (usually higher-degree) B-splines. In this paper, we apply the theory of spline space and discrete B-splines to deduce the representation of the coefficients of all terms of the linear combination, which can

XU Huixia; WANG Guojin

282

Spatially Variant Convolution With Scaled B-Splines  

Microsoft Academic Search

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 Muñoz-Barrutia; Xabier Artaechevarria; Carlos Ortiz-de-Solorzano

2010-01-01

283

Weighted bicubic spline interpolation to rapidly varying data  

Microsoft Academic Search

The weighted bicubic spline that is a C1 piecewise bicubic interpolant to three-dimensional gridded data is introduced. This is a generalization of the univariate weighted spline, developed by Salkauskas, in that a weighted minimization problem is solved. The minimization problem solved is a weighted version of the problem that the natural bicubic spline and Gordon's spline-blended interpolants minimize. The surface

Thomas A. Foley

1987-01-01

284

Application of adaptive hierarchical sparse grid collocation to the uncertainty quantification of nuclear reactor simulators  

SciTech Connect

Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)

Yankov, A.; Downar, T. [University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States)] [University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States)

2013-07-01

285

Splines under tension in integral transfer problems  

NASA Technical Reports Server (NTRS)

Splines under tension are used to develop an interpolatory representation of integral radiation operators. A quantitative measure of the stability of this representation is derived and approximated in terms of local grid lengths and the tension parameter. Cubic splines (zero tension parameter) are shown to be approximately stable when the ratio of successive grid lengths lies within a specific range. Scaling procedures for determining the tension constant from the structure of the grids and the characteristics of the problem are discussed, and the utility of these procedures is illustrated by application to the formation of resonance lines in two-dimensional media with exponential height variation of opacity.

Jones, H. P.

1977-01-01

286

Surface Modeling of Complicated Geometries with Incomplete Erroneous Data Points-An Extension to B-Spline Approach  

Microsoft Academic Search

Based on the analogy between the B-spline curve modeling and the force-deflection behavior of a beam subjected to lateral point loads, an extension to the B-spline surface modeling method was introduced. The proposed method has strong extrapolating capability and can develop accurate surface models over an incomplete net of data points without affecting the original data. Extrapolation of the incomplete

Ali Jafari; Farzam Farahmand; A. Farahmand; A. Meghdari

2005-01-01

287

Spline-based joint gravity and normal mode inversion  

NASA Astrophysics Data System (ADS)

The determination of the mass density function of the Earth from gravity anomalies suffers from a serious non-uniqueness problem. In particular, structures below the Earth's crust cannot be determined from gravity data. However, normal mode data show a certain sensitivity with respect to structures in the Earth's mantle, although the data quality is essentially worse in comparison to gravity data. Therefore, an appropriate balancing of both data types is required for a combined inversion such that gravity data do not dominate the result too much. Moreover, the problem is ill-posed and a null space still remains but is reduced. A new spline based method as a further development of approaches that were already successfully applied to e.g. pure traveltime inversion or pure gravity inversion is presented for the described problem. The method is explained in a comprehensive way and some numerical results are presented and critically evaluated. [1] P. Berkel: Multiscale Methods for the Combined Inversion of Normal Mode and Gravity Variations, PhD thesis, submitted 2009. [2] P. Berkel, V. Michel: On mathematical aspects of a combined inversion of gravity and normal mode variations by a spline method, preprint, Schriften zur Funktionalanalysis und Geomathematik, 41 (2008). [3] V. Michel, A.S. Fokas: A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods, Inverse Problems, 24 (2008), 045019 (25pp). [4] V. Michel, K. Wolf: Numerical aspects of a spline-based multiresolution recovery of the harmonic mass density out of gravity functionals, Geophysical Journal International, 173 (2008), 1-16 .

Michel, V.; Berkel, P.

2009-12-01

288

On hp-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme  

NASA Astrophysics Data System (ADS)

The first purpose of this paper is to provide further illustrations, from both theoretical and numerical perspectives, for the nonconvergence of h-refinement in hp-approximation by the prolate spheroidal wave functions (PSWFs), a surprising convergence property that was first discovered by Boyd et al. (2013) [3]. The second purpose is to offer a new basis that leads to prolate-collocation systems with condition numbers independent of (c,N), the intrinsic bandwidth parameter and the number of collocation points. We highlight that the collocation scheme together with a very practical rule for pairing up (c,N) significantly outperforms the Legendre polynomial-based method (and likewise other Jacobi polynomial-based methods) in approximating highly oscillatory bandlimited functions.

Wang, Li-Lian; Zhang, Jing; Zhang, Zhimin

2014-07-01

289

Partial and interaction spline models for the semiparametric estimation of functions of several variables  

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

290

Proposed Technique for Accurate Detection/Segmentation of Lung Nodules using Spline Wavelet Techniques.  

PubMed

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

2013-03-01

291

Proposed Technique for Accurate Detection/Segmentation of Lung Nodules using Spline Wavelet Techniques  

PubMed Central

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.

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

2013-01-01

292

MAP recovery of polynomial splines from compressive samples and its application to vehicular signals  

NASA Astrophysics Data System (ADS)

We propose a stable reconstruction method for polynomial splines from compressive samples based on the maximum a posteriori (MAP) estimation. The polynomial splines are one of the most powerful tools for modeling signals in real applications. Since such signals are not band-limited, the classical sampling theorem cannot be applied to them. However, splines can be regarded as signals with finite rate of innovation and therefore be perfectly reconstructed from noiseless samples acquired at, approximately, the rate of innovation. In noisy case, the conventional approach exploits Cadzow denoising. Our approach based on the MAP estimation reconstructs the signals more stably than not only the conventional approach but also a maximum likelihood estimation. We show the effectiveness of the proposed method by applying it to compressive sampling of vehicular signals.

Hirabayashi, Akira; Makido, Satoshi; Condat, Laurent

2013-09-01

293

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

294

Mars Mission Optimization Based on Collocation of Resources  

Microsoft Academic Search

A powerful approach for analyzing martian data and optimizing mission site selection is presented. Landing site optimization involves maximizing accessibility to collocated science and resource features within a given mission radius subject to mission constraints.

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

2003-01-01

295

Continuous phase estimation from noisy fringe patterns based on the implicit smoothing splines.  

PubMed

We introduce the algorithm for the direct phase estimation from the single noisy interferometric pattern. The method, named implicit smoothing spline (ISS), can be regarded as a formal generalization of the smoothing spline interpolation for the case when the interpolated data is given implicitly. We derive the necessary equations, discuss the properties of the method and address its application for the direct estimation of the continuous phase in both classical interferometry and digital speckle pattern interferometry (DSPI). The numerical illustrations of the algorithm performance are provided to corroborate the high quality of the results. PMID:24921778

Wielgus, Maciek; Patorski, Krzysztof; Etchepareborda, Pablo; Federico, Alejandro

2014-05-01

296

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

297

Spline smoothing of histograms by linear programming  

NASA Technical Reports Server (NTRS)

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

Bennett, J. O.

1972-01-01

298

A Spline Regression Model for Latent Variables  

ERIC Educational Resources Information Center

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…

Harring, Jeffrey R.

2014-01-01

299

Image Registration Using Hierarchical B-Splines  

Microsoft Academic Search

Hierarchical B-splines have been widely used for shape modeling since their discovery by Forsey and Bartels. 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

Zhiyong Xie; Gerald E. Farin

2004-01-01

300

Improved FFD B-Spline Image Registration  

Microsoft Academic Search

Due to their computational efficiency and other salient properties, B-splines form the basis not only in comprising the de facto standard for curve and surface representation but also for various nonrigid registration techniques frequently employed in medical image analysis. These registration techniques fall under the rubric of Free-Form Deformation (FFD) approaches in which the object to be registered is embedded

Nicholas J. Tustison; Brian B. Avants; James C. Gee

2007-01-01

301

IMAGE COMPRESSION USING SPLINE BASED WAVELET TRANSFORMS  

Microsoft Academic Search

In paper we describe a successful applications of the wavelet transforms to still image compression. The wavelet transforms were designed by the usage of discrete interpolatory splines. These filters outperform the traditional biorthogonal 9\\/7 filters which are frequenty used in wavelet based compression. The new filters and the biorthogonal 9\\/7 are incor- porated into SPIHT in order to measure and

Amir Z. Averbuch; Valery A. Zheludev

302

FORTRAN Subroutines for Bicubic Spline Interpolation.  

National Technical Information Service (NTIS)

Two CDC 3800 FORTRAN subroutines (BICUB1 and BICUB2) which perform bicubic spline interpolation of a tabulated function of two variables are described. Given the values X(1),...,X(N) and Y(1),...,Y(M) of two independent variables and the corresponding fun...

J. J. Cornyn

1973-01-01

303

Nonlinear Dimensionality Reduction with Local Spline Embedding  

Microsoft Academic Search

This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Our algorithm is developed under the conceptual framework of compatible mapping. Each such mapping is a compound of a tangent space projection and a group of splines. Tangent space projection is estimated at each data point on the manifold, through which the data point itself and its neighbors are

Shiming Xiang; Feiping Nie; Changshui Zhang; Chunxia Zhang

2009-01-01

304

Curvilinear Bicubic Spline Fit Interpolation Scheme  

Microsoft Academic Search

When the digital computer is used to design an optical system, the solution is obtained at a set of grid points over a given plane. A reliable interpolation technique is then required to find the values between the grid points, and the bicubic spline fit interpolation technique is often used for this purpose. When the system geometry is circular, a

Changhwi Chi

1973-01-01

305

Penalised regression splines: theory and application to medical research.  

PubMed

Generalised additive models (GAMs) allow for flexible functional dependence of a response variable on covariates. The aim of this article is to provide an accessible overview of GAMs based on the penalised likelihood approach with regression splines. In contrast to the classical backfitting, the penalised likelihood framework taken here provides researchers with an efficient computational method for automatic multiple smoothing parameter selection, which can determine the functional form of any relationship from the data. We illustrate through an example how the use of this methodology can help to gain insights into medical research. PMID:18815162

Marra, Giampiero; Radice, Rosalba

2010-04-01

306

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.

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

2014-06-01

307

Segregated Prediction of 3-D Compressible Subsonic Fluid Flows Using Collocated Grids  

Microsoft Academic Search

A segregated approach for the prediction of three-dimensional, compressible, subsonic flows is presented. The method uses a collocated finite volume scheme in body-fitted coordinates. For computational expediency and ease of implementation of high-order schemes, the continuity, momentum, and state equations are decoupled and solved sequentially. In order to eliminate potential “checkerboard” pressure distributions due to the decoupling of the pressure-velocity

Guoqing Zhang; Dennis N. Assanis; Panos Tamamidis

1996-01-01

308

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

309

Subcell resolution in simplex stochastic collocation for spatial discontinuities  

SciTech Connect

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., 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

310

Analysis of three-dimensional splines and their application to the initial graphics exchange specification  

Microsoft Academic Search

This research develops the fundamental theories associated with three-dimensional splines and the philosophies underlying the Initial Graphics Exchange Specification (IGES). Splines have been classified into three main categories: polynomial splines, splines-in-tension, and blending splines. The importance of a three-dimensional spline standard is given. It is shown that no single spline routine can adequately define a curve for every possible application.

Dolin

1985-01-01

311

Extending cubic uniform B-splines by unified trigonometric and hyperbolic basis  

Microsoft Academic Search

In this paper, the trigonometric basis {sin t, cos t, t, 1} and the hyperbolic basis {sinh t, cosh t, t, 1} are unified by a shape parameter C (0?Csplines (FB-splines) and its corresponding Subdivision B-splines (SB-splines). As well, a geometric proof of curvature continuity for SB-splines is provided. FB-splines and SB-splines inherited nearly all

Jiwen Zhang; Frank-L. Krause

2005-01-01

312

High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces  

Microsoft Academic Search

Spline generated surface Laplacians are introduced as an effective method for estimating neocortical source activity at moderate scales. The method appears to be robust to the unavoidable perturbations of measured potentials and errors of head geometry and resistivity that are certain to occur in clinical or research settings. In particular, the surface Laplacian is derived for general ellipsoidal surfaces in

Samuel K. Law; Paul L. Nunez; Ranjith S. Wijesinghe

1993-01-01

313

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

314

N-dimensional B-spline surface estimated by lofting for locally improving IRI  

NASA Astrophysics Data System (ADS)

N-dimensional surfaces are defined by the tensor product of B-spline basis functions. To estimate the unknown control points of these B-spline surfaces, the lofting method also called skinning method by cross-sectional curve fits is applied. It is shown by an analytical proof and numerically confirmed by the example of a four-dimensional surface that the results of the lofting method agree with the ones of the simultaneous estimation of the unknown control points. The numerical complexity for estimating vn control points by the lofting method is O(vn+1) while it results in O(v3n) for the simultaneous estimation. It is also shown that a B-spline surface estimated by a simultaneous estimation can be extended to higher dimensions by the lofting method, thus saving computer time. An application of this method is the local improvement of the International Reference Ionosphere (IRI), e.g. by the slant total electron content (STEC) obtained by dual-frequency observations of the Global Navigation Satellite System (GNSS). Three-dimensional B-spline surfaces at different time epochs have to be determined by the simultaneous estimation of the control points for this improvement. A four-dimensional representation in space and time of the electron density of the ionosphere is desirable. It can be obtained by the lofting method. This takes less computer time than determining the four-dimensional surface solely by a simultaneous estimation.

Koch, K.; Schmidt, M.

2011-03-01

315

Polynomial interpolation methods for viscous flow calculations  

NASA Technical Reports Server (NTRS)

Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.

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

1977-01-01

316

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

317

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

318

Pseudo-splines, wavelets and framelets  

Microsoft Academic Search

The first type of pseudo-splines were introduced in [I. Daubechies, B. Han, A. Ron, Z. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14 (1) (2003) 1–46; I. Selesnick, Smooth wavelet tight frames with zero moments, Appl. Comput. Harmon. Anal. 10 (2) (2001) 163–181] to construct tight framelets with desired approximation orders via the unitary extension principle

Bin Dong; Zuowei Shen

2007-01-01

319

Power amplifier linearization using cubic spline interpolation  

Microsoft Academic Search

An adaptive RF power amplifier linearization technique is presented. The demodulated amplifier output is compared with the baseband input signal to estimate the amplifier's AM-AM and AM-PM characteristics, using cubic spline interpolation. The input signal is predistorted using these estimated characteristics to compensate for the amplifier's nonlinearity. The proposed technique has nearly 14 dB better suppression of the intermodulation products

Anit Lohtia; Paul A. Goud; Colin G. Englefield

1993-01-01

320

Exact Likelihood Ratio Tests for Penalized Splines  

Microsoft Academic Search

Summary Penalized spline-based additive models allow a simple mixed model representation where the variance components control departures from linear models. The smoothing parameter is the ratio between the random-coe-cient and error variances and tests for linear regression reduce to tests for zero random-coe-cient variances. We propose exact likelihood and restricted likelihood ratio tests, (R)LRTs, for testing polynomial regression versus a

CIPRIAN CRAINICEANU; DAVID RUPPERT; GERDA CLAESKENS; M. P. WAND

2004-01-01

321

Exact likelihood ratio tests for penalised splines  

Microsoft Academic Search

Penalised-spline-based additive models allow a simple mixed model representation where the variance components control departures from linear models. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose exactlikelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by

Ciprian Crainiceanu; David Ruppert; Gerda Claeskens; M. P. Wand

2005-01-01

322

Curvilinear bicubic spline fit interpolation scheme  

NASA Technical Reports Server (NTRS)

Modification of the rectangular bicubic spline fit interpolation scheme so as to make it suitable for use with a polar grid pattern. In the proposed modified scheme the interpolation function is expressed in terms of the radial length and the arc length, and the shape of the patch, which is a wedge or a truncated wedge, is taken into account implicitly. Examples are presented in which the proposed interpolation scheme was used to reproduce the equations of a hemisphere.

Chi, C.

1973-01-01

323

Interobserver reproducibility of quantitative cartilage measurements: comparison of B-spline snakes and manual segmentation  

Microsoft Academic Search

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

324

COLLINARUS: collection of image-derived non-linear attributes for registration using splines  

Microsoft Academic Search

We present a new method for fully automatic non-rigid registration of multimodal imagery, including structural and functional data, that utilizes multiple texutral feature images to drive an automated spline based non-linear image registration procedure. Multimodal image registration is significantly more complicated than registration of images from the same modality or protocol on account of difficulty in quantifying similarity between different

Jonathan Chappelow; B. Nicolas Bloch; Neil Rofsky; Elizabeth Genega; Robert Lenkinski; William Dewolf; Satish Viswanath; Anant Madabhushi

2009-01-01

325

Deformable Image Registration - A Critical Evaluation: Demons, B-Spline FFD and Spring Mass System  

Microsoft Academic Search

This paper describes results of a quantitative evaluation of a flexible spring mass system image registration technique previously proposed by the authors. The method is assessed against two well-known registration algorithms namely the Demons and the B-spline free form deformations (FFD) implemented in Insight Segmentation and Registration Toolkit (ITK). The evaluation has been performed using simulated data as well as

Jian-Kun Shen; Bogdan J. Matuszewski; Lik-Kwan Shark; Andrzej Skalski; T. Zielinski; Christopher J. Moore

2008-01-01

326

Combined Features of Cubic B-Spline Wavelet Moments and Zernike Moments for Invariant Character Recognition  

Microsoft Academic Search

In this paper a new method of combining cubic B-spline wavelet moments (WMs) and Zernike moments (ZMs) into a common feature vector is proposed for invariant pattern classification. By doing so, the ability of ZMs to capture global features and WMs to differentiate between subtle variations in description can be utilized at the same time. Analysis and simulations verify that

Chao Kan; Mandyam D. Srinath

2001-01-01

327

Fusion of 3D B-spline surface patches reconstructed from image sequences  

Microsoft Academic Search

This paper considers the problem of merging a set of distinct three dimensional B-spline surface patches, which are reconstructed from observations of the motion of occluding contours in image sequences. We propose an original method of fusing these partially overlapping patches in order to obtain a whole surface. This approach is based on a triangular mesh and surface interpolation through

Roger Mohr; Chang Sheng Zhao; Gautier Koscielny

1994-01-01

328

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

329

Validation of ocean wind and wave data using triple collocation  

NASA Astrophysics Data System (ADS)

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 random errors of the different systems are independent, but situations where independence is not strictly observed are also considered. The results show that the ERA-40 predictions underestimate high values of significant wave height and, contrary to what would be obtained by less sophisticated statistical methods, wind speed, that the variance of the errors associated with the ERA-40 system is much higher than that of the errors of the measurements, and that the former shows a dependence on the value of the observations not present in the latter. The altimeter measurements of significant wave height are very precise, in contrast to the large uncertainty associated with the altimeter retrieved wind speeds.

Caires, S.; Sterl, A.

2003-03-01

330

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

331

Quintic G2-splines for trajectory planning of autonomous vehicles  

Microsoft Academic Search

Presents a motion planning primitive for car-like vehicles. It is a completely parametrized quintic spline, denoted as ?-spline, that allows interpolation of an arbitrary sequence of points with overall second order geometric (G2-) continuity. Issues such as minimality, regularity, symmetry, and flexibility of these G2-splines are addressed in the exposition. The development of the new primitive is tightly connected to

Aurelio PIAZZI; C. Guarino Lo Bianco

2000-01-01

332

Isotropic polyharmonic B-splines: scaling functions and wavelets  

Microsoft Academic Search

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

333

Development and flight tests of vortex-attenuating splines  

NASA Technical Reports Server (NTRS)

The ground tests and full-scale flight tests conducted during development of the vortex-attenuating spline are described. The flight tests were conducted using a vortex generating aircraft with and without splines; a second aircraft was used to probe the vortices generated in both cases. The results showed that splines significantly reduced the vortex effects, but resulted in some noise and climb performance penalties on the generating aircraft.

Hastings, E. C., Jr.; Patterson, J. C., Jr.; Shanks, R. E.; Champine, R. A.; Copeland, W. L.; Young, D. C.

1975-01-01

334

Reconstruction of convergent G1 smooth B-spline surfaces  

Microsoft Academic Search

Recently, there have been improvements on reconstruction of smooth B-spline surfaces of arbitrary topological type, but the most important problem of smoothly stitching B-spline surface patches (the continuity problem of B-spline surface patches) in surface reconstruction has not been solved in an effective way. Therefore, the motivation of this paper is to study how to better improve and control the

Xiquan Shi; Tianjun Wang; Peiru Wu; Fengshan Liu

2004-01-01

335

High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces.  

PubMed

Spline generated surface Laplacians are introduced as an effective method for estimating neocortical source activity at moderate scales. The method appears to be robust to the unavoidable perturbations of measured potentials and errors of head geometry and resistivity that are certain to occur in clinical or research settings. In particular, we have derived the surface Laplacian for general ellipsoidal surfaces in terms of the spline function. The spline-Laplacian accurately estimates isolated dipoles or distributed sources, is insensitive to subcortical sources and to sources which originate outside the boundaries of the electrode array, and acts as a bandpass spatial filter whose characteristics appear to provide a good match to the volume conduction of intracranial sources through human heads. As a result, spatial resolution is improved over that obtained with conventional EEG by at least a factor of three. This improvement, whether obtained with spline-Laplacian or model-dependent methods, is likely to have a significant impact on both medical and cognitive studies involving EEG. PMID:8319965

Law, S K; Nunez, P L; Wijesinghe, R S

1993-02-01

336

A B-spline approach to phase unwrapping in tagged cardiac MRI for motion tracking.  

PubMed

A novel B-Spline based approach to phase unwrapping in tagged magnetic resonance images is proposed for cardiac motion tracking. A bicubic B-spline surface is used to model the absolute phase. The phase unwrapping problem is formulated as a mixed integer optimization problem that minimizes the sum of the difference between the spatial gradients of absolute and wrapped phases, and the difference between the rewrapped and wrapped phases. In contrast to the existing techniques for motion tracking, the proposed approach can overcome the limitation of interframe half-tag displacement and increase the robustness of motion tracking. The article further presents a hybrid harmonic phase imaging-B-spline method to take the advantage of the harmonic phase imaging method for small motion and the efficiency of the B-Spline approach for large motion. The proposed approach has been successively applied to a full set of cardiac MRI scans in both long and short axis slices with superior performance when compared with the harmonic phase imaging and quality guided path-following methods. PMID:22692944

Chiang, Patricia; Cai, Yiyu; Mak, Koon Hou; Zheng, Jianmin

2013-05-01

337

Approximation by Smooth Bivariate Splines on a Three-Direction Mesh.  

National Technical Information Service (NTIS)

Univariate splines have been proved quite useful in practice. However, if one wants to fit a surface, or solve a partial differential equation numerically, one would naturally think of using multivariate splines. Here splines still mean piecewise polynomi...

R. Jia

1983-01-01

338

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

339

A Step-by-Step Integration Scheme Utilizing the Cardinal B-splines  

Microsoft Academic Search

The authors present a new step-by-step integration scheme by utilizing the cardinal B-splines. The new method organizes conventional implicit methods such as Newmark-beta method and Wilson-theta method and so on, and provides a simple computation procedure so that the step-by-step integration can be carried out efficiently. In addition, when we analyze a nonlinear system with discontinuity the computational accuracy can

Takumi Inoue; Atsuo Sueoka

2002-01-01

340

Spline curves, wire frames and B-value  

NASA Technical Reports Server (NTRS)

The methods that were developed for wire-frame design are described. The principal tools for control of a curve during interactive design are mathematical ducks. The simplest of these devices is an analog of the draftsman's lead weight that he uses to control a mechanical spline also create Ducks for controlling differential and integral properties of curves were created. Other methods presented include: constructing the end of a Bezier polygon to gain quick and reasonably confident control of the end tangent vector, end curvature and end torsion; keeping the magnitude of unwanted curvature oscillations within tolerance; constructing the railroad curves that appear in many engineering design problems; and controlling the frame to minimize errors at mesh points and to optimize the shapes of the curve elements.

Smith, L.; Munchmeyer, F.

1985-01-01

341

An Algebraic Spline Model of Molecular Surfaces for Energetic Computations  

PubMed Central

In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation.

Zhao, Wenqi; Bajaj, Chandrajit; Xu, Guoliang

2009-01-01

342

Image inpainting using cubic spline-based edge reconstruction  

NASA Astrophysics Data System (ADS)

In this paper an image inpainting approach based on the construction of a composite curve for the restoration of the edges of objects in an image using the concepts of parametric and geometric continuity is presented. It is shown that this approach allows to restore the curved edges in damaged image by interpolating the boundaries of objects by cubic splines. A tensor analysis is used for classification of texture and non texture regions. After edge restoration stage, a texture restoration based on exemplar based method is carried out. It finds the best matching patch from another source region and copies it into the damaged region. For non texture regions a Telea method is applied.

Voronin, V. V.; Marchuk, V. I.; Sherstobitov, A. I.; Egiazarian, K. O.

2012-02-01

343

Quantitative analysis of dynamic contrast-enhanced MR images based on Bayesian P-splines.  

PubMed

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the nonlinear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided. PMID:19272996

Schmid, Volker J; Whitcher, Brandon; Padhani, Anwar R; Yang, Guang-Zhong

2009-06-01

344

Cardiac motion tracking with multilevel B-splines and SinMod from tagged MRI  

NASA Astrophysics Data System (ADS)

Cardiac motion analysis can play an important role in cardiac disease diagnosis. Tagged magnetic resonance imaging (MRI) has the ability to directly and non-invasively alter tissue magnetization and produce tags on the deforming tissue. This paper proposes an approach to analysis of tagged MR images using a multilevel B-splines fitting model incorporating phase information. The novelty of the proposed technique is that phase information is extracted from SinMod.1 By using real tag intersections extracted directly from tagged MR image data and virtual tag intersections extracted from phase information, both considered to be scattered data, multilevel B-spline fitting can result in accurate displacement motion fields. The B-spline approximation which also serves to remove noise in the displacement measurements is performed without specifying control point locations explicitly and is very fast. Dense virtual tag intersections based on SinMod were created and incorporated into the multilevel B-spline fitting process. Experimental results on simulated data from the 13- parameter kinematic model of Arts et al.2 and in vivo canine data demonstrate further improvement in accuracy and effectiveness of the proposed method.

Wang, Hui; Amini, Amir A.

2011-03-01

345

B-spline parametrization of the dielectric function applied to spectroscopic ellipsometry on amorphous carbon  

SciTech Connect

The remote plasma deposition of hydrogenated amorphous carbon (a-C:H) thin films is investigated by in situ spectroscopic ellipsometry (SE). The dielectric function of the a-C:H film is in this paper parametrized by means of B-splines. In contrast with the commonly used Tauc-Lorentz oscillator, B-splines are a purely mathematical description of the dielectric function. We will show that the B-spline parametrization, which requires no prior knowledge about the film or its interaction with light, is a fast and simple-to-apply method that accurately determines thickness, surface roughness, and the dielectric constants of hydrogenated amorphous carbon thin films. Analysis of the deposition process provides us with information about the high deposition rate, the nucleation stage, and the homogeneity in depth of the deposited film. Finally, we show that the B-spline parametrization can serve as a stepping stone to physics-based models, such as the Tauc-Lorentz oscillator.

Weber, J. W.; Hansen, T. A. R.; Sanden, M. C. M. van de; Engeln, R. [Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands)

2009-12-15

346

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

347

English Learners' Knowledge of Prepositions: Collocational Knowledge or Knowledge Based on Meaning?  

ERIC Educational Resources Information Center

Second language (L2) learners' successful performance in an L2 can be partly attributed to their knowledge of collocations. In some cases, this knowledge is accompanied by knowledge of the semantic and/or grammatical patterns that motivate the collocation. At other times, collocational knowledge may serve a compensatory role. To determine the…

Mueller, Charles M.

2011-01-01

348

Least-squares collocation with covariance-matching constraints  

NASA Astrophysics Data System (ADS)

Most geostatistical methods for spatial random field (SRF) prediction using discrete data, including least-squares collocation (LSC) and the various forms of kriging, rely on the use of prior models describing the spatial correlation of the unknown field at hand over its domain. Based upon an optimal criterion of maximum local accuracy, LSC provides an unbiased field estimate that has the smallest mean squared prediction error, at every computation point, among any other linear prediction method that uses the same data. However, LSC field estimates do not reproduce the spatial variability which is implied by the adopted covariance (CV) functions of the corresponding unknown signals. This smoothing effect can be considered as a critical drawback in the sense that the spatio-statistical structure of the unknown SRF (e.g., the disturbing potential in the case of gravity field modeling) is not preserved during its optimal estimation process. If the objective for estimating a SRF from its observed functionals requires spatial variability to be represented in a pragmatic way then the results obtained through LSC may pose limitations for further inference and modeling in Earth-related physical processes, despite their local optimality in terms of minimum mean squared prediction error. The aim of this paper is to present an approach that enhances LSC-based field estimates by eliminating their inherent smoothing effect, while preserving most of their local prediction accuracy. Our methodology consists of correcting a posteriori the optimal result obtained from LSC in such a way that the new field estimate matches the spatial correlation structure implied by the signal CV function. Furthermore, an optimal criterion is imposed on the CV-matching field estimator that minimizes the loss in local prediction accuracy (in the mean squared sense) which occurs when we transform the LSC solution to fit the spatial correlation of the underlying SRF.

Kotsakis, Christopher

2007-10-01

349

Mathematical Morphology and P-Splines Fitting: A Robust Combination for the Fully Automated Fluorescence Background Removal and Shot Noise Filtering in Raman Spectroscopy Applied to Pigments Analysis  

NASA Astrophysics Data System (ADS)

A new method has been developed for denoising a Raman spectrum using mathematical morphology combined with P-splines fitting, which requires no user input. It was applied to spectra measured on art works, resolving successfully the Raman information.

González-Vidal, J. J.; Pérez-Pueyo, R.; Soneira, M. J.; Ruiz-Moreno, S.

2014-06-01

350

Nonlinear registration using B-spline feature approximation and image similarity  

NASA Astrophysics Data System (ADS)

The warping methods are broadly classified into the image-matching method based on similar pixel intensity distribution and the feature-matching method using distinct anatomical feature. Feature based methods may fail to match local variation of two images. However, the method globally matches features well. False matches corresponding to local minima of the underlying energy functions can be obtained through the similarity based methods. To avoid local minima problem, we proposes non-linear deformable registration method utilizing global information of feature matching and the local information of image matching. To define the feature, gray matter and white matter of brain tissue are segmented by Fuzzy C-Mean (FCM) algorithm. B-spline approximation technique is used for feature matching. We use a multi-resolution B-spline approximation method which modifies multilevel B-spline interpolation method. It locally changes the resolution of the control lattice in proportion to the distance between features of two images. Mutual information is used for similarity measure. The deformation fields are locally refined until maximize the similarity. In two 3D T1 weighted MRI test, this method maintained the accuracy by conventional image matching methods without the local minimum problem.

Kim, June-Sic; Kim, Jae Seok; Kim, In Young; Kim, Sun Il

2001-07-01

351

Compensator design for stability enhancement with collocated controllers - Explicit solutions  

NASA Technical Reports Server (NTRS)

An explicit closed-form solution is obtained for the compensator transfer function for the compensator designed by Balakrishnan (1991) for stability enhancement of flexible structures with collocated controllers. The solution is positive real but nonrational and yields high stability and robustness.

Balakrishnan, A. V.

1993-01-01

352

Collocation: Integrating Child Welfare and Substance Abuse Services  

Microsoft Academic Search

This article presents findings from a process evaluation of a pilot program to address parental substance abuse in the child welfare system. By placing substance abuse counselors in a local child welfare office, the collocation program was designed to facilitate early identification, timely referral to treatment, and improved treatment engagement of substance-abusing parents. Frontline child welfare workers in 6 of

Eunju Lee; Nina Esaki; Rose Greene

2009-01-01

353

A B-spline Hartree-Fock program  

NASA Astrophysics Data System (ADS)

A B-spline version of a Hartree-Fock program is described. The usual differential equations are replaced by systems of non-linear equations and generalized eigenvalue problems of the form (H-?B)P=0, where a designates the orbital. When orbital a is required to be orthogonal to a fixed orbital, this form assumes that a projection operator has been applied to eliminate the Lagrange multiplier. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthogonal transformations. At such a stationary point, the matrix of Lagrange multipliers, ?=(P|H|P), is symmetric and the off-diagonal Lagrange multipliers may again be eliminated through projection operators. For multiply occupied shells, convergence problems are avoided by the use of a single-orbital Newton-Raphson method. A self-consistent field procedure based on these two possibilities exhibits excellent convergence. A Newton-Raphson method for updating all orbitals simultaneously has better numerical properties and a more rapid rate of convergence but requires more computer processing time. Both ground and excited states may be computed using a default universal grid. Output from a calculation for Al 3s3pP2 shows the improvement in accuracy that can be achieved by mapping results from low-order splines on a coarse grid to splines of higher order onto a refined grid. The program distribution contains output from additional test cases. Program summaryProgram title: SPHF version 1.00 Catalogue identifier: AEIJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 13 925 No. of bytes in distributed program, including test data, etc.: 714 254 Distribution format: tar.gz Programming language: Fortran 95 Computer: Any system with a Fortran 95 compiler. Tested on Intel Xeon CPU X5355, 2.66 GHz Operating system: Any system with a Fortran 95 compiler Classification: 2.1 External routines: LAPACK ( http://www.netlib.org/lapack/) Nature of problem: Non-relativistic Hartree-Fock wavefunctions are determined for atoms in a bound state that may be used to predict a variety atomic properties. Solution method: The radial functions are expanded in a B-spline basis [1]. The variational principle applied to an energy functional that includes Lagrange multipliers for orthonormal constraints defines the Hartree-Fock matrix for each orbital. Orthogonal transformations symmetrize the matrix of Lagrange multipliers and projection operators eliminate the off-diagonal Lagrange multipliers to yield a generalized eigenvalue problem. For multiply occupied shells, a single-orbital Newton-Raphson (NR) method is used to speed convergence with very little extra computation effort. In a final step, all orbitals are updated simultaneously by a Newton-Raphson method to improve numerical accuracy. Restrictions: There is no restriction on calculations for the average energy of a configuration. As in the earlier HF96 program [2], only one or two open shells are allowed when results are required for a specific LS coupling. These include: (ns, where l=0,1,2,3 (nl, where l=0,1,2,3,… (nd)(nf) Unusual features: Unlike HF96, the present program is a Fortran 90/95 program without the use of COMMON. It is assumed that Lapack libraries are available. Running time: For Ac 7s7pP2 the execution time varied from 6.9 s to 9.1 s depending on the iteration method.

Froese Fischer, Charlotte

2011-06-01

354

Interpolation with Splines in Tension: A Green's Function Approach  

Microsoft Academic Search

Interpolation and gridding of data are procedures in the physical sciences and are accomplished typically using an averaging or finite difference scheme on an equidistant grid. Cubic splines are popular because of their smooth appearances; however, these functions can have undesirable oscillations between data points. Adding tension to the spline overcomes this deficiency. Here, we derive a technique for interpolation

Paul Wessel; David Bercovici

1998-01-01

355

Local Control of Bias and Tension in Beta-splines  

Microsoft Academic Search

The Beta-spline introduced recently by Barsky is a generalization of the uniform cubic B-spline: parametric discontinuities are introduced in such a way as to preserve continuity of the unit tangent and curvature vectors at joints (geometric continuity) while providing bias and tension parameters, independent of the position of control vertices, by which the shape of a curve or surface can

Brian A. Barsky; John C. Beatty

1983-01-01

356

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

357

Orthogonal linear local spline discriminant embedding for face recognition  

Microsoft Academic Search

In this paper, an efficient feature extraction algorithm called orthogonal linear local spline discriminant embedding (O-LLSDE) is proposed for face recognition. Derived from local spline embedding (LSE), O-LLSDE not only inherits the advantages of LSE which uses local tangent space as a representation of the local geometry so as to preserve the local structure, but also makes full use of

Ying-Ke Lei; Rong-Xiang Hu; Lei Tang; Shan-Wen Zhang; De-Shuang Huang

2010-01-01

358

Identification of Hammerstein models with cubic spline nonlinearities  

Microsoft Academic Search

This paper considers the use of cubic splines, instead of polynomials, to represent the static nonlinearities in block structured models. It introduces a system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, where cubic splines represent the static nonlinearity and the linear dynamics are modeled using a finite impulse response filter. The algorithm uses

Erika J. Dempsey; David T. Westwick

2004-01-01

359

Inverting travel times with a triplication. [spline fitting technique applied to lunar seismic data reduction  

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

360

Surface mesh to volumetric spline conversion with generalized polycubes.  

PubMed

This paper develops a novel volumetric parameterization and spline construction framework, which is an effective modeling tool for converting surface meshes to volumetric splines. Our new splines are defined upon a novel parametric domain called generalized polycubes (GPCs). A GPC comprises a set of regular cube domains topologically glued together. Compared with conventional polycubes (CPCs), the GPC is much more powerful and flexible and has improved numerical accuracy and computational efficiency when serving as a parametric domain. We design an automatic algorithm to construct the GPC domain while also permitting the user to improve shape abstraction via interactive intervention. We then parameterize the input model on the GPC domain. Finally, we devise a new volumetric spline scheme based on this seamless volumetric parameterization. With a hierarchical fitting scheme, the proposed splines can fit data accurately using reduced number of superfluous control points. Our volumetric modeling scheme has great potential in shape modeling, engineering analysis, and reverse engineering applications. PMID:23846098

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

2013-09-01

361

A degree by degree recursive construction of Hermite spline interpolants  

NASA Astrophysics Data System (ADS)

Based on the classical Hermite spline interpolant H2n-1, which is the piecewise interpolation polynomial of class Cn-1 and degree 2n-1, a piecewise interpolation polynomial H2n of degree 2n is given. The formulas for computing H2n by H2n-1 and computing H2n+1 by H2n are shown. Thus a simple recursive method for the construction of the piecewise interpolation polynomial set {Hj} is presented. The piecewise interpolation polynomial H2n satisfies the same interpolation conditions as the interpolant H2n-1, and is an optimal approximation of the interpolant H2n+1. Some interesting properties are also proved.

Han, Xuli

2009-03-01

362

L1 Influence on the Acquisition of L2 Collocations: Japanese ESL Users and EFL Learners Acquiring English Collocations  

ERIC Educational Resources Information Center

This study investigated first language (L1) influence on the acquisition of second language (L2) collocations using a framework based on Kroll and Stewart (1994) and Jiang (2000), by comparing the performance on a phrase-acceptability judgment task among native speakers of English, Japanese English as a second language (ESL) users, and Japanese…

Yamashita, Junko; Jiang, Nan

2010-01-01

363

Constrained adaptive temporal B-splines (CAT B-splines) for use in medical imaging dynamic curve modelling  

Microsoft Academic Search

Accurate modeling of temporal changes plays important role in several applications in dynamic imaging such as list mode data acquisition, kinetic modeling, deconvolution of dynamic studies, or factor analysis. We present an algorithm that uses B-splines and allows modeling of any time curve. During the optimization the CAT B-spline adaptively reconfigures to model the temporal curve. Both, positions and values

Arkadiusz Sitek; Chun-Shan

2003-01-01

364

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

PubMed

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

365

Coincident collocation of displacement and tangent derivative boundary integral equations in elasticity  

NASA Astrophysics Data System (ADS)

The regular boundary integral equations of elastostatics are combined with regularized versions of the tangent derivative equations and collocated at the same points to formulate the elasticity problem in terms of displacements, tractions and the tangential displacement gradients. Hermitian cubic polynomials are used for functional interpolation on certain elements to formulate the boundary element method in terms of displacements, tractions and their tangent derivatives. Commensurate accuracy of nodal values of these functions and the tangent derivatives is obtained and makes possible the accurate and immediate recovery of all stress components. An example problem demonstrates the accuracy and utility of the approach.

Muci-Kuechler, K. H.; Rudolphi, T. J.

1993-08-01

366

Segregated prediction of 3-D compressible subsonic fluid flows using collocated grids  

SciTech Connect

A segregated approach for the prediction of three-dimensional, compressible, subsonic flows is presented. The method uses a collocated finite volume scheme in body-fitted coordinates. For computational expediency and ease of implementation of high-order schemes, the continuity, momentum, and state equations are decoupled and solved sequentially. In order to eliminate potential ``checkerboard`` pressure distributions due to the decoupling of the pressure-velocity terms in conjunction with a collocated grid, a novel method of nonlinear cell-face interpolation is adopted. The high-order QUICK scheme is implemented for discretizing convective terms, while the central difference scheme is used for discretizing diffusion terms. A four-stage Runge-Kutta explicit scheme is employed to time-march the solution of the governing equations, toward steady state. The finite volume code is applied to the prediction of three-dimensional, laminar flows in a straight duct of square cross section, a cubic driven cavity, a strongly curved duct of square cross section and a two-dimensional airfoil. The ability of the method to eliminate checkerboard pressure distribution and achieve convergence is demonstrated. The method yields accurate results, while at the same time utilizing efficiently the architecture of a vector machine. Finally, the ability of the method to perform satisfactorily near the low Mach number limit is demonstrated through comparisons with incompressible flow measurements.

Zhang, G.; Assanis, D.N. [Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Mechanical Engineering and Applied Mechanics; Tamamidis, P. [Pennsylvania State Univ., University Park, PA (United States). Propulsion Research Center

1996-06-01

367

Regularity and well-posedness of a dual program for convex best C 1 -spline interpolation  

Microsoft Academic Search

An efficient approach to computing the convex best C\\u000a 1-spline interpolant to a given set of data is to solve an associated dual program by standard numerical methods (e.g., Newton’s\\u000a method). We study regularity and well-posedness of the dual program: two important issues that have been not yet well-addressed\\u000a in the literature. Our regularity results characterize the case when the

Houduo Qi; Xiaoqi Yang

2007-01-01

368

Landmark and Intensity-Based, Consistent Thin-Plate Spline Image Registration  

Microsoft Academic Search

Landmark-based thin-plate spline image registration is one of the most commonly used methods for non-rigid medical image registration\\u000a and anatomical shape analysis. It is well known that this method does not produce a unique correspondence between two images\\u000a away from the landmark locations because interchanging the role of source and target landmarks does not produce forward and\\u000a reverse transformations that

Hans J. Johnson; Gary E. Christensen

2001-01-01

369

Free-Form B-spline Deformation Model for Groupwise Registration  

Microsoft Academic Search

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 ecient implementation using stochastic gradient descents in a multi-resolution setting. We demon- strate the method in application to a set of 50 MRI brain scans and compare the results to a pairwise approach using segmentation

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

2007-01-01

370

Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation.  

PubMed

Making sound proteomic inferences using ELISA microarray assay requires both an accurate prediction of protein concentration and a credible estimate of its error. We present a method using monotonic spline statistical models (MS), penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict ELISA microarray protein concentrations and estimate their prediction errors. We contrast the MSMC (monotone spline Monte Carlo) method with a LNLS (logistic nonlinear least squares) method using simulated and real ELISA microarray data sets.MSMC rendered good fits in almost all tests, including those with left and/or right clipped standard curves. MS predictions were nominally more accurate; especially at the extremes of the prediction curve. MC provided credible asymmetric prediction intervals for both MS and LN fits that were superior to LNLS propagation-of-error intervals in achieving the target statistical confidence. MSMC was more reliable when automated prediction across simultaneous assays was applied routinely with minimal user guidance. PMID:18673290

Daly, Don Simone; Anderson, Kevin K; White, Amanda M; Gonzalez, Rachel M; Varnum, Susan M; Zangar, Richard C

2008-01-01

371

Comparing measures of model selection for penalized splines in Cox models  

PubMed Central

This article presents an application and a simulation study of model fit criteria for selecting the optimal degree of smoothness for penalized splines in Cox models. The criteria considered were the Akaike information criterion, the corrected AIC, two formulations of the Bayesian information criterion, and a generalized cross-validation method. The estimated curves selected by the five methods were compared to each other in a study of rectal cancer mortality in autoworkers. In the stimulation study, we estimated the fit of the penalized spline models in six exposure-response scenarios, using the five model fit criteria. The methods were compared based on a mean squared-error score and the power and size of hypothesis tests for any effect and for detecting nonlinearity. All comparisons were made across a range in the total sample size and number of cases.

Malloy, Elizabeth J.; Spiegelman, Donna; Eisen, Ellen A.

2009-01-01

372

Generation of Discrete Bicubic G1 B-Spline Ship Hullform Surfaces from a Given Curve Network Using Virtual IsoParametric Curves  

Microsoft Academic Search

We propose a method that automatically generates discrete bicubic G1 continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are\\u000a classified into two types: boundary curves and “reference curves”. The boundary curves correspond to a set of rectangular\\u000a (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline

Joong-hyun Rhim; Doo-yeoun Cho; Kyu-yeul Lee; Tae-Wan Kim

2006-01-01

373

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

374

Higher order approximations using interpolation applied to collocation solutions of two-point boundary value problems  

NASA Astrophysics Data System (ADS)

When solving a system of first order differential equations involving boundary conditions using collocation at k Gauss points that are the zeros of Pk(x), the kth degree Legendre polynomial, to produce a continuous solution over the problem interval, it is well known that the global error at the mesh points is O(h2k) and at other points the global error is O(hk+1). In addition, it is known that the error in the derivative of the solution at non-mesh points is O(hk). This paper shows that the error in the solution at the zeros of in each subinterval is O(hk+2) and that the error in the derivative of the solution at the zeros of Pk(x) is O(hk+1). This higher order accuracy can be used in various interpolation schemes (Hermite-Birkhoff interpolation in the case that includes derivative data) to produce global errors O(hk+2) in the solution without any additional collocation and without any additional function evaluations. Only the evaluation of the collocation solution or its derivative at certain special points is necessary. Hence, this increased accuracy is almost free compared to other methods which give global errors O(h2k) but at considerable extra expense. Some numerical results illustrating the higher accuracy at these special points are given at the end of the paper along with comparisons, in the form of diagrams, of results produced from the package COLSYS and the results produced from the interpolation schemes (which use COLSYS as a starting point).

Finden, W. F.

2007-09-01

375

Radiation energy budget studies using collocated AVHRR and ERBE observations  

NASA Technical Reports Server (NTRS)

Changes in the energy balance at the top of the atmosphere are specified as a function of atmospheric and surface properties using observations from the Advanced Very High Resolution Radiometer (AVHRR) and the Earth Radiation Budget Experiment (ERBE) scanner. By collocating the observations from the two instruments, flown on NOAA-9, the authors take advantage of the remote-sensing capabilities of each instrument. The AVHRR spectral channels were selected based on regions that are strongly transparent to clear sky conditions and are therefore useful for characterizing both surface and cloud-top conditions. The ERBE instruments make broadband observations that are important for climate studies. The approach of collocating these observations in time and space is used to study the radiative energy budget of three geographic regions: oceanic, savanna, and desert.

Ackerman, Steven A.; Inoue, Toshiro

1994-01-01

376

Quartic Box-Spline Reconstruction on the BCC Lattice.  

PubMed

This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the 7-direction quartic box-spline M7 that has the same approximation order as the 8-direction quintic box-spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations. PMID:22614329

Kim, Minho

2012-05-14

377

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

378

Quantification of spinal cord atrophy from magnetic resonance images via a B-spline active surface model  

Microsoft Academic Search

A method is presented that aims at segmenting and measuring the surface of the spinal cord from MR images in order to detect and quantify atrophy. A semiautomatic segmentation with very little intervention from an operator is proposed. It is based on the optimization of a B-spline active surface. The method al- lows for the computation of orthogonal cross-sections at

O. Coulon; S. J. Hickman; G. J. Parker; G. J. Barker; D. H. Miller; S. R. Arridge

2002-01-01

379

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

2012-05-01

380

Collocation of two GEO satellites and one inclined GSO satellite  

Microsoft Academic Search

Three collocation strategies are planned and analyzed for the cluster of two geostationary orbit (GEO) satellites and one inclined geosynchronous orbit (GSO) satellite in the same longitude control band of 116°E±0.05° . The longitudinal control bands are allocated for the two GEO satellites and one inclined GSO satellite with seven-day East\\/West station-keeping maneuver cycle. The latitudinal control bands are allocated

Byoung-Sun Lee; Kyu-Hong Choi

2000-01-01

381

A new approach for lofted B-spline surface interpolation to serial contours  

Microsoft Academic Search

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface

H. B. Jung; K. Kim

2004-01-01

382

Ordered subsets Bayesian tomographic reconstruction using 2-D smoothing splines as priors.  

PubMed

The ordered subsets expectation maximization (OS-EM) algorithm has enjoyed considerable interest for accelerating the well-known EM algorithm for emission tomography. The OS principle has also been applied to several regularized EM algorithms, such as nonquadratic convex minimization-based maximum a posteriori (MAP) algorithms. However, most of these methods have not been as practical as OS-EM due to their complex optimization methods and difficulties in hyperparameter estimation. We note here that, by relaxing the requirement of imposing sharp edges and using instead useful quadratic spline priors, solutions are much easier to compute, and hyperparameter calculation becomes less of a problem. In this work, we use two-dimensional smoothing splines as priors and apply a method of iterated conditional modes for the optimization. In this case, step sizes or line-search algorithms necessary for gradient-based descent methods are avoided. We also accelerate the resulting algorithm using the OS approach and propose a principled way of scaling smoothing parameters to retain the strength of smoothing for different subset numbers. Our experimental results show that the OS approach applied to our quadratic MAP algorithms provides a considerable acceleration while retaining the advantages of quadratic spline priors. PMID:12850295

Lee, Soo-Jin

2003-09-01

383

Estimation of heat transfer parameters in a trickle-bed reactor using differential evolution and orthogonal collocation  

Microsoft Academic Search

A new non-sequential technique is proposed for the estimation of effective heat transfer parameters using radial temperature profile measurements in a gas–liquid co-current downflow through packed bed reactors (often referred to as trickle bed reactors). Orthogonal collocation method combined with a new optimization technique, differential evolution (DE) is employed for estimation. DE is an exceptionally simple, fast and robust, population

B. V. Babu; K. K. N. Sastry

1999-01-01

384

Bee brains, B-splines and computational democracy: generating an average shape atlas  

Microsoft Academic Search

We describe a method to generate an average atlas from segmented 3-D images of a population of subjects. Using repeated application of an intensity-based non-rigid registration algorithm based on third-order 3-D B-splines, a sequence of average label images is created. Averaging of the non-numerical label data employs a generalization of the mode of sets of corresponding voxels, parameterized by a

Torsten Rohlfing; Robert Brandt; Randolf Menzel

2001-01-01

385

Filling n-sided regions with G1 triangular Coons B-spline patches  

Microsoft Academic Search

Filling n-sided regions is an essential operation in shape and surface modeling. Positional and tangential continuities are highly\\u000a required in designing and manufacturing. We propose a method for filling n-sided regions with untrimmed triangular Coons B-spline patches, preserving G\\u000a 1 continuity exactly. The algorithm first computes a central point, a central normal, the central, and the corner derivative\\u000a vectors. Then

Kan-Le Shi; Jun-Hai Yong; Jia-Guang Sun; Jean-Claude Paul; He-Jin Gu

2010-01-01

386

Detail view of redwood spline joinery of woodframe section against ...  

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Detail view of redwood spline joinery of wood-frame section against adobe addition (measuring tape denotes plumb line from center of top board) - First Theatre in California, Southwest corner of Pacific & Scott Streets, Monterey, Monterey County, CA

387

Composite multi-modal vibration control for a stiffened plate using non-collocated acceleration sensor and piezoelectric actuator  

NASA Astrophysics Data System (ADS)

A novel active method for multi-mode vibration control of an all-clamped stiffened plate (ACSP) is proposed in this paper, using the extended-state-observer (ESO) approach based on non-collocated acceleration sensors and piezoelectric actuators. Considering the estimated capacity of ESO for system state variables, output superposition and control coupling of other modes, external excitation, and model uncertainties simultaneously, a composite control method, i.e., the ESO based vibration control scheme, is employed to ensure the lumped disturbances and uncertainty rejection of the closed-loop system. The phenomenon of phase hysteresis and time delay, caused by non-collocated sensor/actuator pairs, degrades the performance of the control system, even inducing instability. To solve this problem, a simple proportional differential (PD) controller and acceleration feed-forward with an output predictor design produce the control law for each vibration mode. The modal frequencies, phase hysteresis loops and phase lag values due to non-collocated placement of the acceleration sensor and piezoelectric patch actuator are experimentally obtained, and the phase lag is compensated by using the Smith Predictor technology. In order to improve the vibration control performance, the chaos optimization method based on logistic mapping is employed to auto-tune the parameters of the feedback channel. The experimental control system for the ACSP is tested using the dSPACE real-time simulation platform. Experimental results demonstrate that the proposed composite active control algorithm is an effective approach for suppressing multi-modal vibrations.

Li, Shengquan; Li, Juan; Mo, Yueping; Zhao, Rong

2014-01-01

388

Scale-Space Derived From B-Splines  

Microsoft Academic Search

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

389

Smooth piecewise linear regression splines with hyperbolic covariates  

Microsoft Academic Search

We-propose the use of hyperbolas as covariates in piecewise linear regression splines to fit data exhibiting a multi-phase linear response with smooth transitions between phases. The hyperbolic regression spline model, fitted by non-linear regression, provides an intuitive and easy way to extend to multiple phases the two-phase hyperbolic response model previously proposed by others. The small additional effort required to

John Cologne; Richard Sposto

1994-01-01

390

Geometric continuity of parametric curves: constructions of geometrically continuous splines  

Microsoft Academic Search

Some observations are made concerning the source and nature of shape parameters. It is then described how Bezier curve segments can be stitched together with G1 or G2 continuity, using geometric constructions. These constructions lead to the development of geometric constructions for quadratic G1 and cubic G2 Beta-splines. A geometrically continuous subclass of Catmull-Rom splines based on geometric continuity and

Brian A. Barsky; Tony D. DeRose

1990-01-01

391

A flexible B-spline model for multiple longitudinal biomarkers and survival.  

PubMed

Often when jointly modeling longitudinal and survival data, we are interested in a multivariate longitudinal measure that may not fit well by linear models. To overcome this problem, we propose a joint longitudinal and survival model that has a nonparametric model for the longitudinal markers. We use cubic B-splines to specify the longitudinal model and a proportional hazards model to link the longitudinal measures to the hazard. To fit the model, we use a Markov chain Monte Carlo algorithm. We select the number of knots for the cubic B-spline model using the Conditional Predictive Ordinate (CPO) and the Deviance Information Criterion (DIC). The method and model selection approach are validated in a simulation. We apply this method to examine the link between viral load, CD4 count, and time to event in data from an AIDS clinical trial. The cubic B-spline model provides a good fit to the longitudinal data that could not be obtained with simple parametric models. PMID:15737079

Brown, Elizabeth R; Ibrahim, Joseph G; DeGruttola, Victor

2005-03-01

392

Partitioning and mapping B-spline surface fitting algorithm into fixed-size VLSI arrays  

NASA Astrophysics Data System (ADS)

A method of solving the uniform bicubic B-spline surface fitting algorithm is proposed which introduces parallelism in a way that may be effectively exploited by a suitable parallel architecture. This method is based on the observation that a tensor product spline surface fitting problem can be split into two spline curve fitting problems and each of these problems can be realized by a macropipeline of fixed size VLSI arrays. In fact, the heart of curve fitting problem consists of a block tridiagonal linear system. Based on the state-of-art electronic and packaging technologies, the size of VLSI arithmetic devices is limited due to the bounded chip area and I/O packaging constraints. A modular approach to achieve VLSI matrix arithmetic solution for the block tridiagonal linear system is amenable from the viewpoints of feasibility and applicability. A matrix partitioning approach is presented to overcome those technological constraints imposed by the number of I/O pins. A block tridiagonal linear system of size mn is then divided into m simple tridiagonal systems of size n and n simple tridiagonal systems of size m by the Dc Boor partitioning theorem. Each of the simple tridiagonal linear systems could be partitioned and mappied into a series of two fixed size primitive VLSI matrix arithmetic arrays including L-U decomposer and triangular system solver. The L-U decomposer and triangular system solver could be realized by a hex-connected processor array and an inverse perfect shuffle machine respectively. It would be shown that a B-spline surface fitting problem for a grid of mn points can be solved by m hex-connected processor arrays having 4 processors, m inverse perfect shuffle machines having n processors and n inverse perfect shuffle machines having m processors in (3(m+n)+2({logzn1 +flog2n)+4J units of time.

Chang, Po-Rong; Lee, Share-Young

1990-08-01

393

Statistical process control for monitoring non-linear profiles using wavelet filtering and B-Spline approximation  

Microsoft Academic Search

A statistical process control framework is proposed to monitor non-linear profiles. The proposed methodology aims at identifying mean shifts or ‘shape changes’ in a profile. Discrete wavelet transformation (DWT) is applied to separate variation or noise from profile contours. B-splines are adopted to generate critical points to define the shape of a profile. The proposed method is innovative in that

Shing I. Chang; Srikanth Yadama

2010-01-01

394

Wind generation scheduling with pump storage unit by Collocation method  

Microsoft Academic Search

Wind generation is currently undergoing the fastest rate of growth of any form of electricity generation in the world. Integration of wind power into systems could be problematic, however, due to availability and variability of wind supply. As a proven storage technology, pump storage may provide\\/absorb additional capacity so as to hedge against adverse situations. A scheduling software is needed

Feng Gao; Arne Hallam; Chien-Ning Yu

2009-01-01

395

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions  

SciTech Connect

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

396

Results of a triple collocation experiment between the three laser ranging stations of the Grasse observatory, France  

NASA Astrophysics Data System (ADS)

Collocation experiments are incomparable to check geodetic instrument quality and stability. At the Grasse observatory, France, we had the opportunity to have 3 independent laser ranging stations very close one to each other (about 20m): a Satellite Laser Ranging (SLR) station, a Lunar Laser Ranging (LLR) station, and the French Transportable Laser Ranging Station (FTLRS). Thus, we used this unique configuration to perform a triple laser ranging collocation experiment between these 3 instruments from September to November 2001. The prime objective of this experiment was to qualify, to the millimeter level, the new performance of the FTLRS, after its phase of improvements. This validation was of great importance prior to the FTLRS departure to Corsica, where it was to be used to calibrate the altimeter and to validate the orbits of the oceanographic satellite Jason-1 during its initial validation phase (CAL/VAL) in 2002. A secondary objective was to determine, from the common normal point analysis, the systematic biases of the SLR, the LLR, and the FTLRS systems. Finally, the analysis of the raw data acquired during this collocation allowed also to study the difference of LAGEOS satellite response between each station. Our analysis showed the millimeter consistency between the 3 OCA laser stations, result which demonstrated the strength of the SLR technique. The FTLRS range bias value was confirmed with the 2002 Corsica CAL/VAL campaign analysis. The main part of the biases could have been explained with instrumental sources, but raw data and geometrical analysis underscored difference of LAGEOS satellite signature at the level of 3mm between the SLR and the LLR stations, difference linked to the photon detection level of each system. Herein, we summarize the analysis methods, and then we present and discuss the main results obtained from this collocation experiment.

Nicolas, J.; Exertier, P.; Laurain, O.; Bonnefond, P.; Mangin, J. F.; Barlier, F.

397

Landmine detection using B-spline deformable contours in IR images  

NASA Astrophysics Data System (ADS)

Presently, the number of landmines planted around the world totalizes more than 110 million and, far from slowing down, the landmine production planting rate is, at least, one order of magnitude higher than the rate at which they are removed. In this work a technique to detect buried landmines using boundary detection in IR images, is presented. The buried objects have different temperature than the surrounding soil. We find the object contours by means of an algorithm of B-Spline deformable curves. Under a statistical model, regions with different temperatures can be characterized by the values of the statistical parameters of these distributions. Therefore, this information can be used to find boundaries among different regions in the image. The B-Spline approach has been widely used in curve representation for boundary detection, shape approximation, object tracking and contour detection. Contours formulated by means of B-Splines allow local control, require few parameters and are intrinsically smooth. The algorithm consists in estimating the parameters along lines strategically disposed on the image. The true boundary is found when the values of these parameters vary abruptly on both sides. A likelihood function is maximized to determine the position of such boundaries. We present the experimental results, which show the behavior of the detection method, according to the buried object depth and the elapsed time from the cooling initial time. The obtained results exhibit that it is possible to recognize the shape of the objects, buried at different depths, with a low computational effort.

Gambini, Juliana; Buemi, María E.; Abbate, Horacio; Castro, Eduardo; Berllés, Julio Jacobo; Santos, Juan Miguel; Mejail, Marta

2007-05-01

398

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

399

Smoothing spline ANOVA frailty model for recurrent event data.  

PubMed

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

400

Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation  

SciTech Connect

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

401

Communication: Favorable dimensionality scaling of rectangular collocation with adaptable basis functions up to 7 dimensions  

NASA Astrophysics Data System (ADS)

We show that by using a rectangular collocation method with a small basis of parameterized functions, it is possible to compute a vibrational spectrum by solving the Schrödinger equation in 7D from a small number of ab initio calculations without a potential surface. The method is ideal for spectra of molecules adsorbed on a surface. In this paper, it is applied to calculate experimentally relevant energy levels of acetic acid adsorbed on the (101) surface of anatase TiO2. In this case, to obtain levels of experimental accuracy, increasing the number of dimensions from 4 to 7 increases the number of required potential points from about 1000 to about 10 000 and the number of basis functions from 126 to 792: the scaling is very attractive.

Manzhos, Sergei; Chan, Matthew; Carrington, Tucker

2013-08-01

402

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers  

NASA Astrophysics Data System (ADS)

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

403

Composite contour generation for Beta-spline surface reconstruction  

NASA Astrophysics Data System (ADS)

Branching is a process of connecting two adjacent contours called base and branch contours where the numbers of sub contours for each of both contours are different. All points between the contours have to be correctly paired to avoid a twisting surface. In contours connection, continuity is an issue to ensure the surface fit to the required smoothness. Therefore, two main steps to be focused in surface reconstructions are branching technique and surface continuity. This study used composite contour generation as the branching technique which generates an intermediate contour as combination of modified base and branch contours. Although the inserted new contour will disturb the position of original contours, the continuity can be preserved if the fitted surface is Beta-spline. Beta-spline is built with G2 continuity condition, and the changes of the data points position will not affect the continuity. Hence, surface fitting using Beta-spline will simplify the reconstruction process. The result shows several images can be generated using Beta-spline where composite contour is used for branching problem. The result then compared with the original image and it is shown that surface reconstruction using Beta-spline can give a good result especially for the branching case.

Abdul Hadi, Normi; Ibrahim, Arsmah; Yahya, Fatimah; Md Ali, Jamaludin

2013-04-01

404

Analysis, computation, and mitigation of radio systems' mutual interference effects in collocated vehicular transceivers  

Microsoft Academic Search

The recent increase in the use of mobile radios and systems has enhanced the operation probability and harmful mutual interference resulting from the collocation of two transceivers in the same vehicle. Military mobile systems are especially vulnerable to the collocation operation. Civilian systems, however, are now also being affected. This paper provides a better understanding of the effects of mutual

Jacques Gavan

1994-01-01

405

Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations  

ERIC Educational Resources Information Center

Since the late 1980s, collocations have received increasing attention in applied linguistics, especially language teaching, as is evidenced by the many publications on the topic. These works fall roughly into two lines of research (a) those focusing on the identification and use of collocations (Benson, 1989; Hunston, 2002; Hunston & Francis,…

Liu, Dilin

2010-01-01

406

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

407

Collocational Links in the L2 Mental Lexicon and the Influence of L1 Intralexical Knowledge  

ERIC Educational Resources Information Center

This article assesses the influence of L1 intralexical knowledge on the formation of L2 intralexical collocations. Two tests, a primed lexical decision task (LDT) and a test of receptive collocational knowledge, were administered to a group of non-native speakers (NNSs) (L1 Swedish), with native speakers (NSs) of English serving as controls on the…

Wolter, Brent; Gyllstad, Henrik

2011-01-01

408

BOX SPLINE BASED 3D TOMOGRAPHIC RECONSTRUCTION OF DIFFUSION PROPAGATORS FROM MRI DATA.  

PubMed

This paper introduces a tomographic approach for reconstruction of diffusion propagators, P( r ), in a box spline framework. Box splines are chosen as basis functions for high-order approximation of P( r ) from the diffusion signal. Box splines are a generalization of B-splines to multivariate setting that are particularly useful in the context of tomographic reconstruction. The X-Ray or Radon transform of a (tensor-product B-spline or a non-separable) box spline is a box spline - the space of box splines is closed under the Radon transform.We present synthetic and real multi-shell diffusion-weighted MR data experiments that demonstrate the increased accuracy of P( r ) reconstruction as the order of basis functions is increased. PMID:23459604

Ye, Wenxing; Portnoy, Sharon; Entezari, Alireza; Vemuri, Baba C; Blackband, Stephen J

2011-06-01

409

Library of biorthogonal wavelet transforms originated from polynomial splines  

NASA Astrophysics Data System (ADS)

We present a library of biorthogonal wavelet transforms and the related library of biorthogonal symmetric waveforms. For the construction we use interpolatory, quasiinterpolatory and smoothing splines with finite masks (local splines). With this base we designed a set of perfect reconstruction infinite and finite impulse response filter banks with linear phase property. The construction is performed in a lifting manner. The developed technique allows to construct wavelet transforms with arbitrary prescribed properties such as the number of vanishing moments, shape of wavelets, and frequency resolution. Moreover, the transforms contain some scalar control parameters which enable their flexible tuning in either time or frequency domains. The transforms are implemented in a fast way. The transforms, which are based on interpolatory splines, are implemented through recursive filtering. We present encouraging results towards image compression.

Averbuch, Amir Z.; Zheludev, Valery A.

2001-12-01

410

B-LUT: Fast and low memory B-spline image interpolation  

Microsoft Academic Search

We propose a fast alternative to B-splines in image processing based on an approximate calculation using precomputed B-spline weights. During B-spline indirect transformation, these weights are efficiently retrieved in a nearest-neighbor fashion from a look-up table, greatly reducing overall computation time. Depending on the application, calculating a B-spline using a look-up table, called B-LUT, will result in an exact or

David Sarrut; Jef Vandemeulebroucke

2010-01-01

411

Modeling Spatial Smoothness in Fully 3-D SPECT Image Reconstruction Using Multiresolution B-Splines  

Microsoft Academic Search

We investigated the use of B-spline spatial basis functions to model continuous 3-D tracer distributions in cardiac SPECT studies. This approach is motivated by goals of achieving a well-posed image reconstruction problem and computational efficiency. Uniform B-spline basis functions have the noteworthy property that splines having larger spatial support can be composed from a linear combination of splines having smaller

Bryan W. Reutter; G. T. Gullberg; A. Sitek; R. Boutchko; E. H. Botvinick; R. H. Huesman

2006-01-01

412

Reconstructing B-spline Curves from Point Clouds--A Tangential Flow Approach Using Least Squares Minimization  

Microsoft Academic Search

We present a novel algorithm based on least-squares minimization to approximate point cloud data in2D plane with a smooth B-spline curve. The point cloud data may represent an open curve with self intersection and sharp corner. Unlike other existing methods, such as the moving least-squares method and the principle curve method, our algorithm does not need a thinning process. The

Yang Liu; Huaiping Yang; Wenping Wang

2005-01-01

413

Active motion artifact cancellation for wearable health monitoring sensors using collocated MEMS accelerometers  

NASA Astrophysics Data System (ADS)

This paper presents an active noise cancellation technique for recovering wearable biosensor signals corrupted by bodily motion. A finger mounted photoplethysmograph (PPG) ring sensor with a collocated MEMS accelerometer is considered. The system by which finger acceleration disturbs PPG output is identified and a means of modeling this relationship is prescribed using either FIR or Laguerre models. This means of modeling motivates the use of a recursive least squares active noise cancellation technique using the MEMS accelerometer reading as an input for a FIR or Laguerre model. The model parameters are identified and tuned in real time to minimize the power of the recovered PPG signal. Experiments show that the active noise cancellation method can recover pulse information from PPG signals corrupted with up to 2G of acceleration with 85% improvement in mean squared error.

Gibbs, Peter T.; Wood, Levi B.; Asada, H. Harry

2005-05-01

414

On the asymptotic convergence of B-spline wavelets to Gabor functions  

Microsoft Academic Search

A family of nonorthogonal polynomial spline wavelet transforms is considered. These transforms are fully reversible and can be implemented efficiently. The corresponding wavelet functions have a compact support. It is proven that these B-spline wavelets converge to Gabor functions (modulated Gaussian) pointwise and in all Lp -norms with 1⩽p+? as the order of the spline ( n) tends to infinity.

Michael Unser; Akram Aldroubi; Murray Eden

1992-01-01

415

An Automatic Collocation Writing Assistant for Taiwanese EFL Learners: A Case of Corpus-Based NLP Technology  

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

416

B-spline active rays segmentation of microcalcifications in mammography.  

PubMed

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 (Az). 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 +/- .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. PMID:19070250

Arikidis, Nikolaos S; Skiadopoulos, Spyros; Karahaliou, Anna; Likaki, Eleni; Panayiotakis, George; Costaridou, Lena

2008-11-01

417

B-spline active rays segmentation of microcalcifications in mammography  

SciTech Connect

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

418

Optimal spacecraft attitude control using collocation and nonlinear programming  

NASA Astrophysics Data System (ADS)

Direct collocation with nonlinear programming (DCNLP) is employed to find the optimal open-loop control histories for detumbling a disabled satellite. The controls are torques and forces applied to the docking arm and joint and torques applied about the body axes of the OMV. Solutions are obtained for cases in which various constraints are placed on the controls and in which the number of controls is reduced or increased from that considered in Conway and Widhalm (1986). DCLNP works well when applied to the optimal control problem of satellite attitude control. The formulation is straightforward and produces good results in a relatively small amount of time on a Cray X/MP with no a priori information about the optimal solution. The addition of joint acceleration to the controls significantly reduces the control magnitudes and optimal cost. In all cases, the torques and acclerations are modest and the optimal cost is very modest.

Herman, A. L.; Conway, B. A.

1992-10-01

419

Robustness properties of LQG optimized compensators for collocated rate sensors  

NASA Technical Reports Server (NTRS)

In this paper we study the robustness with respect to stability of the closed-loop system with collocated rate sensor using LQG (mean square rate) optimized compensators. Our main result is that the transmission zeros of the compensator are precisely the structure modes when the actuator/sensor locations are 'pinned' and/or 'clamped': i.e., motion in the direction sensed is not allowed. We have stability even under parameter mismatch, except in the unlikely situation where such a mode frequency of the assumed system coincides with an undamped mode frequency of the real system and the corresponding mode shape is an eigenvector of the compensator transfer function matrix at that frequency. For a truncated modal model - such as that of the NASA LaRC Phase Zero Evolutionary model - the transmission zeros of the corresponding compensator transfer function can be interpreted as the structure modes when motion in the directions sensed is prohibited.

Balakrishnan, A. V.

1994-01-01

420

System of linear algebraic equations and Eigen value problems: elimination method, Gauss method, Gauss-Jordan method; Eigen values and Eigen vectors, bounds on Eigen values, Jacobi methods for symmetric matrices, householder's method for symmetric matrices. Interpolation and approximation: interpolation problem, linear interpolation, Lagrange interpolation, Newton interpolation, interpolation with equidistant points, spline interpolation, least square  

Microsoft Academic Search

approximation Numerical differentiation and integration: differentiation of continuous functions, forward difference quotient, central difference quotient, error analysis; derivatives from differences table, higher-order derivatives, Richardson extrapolation techniques, Newton-Cotes method, trapezoidal rule, Simpson's rule, higher order rules, Romberg integration. Numerical solution of ordinary differential equations: Taylor's series method, Euler and modified Euler method, Runge-Kutta methods, Milne's method, Adam-Bashforth- Moultan method. Optimization: basic

Taha H Hamidi; Wiley ISE; Curtis F Gerald; Patrick G Whealley

421

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

422

Low speed wind tunnel investigation of span load alteration, forward-located spoilers, and splines as trailing-vortex-hazard alleviation devices on a transport aircraft model  

NASA Technical Reports Server (NTRS)

The effectiveness of a forward-located spoiler, a spline, and span load alteration due to a flap configuration change as trailing-vortex-hazard alleviation methods was investigated. For the transport aircraft model in the normal approach configuration, the results indicate that either a forward-located spoiler or a spline is effective in reducing the trailing-vortex hazard. The results also indicate that large changes in span loading, due to retraction of the outboard flap, may be an effective method of reducing the trailing-vortex hazard.

Croom, D. R.; Dunham, R. E., Jr.

1975-01-01

423

Thin-plate spline quadrature of geodetic integrals  

NASA Astrophysics Data System (ADS)

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Vangysen, Herman

1989-06-01

424

Thin-plate spline quadrature of geodetic integrals  

NASA Technical Reports Server (NTRS)

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Vangysen, Herman

1989-01-01

425

Numerical solution of nonlinear hyperbolic conservation laws using exponential splines  

NASA Astrophysics Data System (ADS)

Previous theoretical (McCartin 1989a) and computational (McCartin 1989b) results on exponential splines are herein applied to provide approximate solutions of high order accuracy to nonlinear hyperbolic conservation laws. The automatic selection of certain “tension” parameters associated with the exponential spline allows the sharp resolution of shocks and the suppression of any attendant oscillations. Specifically, spatial derivatives are replaced by nodal derivatives of interpolatory splines and temporal discretization is achieved via a Runge-Kutta time stepping procedure. The fourth order accuracy of this scheme in both space and time (for uniform mesh and tension) is established and a linearized stability analysis is provided. The Lax-Wendroff theorem on convergence to weak solutions (Lax and Wendroff 1960) is then extended to spline approximations in conservation form. An implicit artificial viscosity term (Anderson et al. 1984) is included via upwinding in conservation form in order to assure convergence to the physically relevant weak solution. The efficacy of this procedure is illustrated on the inviscid Burgers' equation where the accurate capture of a travelling shockwave is demonstrated.

McCartin, B. J.; Jameson, A.

1990-03-01

426

Construction of Biorthogonal Discrete Wavelet Transforms Using Interpolatory Splines  

Microsoft Academic Search

We present a new family of biorthogonal wavelet and wavelet packet transforms for discrete periodic signals and a related library of biorthogonal periodic symmetric waveforms. The construction is based on the superconvergence property of the interpolatory polynomial splines of even degrees. The construction of the transforms is performed in a “lifting” manner that allows more efficient implementation and provides tools

Amir Z. Averbuch; Valery A. Zheludev

2002-01-01

427

EQUIVALENT CONDITICINS FOB THE CONSISTENCY OF NONPARAMETRIC SPLINE DENSITY ESTIMATORS  

Microsoft Academic Search

We study the nonparametric spline density estimators of probability density. The equivalence of weak convergence for L,-con- sistency of one density and completely for L,-consistency of all densities is proved. It is equivalent also to suitable rates of convergence of window parameter.

GRZEGORZ KRZYKOWSKI

1992-01-01

428

Robust optical flow estimation using B-spline image models  

Microsoft Academic Search

In this paper, we address the problem of robust estimation of the optical flow through a multiresolution energy minimization. Such process involves repeated evaluation of spatial and temporal gradients of image intensity which rely usually on bilinear interpolation and image filtering. We propose to base both computations on a single spline modelization of image intensity. We show empirically improvements in

Guy Le Besnerais; FrCdkric Champagnat; Gilles Rochefort

2003-01-01

429

B-Splines and Linear Combinations of Uniform Order Statistics.  

National Technical Information Service (NTIS)

It is shown in this document that the density of the sum of n independent random variables uniformly distributed on unequal intervals is given by a linear combination of n B-splines with constant coefficients. Another useful representation of the same den...

A. G. Ignatov V. K. Kaishev

1985-01-01

430

Odd-Degree Spline Interpolation at a Biinfinite Knot Sequence.  

National Technical Information Service (NTIS)

It is shown that for an arbitrary strictly increasing knot sequence t = (t sub 1) infinity to minus infinity and for every i, there exists exactly one fundamental spline L sub i (i.e., L sub i)(t sub j) = delta sub ij, all j), of order 2r whose r-th deriv...

C. de Boor

1976-01-01

431

Shape-Preserving MQ-B-Splines Quasi-Interpolation  

Microsoft Academic Search

Based on the definition of MQ-B-splines, this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details. Examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.

Weixiang Zhang; Zongmin Wu

2004-01-01

432

Interpolating Mean Rainfall Using Thin Plate Smoothing Splines  

Microsoft Academic Search

Thin plate smoothing splines provide accurate, operationally straightforward and computationally efficient solutions to the problem of the spatial interpolation of annual mean rainfall for a standard period from point data which contains many short period rainfall means. The analyses depend on developing a statistical model of the spatial variation of the observed rainfall means, considered as noisy estimates of standard

M. F. Hutchinson

1995-01-01

433

Polynomial Spline Approach for Double Integrals with Algebraic Singularity  

NASA Astrophysics Data System (ADS)

In this note, cubature formulas are constructed to evaluate the double integrals on the rectangle with algebraic singularity by replacing the density function f(x,y) with the S?(P) modified spline function interpolation of type (0,2). Rate of convergence are obtained in the classes of function f(x,y) in C2,?(D).

Eshkuvatov, Z. K.; Nik Long, N. M. A.; Midi, Habshah; Khaldjigitov, Abduvali

2013-04-01

434

Quadratic Spline Models for Producer's Supply and Demand Functions  

Microsoft Academic Search

In this paper, the authors propose and estimate a system of producer output supply and input demand functions that generalizes the standard normalized quadratic form. The generalization adds either linear or quadratic splines in a time (or technical change) variable, yet retains the main attractive property of the normalized quadratic, which is that it can provide a local second order

W. E. Diewert; T. J. Wales

1992-01-01

435

Bicubic B-spline blending patches with optimized shape  

Microsoft Academic Search

Two constructions of bicubic B-spline patches with fixed boundary conditions are described. Their goal is to minimize functionals taken for measures of patch badness. The first construction is numerically solving the triharmonic equation ??3p=0. The functional minimized in the second construction is the sum of a term determined by the surface shape (the distribution of mean curvature) and a term

Przemyslaw Kiciak

2011-01-01

436

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation  

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

437

B-spline R-matrix-with-pseudostates calculations for electron-impact excitation and ionization of fluorine  

NASA Astrophysics Data System (ADS)

The B-spline R-matrix method is used to study electron collisions with neutral fluorine over an energy range from threshold to 100 eV. The multiconfiguration Hartree-Fock method in connection with B-spline expansions is employed for an accurate representation of the target wave functions. The sensitivity of the results is checked by comparing data obtained in different approximations, including a large-scale model with over 600 continuum pseudostates. Both correlation and polarization effects are found to be important for accurate calculations of the cross sections. Coupling to the target continuum strongly affects transitions from the ground state, but to a lesser extent the strong transitions between excited states. Cross sections are presented for selected transitions between the lowest 26 states of fluorine, as well as elastic scattering from and ionization of the ground state. The current predictions represent an extensive set of electron scattering data for neutral fluorine.

Gedeon, Viktor; Gedeon, Sergej; Lazur, Vladimir; Nagy, Elizabeth; Zatsarinny, Oleg; Bartschat, Klaus

2014-05-01

438

Fast simulation of x-ray projections of spline-based surfaces using an append buffer  

NASA Astrophysics Data System (ADS)

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, the 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 640 × 480 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.

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

2012-10-01

439

Spectral analysis of GEOS-3 altimeter data and frequency domain collocation. [to estimate gravity anomalies  

NASA Technical Reports Server (NTRS)

The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.

Eren, K.

1980-01-01

440

Collocated Flight Service Station/Air Route Traffic Control Center Aviation Weather Unit.  

National Technical Information Service (NTIS)

A comprehensive study and analysis was performed to determine optimum weather and aeronautical data collection, forecasting, and dissemination methodologies for a collocated Flight Service Station and Air Route Traffic Control Center environment. Special ...

L. J. Wuebker E. Spring E. Mandel J. Langston F. Blake

1976-01-01

441

Fast Medical Image Segmentation Through an Approximation of Narrow-Band B-Spline Level-Set and Multiresolution  

Microsoft Academic Search

We have recently proposed a new level-set formulation, where the level-set is modelled as a continuous parametric function expressed in a B-spline basis. We propose in this paper to adapt this formalism to the class of narrow-band level-set methods, where the implicit function evolves only around its zero-level. For this purpose, we propose to model the interface by two lists

Olivier Bernard; Denis Friboulet

2009-01-01

442

A parallel Vlasov solver based on local cubic spline interpolation on patches  

NASA Astrophysics Data System (ADS)

A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semi-Lagrangian algorithm that approaches the Vlasov equation on a grid of phase space. As this kind of method requires a huge computational effort, the simulations are carried out on parallel machines. To that purpose, we present a local cubic splines interpolation method based on a domain decomposition, e.g. devoted to a processor. Hermite boundary conditions between the domains, using ad hoc reconstruction of the derivatives, provide a good approximation of the global solution. The method is applied on various physical configurations which show the ability of the numerical scheme.

Crouseilles, Nicolas; Latu, Guillaume; Sonnendrücker, Eric

2009-03-01

443

Evaluation of Assumptions in Soil Moisture Triple Collocation Studies  

NASA Astrophysics Data System (ADS)

Error variance information of different products that observe the same geophysical parameter can be obtained using Triple Collocation Analysis (TCA). However, the TCA system of equations has more unknowns than available equations, hence the system is underdetermined. To be able to obtain a solution for the error variance, several assumptions are made; in particular errors are orthogonal with respect to the truth and cross-correlations of errors vanish, while the accuracy of TCA-based errors depend on the degree that the available datasets fit these assumptions. Heavy majority of TCA-based hydrological applications commonly make these assumptions, yet no study has specifically investigated the degree that available soil moisture datasets fit these assumptions. Here we evaluate these assumptions both analytically and numerically using soil moisture data (station-based observations, Noah and API hydrological model simulations, and LPRM and ASCAT retrievals) obtained over four US Department of Agriculture watersheds. In addition to the non-orthogonal and cross-correlated errors, another type of error (leaked signal) is identified, while magnitudes of all error types (non-orthogonal, cross-correlated, leaked signal, true random, and TCA-based errors) are all numerically estimated. Results show widely assumed non-orthogonal and cross-correlated error components are not zero. On the other hand it is analytically shown that the impacts of non-orthogonal and leaked signal errors are largely dampened while error cross-correlations impose a negative bias on the TCA-based error estimates.

Yilmaz, M.; Crow, W. T.

2013-12-01

444

Reuse of B-spline-based shape interrogation tools for triangular mesh models  

NASA Astrophysics Data System (ADS)

In many engineering applications, a smooth surface is often approximated by a mesh of polygons. In a number of downstream applications, it is frequently necessary to estimate the differential invariant properties of the underlying smooth surfaces of the mesh. Such applications include first-order surface interrogation methods that entail the use of isophotes, reflection lines, and highlight lines, and second-order surface interrogation methods such as the computation of geodesics, geodesic offsets, lines of curvature, and detection of umbilics. However, we are not able to directly apply these tools that were developed for B-spline surfaces to tessellated surfaces. This article describes a unifying technique that enables us to use the shape interrogation tools developed for B-spline surface on objects represented by triangular meshes. First, the region of interest of a given triangular mesh is transformed into a graph function (z=h(x,y)) so that we can treat the triangular domain within the rectangular domain. Each triangular mesh is then converted into a cubic graph triangular Bézier patch so that the positions as well as the derivatives of the surface can be evaluated for any given point (x,y) in the domain. A number of illustrative examples are given that show the effectiveness of our algorithm. [Figure not available: see fulltext.

Kobashi, Yuji; Suzuki, Junya; Joo, Han Kyul; Maekawa, Takashi

2012-06-01

445

Cubic spline wavelets with short support adapted to the interval  

NASA Astrophysics Data System (ADS)

Wavelets with the short support and with vanishing moments which form well-conditioned basis are of interest for solving differential equations numerically. The condition number of wavelet bases on the interval depends on the length of the support and it can be further significantly influenced by a proper construction of boundary wavelets. Few years ago, B. Han and Z. Shen constructed Riesz wavelet bases of the space L(R) with the shortest possible support and with m vanishing moments based on B-spline of order m. In this contribution, we start with their another wavelet with two vanishing moments based on cubic B-splines and propose an adaptation of this basis to the interval.

?erná, Dana; Fin?k, Václav

2013-12-01

446

On the role of exponential splines in image interpolation.  

PubMed

A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks. PMID:19520639

Kirshner, Hagai; Porat, Moshe

2009-10-01

447

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

448

Potential-Field Transformations and Modeling Using Splines  

Microsoft Academic Search

Potential-field transformations facilitate geologic interpretations by transforming measured data into new forms. Potential-field modeling is able to construct useful source models that match observed anomalies. The widely used FFT algorithms for transformations and modeling have limitations, however. We advance new unified formulas for interpolation, differentiation and integration using splines and propose new space-domain approaches to 2D and 3D potential-field transformations

B. Wang

2005-01-01

449

A rational B-spline hypervolume for multidimensional multivariate modeling  

Microsoft Academic Search

This paper proposes a rational B-spline hypervolume that represents a volume object which has multiple attributes defined\\u000a in a multidimensional space. This representation provides a mathematical framework for modeling and visualizing a multidimensional\\u000a multivariate object as well as analyzing the object interiors to extract its intrinsic features that are directly inaccessible.\\u000a We discuss the NURBS extension procedure showing that the

2009-01-01

450

Polynomial C 2 Spline Surfaces Guided by Rational Multisided Patches  

Microsoft Academic Search

An algorithm is presented for approximating a rational multi-sided M-patch by a C2 spline surface. The motivation is that the multi-sided patch can be assumed to have good shape but is in nonstandard representation or of too high a degree. The algorithm generates a finite approximation of the M-patch, by a sequence of patches of bidegree (5,5) capped off by

Ke?stutis Kar?ciauskas; Jörg Peters

451

Adaptation of a cubic smoothing spline algorithm for multi-channel data stitching at the National Ignition Facility  

NASA Astrophysics Data System (ADS)

Some diagnostics at the National Ignition Facility (NIF), including the Gamma Reaction History (GRH) diagnostic, require multiple channels of data to achieve the required dynamic range. These channels need to be stitched together into a single time series, and they may have non-uniform and redundant time samples. We chose to apply the popular cubic smoothing spline technique to our stitching problem because we needed a general non-parametric method. We adapted one of the algorithms in the literature, by Hutchinson and deHoog, to our needs. The modified algorithm and the resulting code perform a cubic smoothing spline fit to multiple data channels with redundant time samples and missing data points. The data channels can have different, timevarying, zero-mean white noise characteristics. The method we employ automatically determines an optimal smoothing level by minimizing the Generalized Cross Validation (GCV) score. In order to automatically validate the smoothing level selection, the Weighted Sum-Squared Residual (WSSR) and zero-mean tests are performed on the residuals. Further, confidence intervals, both analytical and Monte Carlo, are also calculated. In this paper, we describe the derivation of our cubic smoothing spline algorithm. We outline the algorithm and test it with simulated and experimental data.

Brown, Charles G., Jr.; Adcock, Aaron B.; Azevedo, Stephen G.; Liebman, Judith A.; Bond, Essex J.

2011-02-01

452

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

453