Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
B-spline Collocation with Domain Decomposition Method
NASA Astrophysics Data System (ADS)
Hidayat, M. I. P.; Ariwahjoedi, B.; Parman, S.
2013-04-01
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.
Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere
Christara, Christina C.
Optimal Quadratic Spline Collocation Methods for the Shallow Water Equations on the Sphere Anita T, for solving the shallow water equations (SWEs) in spherical coÂ ordinates. A quadratic spline collocation formulation, the quadratic spline is computed by making the residual of the differential equations zero
NASA Astrophysics Data System (ADS)
Horvat, Vilmos; Rogina, Mladen
2002-03-01
We consider the numerical discretization of singularly perturbed Volterra integro-differential equations (VIDE) and Volterra integral equations (VIE) by tension spline collocation methods in certain tension spline spaces, where [var epsilon] is a small parameter satisfying 0<[var epsilon]<<1, and q1, q2, g and K are functions sufficiently smooth on their domains to ensure that Eqs. (*) and (**) posses a unique solution. We give an analysis of the global convergence properties of a new tension spline collocation solution for 0<[var epsilon]<<1 for singularly perturbed VIDE and VIE; thus, extending the existing theory for [var epsilon]=1 to the singularly perturbed case.
Domain identification in impedance computed tomography by spline collocation method
NASA Technical Reports Server (NTRS)
Kojima, Fumio
1990-01-01
A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.
Basis spline collocation method for solving the Schroedinger equation in axillary symmetric systems
Kegley, D.R. Jr.; Oberacker, V.E.; Umar, A.S. [Oak Ridge National Lab., TN (United States)]|[Vanderbilt Univ., Nashville, TN (United States)] [and others
1996-10-01
We use basis spline collocation to solve the Schroedinger equation on a lattice for axially symmetric systems, with and without spin. The focus of the present work is on systems which have continuum states, weakly bound states, or strong spin-orbit coupling, since these are the most difficult to solve on the lattice. A brief overview of the basis spline collocation method is included which concentrates primarily on those aspects of the theory which are relevant to its application in cylindrical coordinates. To demonstrate the method, we solve several model problems selected from the fields of atomic and nuclear physics. 25 refs., 6 figs., 5 tabs.
Parameter estimation technique for boundary value problems by spline collocation method
NASA Technical Reports Server (NTRS)
Kojima, Fumio
1988-01-01
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.
QuarticSpline Collocation Methods for FourthOrder TwoPoint Boundary Value Problems
Christara, Christina C.
Ji Dai and Zhu Guo Ping, who are also my best friends. iii #12; Acknowledgements I would especiallyQuarticÂSpline Collocation Methods for FourthÂOrder TwoÂPoint Boundary Value Problems by Ying Zhu Department of Computer Science University of Toronto Copyright c fl 2001 by Ying Zhu #12; Abstract Quartic
Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation
Hui-Chol Choe; Yong-Suk Kang
2013-03-20
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimation. The approximate solution of fractional differential equation is obtained by fractional integration of the approximate solution for fractional integral equation.
Higher Order B-Spline Collocation at the Greville Abscissae
Johnson, Richard Wayne
2005-01-01
Collocation methods are investigated because of their simplicity and inherent efficiency for application to a model problem with similarities to the equations of fluid dynamics. The model problem is a steady, one-dimensional convection-diffusion equation with constant coefficients. The objective of the present research is to compare the efficiency and accuracy of several collocation schemes as applied to the model problem for values of 15 and 50 for the associated Peclet number. The application of standard nodal and orthogonal collocation is compared to the use of the Greville abscissae for the collocation points, in conjunction with cubic and quartic B-splines. The continuity of the B-spline curve solution is varied from C1 continuity for traditional orthogonal collocation of cubic and quartic splines to C2-C3 continuity for cubic and quartic splines employing nodal, orthogonal and Greville point collocation. The application of nodal, one-point orthogonal, and Greville collocation for smoothest quartic B-splines is found to be as accurate as for traditional two-point orthogonal collocation using cubics, while having comparable or better efficiency based on operation count. Greville collocation is more convenient than nodal or 1-point orthogonal collocation because exactly the correct number of collocation points is available.
Quartic B-spline collocation method applied to Korteweg de Vries equation
NASA Astrophysics Data System (ADS)
Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md
2014-07-01
The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+?uux+?uxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L?-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L?-norm are also increase.
Christara, Christina C.
1 Quadratic spline collocation for oneÂdimensional linear parabolic partial differential equations general linear parabolic partial differential equations (PDEs) in one space dimenÂ sion are developed. The methods combine quadraticÂspline collocation for the space discretization and classical finite differences
Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework
Chen, Yanlai
2012-01-01
In this paper, we present {\\em the first} reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced Collocation Method (ERCM). This work provides a reduced basis strategy to practitioners who require a collocation, rather than Galerkin, approach. Furthermore, the empirical reduced collocation method {\\em eliminates} a potentially costly online procedure that is needed for non-affine problems with Galerkin approach. Numerical results demonstrate the high efficiency and accuracy of the reduced collocation methods, which match or exceed that of the traditional reduced basis method in the Galerkin framework.
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.
1987-01-01
This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.
Johnson, Richard Wayne
2003-05-01
The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effectiveness and accuracy of B-spline collocation for solving differential equations include which points to use for collocation, what degree B-spline to use and what level of continuity to maintain. Success using higher degree B-spline curves having higher continuity at the knots, as opposed to more traditional approaches using orthogonal collocation, have recently been investigated along with collocation at the Greville points for linear (1D) and rectangular (2D) geometries. The development of automatic knot insertion techniques to provide sufficient accuracy for B-spline collocation has been underway. The present article reviews recent progress for the application of B-spline collocation to fluid motion equations as well as new work in developing a novel adaptive knot insertion algorithm for a 1D convection-diffusion model equation.
NASA Technical Reports Server (NTRS)
Guseman, L. F., Jr.; Schumaker, L. L.
1983-01-01
The use of spline functions in the development of classification algorithms is discussed. A method is formulated for producing spline approximations to univariate density functions when each density function is described by a histogram of measurements. The resulting approximations are then incorporated into a Bayesian classification procedure for which the probability of misclassification can be readily computed. Some preliminary numerical results are presented to illustrate the method.
Positivity conditions in meshless collocation methods
Xiaozhong Jin; Gang Li; N. R. Aluru
2004-01-01
Collocation meshless methods are conceptually simple, easy-to-implement and fast numerical methods. The robustness of collocation methods has, however, been an issue especially for scattered set of points. In this paper we show that the robustness of collocation meshless methods can be improved by ensuring that certain conditions, defined as the positivity conditions, are satisfied when constructing approximation functions and their
Least?squares collocation meshless method
Xiong Zhang; Ming-Wan Lu
2001-01-01
SUMMARY A 1nite point method, least-squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satis1ed not only at the collocation points but also at the auxiliary points in a least-squares sense. The moving
Stable and Convergent Unsymmetric Meshless Collocation Methods
Schaback, Robert
Stable and Convergent Unsymmetric Meshless Collocation Methods Leevan Ling and Robert Schaback July for error bounds and convergence of a variation of E. Kansa's well-known unsymmetric meshless collocation-dependent meshless selection of test and trial spaces. The new method satisfies the assumptions of the background
A B-Spline Method for Solving the Navier Stokes Equations
Johnson, Richard Wayne
2005-01-01
Collocation methods using piece-wise polynomials, including B-splines, have been developed to find approximate solutions to both ordinary and partial differential equations. Such methods are elegant in their simplicity and efficient in their application. The spline collocation method is typically more efficient than traditional Galerkin finite element methods, which are used to solve the equations of fluid dynamics. The collocation method avoids integration. Exact formulae are available to find derivatives on spline curves and surfaces. The primary objective of the present work is to determine the requirements for the successful application of B-spline collocation to solve the coupled, steady, 2D, incompressible Navier–Stokes and continuity equations for laminar flow. The successful application of B-spline collocation included the development of ad hoc method dubbed the Boundary Residual method to deal with the presence of the pressure terms in the Navier–Stokes equations. Historically, other ad hoc methods have been developed to solve the incompressible Navier–Stokes equations, including the artificial compressibility, pressure correction and penalty methods. Convergence studies show that the ad hoc Boundary Residual method is convergent toward an exact (manufactured) solution for the 2D, steady, incompressible Navier–Stokes and continuity equations. C1 cubic and quartic B-spline schemes employing orthogonal collocation and C2 cubic and C3 quartic B-spline schemes with collocation at the Greville points are investigated. The C3 quartic Greville scheme is shown to be the most efficient scheme for a given accuracy, even though the C1 quartic orthogonal scheme is the most accurate for a given partition. Two solution approaches are employed, including a globally-convergent zero-finding Newton's method using an LU decomposition direct solver and the variable-metric minimization method using BFGS update.
CONVERGENCE OF UNSYMMETRIC KERNELBASED MESHLESS COLLOCATION METHODS
Schaback, Robert
CONVERGENCE OF UNSYMMETRIC KERNELÂBASED MESHLESS COLLOCATION METHODS ROBERT SCHABACK Abstract of approximation to the residuals by non- stationary meshless-kernel-based trial spaces, and they are independent problem via an unsymmetric or even non-square system of linear collocation equations involving meshless
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
NASA Astrophysics Data System (ADS)
Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo
2014-04-01
We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.
Numerical Methods Using B-Splines
NASA Technical Reports Server (NTRS)
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
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.
Spline Smoothing: The Equivalent Variable Kernel Method
B. W. Silverman
1984-01-01
The spline smoothing approach to nonparametric regression and curve estimation is considered. It is shown that, in a certain sense, spline smoothing corresponds approximately to smoothing by a kernel method with bandwidth depending on the local density of design points. Some exact calculations demonstrate that the approximation is extremely close in practice. Consideration of kernel smoothing methods demonstrates that the
B-spline Method in Fluid Dynamics
NASA Technical Reports Server (NTRS)
Botella, Olivier; Shariff, Karim; Mansour, Nagi N. (Technical Monitor)
2001-01-01
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.
Statistical methods of collocation detection Aleksander Buczyski
Tabela: Top 20 collocations from Jane Austen books according to different frequency-like measures Freq are her own her own #12;Dependency-like tests Tabela: Top 20 collocations from Jane Austen books according
Chebyshev collocation methods in thermoconvective problems
H. Herrero
2007-01-01
. Chebyshev collocation methods are high-order methods.\\u000a This means that high precision is obtained with low-order\\u000a expansions. Then `small' matrices appear in the numerical\\u000a implementation and reduced computing resources become necessary.\\u000a Thermoconvective fluid dynamics problems are large ones, involving\\u000a various partial differential equations for several fields in large\\u000a dimensions. The models present a number of difficulties, such as\\u000a the different orders
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
M. D. Landon; R. W. Johnson
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics
Johnson, Richard Wayne; Landon, Mark Dee
1999-07-01
The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.
Meshless methods based on collocation with radial basis functions
X. Zhang; K. Z. Song; M. W. Lu; X. Liu
2000-01-01
Meshless methods based on collocation with radial basis functions (RBFs) are investigated in detail in this paper. Both globally\\u000a supported and compactly supported radial basis functions are used with collocation to solve partial differential equations\\u000a (PDEs). Using RBFs as a meshless collocation method to solve PDEs possesses some advantages. It is a truly mesh-free method,\\u000a and is space dimension independent.
An enhanced splined saddle method
NASA Astrophysics Data System (ADS)
Ghasemi, S. Alireza; Goedecker, Stefan
2011-07-01
We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)], 10.1063/1.2916716. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C60 fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time.
An enhanced splined saddle method.
Ghasemi, S Alireza; Goedecker, Stefan
2011-07-01
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
Multivariate spline methods in surface fitting
NASA Technical Reports Server (NTRS)
Guseman, L. F., Jr. (principal investigator); Schumaker, L. L.
1984-01-01
The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
NASA Astrophysics Data System (ADS)
Buffa, A.; Sangalli, G.; Vázquez, R.
2014-01-01
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.
A collocation method for certain elliptic boundary-value problems
Hord, Susan Kathleen
1974-01-01
A COLLOCATION METHOD FOR CERTAIN ELLIPTIC BOUNDARY-VALUE PROBLEMS A Thesis Susan Kathleen Hard Submitted to the Graduate Co ilepe of Texas ABM University in partial fulfillment of the requirement for. the ilegreu of, MASTER OF SCIENCE May... 1974 Major Subject: Mathematics A COLLOCATION METHOD FOR CERTAIN ELLIPTIC BOUNDARY-VALUE PROBLEMS A Thesis by Susan Kathleen Hord Approved as to style and content by: (Chairman o Committee) (Head of Department) (Member) (Member) May 1974...
The Fourier collocation method for the Cahn-Hilliard equation
Xingde Ye
2002-01-01
In this paper, a Fourier collocation method for numerically solving Cahn-Hilliard equations with periodic boundary conditions is developed. We establish their semidiscrete and fully discrete schemes that inherit the energy dissipation property and mass conservation property from the associated continuous problem. We prove existence and uniqueness of the numerical solution and derive the optimal error bounds. We perform some numerical
Collocation Model Reduction for Moving-least-square method
Paris-Sud XI, UniversitÃ© de
Collocation Model Reduction for Moving-least-square method B. Khoshnoudirad,P.Joyot,F. Chinesta, P. Villon December 2, 2008 Abstract Proper orthogonal decomposition (POD) and moving least-square- square data in a certain least-square optimal sense. In addition to being optimal in a least-square sense, POD
Domain decomposition preconditioners for the spectral collocation method
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio; Sacchilandriani, Giovanni
1988-01-01
Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.
A family of Multistep Collocation Methods for Volterra Integro-Differential Equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Conte, D.; Paternoster, B.
2009-09-01
In this paper we analyze a family of multistep collocation methods for Volterra Integro-Differential Equations, with the aim of increasing the order of classical one-step collocation methods without increasing the computational cost. We discuss the order of the constructed methods and present the stability analysis.
The chain collocation method: A spectrally accurate calculus of forms
NASA Astrophysics Data System (ADS)
Rufat, Dzhelil; Mason, Gemma; Mullen, Patrick; Desbrun, Mathieu
2014-01-01
Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.
Testing Generalized Linear Models Using Smoothing Spline Methods
Meiring, Wendy
Testing Generalized Linear Models Using Smoothing Spline Methods Anna Liu, Wendy Meiring to data from the Wisconsin Epidemiology Study of Diabetic Retinopathy, the results of which con#12;rm tools are especially important in practice. In this pa- per, we propose and compare three methods
Multi-element probabilistic collocation method in high dimensions
NASA Astrophysics Data System (ADS)
Foo, Jasmine; Karniadakis, George Em
2010-03-01
We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM [1] and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order ? and the effective dimension ?, with ??N, and N the nominal dimension. Numerical tests for multi-dimensional integration and for stochastic elliptic problems suggest that ??? for monotonic convergence of the method. We also employ MEPCM-A to obtain error bars for the piezometric head at the Hanford nuclear waste site under stochastic hydraulic conductivity conditions. Finally, we compare the cost of MEPCM-A against Monte Carlo in several hundred dimensions, and we find MEPCM-A to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.
Multilevel fast multipole method for thin plate spline evaluation
Ali Zandifar; Ser-nam Lirn; Ramani Duraiswami; Nail A. Gumerov; Larry S. Davis
2004-01-01
Image registration is an important problem in image pro- cessing and computer vision. Much recent work in image registration is on matching non-rigid deformations. Thin Plate Splines are an effective image registration method when the deformation between two images can be modeled as the bending of a thin metal plate on point constraints such that the topology is preserved (non-rigid
Three dimensional distorted black holes: using the Galerkin-Collocation method
H. P. de Oliveira; E. L. Rodrigues
2015-02-20
We present an implementation of the Galerkin-Collocation method to determine the initial data for non-rotating distorted three dimensional black holes in the inversion and puncture schemes. The numerical method combines the key features of the Galerkin and Collocation methods which produces accurate initial data. We evaluated the ADM mass of the initial data sets, and we have provided the angular structure of the gravitational wave distribution at the initial hypersurface by evaluating the scalar $\\Psi_4$ for asymptotic observers.
Convergence order estimates of meshless collocation methods using radial basis functions
Carsten Franke; Robert Schaback
1998-01-01
IntroductionWe will treat systems of linear equations, each of the formLu = fon\\\\Omega; (1.1)where\\\\Omegais a domain in IRdand L is a linear operator, acting on complex valuedfunctions on \\\\Omega\\\\Gamma The function f is given ("data") and each equation should havea nonempty space of solutions.2 1. Introduction1.1 Collocation Method for Single EquationsCollocation is a well-known method to approximate the solution of
NASA Astrophysics Data System (ADS)
Tu, Lianghui; Yuan, Jianping; Luo, Jianjun; Ning, Xin; Zhou, Ruiwu
2007-11-01
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 some reasonable hypotheses. Performance is selected to minimize the fuel consumption. The control variables are thrust attack angle and thrust of engine. Terminal state variable constraints are velocity and altitude constraints. Then, the optimal control problem is transformed into nonlinear programming problem using direct collocation method. The state variables and control variables are selected as optimal parameters at all nodes and collocation nodes. Parameter optimization problem is solved using the SNOPT software package. The simulation results demonstrate that the direct collocation method is not sensitive to lunar soft landing initial conditions; they also show that the optimal solutions of trajectory optimization problem are fairly good in real-time. Therefore, the direct collocation method is a viable approach to lunar probe soft landing trajectory optimization problem.
ERIC Educational Resources Information Center
Cui, Zhongmin; Kolen, Michael J.
2009-01-01
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…
NASA Technical Reports Server (NTRS)
Zhang, Zhimin; Tomlinson, John; Martin, Clyde
1994-01-01
In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.
Webster, Clayton G [ORNL; Tran, Hoang A [ORNL; Trenchea, Catalin S [ORNL
2013-01-01
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.
Two methods of selecting smoothing splines applied to fermentation process data
Thornhill, N.F.; Manela, M.; Campbell, J.A.; Stone, K.M. (University College London (United Kingdom))
1994-04-01
Two methods for generating smoothing splines are compared and applied to data from a fed-batch fermentation process. One method chose both the degree of the spline and its parameters by minimizing the generalized cross validation (GCV) function using a genetic algorithm (GA). The other method adjusted the smoothing spline to a specified chi-square goodness-of-fit requiring prior knowledge of the measurement variability. The GCV/GA method led to excellent results with all the fermentation data records. The goodness-of-fit method gave a family of spline fits; splines with a low percentage fit extracted trends from the data, while for general use a 50% fit appeared satisfactory. The goodness-of-fit method executed more quickly than the GCV/GA method, but the GCV/GA method was more generally applicable as it chose both the degree of the spline and the amount of smoothing automatically.
NASA Technical Reports Server (NTRS)
Khorrami, Mehdi R.
1991-01-01
A staggered spectral collocation method for the stability of cylindrical flows is developed. In this method the pressure is evaluated at different nodal points than the three velocity components. These modified nodal points do not include the two boundary nodes; therefore the need for the two artificial pressure boundary conditions employed by Khorrami et al. is eliminated. It is shown that the method produces very accurate results and has a better convergence rate than the spectral tau formulation. However, through extensive convergence tests it was found that elimination of the artificial pressure boundary conditions does not result in any significant change in the convergence behavior of spectral collocation methods.
C. H. Tsai; Joseph Kolibal; Ming Li
2010-01-01
In this paper we propose to apply the golden section search algorithm to determining a good shape parameter of multiquadrics (MQ) for the solution of partial differential equations. We use two radial basis function based meshless collocation methods, the method of approximate particular solutions (MAPS) and Kansa's method, to solve partial differential equations. Due to the severely ill-conditioned matrix system
Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid
Xu, Zhenli; Cai, Wei
2009-01-01
This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from 𝒪(M2N4) to 𝒪(MN4), where N2 is the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method. PMID:20414359
A meshless collocation method based on radial basis functions and wavelets
S. L. Ho; Shiyou Yang; H. C. Wong; Guangzheng Ni
2004-01-01
A meshless method based on collocation with radial basis functions (RBFs) and wavelets is proposed. It is shown that the proposed method takes full advantage of both RBFs and wavelets. The bridging scales are employed to preserve the mathematical properties of the entire bases in terms of consistency and linear independence. A numerical example that is used to validate the
NOKIN1D: one-dimensional neutron kinetics based on a nodal collocation method
NASA Astrophysics Data System (ADS)
Verdú, G.; Ginestar, D.; Miró, R.; Jambrina, A.; Barrachina, T.; Soler, Amparo; Concejal, Alberto
2014-06-01
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.
An analytic reconstruction method for PET based on cubic splines
NASA Astrophysics Data System (ADS)
Kastis, George A.; Kyriakopoulou, Dimitra; Fokas, Athanasios S.
2014-03-01
PET imaging is an important nuclear medicine modality that measures in vivo distribution of imaging agents labeled with positron-emitting radionuclides. Image reconstruction is an essential component in tomographic medical imaging. In this study, we present the mathematical formulation and an improved numerical implementation of an analytic, 2D, reconstruction method called SRT, Spline Reconstruction Technique. This technique is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of 'custom made' cubic splines. It also imposes sinogram thresholding which restricts reconstruction only within object pixels. Furthermore, by utilizing certain symmetries it achieves a reconstruction time similar to that of FBP. We have implemented SRT in the software library called STIR and have evaluated this method using simulated PET data. We present reconstructed images from several phantoms. Sinograms have been generated at various Poison noise levels and 20 realizations of noise have been created at each level. In addition to visual comparisons of the reconstructed images, the contrast has been determined as a function of noise level. Further analysis includes the creation of line profiles when necessary, to determine resolution. Numerical simulations suggest that the SRT algorithm produces fast and accurate reconstructions at realistic noise levels. The contrast is over 95% in all phantoms examined and is independent of noise level.
Spline methods for approximating quantile functions and generating random samples
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Matthews, C. G.
1985-01-01
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.
Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Halem, Milton (Technical Monitor)
2000-01-01
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.
An effective dynamic optimization method based on modified orthogonal collocation and reduced SQP
Xinggao Liu; Long Chen; Yunqing Hu
2011-01-01
An effective dynamic optimization solution method based on the modified orthogonal collocation (mOC) and reduced successive quadratic programming (rSQP) is proposed, where the mOC is proposed to decrease the approximation error of the discrete optimal problem while traditional OC method converts the dynamic optimization problem to a regular but discrete nonlinear programming (NLP) problem, and the rSQP method is introduced
GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD
New Hampshire, University of
GRADUAL GENERALIZATION OF NAUTICAL CHART CONTOURS WITH A B-SPLINE SNAKE METHOD BY DANDAN MIAO BS...............................................................................................39 2.2 Snake Method....................................................................................................................40 2.2.1 Snake Method Definition...............................................
Domain decomposition methods for systems of conservation laws: Spectral collocation approximations
NASA Technical Reports Server (NTRS)
Quarteroni, Alfio
1989-01-01
Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.
Multi-Symplectic Runge-Kutta Collocation Methods for Hamiltonian Wave Equations
Sebastian Reich
1999-01-01
A number of conservative PDEs, like various wave equations, allow for a multi-symplecticformulation which can be viewed as a generalization of the symplectic structure of HamiltonianODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplecticintegrators, i.e., to numerical methods that preserve a symplectic conservation law similar tothe conservation of symplecticity under a symplectic method for Hamiltonian ODEs.
Nasser S. Elgazery; Nader Y. Abd Elazem
2009-01-01
In this article, the authors analyzed the effect of thermal conductivity on unsteady magnetohydrodynamic (MHD) free convection in a micro-polar fluid past a semi-infinite vertical porous plate. The fluid thermal conductivity is assumed to vary as a linear function of temperature. By using the Chebyshev collocation method in the spatial direction and the Crank-Nicolson method in the time direction, the
Multi-Symplectic Runge–Kutta Collocation Methods for Hamiltonian Wave Equations
Sebastian Reich
2000-01-01
A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss–Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplecticity under a symplectic
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1980-01-01
The coupled strongly implicit (CSIP) method described previously is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equations. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered (equal to or less than 1000). In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.
Convergence of Unsymmetric Kernel-Based Meshless Collocation Methods
Robert Schaback
2007-01-01
This paper proves convergence of variations of the unsymmetric kernel-based collo- cation method introduced by E. Kansa in 1986. Since then, this method has been very successfully used in many applications, though it may theoretically fail in special situations, and though it had no error bound or convergence proof up to now. Thus it is necessary to add assumptions or
NASA Astrophysics Data System (ADS)
Dai, Honghua; Yue, Xiaokui; Yuan, Jianping; Atluri, Satya N.
2014-08-01
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.
NASA Astrophysics Data System (ADS)
Marzban, H. R.; Tabrizidooz, H. R.; Razzaghi, M.
2011-03-01
This paper presents a computational technique for the solution of the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. The method is based on the composite collocation method. The properties of hybrid of block-pulse functions and Lagrange polynomials are discussed and utilized to define the composite interpolation operator. The estimates for the errors are given. The composite interpolation operator together with the Gaussian integration formula are then used to transform the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations into a system of nonlinear equations. The efficiency and accuracy of the proposed method is illustrated by four numerical examples.
A Fourier collocation time domain method for numerically solving Maxwell's equations
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1991-01-01
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.
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
NASA Technical Reports Server (NTRS)
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
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.
Webster, Clayton G [ORNL; Zhang, Guannan [ORNL; Gunzburger, Max D [ORNL
2012-10-01
Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
NASA Astrophysics Data System (ADS)
Parand, K.; Delafkar, Z.; Pakniat, N.; Pirkhedri, A.; Kazemnasab Haji, M.
2011-04-01
This paper proposes two approximate methods to solve Volterra's population model for population growth of a species in a closed system. Volterra's model is a nonlinear integro-differential equation on a semi-infinite interval, where the integral term represents the effect of toxin. The proposed methods have been established based on collocation approach using Sinc functions and Rational Legendre functions. They are utilized to reduce the computation of this problem to some algebraic equations. These solutions are also compared with some well-known results which show that they are accurate.
Numerical Algorithm Based on Haar-Sinc Collocation Method for Solving the Hyperbolic PDEs
Javadi, H. H. S.; Navidi, H. R.
2014-01-01
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed. PMID:25485295
Orthogonal grid generation of an irregular region using a local polynomial collocation method
NASA Astrophysics Data System (ADS)
Wu, Nan-Jing; Tsay, Ting-Kuei; Yang, Tun-Chi; Chang, Hung-Yuan
2013-06-01
In this study, a 2-D orthogonal grid generation model is developed by solving the governing equations of coordinate transformation with a local polynomial collocation method accompanied with the moving least squares (MLS) approach. This method was developed in a way that on the boundaries both the governing equation and boundary condition are satisfied, so it is more robust and accurate than conventional collocation methods. Though the method used to solve the coordinate transforming equations is meshless, it does not deteriorate the value of present work, because most numerical models in modern use are grid-dependent, and grid generation of service to these models is still strongly desired, particularly for finite difference models in irregular domains. Before applying to grid generation problems, the performance of present method is tested by a bench mark potential flow problem. Additional to two basic grid generation problems, a bottleneck problem of previous works, which contains zero-degree corners in the domain, is carried out. Finally, the model is applied to the orthogonal grid generation in a multi-connected domain. The correctness is testified by checking the orthogonality of the generated results.
Motsa, S. S.; Magagula, V. M.; Sibanda, P.
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Regional Ionosphere Mapping with Kriging and B-spline Methods
NASA Astrophysics Data System (ADS)
Grynyshyna-Poliuga, O.; Stanislawska, I. M.
2013-12-01
This work demonstrates the concept and practical examples of mapping of regional ionosphere, based on GPS observations from the EGNOS Ranging and Integrity Monitoring Stations (RIMS) network and permanent stations near to them. Interpolation/prediction techniques, such as kriging (KR) and the cubic B-spline, which are suitable for handling multi-scale phenomena and unevenly distributed data, were used to create total electron content (TEC) maps. Their computational efficiency (especially the B-spline) and the ability to handle undersampled data (especially kriging) are particularly attractive. The data sets have been collect into seasonal bins representing June, December solstices and equinox (March, September). TEC maps have a spatial resolution of 2.50 and 2.50 in latitude and longitude, respectively, and a 15-minutes temporal resolution. The time series of the TEC maps can be used to derive average monthly maps describing major ionospheric trends as a function of time, season, and spatial location.
Chebyshev collocation Dirichlet-to-Neumann map method for diffraction gratings.
Song, Dawei; Lu, Ya Yan
2009-09-01
For diffraction gratings with layered refractive index profiles, the Fourier modal method is widely used. However, it is quite expensive to calculate the eigenmodes for each layer, especially when the structure involves absorptive media. We develop an efficient method that avoids the eigenvalue problems based on the so-called Dirichlet-to-Neumann (DtN) map. For each layer, the DtN map is an operator that maps the wave field to its normal derivative on one period of the boundaries of the layer, and it is approximated by a matrix. An efficient procedure for computing the DtN map is developed based on a Chebyshev collocation method and a fourth-order finite difference method for discretizing the uniform and the periodic directions, respectively. The efficiency and accuracy of our method are illustrated by numerical examples. PMID:19721683
NASA Technical Reports Server (NTRS)
Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.
1994-01-01
Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.
Numerical methods for solving systems of Fredholm integral equations with cardinal splines
NASA Astrophysics Data System (ADS)
Liu, Xiaoyan; Xie, Jin
2014-12-01
The aim of this paper is to develop numerical methods for solving systems of integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is obtained for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are used in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. Examples are given to demonstrate the benefits of the methods.
Sankaran, Sethuraman [Department of Mechanical and Aerospace Engineering, EBU II 569, University of California San Diego, La Jolla, CA 92093-0411 (United States); Audet, Charles [GERAD and Departement de mathematiques et de genie industriel, Ecole Polytechnique de Montreal, C.P. 6079, Succ. Centre-ville, Montreal (Quebec), H3C 3A7 (Canada); Marsden, Alison L. [Department of Mechanical and Aerospace Engineering, EBU II 569, University of California San Diego, La Jolla, CA 92093-0411 (United States)], E-mail: amarsden@ucsd.edu
2010-06-20
Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realistic engineering design problems. A large computational overhead is associated with computing the cost function for most practical problems involving complex physical phenomena. Such problems are also plagued with uncertainties in a diverse set of parameters. We present a novel stochastic derivative-free optimization approach for tackling such problems. Our method extends the previously developed surrogate management framework (SMF) to allow for uncertainties in both simulation parameters and design variables. The stochastic collocation scheme is employed for stochastic variables whereas Kriging based surrogate functions are employed for the cost function. This approach is tested on four numerical optimization problems and is shown to have significant improvement in efficiency over traditional Monte-Carlo schemes. Problems with multiple probabilistic constraints are also discussed.
Solving non-linear Lane-Emden type equations using Bessel orthogonal functions collocation method
NASA Astrophysics Data System (ADS)
Parand, Kourosh; Nikarya, Mehran; Rad, Jamal Amani
2013-05-01
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.
Lesage, Jonathan C; Bond, Jill V; Sinclair, Anthony N
2014-09-01
The problem of elastic wave propagation in an infinite bar of arbitrary cross section is studied via a generalized version of the Fourier expansion collocation method. In the current formulation, the exact three dimensional solution to Navier's equation in cylindrical coordinates is used to obtain the boundary traction vector as a periodic, piecewise continuous/differentiable function of the angular coordinate. Traction free conditions are then met by setting the Fourier coefficients of the boundary traction vector to zero without approximating the bounding surface by multi-sided polygons as in the method presented by Nagaya. The method is derived for a general cross section with no axial planes of symmetry. Using the general formulation it is shown that the symmetric and asymmetric modes decouple for cross sections having one axial plane of symmetry. An efficient algorithm for computing dispersion curves based on the current method is presented and used to obtain the fundamental longitudinal and flexural wave speeds for a bar of elliptical cross section. The results are compared to those obtained by previous researchers using exact and approximate treatments. PMID:25190374
NASA Astrophysics Data System (ADS)
Soghrati, Soheil; Mai, Weijie; Liang, Bowen; Buchheit, Rudolph G.
2015-01-01
A new meshfree method based on a discrete transformation of Green's basis functions is introduced to simulate Poisson problems with complex morphologies. The proposed Green's Discrete Transformation Method (GDTM) uses source points that are located along a virtual boundary outside the problem domain to construct the basis functions needed to approximate the field. The optimal number of Green's functions source points and their relative distances with respect to the problem boundaries are evaluated to obtain the best approximation of the partition of unity condition. A discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions. A comprehensive convergence study is presented to investigate the accuracy and convergence rate of the GDTM. We will also demonstrate the application of this meshfree method for simulating the conductive heat transfer in a heterogeneous materials system and the dissolved aluminum ions concentration in the electrolyte solution formed near a passive corrosion pit.
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential convergence is achieved rather than polynomial rates. The solution methodology proposed, the CCSLBM, is also extended to three dimensions and a 3D regularized cavity is simulated; the corresponding results are presented and validated. Indications are that the CCSLBM developed and applied herein is robust, efficient, and accurate for computing 2D and 3D low-speed flows. Note also that high-accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the assessment of other LBM-based flow solvers. PMID:25679733
Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows
NASA Astrophysics Data System (ADS)
Hejranfar, Kazem; Hajihassanpour, Mahya
2015-01-01
In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential convergence is achieved rather than polynomial rates. The solution methodology proposed, the CCSLBM, is also extended to three dimensions and a 3D regularized cavity is simulated; the corresponding results are presented and validated. Indications are that the CCSLBM developed and applied herein is robust, efficient, and accurate for computing 2D and 3D low-speed flows. Note also that high-accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the assessment of other LBM-based flow solvers.
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
NASA Technical Reports Server (NTRS)
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
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.
Modeling guided elastic waves in generally anisotropic media using a spectral collocation method.
Quintanilla, F Hernando; Lowe, M J S; Craster, R V
2015-03-01
Guided waves are now well established for some applications in the non-destructive evaluation of structures and offer potential for deployment in a vast array of other cases. For their development, it is important to have reliable and accurate information about the modes that propagate for particular waveguide structures. Essential information that informs choices of mode transducer, operating frequencies, and interpretation of signals, among other issues, is provided by the dispersion curves of different modes within various combinations of geometries and materials. In this paper a spectral collocation method is successfully used to handle the more complicated and realistic waveguide problems that are required in non-destructive evaluation; many pitfalls and limitations found in root-finding routines based on the partial wave method are overcome by using this approach. The general cases presented cover anisotropic homogeneous perfectly elastic materials in flat and cylindrical geometry. Non-destructive evaluation applications include complex waveguide structures, such as single or multi-layered fiber composites, lined, bonded and buried structures. For this reason, arbitrarily multi-layered systems with both solid and fluid layers are also addressed as well as the implementation of interface models of imperfect boundary conditions between layers. PMID:25786933
Preston, J. Samuel; Tasdizen, Tolga; Terry, Christi M.; Cheung, Alfred K.
2010-01-01
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. PMID:19272865
Preston, J Samuel; Tasdizen, Tolga; Terry, Christi M; Cheung, Alfred K; Kirby, Robert M
2009-03-01
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. PMID:19272865
NASA Astrophysics Data System (ADS)
Cherry, M. R.; Knopp, J. S.; Blodgett, M. P.
2012-05-01
In order to quantify the reliability of NDE systems, large numbers of experiments are performed to develop a probability of detection (POD) curve for the system. These POD studies require a substantial amount of experimentation which can sometimes be cost prohibitive. To expedite the process of developing these curves, highly precise numerical models are used in conjunction with NDE sensors to understand the uncertainties associated with the inspections. Numerical models are also used in stochastic inversion methods such as Bayesian inversion, which provide a means of characterizing system properties with uncertainties. A strong basis has been developed in the modeling and simulation community for deterministic forward models in NDE, but to fully incorporate these models in model-assisted probability of detection (MAPOD) studies or stochastic inversion schemes, the models must be treated in a stochastic sense. A method of taking random inputs to a "black box" forward model and developing the full probability distribution function (PDF) of the response has been proposed. This method, called the probabilistic collocation method (PCM), takes random inputs to a forward model and uses orthogonal polynomials to construct a surrogate model in the area of the expected values of the inputs which is solved much quicker than the original forward model. In the NDE community, this method has only been used with inputs of known, named distributions. In this work, inputs of arbitrary distribution were used and the orthogonal polynomials for these inputs were developed with a recursion relationship that has been shown to produce orthogonal polynomials with respect to a given, continuous function. A concise code was written to make testing the method and incorporating it into MAPOD studies and inversion schemes relatively easy. The routine was tested with academic problems as well as eddy current problems.
Estimation of CRF and TRF from VLBI observations by the Least Square Collocation method
NASA Astrophysics Data System (ADS)
Kurdubov, S. L.
2006-08-01
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.
H. F. Meier; J. J. N. Alves; M. Mori
1999-01-01
This work presents the numerical results obtained when staggered and collocated grids were used in the finite-volume methods (FVMs) for four standard flows: developing laminar single-phase flow at the entrance of the tube; developing turbulent single-phase flow at the entrance of the tube; incompressible laminar flow through an orifice plate; and developing turbulent gas–solid flow in a vertical pipe. These
NASA Astrophysics Data System (ADS)
Karkar, Sami; Cochelin, Bruno; Vergez, Christophe
2014-06-01
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.
Two-dimensional mesh embedding for Galerkin B-spline methods
NASA Technical Reports Server (NTRS)
Shariff, Karim; Moser, Robert D.
1995-01-01
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.
Butcher, Eric A.
Free Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation for the free vibration analysis of slender Kirchoff plates with both mixed and damaged boundaries an important role in applications of mechanical, aerospace and civil engineering. Studying the free vibration
[Baseline correction method for Raman spectroscopy based on B-spline fitting].
Wang, Xin; Fan, Xian-guang; Xu, Ying-jie; Wu, Jing-lin; Liang, Jun; Zuo, Yong
2014-08-01
Baseline drift is a widespread phenomenon in modern spectroscopy instrumentation, which would bring a very negative impact to the feature extraction of spectrum signal, and the baseline correction method is an important means to solve the problem, which is also the important part of Raman signal preprocessing. The general principle of baseline drift elimination is using the fitting method to the fit the baseline. The traditional fitting method is polynomial fitting, but this method is prone to over-fitting and under-fitting, and the fitting order is difficult to be determined. In this paper, the traditional method is improved; the B-spline fitting method is used to approach the baseline of Raman signal through constant iteration The advantages of B-spline, namely low-order and smoothness, can help the method overcome the shortcomings of polynomial method. In the experiments, the Raman signal of malachite green and rhodamine B were detected, and then the proposed method and traditional method were applied to perform baseline correction Experimental results showed that the proposed method can eliminate the Raman signal baseline drift effectively without over- and under-fitting, and the same order can be used in both positions where large or small baseline drift occurred. Therefore, the proposed method provided more accurate and reliable information for the further analysis of spectral data. PMID:25474946
[Baseline correction method for Raman spectroscopy based on B-spline fitting].
Wang, Xin; Fan, Xian-guang; Xu, Ying-jie; Wu, Jing-lin; Liang, Jun; Zuo, Yong
2014-08-01
Baseline drift is a widespread phenomenon in modern spectroscopy instrumentation, which would bring a very negative impact to the feature extraction of spectrum signal, and the baseline correction method is an important means to solve the problem, which is also the important part of Raman signal preprocessing. The general principle of baseline drift elimination is using the fitting method to the fit the baseline. The traditional fitting method is polynomial fitting, but this method is prone to over-fitting and under-fitting, and the fitting order is difficult to be determined. In this paper, the traditional method is improved; the B-spline fitting method is used to approach the baseline of Raman signal through constant iteration The advantages of B-spline, namely low-order and smoothness, can help the method overcome the shortcomings of polynomial method. In the experiments, the Raman signal of malachite green and rhodamine B were detected, and then the proposed method and traditional method were applied to perform baseline correction Experimental results showed that the proposed method can eliminate the Raman signal baseline drift effectively without over- and under-fitting, and the same order can be used in both positions where large or small baseline drift occurred. Therefore, the proposed method provided more accurate and reliable information for the further analysis of spectral data. PMID:25508725
Swenson, Darrell J.; Geneser, Sarah E.; Stinstra, Jeroen G.; Kirby, Robert M.; MacLeod, Rob S.
2012-01-01
The electrocardiogram (ECG) is ubiquitously employed as a diagnostic and monitoring tool for patients experiencing cardiac distress and/or disease. It is widely known that changes in heart position resulting from, for example, posture of the patient (sitting, standing, lying) and respiration significantly affect the body-surface potentials; however, few studies have quantitatively and systematically evaluated the effects of heart displacement on the ECG. The goal of this study was to evaluate the impact of positional changes of the heart on the ECG in the specific clinical setting of myocardial ischemia. To carry out the necessary comprehensive sensitivity analysis, we applied a relatively novel and highly efficient statistical approach, the generalized polynomial chaos-stochastic collocation method, to a boundary element formulation of the electrocardiographic forward problem, and we drove these simulations with measured epicardial potentials from whole-heart experiments. Results of the analysis identified regions on the body-surface where the potentials were especially sensitive to realistic heart motion. The standard deviation (STD) of ST-segment voltage changes caused by the apex of a normal heart, swinging forward and backward or side-to-side was approximately 0.2 mV. Variations were even larger, 0.3 mV, for a heart exhibiting elevated ischemic potentials. These variations could be large enough to mask or to mimic signs of ischemia in the ECG. Our results suggest possible modifications to ECG protocols that could reduce the diagnostic error related to postural changes in patients possibly suffering from myocardial ischemia. PMID:21909818
B-spline-based complex-rotation method with spin-dependent interaction
Fang, T. K. [Department of Physics, Fu Jen Catholic University, Taipei, Taiwan 242 (China); Chang, T. N. [Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484 (United States); National Center of Theoretical Sciences, Hsinchu, Taiwan 30039 (China)
2007-07-15
We present a B-spline-based complex-rotation (BSCR) method with spin-dependent interaction for the study of atomic photoionization leading to multiple ionization channels dominated by doubly excited resonances for two-electron and divalent atoms. The degree of mixing between different spin states and between the bound and continuum components of the state function of the resonance state can be easily identified in the BSCR method. Its application to Mg photoionization gives good agreement with observed singlet-triplet mixed Mg spectra.
H. S. Shukla; Mohammad Tamsir; Vineet K. Srivastava
2014-10-01
In this article, we study the numerical solution of the one dimensional nonlinear sine-Gordon by using the modified cubic B-spline differential quadrature method. The scheme is a combination of a modified cubic B spline basis function and the differential quadrature method. The modified cubic B spline is used as a basis function in the differential quadrature method to compute the weighting coefficients. Thus, the sine Gordon equation is converted into a system of ordinary differential equations (ODEs). The resulting system of ODEs is solved by an optimal five stage and fourth order strong stability preserving Runge Kutta scheme. The accuracy and efficiency of the scheme are successfully described by considering the three numerical examples of the nonlinear sine Gordon equation having the exact solutions.
Sankaran, Sethuraman; Marsden, Alison L
2011-03-01
Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input parameters. In this work, we develop a general set of tools to evaluate the sensitivity of output parameters to input uncertainties in cardiovascular simulations. Uncertainties can arise from boundary conditions, geometrical parameters, or clinical data. These uncertainties result in a range of possible outputs which are quantified using probability density functions (PDFs). The objective is to systemically model the input uncertainties and quantify the confidence in the output of hemodynamic simulations. Input uncertainties are quantified and mapped to the stochastic space using the stochastic collocation technique. We develop an adaptive collocation algorithm for Gauss-Lobatto-Chebyshev grid points that significantly reduces computational cost. This analysis is performed on two idealized problems--an abdominal aortic aneurysm and a carotid artery bifurcation, and one patient specific problem--a Fontan procedure for congenital heart defects. In each case, relevant hemodynamic features are extracted and their uncertainty is quantified. Uncertainty quantification of the hemodynamic simulations is done using (a) stochastic space representations, (b) PDFs, and (c) the confidence intervals for a specified level of confidence in each problem. PMID:21303177
A Stochastic Collocation Algorithm for Uncertainty Analysis
NASA Technical Reports Server (NTRS)
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
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.
NASA Astrophysics Data System (ADS)
Chen, Shang-Shang; Li, Ben-Wen
2014-12-01
A collocation spectral domain decomposition method (CSDDM) based on the influence matrix technique is developed to solve radiative transfer problems within a participating medium of 2D partitioned domains. In this numerical approach, the spatial domains of interest are decomposed into rectangular sub-domains. The radiative transfer equation (RTE) in each sub-domain is angularly discretized by the discrete ordinates method (DOM) with the SRAPN quadrature scheme and then is solved by the CSDDM directly. Three test geometries that include square enclosure and two enclosures with one baffle and one centered obstruction are used to validate the accuracy of the developed method and their numerical results are compared to the data obtained by other researchers. These comparisons indicate that the CSDDM has a good accuracy for all solutions. Therefore this method can be considered as a useful approach for the solution of radiative heat transfer problems in 2D partitioned domains.
NASA Astrophysics Data System (ADS)
Gao, Wen-Wu; Wang, Zhi-Gang
2014-11-01
Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions.
NASA Astrophysics Data System (ADS)
Cuomo, S.; D'Amore, L.; Murli, A.
2007-12-01
In [S. Cuomo, L. D'Amore, A. Murli, M.R. Rizzardi, Computation of the inverse Laplace transform based on a collocation method which uses only real values, J. Comput. Appl. Math., 198 (1) (2007) 98-115] the authors proposed a Collocation method (C-method) for real inversion of Laplace transforms (Lt), based on the truncated Laguerre expansion of the inverse function:where [sigma], b are parameters and ck, k[set membership, variant]N, are the MacLaurin coefficients of a function depending on the Lt. The computational kernel of a C-method is the solution of a Vandermonde linear system, where the right hand side is obtained evaluating the Lt on the real axis. The Bjorck Pereira algorithm has been used for solving the Vandermonde linear system, providing a computable componentwise error bound on the solution. For an inversion problem on discrete data F is known on a pre-assigned set of points (we refer to these points as samples of F) only and the major challenge is to deal with a significative loss of information. A natural approach to overcome this intrinsic difficulty is to construct a suitable fitting model that approximates the given data. In this case, we show that such approach leads to a C-method with perturbed right hand side, and then we use again the Bjorck Pereira algorithm. Starting from the error introduced by the fitting model, we study its propagation in order to determine the maximum attainable accuracy on fN. Moreover we derive a computable error bound that allows to get the suitable value of the parameter N that gives the maximum attainable accuracy.
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2015-01-01
Reliable quantification of air-biosphere exchange flux of elemental mercury vapor (Hg0) is crucial for understanding the global biogeochemical cycle of mercury. However, there has not been a standard analytical protocol for flux quantification, and little attention has been devoted to characterize the temporal variability and comparability of fluxes measured by different methods. In this study, we deployed a collocated set of micrometeorological (MM) and dynamic flux chamber (DFC) measurement systems to quantify Hg0 flux over bare soil and low standing crop in an agricultural field. The techniques include relaxed eddy accumulation (REA), modified Bowen ratio (MBR), aerodynamic gradient (AGM) as well as dynamic flux chambers of traditional (TDFC) and novel (NDFC) designs. The five systems and their measured fluxes were cross-examined with respect to magnitude, temporal trend and correlation with environmental variables. Fluxes measured by the MM and DFC methods showed distinct temporal trends. The former exhibited a highly dynamic temporal variability while the latter had much more gradual temporal features. The diurnal characteristics reflected the difference in the fundamental processes driving the measurements. The correlations between NDFC and TDFC fluxes and between MBR and AGM fluxes were significant (R>0.8, p<0.05), but the correlation between DFC and MM fluxes were from weak to moderate (R=0.1-0.5). Statistical analysis indicated that the median of turbulent fluxes estimated by the three independent MM techniques were not significantly different. Cumulative flux measured by TDFC is considerably lower (42% of AGM and 31% of MBR fluxes) while those measured by NDFC, AGM and MBR were similar (<10% difference). This suggests that incorporating an atmospheric turbulence property such as friction velocity for correcting the DFC-measured flux effectively bridged the gap between the Hg0 fluxes measured by enclosure and MM techniques. Cumulated flux measured by REA was ~60% higher than the gradient-based fluxes. Environmental factors have different degrees of impacts on the fluxes observed by different techniques, possibly caused by the underlying assumptions specific to each individual method. Recommendations regarding the application of flux quantification methods were made based on the data obtained in this study.
LEON GRADO?; ANDRZEJ D?UGOSZ
1984-01-01
The convective diffusion equation of aerosols in the case of gas stream slip on the fibre cylindrical surface has been solved by means of the finite element collocation method. Half-analytical form of the solution makes it possible to examine directly changes the slip causes in the distribution of solids around the fibre surface. Concentration profiles and deposition efficiency computed by
Spline histogram method for reconstruction of probability density function of clusters of galaxies
Dmitrijs Docenko; Karlis Berzins
2003-02-28
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 http://www.virac.lv/en/soft.html
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Kumar, Jai
2014-11-01
In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Examination of the Circle Spline Routine
NASA Technical Reports Server (NTRS)
Dolin, R. M.; Jaeger, D. L.
1985-01-01
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).
Christophe Reboud; Denis Prémel; Dominique Lesselier; Bernard Bisiaux
2008-01-01
Purpose – A numerical model dedicated to external eddy current inspection of tubes has been developed using the volume integral method (VIM). The purpose of this paper is to suggest new discretization schemes based on non-uniform B-splines for the solution of the state equation with the method of moments (MoM). Design\\/methodology\\/approach – VIM is a semi-analytical approach providing fast and
NASA Astrophysics Data System (ADS)
Wang, Chunqi; Huang, Lixi
2012-09-01
A time-domain Chebyshev collocation (ChC) method is used to simulate acoustic wave propagation and its interaction with flexible structures in ducts. The numerical formulation is described using a two-dimensional duct noise control system, which consists of an expansion chamber and a tensioned membrane covering the side-branch cavity. Full coupling between the acoustic wave and the structural vibration of the tensioned membrane is considered in the modelling. A systematic method of solution is developed for the discretized differential equations over multiple physical domains. The time-domain ChC model is tested against analytical solutions under two conditions: one with an initial state of wave motion; the other with a time-dependent acoustic source. Comparisons with the finite-difference time-domain (FDTD) method are also made. Results show that the time-domain ChC method is highly accurate and computationally efficient for the time-dependent solution of duct acoustic problems. For illustrative purposes, the time-domain ChC method is applied to investigate the acoustic performance of three typical duct noise control devices: the expansion chamber, the quarter wavelength resonator and the drum silencer. The time-dependent simulation of the sound-structure interaction in the drum silencer reveals the delicate role of the membrane mass and tension in its sound reflection capability.
Solution of three-dimensional flow problems using a flux-spline method
NASA Technical Reports Server (NTRS)
Karki, K.; Mongia, H.; Patankar, S.
1989-01-01
This paper reports the application of a flux-spline scheme to three-dimensional fluid flow problems. The performance of this scheme is contrasted with that of the power-law differencing scheme. The numerical results are compared with reference solutions available in the literature. For the problems considered in this study, the flux-spline scheme is significantly more accurate than the power-law scheme.
B-spline methods and zonal grids for numerical simulations of turbulent flows
NASA Astrophysics Data System (ADS)
Kravchenko, Arthur Grigorievich
1998-12-01
A novel numerical technique is developed for simulations of complex turbulent flows on zonal embedded grids. This technique is based on the Galerkin method with basis functions constructed using B-splines. The technique permits fine meshes to be embedded in physically significant flow regions without placing a large number of grid points in the rest of the computational domain. The numerical technique has been tested successfully in simulations of a fully developed turbulent channel flow. Large eddy simulations of turbulent channel flow at Reynolds numbers up to Rec = 110,000 (based on centerline velocity and channel half-width) show good agreement with the existing experimental data. These tests indicate that the method provides an efficient information transfer between zones without accumulation of errors in the regions of sudden grid changes. The numerical solutions on multi-zone grids are of the same accuracy as those on a single-zone grid but require less computer resources. The performance of the numerical method in a generalized coordinate system is assessed in simulations of laminar flows over a circular cylinder at low Reynolds numbers and three-dimensional simulations at ReD = 300 (based on free-stream velocity and cylinder diameter). The drag coefficients, the size of the recirculation region, and the vortex shedding frequency all agree well with the experimental data and previous simulations of these flows. Large eddy simulations of a flow over a circular cylinder at a sub-critical Reynolds number, ReD = 3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the very near-wake, all three simulations are in agreement with each other and agree fairly well with the PIV experimental data of Lourenco & Shih (1993). Farther downstream, the results of the B- spline computations are in better agreement with the hot- wire experiment of Ong & Wallace (1996) than those obtained in finite-difference simulations. In particular, the power spectra of velocity fluctuations are in excellent agreement with the experimental data. The study also shows the impact of grid resolution on simulations of this flow.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1986-01-01
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 used to argue convergence and establish rates of convergence. An example and numerical results are discussed.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1985-01-01
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.
Dorje C. Brody; Darryl D. Holm; David M. Meier
2012-09-04
A quantum spline is a smooth curve parameterised by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm of the time rate of change of the associated Hamiltonian is minimised. The solution to the quantum spline problem is obtained, and is applied in an example that illustrates quantum control of coherent states. An efficient numerical scheme for computing quantum splines is discussed and implemented in the examples.
NASA Astrophysics Data System (ADS)
Totis, G.; Albertelli, P.; Sortino, M.; Monno, M.
2014-02-01
Chatter is a vibrational problem affecting machining operations, which may cause bad surface quality and damages to the machining system. In recent decades, several techniques for avoiding chatter onset were developed. Among other techniques, the continuous modulation of spindle speed during the cutting process (also called Spindle Speed Variation - SSV) has been demonstrated to be very effective for reducing the chance of chatter onset. However, spindle speed modulation parameters should be adequately chosen before machining, in order to effectively increase the material removal rate. In this perspective, chatter prediction algorithms play a crucial role, since they allow a preventive evaluation of process stability for any given spindle speed regime. State of the art algorithms for chatter prediction in milling with SSV are characterized by extremely long computation times, hindering their practical application in industry. In this paper, an innovative and fast algorithm for chatter prediction in milling with SSV, based on the Chebyshev Collocation Method, is presented. The algorithm was successfully compared with a state of the art algorithm - the Semi Discretization Method - in different experimental configurations and cutting conditions. The results showed that the new method is generally more accurate and from ten to one thousand times faster than the Semi Discretization Method.
Results on meshless collocation techniques
Leevan Ling; Roland Opfer; Robert Schaback
2006-01-01
Though the technique introduced by Kansa is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail-safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test spaces.
NASA Astrophysics Data System (ADS)
Lee, W. M.
2011-09-01
This paper presents a semi-analytical approach to solve the eigenproblem of an acoustic cavity with multiple elliptical boundaries. To satisfy the Helmholtz equation in the elliptical coordinate system, the multipole expansion for the acoustic pressure is formulated in terms of angular and radial Mathieu functions. The boundary conditions are satisfied by uniformly collocating points on the boundaries. The acoustic pressure at each point is directly calculated in each elliptical coordinate system. In different coordinate systems, the normal derivative of the acoustic pressure is calculated by using the appropriate directional derivative, an alternative to the addition theorem. By truncating the multipole expansion, a finite linear algebraic system is derived. The direct searching approach is employed to determine the natural frequencies by using the singular value decomposition (SVD). Numerical results are widely discussed for several examples including an elliptical cavity, a confocal elliptical annulus cavity and an elliptical cavity with two elliptical cylinders. The accuracy and numerical convergence of the presented method is validated by comparison with available results from the analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Excellent accuracy and fast rate of convergence are the key features of the present method thanks to its semi-analytical feature.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.
2015-01-01
In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM) is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs). The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme (SSP-RK54). Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
H. S. Shukla; Mohammad Tamsir; Vineet K. Srivastava
2014-09-30
In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Neumann boundary condition is obtained by using a composite scheme referred to as a modified cubic B spline differential quadrature method. The modified cubic B-spline serves as a basis function in the differential quadrature method to compute the weighting coefficients. Thus, the sine-Gordon equation is converted into a system of second order ordinary differential equations (ODEs). We solve the resulting system of ODEs by an optimal five stage and fourth-order strong stability preserving Runge Kutta scheme. Both damped and undamped cases are considered for the numerical simulation with Josephson current density function with value minus one. The computed results are found to be in good agreement with the exact solutions and other numerical results available in literature.
NASA Astrophysics Data System (ADS)
Wu, Bin; Zheng, Yi; Tian, Yong; Wu, Xin; Yao, Yingying; Han, Feng; Liu, Jie; Zheng, Chunmiao
2014-07-01
Systematic uncertainty analysis (UA) has rarely been conducted for integrated modeling of surface water-groundwater (SW-GW) systems, which is subject to significant uncertainty, especially at a large basin scale. The main objective of this study was to explore an innovative framework in which a systematic UA can be effectively and efficiently performed for integrated SW-GW models of large river basins and to illuminate how process understanding, model calibration, data collection, and management can benefit from such a systematic UA. The framework is based on the computationally efficient Probabilistic Collocation Method (PCM) linked with a complex simulation model. The applicability and advantages of the framework were evaluated and validated through an integrated SW-GW model for the Zhangye Basin in the middle Heihe River Basin, northwest China. The framework for systematic UA allows for a holistic assessment of the modeling uncertainty, yielding valuable insights into the hydrological processes, model structure, data deficit, and potential effectiveness of management. The study shows that, under the complex SW-GW interactions, the modeling uncertainty has great spatial and temporal variabilities and is highly output-dependent. Overall, this study confirms that a systematic UA should play a critical role in integrated SW-GW modeling of large river basins, and the PCM-based approach is a promising option to fulfill this role.
Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces.
Chen, Xi; He, Si-Yuan; Yu, Ding-Feng; Yin, Hong-Cheng; Hu, Wei-Dong; Zhu, Guo-Qiang
2013-04-01
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
NASA Astrophysics Data System (ADS)
Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton
2013-10-01
Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by 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, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.
Algebraic grid adaptation method using non-uniform rational B-spline surface modeling
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, B. K.
1992-01-01
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.
Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2012-09-01
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.
K. Wright
1970-01-01
In this paper relationships between various one-step methods for the initial value problem in ordinary differential equations are discussed and a unified treatment of the stability properties of the methods is given. The analysis provides some new results on stability as well as alternative derivations for some known results. The term stability is used in the sense ofA-Stability as introduced
Quirós, Elia; Felicísimo, Ángel M.; Cuartero, Aurora
2009-01-01
This work proposes a new method to classify multi-spectral satellite images based on multivariate adaptive regression splines (MARS) and compares this classification system with the more common parallelepiped and maximum likelihood (ML) methods. We apply the classification methods to the land cover classification of a test zone located in southwestern Spain. The basis of the MARS method and its associated procedures are explained in detail, and the area under the ROC curve (AUC) is compared for the three methods. The results show that the MARS method provides better results than the parallelepiped method in all cases, and it provides better results than the maximum likelihood method in 13 cases out of 17. These results demonstrate that the MARS method can be used in isolation or in combination with other methods to improve the accuracy of soil cover classification. The improvement is statistically significant according to the Wilcoxon signed rank test. PMID:22291550
Dolin, R.M.
1985-08-01
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.
Duong Pham; Thanh Tran
We present an overlapping domain decomposition technique for solving the hypersingular integral equation on the sphere with\\u000a spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O(H\\/?), where H is the size of the coarse mesh and ? is the overlap size, which is chosen to be proportional to the size of the
Multivariate Adaptive Regression Splines
Jerome H. Friedman
1991-01-01
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
Interchangeable spline reference guide
Dolin, R.M.
1994-05-01
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.
Number systems, ?-splines and refinement
NASA Astrophysics Data System (ADS)
Zube, Severinas
2004-12-01
This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case ?=1+i, we prove better results. We introduce ?-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of ?-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of ?-splines to subdivision with several examples. It turns out that ?-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of ?-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of ?-splines: partition of unity and the refinement equation.
NASA Technical Reports Server (NTRS)
Vranish, John M. (inventor)
1993-01-01
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.
December 13, 1997 Convergence Order Estimates of Meshless Collocation
Schaback, Robert
December 13, 1997 Convergence Order Estimates of Meshless Collocation Methods using Radial Basis@math.uni-goettingen.de We study meshless collocation methods using radial basis functions to approximate regular solutions of the emerging meshless methods, cf. 1]. Its range of application is not con- ned to elliptic problems. However
Monotone and convex quadratic spline interpolation
NASA Technical Reports Server (NTRS)
Lam, Maria H.
1990-01-01
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.
Regularization of B-Spline Objects*
Xu, Guoliang; Bajaj, Chandrajit
2010-01-01
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. PMID:21218183
A Collocational Dictionary of Russian.
ERIC Educational Resources Information Center
Benson, Morton
1989-01-01
Describes an adequate collocational dictionary for learners of Russian. Recommendations are made regarding what should and should not be included in a collocational dictionary, and a discussion looks at under which headwords collocations should be entered in the dictionary. (44 references) (GLR)
Estimation of divergence and vorticity using multidimensional smoothing splines
NASA Technical Reports Server (NTRS)
Wendelberger, J. G.
1982-01-01
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.
Results on Meshless Collocation Techniques , and R. Schaback
Schaback, Robert
Results on Meshless Collocation Techniques L. Ling , R. Opfer , and R. Schaback , March 15, 2004 applications, there were no proven results so far on the unsymmetric meshless collocation method for solvingÂdependent meshless selection of the test and trial spaces. 1 Introduction The general idea for solving PDE problems
NASA Astrophysics Data System (ADS)
Mohd Fauzi, Norizyan Izzati; Sulaiman, Jumat
2013-04-01
The aim of this paper is to describe the application of Quarter-Sweep Gauss-Seidel (QSGS) iterative method using quadratic spline scheme for solving fourth order two-point linear boundary value problems. In the line to derive approximation equations, firstly the fourth order problems need to be reduced onto a system of second-order two-point boundary value problems. Then two linear systems have been constructed via discretization process by using the corresponding quarter-sweep quadratic spline approximation equations. The generated linear systems have been solved using the proposed QSGS iterative method to show the superiority over Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods. Computational results are provided to illustrate that the effectiveness of the proposed QSGS method is more superior in terms of computational time and number of iterations as compared to other tested methods.
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method
NASA Astrophysics Data System (ADS)
Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Düster, Alexander; Rank, Ernst
2012-10-01
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.
The L2Polynomial Spline Pyramid
Michael Unser; Akram Aldroubi; Murray Eden
1993-01-01
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
Smoothing noisy data with spline functions
Peter Craven; Grace Wahba
1978-01-01
Summary Smoothing splines are well known to provide nice curves which smooth discrete, noisy data. We obtain a practical, effective method for estimating the optimum amount of smoothing from the data. Derivatives can be estimated from the data by differentiating the resulting (nearly) optimally smoothed spline.
Cubic splines for image interpolation and digital filtering
Hsieh Hou; H. C. Andrews
1978-01-01
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
Wu, Hulin; Xue, Hongqi; Kumar, Arun
2012-06-01
Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. PMID:22376200
Interpolating splines with local tension, continuity, and bias control
Doris H. U. Kochanek; Richard H. Bartels
1984-01-01
This paper presents a new method for using cubic interpolating splines in a key frame animation system. Three control parameters allow the animator to change the tension, continuity, and bias of the splines. Each of these three parameters can be used for either local or global control. Our technique produces a very general class of interpolating cubic splines which includes
Shape Preserving Spline Interpolation
NASA Technical Reports Server (NTRS)
Gregory, J. A.
1985-01-01
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.
McCartin, B.J.
1996-12-31
Herein, we discuss a generalization of the semiclassical cubic spline known in the literature as the exponential spline. 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 {open_quotes}tension{close_quotes} parameters. We first outline the theoretical underpinnings of the exponential spline. 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. We next discuss the numerical computation of the exponential spline. 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. We conclude with a consideration of the broad spectrum of possible uses of exponential splines in the applications. Our primary emphasis is on computational fluid dynamics although the imaginative reader will recognize the wider generality of the techniques developed.
Spline approximation of quantile functions
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Matthews, C. G.
1983-01-01
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.
NASA Astrophysics Data System (ADS)
Owusu-Banson, Derek
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.
Ronglin Li; Guangzheng Ni; Jihui Yu; Zejia Jiang
1996-01-01
A new numerical technique is presented for calculating the current distributions on wire antennas with a high degree of curvature. The geometry of the wire antenna is expressed by a parametric equation and the current is directly expanded into a series of quadratic B-spline basis functions of the parameter, so that the truncation error in modeling the curved wire structure
Galerkin-Basis-Spline method for lattice representation of quantum many-particle systems
V. E. Oberacker; D. R. Kegley; A. S. Umar
1997-01-01
Our goal is to represent the Hamiltonian, single-particle wave functions and other observables of quantum many-particle systems on 2-D or 3-D lattices. These lattices may be comprised of either cartesian or curvilinear coordinates, with periodic or fixed boundary conditions. Our computational approach may be thought of as a hybrid method which uses the Galerkin method (global reduction of the residual)
NASA Technical Reports Server (NTRS)
Schiess, James R.; Kerr, Patricia A.; Smith, Olivia C.
1988-01-01
Smooth curves drawn among plotted data easily. Rational-Spline Approximation with Automatic Tension Adjustment algorithm leads to flexible, smooth representation of experimental data. "Tension" denotes mathematical analog of mechanical tension in spline or other mechanical curve-fitting tool, and "spline" as denotes mathematical generalization of tool. Program differs from usual spline under tension, allows user to specify different values of tension between adjacent pairs of knots rather than constant tension over entire range of data. Subroutines use automatic adjustment scheme that varies tension parameter for each interval until maximum deviation of spline from line joining knots less than or equal to amount specified by user. Procedure frees user from drudgery of adjusting individual tension parameters while still giving control over local behavior of spline.
Biomechanical Analysis with Cubic Spline Functions
ERIC Educational Resources Information Center
McLaughlin, Thomas M.; And Others
1977-01-01
Results of experimentation suggest that the cubic spline is a convenient and consistent method for providing an accurate description of displacement-time data and for obtaining the corresponding time derivatives. (MJB)
Miguel F. Paulos
2013-04-22
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 an $n$-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.
SMOOTHING SPLINE GROWTH CURVES WITH COVARIATES
SMOOTHING SPLINE GROWTH CURVES WITH COVARIATES Kurt S. Riedel and Kaya Imre Courant Institute splines, Multivariate analysis, Generalized crossvalidation, Adaptive splines, Fusion physics. ABSTRACT We adapt the interactive spline model of Wahba to growth curves with covariates. The smoothing spline
J. T. CHEN; M. H. CHANG; K. H. CHEN; S. R. LIN
2002-01-01
In this paper, a meshless method for the acoustic eigenfrequencies using radial basis function (RBF) is proposed. The coefficients of influence matrices are easily determined by the two-point functions. In determining the diagonal elements of the influence matrices, two techniques, limiting approach and invariant method, are employed. Based on the RBF in the imaginary-part kernel, the method results in spurious
Li, Xin; Miller, Eric L.; Rappaport, Carey; Silevich, Michael
2000-04-11
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.
Detection of defects on apple using B-spline lighting correction method
NASA Astrophysics Data System (ADS)
Li, Jiangbo; Huang, Wenqian; Guo, Zhiming
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.
NASA Astrophysics Data System (ADS)
Adachi, Junpei; Okubo, Kan; Tagawa, Norio; Tsuchiya, Takao; Ishizuka, Takashi
2013-07-01
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.
Collocating satellite-based radar and radiometer measurements - methodology and usage examples
G. Holl; S. A. Buehler; B. Rydberg; C. Jiménez
2010-01-01
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
Priors for Bayesian adaptive spline smoothing
Yu Ryan Yue; Paul L. Speckman; Dongchu Sun
2012-01-01
Adaptive smoothing has been proposed for curve-fitting problems where the underlying function is spatially inhomogeneous.\\u000a Two Bayesian adaptive smoothing models, Bayesian adaptive smoothing splines on a lattice and Bayesian adaptive P-splines,\\u000a are studied in this paper. Estimation is fully Bayesian and carried out by efficient Gibbs sampling. Choice of prior is critical\\u000a in any Bayesian non-parametric regression method. We use
Image interpolation by multivariate B-splines
Chan, Ki Bun
1986-01-01
two-dimensional interpolation schemes. (2) The grid lines of the support of the B-spline approximant can be varied according to the data point locations. This research also uses the FFT and performs calculations in the spatial frequency domain... of Bivariate B-spline B. Computational Implementation III IMAGE INTERPOLATION 17 A. Comparison Between Interpolating Methods B. Comparison Of The Reconstructed Images C. The Iterative Scheme 17 18 19 IV FOVEAL SPOT APPLICATIONS 34 V APPLICATION OF FFT...
NASA Astrophysics Data System (ADS)
Zhu, W.; Sommar, J.; Lin, C.-J.; Feng, X.
2015-02-01
Dynamic flux chambers (DFCs) and micrometeorological (MM) methods are extensively deployed for gauging air-surface Hg0 gas exchange. However, a systematic evaluation of the precision of the contemporary Hg0 flux quantification methods is not available. In this study, the uncertainty in Hg0 flux measured by relaxed eddy accumulation (REA) method, aerodynamic gradient method (AGM), modified Bowen-ratio (MBR) method, as well as DFC of traditional (TDFC) and novel (NDFC) designs is assessed using a robust data-set from two field intercomparison campaigns. The absolute precision in Hg0 concentration difference (? C) measurements is estimated at 0.064 ng m-3 for the gradient-based MBR and AGM system. For the REA system, the parameter is Hg0 concentration (C) dependent at 0.069+0.022C. 57 and 62% of the individual vertical gradient measurements were found to be significantly different from zero during the campaigns, while for the REA-technique the percentage of significant observations was lower. For the chambers, non-significant fluxes are confined to a few nighttime periods with varying ambient Hg0 concentration. Relative bias for DFC-derived fluxes is estimated to be ~ ±10%, and ~ 85% of the flux bias are within ±2 ng m-2 h-1 in absolute term. The DFC flux bias follows a diurnal cycle, which is largely dictated by temperature controls on the enclosed volume. Due to contrasting prevailing micrometeorological conditions, the relative uncertainty (median) in turbulent exchange parameters differs by nearly a factor of two between the campaigns, while that in ? C measurements is fairly stable. The estimated flux uncertainties for the triad of MM-techniques are 16-27, 12-23 and 19-31% (interquartile range) for the AGM, MBR and REA method, respectively. This study indicates that flux-gradient based techniques (MBR and AGM) are preferable to REA in quantifying Hg0 flux over ecosystems with low vegetation height. A limitation of all Hg0 flux measurement systems investigated is their incapability to obtain synchronous samples for the calculation of ? C. This reduces the precision of flux quantification, particularly the MM-systems under non-stationarity of ambient Hg0 concentration. For future applications, it is recommended to accomplish ? C derivation from simultaneous collected samples.
Meshless Parameterization and B-spline Surface Approximation
Floater, Michael S.
Meshless Parameterization and B-spline Surface Approximation Michael S. Floater1 SINTEF, P.O. Box points in lR3 with smooth B-spline surfaces. The method involves: meshless parameteri- zation method we propose consists of several sequen- tial steps: meshless parameterization; triangulation
NASA Astrophysics Data System (ADS)
M Ali, M. K.; Ruslan, M. H.; Muthuvalu, M. S.; Wong, J.; Sulaiman, J.; Yasir, S. Md.
2014-06-01
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., E-mail: majidkhankhan@ymail.com, E-mail: eutoco@gmail.com; Ruslan, M. H., E-mail: majidkhankhan@ymail.com, E-mail: eutoco@gmail.com [Solar Energy Research Institute (SERI), Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Muthuvalu, M. S., E-mail: sudaram-@yahoo.com, E-mail: jumat@ums.edu.my; Wong, J., E-mail: sudaram-@yahoo.com, E-mail: jumat@ums.edu.my [Unit Penyelidikan Rumpai Laut (UPRL), Sekolah Sains dan Teknologi, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah (Malaysia); Sulaiman, J., E-mail: ysuhaimi@ums.edu.my, E-mail: hafidzruslan@eng.ukm.my; Yasir, S. Md., E-mail: ysuhaimi@ums.edu.my, E-mail: hafidzruslan@eng.ukm.my [Program Matematik dengan Ekonomi, Sekolah Sains dan Teknologi, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah (Malaysia)
2014-06-19
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/m{sup 2} 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 (R{sup 2}), 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.
Multivariate Spline Algorithms for CAGD
NASA Technical Reports Server (NTRS)
Boehm, W.
1985-01-01
Two special polyhedra present themselves for the definition of B-splines: a simplex S and a box or parallelepiped B, where the edges of S project into an irregular grid, while the edges of B project into the edges of a regular grid. More general splines may be found by forming linear combinations of these B-splines, where the three-dimensional coefficients are called the spline control points. Univariate splines are simplex splines, where s = 1, whereas splines over a regular triangular grid are box splines, where s = 2. Two simple facts render the development of the construction of B-splines: (1) any face of a simplex or a box is again a simplex or box but of lower dimension; and (2) any simplex or box can be easily subdivided into smaller simplices or boxes. The first fact gives a geometric approach to Mansfield-like recursion formulas that express a B-spline in B-splines of lower order, where the coefficients depend on x. By repeated recursion, the B-spline will be expressed as B-splines of order 1; i.e., piecewise constants. In the case of a simplex spline, the second fact gives a so-called insertion algorithm that constructs the new control points if an additional knot is inserted.
Supporting Sensemaking during Collocated Collaborative Visual Analytics
Tory, Melanie
Supporting Sensemaking during Collocated Collaborative Visual Analytics by Narges Mahyar B Narges Mahyar, 2014 University of Victoria All rights reserved. This dissertation may not be reproduced Supporting Sensemaking during Collocated Collaborative Visual Analytics by Narges Mahyar B.Sc., Azad
Oceanographic data interpolation: Objective analysis and splines
Peter C. McIntosh
1990-01-01
Two data interpolation methods are reviewed and compared. They are objective analysis (also known as objective mapping, statistical interpolation or Gauss-Markov interpolation), and spline interpolation. The former is a statistical method based on minimizing the interpolation error variance; the latter is a deterministic method which seeks to obtain the smoothest interpolated field consistent with the data. The two methods are
Matuschek, Hannes; Kliegl, Reinhold; Holschneider, Matthias
2015-01-01
The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading. PMID:25816246
Fairing Bicubic B-Spline Surfaces using Simulated Annealing
Hahmann, Stefanie
Fairing Bicubic B-Spline Surfaces using Simulated Annealing Stefanie Hahmann and Stefan Konz Abstract. In this paper we present an automatic fairing algorithm for bicubic B-spline surfaces. The fairing method consists of a knot re- moval and knot reinsertion step which locally smoothes the surface
Mr. Stockdale's Dictionary of Collocations.
ERIC Educational Resources Information Center
Stockdale, Joseph Gagen, III
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…
Interlanguage Development and Collocational Clash
ERIC Educational Resources Information Center
Shahheidaripour, Gholamabbass
2000-01-01
Background: Persian English learners committed mistakes and errors which were due to insufficient knowledge of different senses of the words and collocational structures they formed. Purpose: The study reported here was conducted for a thesis submitted in partial fulfillment of the requirements for The Master of Arts degree, School of Graduate…
Scalar and planar-valued curve fitting using splines under tension
A. K. Cline
1974-01-01
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
Spline-based deformable models
NASA Astrophysics Data System (ADS)
Green, William D. K.
1995-08-01
There are well established techniques for the biomathematical analysis of sets of homologous images with landmarks. These include the construction of the average configuration of landmarks, the statistical analysis of the procrustes residuals of the landmark positions and the averaging of the images themselves. This paper outlines a method of performing similar steps on sets of images with homologous 1D features as well as landmarks. The basis of the method is the expanded and consistent application of the thin-plate spline, a tool already used in the analysis of landmark images.
NASA Technical Reports Server (NTRS)
Schiess, J. R.
1994-01-01
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.
Spline Functions in Data Analysis
Svante Wold
1974-01-01
The use of spline functions in the analysis of empirical two-dimensional data (yi, xi) is described. The definition of spline functions as piecewise polynomials with continuity conditions give them unique properties as empirical function. They can represent any variation of y with x arbitrarily well over wide intervals of x. Furthermore, due to the local properties of the spline functions,
Function Estimation Employing Exponential Splines
NASA Astrophysics Data System (ADS)
Dose, V.; Fischer, R.
2005-11-01
We introduce and discuss the use of the exponential spline family for Bayesian nonparametric function estimation. Exponential splines span the range of shapes between the limiting cases of traditional cubic spline and piecewise linear interpolation. They are therefore particularly suited for problems where both, smooth and rapid function changes occur.
Extracting Terminologically Relevant Collocations in the Translation of Chinese Monograph
Byeong-Kwu Kang; Bao-bao Chang; Yi-rong Chen; Shi-Wen Yu
2005-01-01
This paper suggests a methodology which is aimed to extract the terminologically relevant collocations for translation purposes. Our basic idea is to use a hybrid method which combines the statistical method and linguistic rules. The extraction system used in our work operated at three steps: (1) Tokenization and POS tagging of the corpus; (2) Extraction of multi-word units using statistical
Siefert, Andrew W.; Icenogle, David A.; Rabbah, Jean-Pierre; Saikrishnan, Neelakantan; Rossignac, Jarek; Lerakis, Stamatios; Yoganathan, Ajit P.
2013-01-01
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. PMID:23460042
Collocating satellite-based radar and radiometer measurements - methodology and usage examples.
NASA Astrophysics Data System (ADS)
Holl, G.; Buehler, S. A.; Rydberg, B.; Jiménez, C.
2010-05-01
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.
{L(1}) Control Theoretic Smoothing Splines
NASA Astrophysics Data System (ADS)
Nagahara, Masaaki; Martin, Clyde F.
2014-11-01
In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1 optimality, that is, we use the L1 norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.
Smoothing spline primordial power spectrum reconstruction
Carolyn Sealfon; Licia Verde; Raul Jimenez
2005-11-01
We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with WMAP first-year data that the PPS deviates from Harrison-Zeldovich and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.
Smoothing spline primordial power spectrum reconstruction
Sealfon, Carolyn; Verde, Licia; Jimenez, Raul [Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
2005-11-15
We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with Wilkinson Microwave Anisotropy Probe first-year data that the PPS deviates from a Harrison-Zeldovich spectrum and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.
SURVIVAL ESTIMATION USING SPLINES
A non parametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. t approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. pecial case is that proposed by...
Christian H. Reinsch
1967-01-01
During the last years, spline functions have found widespread application, mainly for the purpose of interpolation []. However, there may be a demand to replace strict interpolation by some kind of smoothing. Usually, such a situation occurs if the values of the ordinates are given only approximately, for example if they stem from experimental data. In the case in which,
Numerical Solution of Elliptic Boundary Value Problems by Spline Functions
Shah, Jayant M.
1968-04-01
A numerical method for solving linear, two-dimensional elliptic boundary value problems is presented. The method is essentially the Ritz procedure which uses; polynomial spline functions to approximate the exact solution. ...
Solving the Laplace Equation by Meshless Collocation Using Harmonic Kernels
Schaback, Robert
Solving the Laplace Equation by Meshless Collocation Using Harmonic Kernels Robert Schaback February 13, 2008 Abstract We present a meshless technique which can be seen as an alter- native, and there is a fairly general and complete error analysis using standard techniques from meshless methods
Time Domain BEM: Numerical Aspects of Collocation and Galerkin Formulations
Cirak, Fehmi
Time Domain BEM: Numerical Aspects of Collocation and Galerkin Formulations Martin Schanz, Thomas R Method (BEM) in time domain is especially important to treat wave propagation problems in semi BEM but very often the main motivation as, e.g., in earthquake engineering. The first boundary
Multidimensional Elastic Registration of Images Using Splines
Jan Kybic; Michael Unser
2000-01-01
We present an algorithm for nonlinear multidimensionalregistration. The correspondence function isrepresented in a spline space. We also use the cubic splinesto interpolate the volumetric data to be registered. We usea multiresolution strategy, which gives us robustness andadditional speedup. We analyze the computational complexityof the algorithm and its performance using di#erentmultidimensional optimization methods. Finally, we presentan application of the algorithm for
Cartesian spline interpolation for industrial robots
Thomas Horsch; Bert Jüttler
1998-01-01
We describe an algorithm for interpolation of positions by a rational spline motion. A reparameterization of the resulting motion is applied in order to achieve the desired distribution of the velocity. For the ease of presentation we discuss trapezoidal velocity profiles, i.e. piecewise constant and linear velocity distribution. The method can be generalized to more general velocity profiles. The whole
WFSFIT. Wilson-Fowler Spline Fit Algorithm
Fritsch, F [Lawrence Livermore National Lab, CA (United States)
1992-01-01
WFSFIT is a legacy algorithm introduced in the early 1960`s for passing a smooth curve through a planar set of design points. WFSFIT predates b-spline methods, but is still used in some numeric control systems, e.g. APT.
DISCOUNT CURVE ESTIMATION BY MONOTONIZING MCCULLOCH SPLINES
HOLGER DETTE; DANIEL ZIGGEL
2008-01-01
In this paper a new method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) McCulloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the
A Localized Tau Method PDE Solver
NASA Technical Reports Server (NTRS)
Cottam, Russell
2002-01-01
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.
Curve fitting and fairing using conic splines
Xunnian Yang
2004-01-01
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
SMOOTHING SPLINE GROWTH CURVES WITH COVARIATES
SMOOTHING SPLINE GROWTH CURVES WITH COVARIATES Kurt S. Riedel and Kaya Imre #3; Courant Institute splines, Multivariate analysis, Generalized crossvalidation, Adaptive splines, Fusion physics. ABSTRACT We adapt the interactive spline model of Wahba to growth curves with covariates. The smoothing spline
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
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.
Spline screw payload fastening system
NASA Technical Reports Server (NTRS)
Vranish, John M. (inventor)
1993-01-01
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.
Covariance modeling in geodetic applications of collocation
NASA Astrophysics Data System (ADS)
Barzaghi, Riccardo; Cazzaniga, Noemi; De Gaetani, Carlo; Reguzzoni, Mirko
2014-05-01
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.
NASA Technical Reports Server (NTRS)
Fang, Ming; Bowin, Carl
1992-01-01
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.
Fitting multidimensional splines using statistical variable selection techniques
NASA Technical Reports Server (NTRS)
Smith, P. L.
1982-01-01
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.
Integral resonant control of collocated smart structures
Sumeet S. Aphale; Andrew J. Fleming; S. O. Reza Moheimani
2007-01-01
This paper introduces integral resonant control, IRC, a simple, robust and well-performing technique for vibration control in smart structures with collocated sensors and actuators. By adding a direct feed-through to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. It is shown that this modification permits
Integral control of collocated smart structures
Sumeet S. Aphale; Andrew J. Fleming; S. O. Reza Moheimani
2007-01-01
This paper introduces a simple and robust technique for vibration control in smart structures with collocated sensors and actuators. The technique is called Integral Resonant Control (IRC). We show that by adding a direct feed-through to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. This
Validation of significant wave height product from Envisat ASAR using triple collocation
NASA Astrophysics Data System (ADS)
Wang, H.; Shi, C. Y.; Zhu, J. H.; Huang, X. Q.; Chen, C. T.
2014-03-01
Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height. Traditionally, validation of SAR derived ocean wave height has been carried out against buoy measurements or model outputs, which only yield a inter-comparison, but not an 'absolute' validation. In this study, the triple collocation error model has been introduced in the validation of Envisat ASAR level 2 data. Significant wave height data from ASAR were validated against in situ buoy data, and wave model hindcast results from WaveWatch III, covering a period of six years. The impact of the collocation distance on the error of ASAR wave height was discussed. From the triple collocation validation analysis, it is found that the error of Envisat ASAR significant wave height product is linear to the collocation distance, and decrease with the decreasing collocation distance. Using the linear regression fit method, the absolute error of Envisat ASAR wave height was obtained with zero collocation distance. The absolute Envisat ASAR wave height error of 0.49m is presented in deep and open ocean from this triple collocation validation work.
C1 Hermite shape preserving polynomial splines in R3
NASA Astrophysics Data System (ADS)
Gabrielides, Nikolaos C.
2012-06-01
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.
Surface deformation over flexible joints using spline blending techniques
NASA Astrophysics Data System (ADS)
Haavardsholm, Birgitte; Bratlie, Jostein; Dalmo, Rune
2014-12-01
Skinning over a skeleton joint is the process of skin deformation based on joint transformation. Popular geometric skinning techniques include implicit linear blending and dual quaternions. Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended by Ck-smooth basis functions. A smooth skinning surface can be constructed over a transformable skeleton joint by combining various types of local surface constructions and applying local Hermite interpolation. Compared to traditional spline methods, increased flexibility and local control with respect to surface deformation can be achieved using the GERBS blending construction. We present a method using a blending-type spline surface for skinning over a flexible joint, where local geometry is individually adapted to achieve natural skin deformation based on skeleton transformations..
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
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.
Mathematical research on spline functions
NASA Technical Reports Server (NTRS)
Horner, J. M.
1973-01-01
One approach in spline functions is to grossly estimate the integrand in J and exactly solve the resulting problem. If the integrand in J is approximated by Y" squared, the resulting problem lends itself to exact solution, the familiar cubic spline. Another approach is to investigate various approximations to the integrand in J and attempt to solve the resulting problems. The results are described.
Monotone Regression Splines in Action
J. O. Ramsay
1988-01-01
Piecewise polynomials or splines extend the advantages of polynomials to include greater flexibility, local effects of parameter changes and the possibility of imposing useful constraints on estimated functions. Among these constraints is monotonicity, which can be an important property in many curve estimation problems. This paper shows the virtues of monotone splines through a number of statistical applications, including response
Using parametric {ital B} splines to fit specular reflectivities
Berk, N.F.; Majkrzak, C.F. [Materials Science and Engineering Laboratory, National Insitute of Standards and Technology, Gaithersburg, Maryland 20899-0001 (United States)] [Materials Science and Engineering Laboratory, National Insitute of Standards and Technology, Gaithersburg, Maryland 20899-0001 (United States)
1995-05-01
Parametric {ital B}-spline curves offer a flexible and appropriate mathematical description of scattering length density profiles in specular reflectivity analysis. Profiles combining smooth and sharp features can be defined in low dimensional representations using control points in the density-depth plane which provide graded local influence on profile shape. These profiles exist in vector spaces defined by {ital B}-spline order and parameter knot set, which can be systematically densified during analysis. Such profiles can easily be rendered as adaptive histograms for reflectivity computation. {ital B}-spline order can be chosen to accommodate the asymptotic (large-{ital Q}) behavior indicated by reflectivity data. We describe an interactive fitting strategy in which the Nelder and Mead simplex method is used in the {ital B}-spline control point space to guide the discovery of profiles that can produce given reflectivity data. Examples using actual and simulated spectra are discussed.
Self-Aligning, Spline-Locking Fastener
NASA Technical Reports Server (NTRS)
Vranish, John M.
1992-01-01
Self-aligning, spline-locking fastener is two-part mechanism operated by robot, using one tool and simple movements. Spline nut on springloaded screw passes through mating spline fitting. Operator turns screw until vertical driving surfaces on spline nut rest against corresponding surfaces of spline fitting. Nut rides upward, drawing pieces together. Used to join two parts of structure, to couple vehicles, or to mount payload in vehicle.
Fragment-based Evaluation of Non-Uniform B-spline Surfaces on GPUs
Takashi Kanai
2007-01-01
In this paper, we propose a fragment-based evaluation method for non-uniform B-spline surfaces using recent programmable graphics hardware (GPU). A position on a non-uniform B-spline surface is evaluated by the linear combination of both control points and B-spline basis functions. Hence the computational costs can be reduced by pre-computing a knot interval of a parameter from a knot vector. We
Spline-interpolation solution of 3D Dirichlet problem for one class of solids
Pyotr Ivanshin; Elena Shirokova
2011-03-20
We present the spline-interpolation approximate solution of the Dirichlet problem for the Laplace equation in the bodies of revolution, cones and cylinders. Our method is based on reduction of the 3D problem to the sequence of 2D Dirichlet problems. The main advantage of the spline-interpolation solution of the 3D Dirichlet problem is its continuity in the whole domain up to the boundary even for the case of the linear spline.
Multilingual collocation extraction with a syntactic parser
Violeta Seretan; Eric Wehrli
2009-01-01
An impressive amount of work was devoted over the past few decades to collocation extraction. The state of the art shows that\\u000a there is a sustained interest in the morphosyntactic preprocessing of texts in order to better identify candidate expressions;\\u000a however, the treatment performed is, in most cases, limited (lemmatization, POS-tagging, or shallow parsing). This article\\u000a presents a collocation extraction
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.
2013-12-01
This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior. The local collocation of the PDE governing operator allows the method to operate on centred stencils in the presence of strong convective fields; the reconstruction weights assigned to nodes in the stencils being automatically adjusted to represent the flow of information as dictated by the problem physics. This "implicit upwinding" effect mitigates the need for ad-hoc upwinding stencils in convective dominant problems. Boundary conditions are also enforced within the local collocation systems, allowing arbitrary boundary operators to be imposed naturally within the solution construction. The performance of the method is assessed using a large number of numerical examples with two steady PDEs; the convection-diffusion equation, and the Lamé-Navier equations for linear elasticity. The method exhibits high-order convergence in each case tested (greater than sixth order), and the use of centred stencils is demonstrated for convective-dominant problems. In the case of linear elasticity, the stress fields are reproduced to the same degree of accuracy as the displacement field, and exhibit the same order of convergence. The method is also highly stable towards variations in basis function flatness, demonstrating significantly improved stability in comparison to finite-difference type RBF collocation methods.
Locating CVBEM collocation points for steady state heat transfer problems
Hromadka, T.V., II
1985-01-01
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.
A Two-Timescale Discretization Scheme for Collocation
NASA Technical Reports Server (NTRS)
Desai, Prasun; Conway, Bruce A.
2004-01-01
The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.
Quadratic spline subroutine package
Rasmussen, L.A.
1982-01-01
A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)
Parametric Curves parametric curves (Splines)
Treuille, Adrien
curves (Splines) Â· polygonal meshes #12;2 Roller coaster Â· Next programming assignment involves creating a 3D roller coaster animation Â· We must model the 3D curve describing the roller coaster, but how
NASA Technical Reports Server (NTRS)
Stacy, J. E.
1984-01-01
Asymmetric spline surfaces appear useful for the design of high-quality general optical systems (systems without symmetries). A spline influence function defined as the actual surface resulting from a simple perturbation in the spline definition array shows that a subarea is independent of others four or more points away. Optimization methods presented in this paper are used to vary a reflective spline surface near the focal plane of a decentered Schmidt-Cassegrain to reduce rms spot radii by a factor of 3 across the field.
NASA Astrophysics Data System (ADS)
Gutierrez, Ronald R.; Abad, Jorge D.; Parsons, Daniel R.; Best, James L.
2013-09-01
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.
Grigorenko, Ya.M.; Kryukov, N.N.; Ivanova, Yu.I. [S.P. Timoshenko Institute of Mechanics, Kiev (Ukraine)
1995-10-01
Spline functions have come into increasingly wide use recently in the solution of boundary-value problems of the theory of elasticity of plates and shells. This development stems from the advantages offered by spline approximations compared to other methods. Among the most important advantages are the following: (1) the behavior of the spline in the neighborhood of a point has no effect on the behavior of the spline as a whole; (2) spline interpolation converges well compared to polynomial interpolation; (3) algorithms for spline construction are simple and convenient to use. The use of spline functions to solve linear two-dimensional problems on the stress-strain state of shallow shells and plates that are rectangular in plan has proven their efficiency and made it possible to expand the range of problems that can be solved. The approach proposed in these investigations is based on reducing a linear two-dimensional problem to a unidimensional problem by the spline unidimensional problem by the method of discrete orthogonalization in the other coordinate direction. Such an approach makes it possible to account for local and edge effects in the stress state of plates and shells and obtain reliable solutions with complex boundary conditions. In the present study, we take the above approach, employing spline functions to solve linear problems, and use it to also solve geometrically nonlinear problems of the statics of shallow shells and plates with variable parameters.
Multidimensional spline integration of scattered data
Gergely Endrodi
2011-03-01
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing the deviation between its derivatives and the measured gradient. Unlike a multidimensional integration along some path, the present method results in a continuous, smooth surface, furthermore, it also applies to input data that are non-equidistant and not aligned on a rectangular grid. Function values, first and second derivatives and integrals are easy to calculate. The proper estimation of the statistical and systematical errors is also incorporated in the method.
ERIC Educational Resources Information Center
Wolter, Brent; Gyllstad, Henrik
2013-01-01
This study investigated the influence of frequency effects on the processing of congruent (i.e., having an equivalent first language [L1] construction) collocations and incongruent (i.e., not having an equivalent L1 construction) collocations in a second language (L2). An acceptability judgment task was administered to native and advanced…
Mars Mission Optimization Based on Collocation of Resources
NASA Technical Reports Server (NTRS)
Chamitoff, G. E.; James, G. H.; Barker, D. C.; Dershowitz, A. L.
2003-01-01
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.
Triangle Mesh Compression using B-Spline Curves
We present a new method to compress triangle meshes in a lossless manner. Triangle compression requires compression of the geometry (vertices) as well as the topology (connectivity). The method is loosely based on the Edgebreaker algorithm by Rossignac et al. in the sense that the traversal of the mesh is done the same way during compression. We use B-Spline curves to store, compute and predict the geometry or the vertices. We do not need to store the connectivity in our method unlike Edgebreaker. The resulting compressed files are roughly 10 % smaller than that from Edgebreaker. Keywords: Triangle compression, B-Spline curves. 1
Connecting the Dots Parametrically: An Alternative to Cubic Splines.
ERIC Educational Resources Information Center
Hildebrand, Wilbur J.
1990-01-01
Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)
ERIC Educational Resources Information Center
Woods, Carol M.; Thissen, David
2006-01-01
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…
Results of laser ranging collocations during 1983
NASA Technical Reports Server (NTRS)
Kolenkiewicz, R.
1984-01-01
The objective of laser ranging collocations is to compare the ability of two satellite laser ranging systems, located in the vicinity of one another, to measure the distance to an artificial Earth satellite in orbit over the sites. The similar measurement of this distance is essential before a new or modified laser system is deployed to worldwide locations in order to gather the data necessary to meet the scientific goals of the Crustal Dynamics Project. In order to be certain the laser systems are operating properly, they are periodically compared with each other. These comparisons or collocations are performed by locating the lasers side by side when they track the same satellite during the same time or pass. The data is then compared to make sure the lasers are giving essentially the same range results. Results of the three collocations performed during 1983 are given.
Technology Transfer Automated Retrieval System (TEKTRAN)
In the US, regional air quality compliance with national ambient air quality standards (NAAQS) for PM10 is based on concentration measurements taken by federal reference method (FRM) PM10 samplers. The EPA specifies the performance characteristics of the FRM PM10 sampler by defining ranges for the p...
History of the Wilson-Fowler spline
Fritsch, F.N.
1986-04-01
The Wilson-Fowler spline (abbreviated WF-spline) was introduced in the early 1960's as a means for drawing a smooth curve through a planar set of data. It has been used as the spline entity in the APT system's TABCYL since its inception. The history of the WF-spline is briefly described and a chronologically arranged annotated bibliography of all known references to it are featured. 6 refs.
Curvature continuous spline surfaces over irregular meshes
Jörg Peters
1996-01-01
Concepts and techniques for the construction of smooth surfaces over irregular meshes are developed and made concrete by defining curvature continuous splines based on 3-sided patches. These splines extend the B-spline paradigm for the construction of parametric piecewise polynomial surfaces to control meshes with nonquadrilateral cells and more or fewer than four cells meeting at a point. Mesh points serve
Refinability of splines derived from regular tessellations
Peters, JÃ¶rg
,1,2 H (b) half-scaled hex-tiling Figure 1: (a) Splines by convolution of the hexagonal Voronoi cell (http://bigwww.epfl.ch/demo/hexsplines) (b) Non-nesting of the hex parti- tion in Example 1-product and box splines. Among the many non- refinable constructions are hex-splines and their generalization
Properties of the Wilson-Fowler spline
Emery, J.D.
1982-07-01
The Wilson-Fowler spline, a piecewise cubic curve with continuous tangent and curvature, is described. The spline is used in the APT numerical machining program and several CAD-CAM systems. This report gives information on existence, uniqueness, invariance properties, and gives some comparison with other spline types. Fortran subroutines are included.
Smooth spline surfaces over irregular meshes
Charles T. Loop
1994-01-01
An algorithm for creating smooth spline surfaces over irregular meshes is presented. The algorithm is a generalization of quadratic B-splines; that is, if a mesh is (locally) regular, the resulting surface is equivalent to a B-spline. Otherwise, the resulting surface has a degree 3 or 4 parametric polynomial representation. A construction is given for representing the surface as a collection
Various collocated circular loop antennas: theory, analysis and design
Li Le-Wei; Leong Mook-Sengl; S. Krishnan
2004-01-01
Collocated circular loops form an important class of antenna structures with potential for use in direction-finding and many other applications. In this paper, a general formulation for analyzing a set of arbitrarily oriented circular loops is first presented. The formulation is then used to analyze various collocated loop configurations. In particular, collocated orthogonal and skewed loops are discussed. Two new
Gauging the Effects of Exercises on Verb-Noun Collocations
ERIC Educational Resources Information Center
Boers, Frank; Demecheleer, Murielle; Coxhead, Averil; Webb, Stuart
2014-01-01
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…
Corpus-Based versus Traditional Learning of Collocations
ERIC Educational Resources Information Center
Daskalovska, Nina
2015-01-01
One of the aspects of knowing a word is the knowledge of which words it is usually used with. Since knowledge of collocations is essential for appropriate and fluent use of language, learning collocations should have a central place in the study of vocabulary. There are different opinions about the best ways of learning collocations. This study…
Analysis of Pairwise Preference Data Using Integrated B-SPLINES.
ERIC Educational Resources Information Center
Winsberg, Suzanne; Ramsay, James O.
1981-01-01
A general method of scaling pairwise preference data is presented that may be used without prior knowledge about the nature of the relationship between an observation and the process giving rise to it. The method involves a monotone transformation and is similar to the B-SPLINE approach. (Author/JKS)
Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture
NASA Technical Reports Server (NTRS)
Desai, Prasun N.; Conway, Bruce A.
2005-01-01
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.
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2012 CFR
2012-10-01
...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;...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2011 CFR
2011-10-01
...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;...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2014 CFR
2014-10-01
...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;...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2013 CFR
2013-10-01
...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;...
47 CFR 51.323 - Standards for physical collocation and virtual collocation.
Code of Federal Regulations, 2010 CFR
2010-10-01
...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;...
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
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
The computation of Laplacian smoothing splines with examples
NASA Technical Reports Server (NTRS)
Wendelberger, J. G.
1982-01-01
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.
Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline
NASA Astrophysics Data System (ADS)
Wang, Wenyan; Zhang, Yongjie; Xu, Guoliang; Hughes, Thomas J. R.
2012-07-01
This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To construct a gap-free T-spline, templates are designed for each type of node and applied to elements in the input mesh. In the geometry stage, an efficient surface fitting technique is developed to improve the surface accuracy with sharp feature preservation. The constructed T-spline surface and solid T-spline interpolate every boundary node in the input mesh, with C 2-continuity everywhere except the local region around irregular nodes. Finally, a Bézier extraction technique is developed and linear independence of the constructed T-splines is studied to facilitate T-spline based isogeometric analysis.
Smoothing Strange Attractors Using Splines
Junheng Luo; Dominique Thiebaut
1995-12-31
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical and experimental data. It is linear in complexity, and can be applied to embeddings of any dimension.
Spline-Based Image Registration
Richard Szeliski; James Coughlan
1997-01-01
Abstract. The problem of image registration subsumes a number of problems and techniques in multiframe image analysis, including the computation of optic flow (general pixel-based motion), stereo correspondence, structure from motion, and feature tracking. We present a new registration algorithm based on spline representations of the displacement field which can be specialized to solve all of the above mentioned problems.
Spline Approximation of Thin Shell Dynamics
NASA Technical Reports Server (NTRS)
delRosario, R. C. H.; Smith, R. C.
1996-01-01
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.
Accuracy and speed in computing the Chebyshev collocation derivative
NASA Technical Reports Server (NTRS)
Don, Wai-Sun; Solomonoff, Alex
1991-01-01
We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.
NASA Astrophysics Data System (ADS)
Meyer, Daniel W.; Müller, Florian; Jenny, Patrick
2014-05-01
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.
Generalized T-splines and VMCR T-meshes
NASA Astrophysics Data System (ADS)
Bracco, Cesare; Cho, Durkbin
2014-10-01
The paper considers the extension of the T-spline approach to the Generalized B-splines (GB-splines), a relevant class of non-polynomial splines. The Generalized T-splines (GT-splines) are based both on the framework of classical polynomial T-splines and on the Trigonometric GT-splines (TGT-splines), a particular case of GT-splines. Our study of GT-splines introduces a class of T-meshes (named VMCR T-meshes) for which both the corresponding GT-splines and the corresponding polynomial T-splines are linearly independent. A practical characterization can be given for a sub-class of VMCR T-meshes, which we refer to as weakly dual-compatible T-meshes, which properly includes the class of dual-compatible (equivalently, analysis-suitable) T-meshes for an arbitrary (polynomial) order.
Spline interpolation techniques applied to the study of geophysical data
NASA Astrophysics Data System (ADS)
Mariani, Maria C.; Basu, Kanadpriya
2015-06-01
This work is devoted to the study of geophysical data by using different spline interpolation techniques. A spatial analysis of the California earthquakes geological data was performed, some of the methods proved to be more efficient than others depending on the number of data points considered. Overall, this class of interpolation surface proved to be a very powerful tool for analyzing geophysical data.
Discount curve estimation by monotonizing McCulloch Splines
Holger Dette; Daniel Ziggel
2006-01-01
In this paper a new and very simple method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) Mc-Culloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the
Daly, Don S.; Anderson, Kevin K.; White, Amanda M.; Gonzalez, Rachel M.; Varnum, Susan M.; Zangar, Richard C.
2008-07-14
Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensity that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting, and reliably estimates believable prediction errors. For the 50% of the real data sets fit well by both methods, spline and logistic predictions are practically indistinguishable, varying in accuracy by less than 15%. The spline method may be useful when automated prediction across simultaneous assays of numerous proteins must be applied routinely with minimal user intervention.
Spline interpolation on networks
Hisamoto Hiyoshi
2010-01-01
So far, spatial data analysis methods have been designed and developed mainly for manifold-like spaces such as the Euclidean\\u000a plane. Recently, spatial data analysis methods for networks, called network spatial methods, have been gaining attentions\\u000a since they are convenient for micro-scale analysis. In this paper, interpolation methods over networks are explored. Shiode\\u000a extended the inverse distance-weighted method to networks, compared
NASA Astrophysics Data System (ADS)
Kuczy?ski, Pawe?; Bia?ecki, Ryszard
2014-06-01
The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD). The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS) surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.
Examination of the Circle Spline routine
Dolin, R.M.; Jaeger, D.L.
1985-11-01
The Circle Spline routine is a library file with several subroutines, which can generate splines in two and three dimensions. By using two programs, FUNCTION and CSPLINE, we generated data points, output a data file, and produced a series of blended arcs linking data points. The insertion of the proper number of subpoints allows the blending of two arcs into one spline segment. Up to the critical number of subpoints, the accuracy and smoothness of the spline increased as more subpoints were used. Experiments revealed, however, that the blending process began to develop errors if too many subpoints were used and that persistent errors developed in cases of extreme variation of curvature (as in a cigar-shaped ellipse). The Circle Spline routine generally compares favorably with the Wilson-Fowler routine, the current DOE-NWC standard spline routine.
ERIC Educational Resources Information Center
Chatpunnarangsee, Kwanjira
2013-01-01
The purpose of this study is to explore ways of incorporating web-based concordancers for the purpose of teaching English collocations. A mixed-methods design utilizing a case study strategy was employed to uncover four specific dimensions of corpus use by twenty-four students in two classroom sections of a writing course at a university in…
Larry C. Young; Bruce A. Finlayson
1976-01-01
The orthogonal collocation method is applied to solve the mathematical model of a monolith catalytic converter, in which the reaction takes place in a porous catalytic layer deposited on the wall of a tube. A sequence of models is developed, with the most complicated one involving transient heat and mass transfer in three dimensions.
Technology Transfer Automated Retrieval System (TEKTRAN)
Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in heat production, or energy expenditure (EE). Multivariate adaptive regression splines (MARS), is a nonparametric method that estimates complex nonlinear relationships by a seri...
Improved Spline Coupling For Robotic Docking
NASA Technical Reports Server (NTRS)
Vranish, John M.
1995-01-01
Robotic docking mechanism like one described in "Self-Aligning Mechanical and Electrical Coupling" (GSC-13430) improved. Spline coupling redesigned to reduce stresses, enchancing performance and safety of mechanism. Does not involve significant increase in size. Convex spherical surfaces on spline driver mate with concave spherical surfaces on undersides on splines in receptacle. Spherical surfaces distribute load stresses better and tolerate misalignments better than flat and otherwise shaped surfaces.
Spline screw multiple rotations mechanism
NASA Technical Reports Server (NTRS)
Vranish, John M. (inventor)
1993-01-01
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.
Reconstruction from contour lines based on bi-cubic Bézier spline surface
Zhong Li; Li-zhuang Ma; Wu-zheng Tan; Ming-xi Zhao
2006-01-01
A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points\\u000a on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different contours,\\u000a we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic
Geometry modeling of ship hull based on non-uniform B-spline
Hu Wang; Zao-jian Zou
2008-01-01
In order to generate the three-dimensional (3-D) hull surface accurately and smoothly, a mixed method which is made up of\\u000a non-uniform B-spline together with an iterative procedure was developed. By using the iterative method the data points on\\u000a each section curve are calculated and the generalized waterlines and transverse section curves are determined. Then using\\u000a the non-uniform B-spline expression, the
Curve fitting and modeling with splines using statistical variable selection techniques
NASA Technical Reports Server (NTRS)
Smith, P. L.
1982-01-01
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.
Moving Surface Spline Interpolation Based on Green’s Function
Xingsheng Deng; Zhong-an Tang
2011-01-01
Some commonly used interpolation algorithms are analyzed briefly in this paper. Among all of the methods, biharmonic spline\\u000a interpolation, which is based on Green’s function and proposed by Sandwell, has become the mainstream method for its high\\u000a precision, simplicity and flexibility. However, the minimum curvature method has two flaws. First, it suffers from undesirable\\u000a oscillations between data points, which is
Modelling Childhood Growth Using Fractional Polynomials and Linear Splines
Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.
2014-01-01
Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651
NASA Astrophysics Data System (ADS)
Wielgus, Maciek; Patorski, Krzysztof
2014-12-01
We discuss a recently proposed method of the implicit smoothing splines in the context of the interferometric fringe pattern processing. The algorithm extends classic smoothing spline method to the case of the measurements being in some non-trivial functional relation to the estimated distribution, i.e., to the case of the implicitly given data. This is the case of the phase estimation based on the intensity of the related fringe pattern. While there are certain preprocessing complications involved in the application of the implicit smoothing splines, the method offers very accurate continuous (unwrapped) phase estimation and outperforms well-established fringe pattern analysis tools. In this paper we present theoretical background of the implicit smoothing splines as well as numerical results related to their application to the fringe pattern phase estimation problem.
McCurdy, C. William; Martin, Fernando
2003-11-18
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.
Spline Curves, Wire Frames and Bvalue
NASA Technical Reports Server (NTRS)
Smith, L.; Munchmeyer, F.
1985-01-01
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.
Implicit B-spline surface reconstruction.
Rouhani, Mohammad; Sappa, Angel D; Boyer, Edmond
2015-01-01
This paper presents a fast and flexible curve, and surface reconstruction technique based on implicit B-spline. This representation does not require any parameterization and it is locally supported. This fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations. This method is further accelerated to reduce the dimension to the active control lattice. Moreover, the surface smoothness and user interaction are allowed for controlling the surface. Finally, a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions. The whole framework is very fast and efficient and can handle large cloud of points with very low computational cost. The experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies. Comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data. PMID:25373084
Code of Federal Regulations, 2014 CFR
2014-10-01
...Agreement for the Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication...Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal...
Code of Federal Regulations, 2010 CFR
2010-10-01
...Agreement for the Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication...Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal...
Code of Federal Regulations, 2013 CFR
2013-10-01
...Agreement for the Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication...Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal...
Code of Federal Regulations, 2011 CFR
2011-10-01
...Agreement for the Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication...Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal...
Code of Federal Regulations, 2012 CFR
2012-10-01
...Agreement for the Collocation of Wireless Antennas B Appendix B to Part 1 Telecommunication...Agreement for the Collocation of Wireless Antennas Nationwide Programmatic Agreement for the Collocation of Wireless Antennas Executed by the Federal...
Registration of sliding objects using direction dependent B-splines decomposition
NASA Astrophysics Data System (ADS)
Delmon, V.; Rit, S.; Pinho, R.; Sarrut, D.
2013-03-01
Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those interfaces to match. The method was evaluated on 16 lung cancer patients against a single B-spline transform approach and a multi B-spline transforms approach without the sliding constraint at the interface. The target registration error (TRE) was significantly lower with the proposed method (TRE = 1.5 mm) than with the single B-spline approach (TRE = 3.7 mm) and was comparable to the multi B-spline approach without the sliding constraint (TRE = 1.4 mm). The proposed method was also more accurate along region interfaces, with 37% less gaps and overlaps when compared to the multi B-spline transforms without the sliding constraint. This work was presented in part at the 4th International Workshop on Pulmonary Image Analysis during the Medical Image Computing and Computer Assisted Intervention (MICCAI) in Toronto, Canada (2011).
Optimization of Low-Thrust Spiral Trajectories by Collocation
NASA Technical Reports Server (NTRS)
Falck, Robert D.; Dankanich, John W.
2012-01-01
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.
Flexible joint control: Robustness analysis of the collocated and non-collocated feedbacks
D. Alazard; J. P. Chretien
1993-01-01
The robustness and performance properties of a proportional-derivative controller applied to a very flexible joint are discussed. Because of a flexible mode due to in-joint compliance, the classical collocated control does yield good rigid mode dynamics with a correct phase margin in low and high frequency, and noncollocated control does not allow correct damping of the rotor mode. The simultaneous
Group-Lasso on Splines for Spectrum Cartography
NASA Astrophysics Data System (ADS)
Bazerque, Juan Andrés; Mateos, Gonzalo; Giannakis, Georgios B.
2011-10-01
The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finitely-parameterized (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that ``better'' explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Simulated tests corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.
Flexible coiled spline securely joins mating cylinders
NASA Technical Reports Server (NTRS)
Coppernol, R. W.
1966-01-01
Mating cylindrical members are joined by spline to form an integral structure. The spline is made of tightly coiled, high tensile-strength steel spiral wire that fits a groove between the mating members. It provides a continuous bearing surface for axial thrust between the members.
Multivariate Spline Bibliography 21 December 2006
Schumaker, Larry
to the book Splines on Tri- angulations by Ming-Jun Lai and Larry L. Schumaker, Cambridge Uni- versity Press is urged to email us with corrections and or additions (larry.schumaker@vanderbilt.edu). A similar;2 Alaylioglu, A., D. Eyre, M. Brannigan, and J. P. Svenne (1986) Spline-Galerkin solution of integral equations
Smoothing splines: Regression, derivatives and deconvolution
NASA Technical Reports Server (NTRS)
Rice, J.; Rosenblatt, M.
1982-01-01
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.
Multicategorical Spline Model for Item Response Theory.
ERIC Educational Resources Information Center
Abrahamowicz, Michal; Ramsay, James O.
1992-01-01
A nonparametric multicategorical model for multiple-choice data is proposed as an extension of the binary spline model of J. O. Ramsay and M. Abrahamowicz (1989). Results of two Monte Carlo studies illustrate the model, which approximates probability functions by rational splines. (SLD)
Animated face modeling and adaptation with triangular B-spline
Guangyou Xu; Hui Zhang; Qiang Wang
2001-01-01
This paper concentrates on creating individual faces for MPEG4 compliant animation with triangular B-spline. We reconstruct 3D face by adapting a generic face model. A semi-automatic method, which creates human face from Cyberware range and texture dat, and deformation primitive, an auxiliary tool for face editing, are presented. In both tools triangular method more robust to range data errors and
3D Shape Metamorphosis Based on T-spline Level Sets
Huaiping Yang; B. Jilttler
2007-01-01
Summary form only given. We propose a new method for 3D shape metamorphosis, where the in-between objects are constructed by using T-spline scalar functions. The use of T-spline level sets offers several advantages: First, it is convenient to handle complex topology changes without the need of model parameterization. Second, the constructed objects are smooth (C2 in our case). Third, high
3D shape metamorphosis based on T-spline level sets
Huaiping Yang; Bert Jüttler
2007-01-01
We propose a new method for 3D shape meta- morphosis, where the in-between objects are constructed by using T-spline scalar functions. The use of T-spline level sets offers several advantages: First, it is convenient to handle complex topology changes without the need of model parametrization. Second, the constructed objects are smooth (C2 in our case). Third, high quality meshes can
Radial spline assembly for antifriction bearings
NASA Technical Reports Server (NTRS)
Moore, Jerry H. (inventor)
1993-01-01
An outer race carrier is constructed for receiving an outer race of an antifriction bearing assembly. The carrier in turn is slidably fitted in an opening of a support wall to accommodate slight axial movements of a shaft. A plurality of longitudinal splines on the carrier are disposed to be fitted into matching slots in the opening. A deadband gap is provided between sides of the splines and slots, with a radial gap at ends of the splines and slots and a gap between the splines and slots sized larger than the deadband gap. With this construction, operational distortions (slope) of the support wall are accommodated by the larger radial gaps while the deadband gaps maintain a relatively high springrate of the housing. Additionally, side loads applied to the shaft are distributed between sides of the splines and slots, distributing such loads over a larger surface area than a race carrier of the prior art.
An automatic Chinese collocation extraction algorithm based on lexical statistics
Ruifeng Xu; Qin Lu; Yin Li
2003-01-01
We present an automatic Chinese collocation extraction system using lexical statistics and syntactical knowledge. This system extracts collocations from manually segmented and tagged Chinese news corpus in three stages. First, the bidirectional bigram statistical measures, including bidirectional strength and spread, and ?2 test value, are employed to extract candidate two-word pairs. These candidate word pairs are then used to extract
NASA Astrophysics Data System (ADS)
Luo, Kang; Cao, Zhi-Hong; Yi, Hong-Liang; Tan, He-Ping
2014-03-01
A direct collocation meshless (DCM) method with upwind scheme is employed for solving the radiative transfer equation (RTE) for strongly inhomogeneous media. The trial function is constructed by a moving least-squares (MLS) approximation. The upwind scheme is implemented by moving the support domain of MLS approximation to the opposite direction of each streamline. To test computational accuracy and efficiency of the upwind direct collocation meshless (named UPCM) method, various problems in 1-D and 2-D geometries are analyzed. For the comparison, we also present cases of both the DCM method for the first-order RTE (employed by Tan et al. [1]) and the DCM for the MSORTE (a new second-order form of radiative transfer equation proposed by Zhao et al. [2]). The results show that the proposed method is more accurate and stable than the DCM method (no upwinding) based on both the RTE and MSORTE. Computationally, it is also faster.
Yankov, A.; Downar, T. [University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States)
2013-07-01
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)
Rational-spline approximation with automatic tension adjustment
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Kerr, P. A.
1984-01-01
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.
Spline-based procedures for dose-finding studies with active control.
Helms, Hans-Joachim; Benda, Norbert; Zinserling, Jörg; Kneib, Thomas; Friede, Tim
2015-01-30
In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the dose-response relationship and to find the smallest target dose concentration d(*), which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean dose-response function with the expected efficacy of the active control has to be estimated. The focus of this paper is a cubic spline-based method for deriving an estimator of the target dose without assuming a specific dose-response function. Furthermore, the construction of a spline-based bootstrap CI is described. Estimator and CI are compared with other flexible and parametric methods such as linear spline interpolation as well as maximum likelihood regression in simulation studies motivated by a real clinical trial. Also, design considerations for the cubic spline approach with focus on bias minimization are presented. Although the spline-based point estimator can be biased, designs can be chosen to minimize and reasonably limit the maximum absolute bias. Furthermore, the coverage probability of the cubic spline approach is satisfactory, especially for bias minimal designs. PMID:25319931
CNC tool path in terms of B-spline curves
Claire Lartigue; François Thiebaut; Takashi Maekawa
2001-01-01
We present an accurate and efficient method to generate a CNC tool path for a smooth free-form surface in terms of planar cubic B-spline curves which will be fed into a free-form curve interpolator. We assume the use of a three-axis CNC machine tool with a ball end-mill cutter. We first interpolate break points, which are generated by computing the
Spline-based feature curves from point-sampled geometry
Joel Daniels II; Tilo Ochotta; Linh K. Ha; Cláudio T. Silva
2008-01-01
Defining sharp features in a 3D model facilitates a better understanding of the surface and aids geometric processing and\\u000a graphics applications, such as reconstruction, filtering, simplification, reverse engineering, visualization, and non-photo\\u000a realism. We present a robust method that identifies sharp features in a point-based model by returning a set of smooth spline\\u000a curves aligned along the edges. Our feature extraction
Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Capilla, M.; Talavera, C. F.; Ginestar, D. [Dept. of Nuclear Engineering, Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)
2012-07-01
PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)
Comparison between the Wilson-Fowler Spline and the Circle Spline routines
Dolin, R.M.; Oakes, W.R.
1985-11-01
The Nuclear Weapons Complex has used the Wilson-Fowler Spline as its standard curve-fitting routine. This routine can be used effectively only in two dimensions since it requires an unacceptable amount of computer power to be adapted for use in three dimensions due mainly to the extra computations involved with an additional dimension. The Circle Spline routine can be used effectively in both two and three dimensions. Because a standard spline routine should possess the ability to work in two- and three-dimensional space, the Circle Spline routine was compared with the Wilson-Fowler routine to determine which procedure would better approximate a curve. In our experiments the Wilson-Fowler routine was generally smooth and had smaller errors; it handled reverse curvatures well. The Circle Spline had smaller errors at points of extreme curvature and compared favorably with the Wilson-Fowler Spline for most applications. 27 refs., 4 figs.
B-Spline Signal Processing: Part I-Theory
Michael Unser; Akram Aldroubi; Murray Eden
1993-01-01
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
NASA Technical Reports Server (NTRS)
Goldman, R. N.
1985-01-01
Some insight into the properties of beta-splines is gained by applying the techniques of urn models. Urn models are used to construct beta-spline basis functions and to derive the basic properties of these blending functions and the corresponding beta-spline curves. Only the simple notion of linear geometric continuity and with the most elementary beta parameter are outlined. Non-linear geometric continuity leads to additional beta parameters and to more complicated basis functions. Whether urn models can give us any insight into these higher order concepts still remains to be investigated.
Data reduction using cubic rational B-splines
NASA Technical Reports Server (NTRS)
Chou, Jin J.; Piegl, Les A.
1992-01-01
A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.
Analysis of harmonic spline gravity models for Venus and Mars
NASA Technical Reports Server (NTRS)
Bowin, Carl
1986-01-01
Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.
Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers
ERIC Educational Resources Information Center
Chen, Hao-Jan Howard
2011-01-01
The development of adequate collocational knowledge is important for foreign language learners; nonetheless, learners often have difficulties in producing proper collocations in the target language. Among the various ways of learning collocations, the DDL (data-driven learning) approach encourages independent learning of collocations and allows…
Convex Interpolating Splines of Arbitrary Degree
NASA Technical Reports Server (NTRS)
Neuman, E.
1985-01-01
Shape preserving approximations are constructed by interpolating the data with polynomial splines of arbitrary degree. A regularity condition is formulated on the data which insures the existence of such a shape preserving spline, an algorithm is presented for its construction, and the uniform norm of the error is bound which results when the algorithm is used to produce an approximation to a given f epsilon Ca,b.
Single-grid spectral collocation for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte
1988-01-01
The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.
A preliminary harmonic spline model from Magsat data
NASA Technical Reports Server (NTRS)
Shure, L.; Parker, R. L.; Langel, R. A.
1985-01-01
A preliminary main field model for 1980 derived from a carefully selected subset of Magsat vector measurements, using the method of harmonic splines, is presented. This model (PHS /80/) for preliminary harmonic splines is the smoothest model (in the sense that the rms radial field at the core surface is minimum) consistent with the measurements (with an rms misfit of 10 nT to account for crustal and external fields as well as noise in the measurement procedure). Therefore PHS (80) is more suitable for studies of the core than models derived with the traditional least squares approach (e.g., GSFC /9/80/). A comparison is conducted of the characteristics of the harmonic spline spectrum, topology of the core field and especially the null-flux curves (loci where the radial field is zero) and the flux through patches bounded by such curves. PHS (80) is less complex than GSFC (9/80) and is therefore more representative of that part of the core field that the data constrain.
Usability Study of Two Collocated Prototype System Displays
NASA Technical Reports Server (NTRS)
Trujillo, Anna C.
2007-01-01
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.
Subcell resolution in simplex stochastic collocation for spatial discontinuities
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
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.
Achieving high data reduction with integral cubic B-splines
NASA Technical Reports Server (NTRS)
Chou, Jin J.
1993-01-01
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.
Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles
NASA Astrophysics Data System (ADS)
Fassò, A.; Ignaccolo, R.; Madonna, F.; Demoz, B. B.; Franco-Villoria, M.
2014-06-01
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.
Solution of problems of the theory of plates and shells with spline functions (survey)
Grogorenko, Ya.M.; Kryukov, N.N. [National Academy of Sciences of Ukraine, Kiev (Russian Federation)
1995-12-01
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.
SPLPKG,WFCMPR,WFAPPX. Wilson-Fowler Spline Use
Fletcher, S.K. [Sandia National Labs., Albuquerque, NM (United States)
1985-02-01
The three programs SPLPKG, WFCMPR, and WFAPPX provide the capability for interactively generating, comparing, and approximating Wilson-Fowler splines. The Wilson-Fowler spline is widely used in Computer Aided Design and Manufacturing (CAD/CAM) systems. It is favored for many applications because it produces a smooth, low curvature fit to planar data points. Program SPLPKG generates a Wilson-Fowler spline passing through given nodes (with given end conditions) and also generates a piecewise linear approximation to that spline within a user-defined tolerance. The program may be used to generate a `desired` spline against which to compare other splines generated by CAD/CAM systems. It may also be used to generate an acceptable approximation to a desired spline in the event that an acceptable spline cannot be generated by the receiving CAD/CAM system. SPLPKG writes an IGES file of points evaluated on the spline and/or a file containing the spline description. Program WFCMPR computes the maximum difference between two Wilson-Fowler splines and may be used to verify the spline recomputed by a receiving system. It compares two Wilson-Fowler splines with common nodes and reports the maximum distance between curves (measured perpendicular to segments) and the maximum difference of their tangents (or normals), both computed along the entire length of the splines. Program WFAPPX computes the maximum difference between a Wilson-Fowler spline and a piecewise linear curve. It may be used to accept or reject a proposed approximation to a desired Wilson-Fowler spline, even if the origin of the approximation is unknown. The maximum deviation between these two curves, and the parameter value on the spline where it occurs are reported.
Application of splines to the calculation of bacterial swimming speed distributions.
Stock, G B
1976-01-01
A new method of extracting information about bacterial speeds from photon correlation spectroscopy is presented. This method has the advantage that an estimation of the translational speed distribution is directly varied so as to achieve a best least-squares fit to the experimental autocorrelation function. The theory of spline approximations to continuous functions is briefly outlined. The importance of the previously disregarded diffusional component of bacterial motion is discussed. Experimental data from Salmonella at a low scattering angle is analyzed by this method of spline approximation and the distribution of translational speeds is obtained. PMID:1276382
Spline-based joint gravity and normal mode inversion
NASA Astrophysics Data System (ADS)
Michel, V.; Berkel, P.
2009-12-01
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 .
Digraph and matrix representation or nonuniform B-spline functions
NASA Astrophysics Data System (ADS)
Santoro, Esamuele
1996-03-01
For many purposes, problems appear easier to understand when they are formulated by graph theory. In this paper, the recurrence relation of B-spline is modeled by a weighted digraph and a one-to-one correspondence between B-spline functions and weighted digraph paths is proved. A matrix representation of the B-spline digraph is utilized, which yields to compute the B- spline functions as matrix products.
The studies of spline interpolation for five-axis machining
Liang Quan; Wang Yongzhang
2009-01-01
The study proposed a dual uniform B-spline interpolator architecture for computer numerical control (CNC) machines spline machining. For solving the different transformation in machining sculpture surface with five-axis machine tool, the format of G codes for five-axis spline interpolation is presented. Quaternion B-spline curves are adopted to describe the movement of rotary axis of five-axis machine, relative to conventional five-axis
Sparse and Efficient Estimation for Partial Spline Models with Increasing Dimension
Zhang, Hao Helen; Shang, Zuofeng
2014-01-01
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on the nonparametric component and shrinkage penalty on the parametric components, which can achieve function smoothing and sparse estimation simultaneously. We establish the convergence rate and oracle properties of the estimator under weak regularity conditions. Remarkably, the estimated parametric components are sparse and efficient, and the nonparametric component can be estimated with the optimal rate. The procedure also has attractive computational properties. Using the representer theory of smoothing splines, we reformulate the objective function as a LASSO-type problem, enabling us to use the LARS algorithm to compute the solution path. We then extend the procedure to situations when the number of predictors increases with the sample size and investigate its asymptotic properties in that context. Finite-sample performance is illustrated by simulations. PMID:25620808
Error Estimates Derived from the Data for Least-Squares Spline Fitting
Jerome Blair
2007-06-25
The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.
NASA Technical Reports Server (NTRS)
Wahba, Grace
1987-01-01
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.
Quantifying cervical-spine curvature using Be?zier splines.
Klinich, Kathleen D; Ebert, Sheila M; Reed, Matthew P
2012-11-01
Knowledge of the distributions of cervical-spine curvature is needed for computational studies of cervical-spine injury in motor-vehicle crashes. Many methods of specifying spinal curvature have been proposed, but they often involve qualitative assessment or a large number of parameters. The objective of this study was to develop a quantitative method of characterizing cervical-spine curvature using a small number of parameters. 180 sagittal X-rays of subjects seated in automotive posture with their necks in neutral, flexed, and extended postures were collected in the early 1970s. Subjects were selected to represent a range of statures and ages for each gender. X-rays were reanalyzed using advanced technology and statistical methods. Coordinates of the posterior margins of the vertebral bodies and dens were digitized. Be?zier splines were fit through the coordinates of these points. The interior control points that define the spline curvature were parameterized as a vector angle and length. By defining the length as a function of the angle, cervical-spine curvature was defined with just two parameters: superior and inferior Be?zier angles. A classification scheme was derived to sort each curvature by magnitude and type of curvature (lordosis versus S-shaped versus kyphosis; inferior or superior location). Cervical-spine curvature in an automotive seated posture varies with gender and age but not stature. Average values of superior and inferior Be?zier angles for cervical spines in flexion, neutral, and extension automotive postures are presented for each gender and age group. Use of Be?zier splines fit through posterior margins offers a quantitative method of characterizing cervical-spine curvature using two parameters: superior and inferior Be?zier angles. PMID:23387791
Procedure for converting a Wilson-Fowler spline to a cubic B-spline with double knots
Fritsch, F.N.
1987-10-14
The Wilson-Fowler spline (WF-spline) has been used by the DOE Weapons Complex for over twenty years to represent point-defined smooth curves. Most modern CADCAM systems use parametric B-spline curves (or, more recently, rational B-splines) for this same purpose. The WF-spline is a parametric piecewise cubic curve. It has been shown that a WF-spline can be reparametrized so that its components are C/sup 1/ piecewise cubic functions (functions that are cubic polynomials on each parameter interval, joined so the function and first derivative are continuous). The purpose of these notes is to show explicitly how to convert a given WF-spline to a cubic B-spline with double knots. 7 refs.
Surface reconstruction using bivariate simplex splines on Delaunay configurations
Juan Cao; Xin Li; Guozhao Wang; Hong Qin
2009-01-01
Recently, a new bivariate simplex spline scheme based on Delaunay configuration has been introduced into the geometric computing community, and it defines a complete spline space that retains many attractive theoretic and computational properties. In this paper, we develop a novel shape modeling framework to reconstruct a closed surface of arbitrary topology based on this new spline scheme. Our framework
B-spline finite elements for plane elasticity problems
Aggarwal, Bhavya
2007-04-25
............................................................................................ 56 37 Difference in ? 22 value with respect to the reference value for conventional and B-spline finite elements. .....................................................58 38 Solution time vs number of degrees of freedom for conventional and B... value for B-spline finite elements............................................................................. 69 51 Solution time vs number of degrees of freedom for conventional and B-spline finite elements...
Bernuau spline wavelets and Sturmian sequences
Miroslav Andrle; Cestmir Burdik; Jean-Pierre Gazeau
2003-09-24
A spline wavelets construction of class C^n(R) supported by sequences of aperiodic discretizations of R is presented. The construction is based on multiresolution analysis recently elaborated by G. Bernuau. At a given scale, we consider discretizations that are sets of left-hand ends of tiles in a self-similar tiling of the real line with finite local complexity. Corresponding tilings are determined by two-letter Sturmian substitution sequences. We illustrate the construction with examples having quadratic Pisot-Vijayaraghavan units (like tau = (1 + sqrt{5})/2 or tau^2 = (3 + sqrt{5})/2) as scaling factor. In particular, we present a comprehensive analysis of the Fibonacci chain and give the analytic form of related scaling functions and wavelets as splines of second order. We also give some hints for the construction of multidimensional spline wavelets based on stone-inflation tilings in arbitrary dimension.
Continuous Groundwater Monitoring Collocated at USGS Streamgages
NASA Astrophysics Data System (ADS)
Constantz, J. E.; Eddy-Miller, C.; Caldwell, R.; Wheeer, J.; Barlow, J.
2012-12-01
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.
A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion.
Steininger, Gavin; Dosso, Stan E; Holland, Charles W; Dettmer, Jan
2014-10-01
This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.]. PMID:25324060
Spline-Screw Multiple-Rotation Mechanism
NASA Technical Reports Server (NTRS)
Vranish, John M.
1994-01-01
Mechanism functions like combined robotic gripper and nut runner. Spline-screw multiple-rotation mechanism related to spline-screw payload-fastening system described in (GSC-13454). Incorporated as subsystem in alternative version of system. Mechanism functions like combination of robotic gripper and nut runner; provides both secure grip and rotary actuation of other parts of system. Used in system in which no need to make or break electrical connections to payload during robotic installation or removal of payload. More complicated version needed to make and break electrical connections. Mechanism mounted in payload.
Collocation and Pattern Recognition Effects on System Failure Remediation
NASA Technical Reports Server (NTRS)
Trujillo, Anna C.; Press, Hayes N.
2007-01-01
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.
Control Theoretic Splines with Deterministic and Random Data Y. Zhou M. Egerstedt C. Martin
Egerstedt, Magnus
Control Theoretic Splines with Deterministic and Random Data Y. Zhou M. Egerstedt C. Martin in papers by Egerstedt and Martin, [11], [6], [3] and their colleagues. The main technical contribution and Martin, [14], [15], [16]. We will see that this method rests on the Hilbert space methods developed
Smoothing B-spline active contour for fast and robust image and video segmentation
Frédéric Precioso; Michel Barlaud; Thierry Blu; Michael Unser
2003-01-01
This paper deals with fast image and video segmentation using active contours. Region based active contours using level-sets are powerful techniques for video segmentation but they suffer from large computational cost. A paramet- ric active contour method based on B-Spline interpolation has been proposed in (1) to highly reduce the computational cost but this method is sensitive to noise. Here,
NASA Technical Reports Server (NTRS)
Rogers, David
1991-01-01
G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.
ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALISED SPLINES
M. P. Wand; J. T. Ormerod
2010-01-01
This is an expos\\\\'e on the use of O'Sullivan penalised splines in\\u000acontemporary semiparametric regression, including mixed model and Bayesian\\u000aformulations. O'Sullivan penalised splines are similar to P-splines, but have\\u000aan advantage of being a direct generalisation of smoothing splines. Exact\\u000aexpressions for the O'Sullivan penalty matrix are obtained. Comparisons between\\u000athe two reveals that O'Sullivan penalised splines more closely
An algorithm for surface smoothing with rational splines
NASA Technical Reports Server (NTRS)
Schiess, James R.
1987-01-01
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.
Smoothing two-dimensional Malaysian mortality data using P-splines indexed by age and year
NASA Astrophysics Data System (ADS)
Kamaruddin, Halim Shukri; Ismail, Noriszura
2014-06-01
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.
High-quality rendering of quartic spline surfaces on the GPU.
Reis, Gerd; Zeilfelder, Frank; Hering-Bertram, Martin; Farin, Gerald; Hagen, Hans
2008-01-01
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 in the sense that since we do not use an intermediate tessellation but rather compute ray-surface intersections (by solving quartic equations numerically) as well as surface normals (by using Bernstein-Bézier techniques) for Phong illumination on the GPU. Inaccurate shading and artifacts appearing for triangular tesselated surfaces are completely avoided. Level of detail is automatic since all computations are done on a per fragment basis. We compare three different (quasi-) interpolating schemes for uniformly sampled gridded data, which differ in the smoothness and the approximation properties of the splines. The results show that our hardware based renderer leads to visualizations (including texturing, multiple light sources, environment mapping, etc.) of highest quality. PMID:18599922
Statistical modelling of collocation uncertainty in atmospheric thermodynamic profiles
NASA Astrophysics Data System (ADS)
Fassò, A.; Ignaccolo, R.; Madonna, F.; Demoz, B. B.
2013-08-01
The uncertainty of important atmospheric parameters is a key factor for assessing the uncertainty of global change estimates given by numerical prediction models. One of the critical points of the uncertainty budget is related to the collocation mismatch in space and time among different observations. This is particularly important for vertical atmospheric profiles obtained by radiosondes or LIDAR. In this paper we consider a statistical modelling approach to understand at which extent collocation uncertainty is related to environmental factors, height and distance between the trajectories. To do this we introduce a new statistical approach, based on the heteroskedastic functional regression (HFR) model which extends the standard functional regression approach and allows us a natural definition of uncertainty profiles. Moreover, using this modelling approach, a five-folded uncertainty decomposition is proposed. Eventually, the HFR approach is illustrated by the collocation uncertainty analysis of relative humidity from two stations involved in GCOS reference upper-air network (GRUAN).
A 2D time-domain collocation-Galerkin BEM for dynamic crack analysis in piezoelectric solids
M. Wünsche; F. García-Sánchez; A. Sáez; Ch. Zhang
2010-01-01
A time-domain boundary element method (TDBEM) for transient dynamic analysis of two-dimensional (2D), homogeneous, anisotropic and linear piezoelectric cracked solids is presented in this paper. The present analysis uses a combination of the strongly singular displacement boundary integral equations (BIEs) and the hypersingular traction boundary integral equations. The spatial discretization is performed by a Galerkin-method, while a collocation method is
Image inpainting using cubic hermit spline
NASA Astrophysics Data System (ADS)
Farid, M. Shahid; Khan, Hassan; Mahmood, Arif
2011-10-01
Image inpainting is a technique used to automatically recover the damaged or missing regions in digital images and is used to remove the unwanted objects from images. This paper presents a novel approach for recovering the damaged regions of digital images using splines. The proposed technique is divided into two steps. In the first step structure of the object in the damaged region is recovered using splines. The animator marks a reasonable number of points on the structure of the object around the damaged region. Using these points a spline is constructed and the isophote lines arriving at the contours of the damaged region are interpolated into the damaged regions using that spline. After recovering the structure of the object in the damaged or missing region, in the second step, a fill in process is done to fill in the color information in the damaged region. Any interpolation technique can be used in the second step to flow the color information into the damaged region. The proposed algorithm is tested over a large variety of images and has sown excellent results to restore the small damaged regions and satisfactory results for large damaged regions
A Spline Regression Model for Latent Variables
ERIC Educational Resources Information Center
Harring, Jeffrey R.
2014-01-01
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…
Spline smoothing of histograms by linear programming
NASA Technical Reports Server (NTRS)
Bennett, J. O.
1972-01-01
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.
Jörg Peters; Michael Wittman
1997-01-01
The zero set of a trivariate spline is used to blend basic CSG surfaces of algebraic degree up to four. The resulting volume-bounded blend surface is generically curvature continuous, and piecewise of algebraic degree four itself, independent of the number of surfaces joined. The algorithm consists of two parts: representing each of the n basic surfaces within the blend volume
Tensegrity spline beam and grid shell structures
S. M. L Adriaenssens; M. R Barnes
2001-01-01
This paper considers a class of tensegrity structures with continuous tubular compression booms forming curved splines, which may be deployed from straight by prestressing a cable bracing system. A free-form arch structure for the support of prestressed membranes is reviewed and the concepts are extended to a two-way spanning system for double layer grid shell structures. A numerical analysis based
The hat matrix for smoothing splines
R. L. Eubank
1984-01-01
The matrix which transforms the data vector to the vector of fitted values for smoothing splines is termed the hat matrix. This matrix is shown to have many of the same properties, and is seen to play the same role in the variances and covariances of the residuals, as its regression analysis counterpart. This fact is utilized to propose several
Shaft Coupler With Friction and Spline Clutches
NASA Technical Reports Server (NTRS)
Thebert, Glenn W.
1987-01-01
Coupling, developed for rotor of lift/cruise aircraft, employs two clutches for smooth transmission of power from gas-turbine engine to rotor. Prior to ascent, coupling applies friction-type transition clutch that accelerates rotor shaft to speeds matching those of engine shaft. Once shafts synchronized, spline coupling engaged and friction clutch released to provide positive mechanical drive.
Hierarchical spline-based image registration
Richard Szeliski; James Coughlan
1994-01-01
The problem of image registration subsumes a number of topics in multiframe image analysis, including the computation of optic flow (general pixel-based motion), stereo correspondence, structure from motion, and feature tracking. We present a new registration algorithm based on a spline representation of the displacement field which can be specialized to solve all of the above mentioned problems. In particular,
Nonlinear Dimensionality Reduction with Local Spline Embedding
Shiming Xiang; Feiping Nie; Changshui Zhang; Chunxia Zhang
2009-01-01
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
Semisupervised feature selection via spline regression for video semantic recognition.
Han, Yahong; Yang, Yi; Yan, Yan; Ma, Zhigang; Sebe, Nicu; Zhou, Xiaofang
2015-02-01
To improve both the efficiency and accuracy of video semantic recognition, we can perform feature selection on the extracted video features to select a subset of features from the high-dimensional feature set for a compact and accurate video data representation. Provided the number of labeled videos is small, supervised feature selection could fail to identify the relevant features that are discriminative to target classes. In many applications, abundant unlabeled videos are easily accessible. This motivates us to develop semisupervised feature selection algorithms to better identify the relevant video features, which are discriminative to target classes by effectively exploiting the information underlying the huge amount of unlabeled video data. In this paper, we propose a framework of video semantic recognition by semisupervised feature selection via spline regression (S(2)FS(2)R) . Two scatter matrices are combined to capture both the discriminative information and the local geometry structure of labeled and unlabeled training videos: A within-class scatter matrix encoding discriminative information of labeled training videos and a spline scatter output from a local spline regression encoding data distribution. An l2,1 -norm is imposed as a regularization term on the transformation matrix to ensure it is sparse in rows, making it particularly suitable for feature selection. To efficiently solve S(2)FS(2)R , we develop an iterative algorithm and prove its convergency. In the experiments, three typical tasks of video semantic recognition, such as video concept detection, video classification, and human action recognition, are used to demonstrate that the proposed S(2)FS(2)R achieves better performance compared with the state-of-the-art methods. PMID:25608288
Tobias Stammberger; Felix Eckstein; Markus Michaelis; Karl-Hans Englmeier; Maximilian Reiser
1999-01-01
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.
Classification by means of B-spline potential functions with applications to remote sensing
NASA Technical Reports Server (NTRS)
Bennett, J. O.; Defigueiredo, R. J. P.; Thompson, J. R.
1974-01-01
A method is presented for using B-splines as potential functions in the estimation of likelihood functions (probability density functions conditioned on pattern classes), or the resulting discriminant functions. The consistency of this technique is discussed. Experimental results of using the likelihood functions in the classification of remotely sensed data are given.
Triangle Mesh Compression using B-Spline Curves Anshuman Razdan1
Triangle Mesh Compression using B-Spline Curves Anshuman Razdan1 , Vinodth Kumar Mohanam2 , Gerald Farin3 Abstract We present a new method to compress triangle meshes in a lossless manner. Triangle compressed files are roughly 10% smaller than that from Edgebreaker. Keywords: Triangle compression, B
G. H. Hoffman
1982-01-01
A model strong interaction problem for two-dimensional laminar flow is solved numerically. The method makes use of the parabolized vorticity approximation in conjunction with fourth-order accurate polynomial splines to resolve the wall shear layer with a relatively sparse grid. A sheared wall fitted coordinate mapping is used which produces discontinous coefficients in the governing differential equations. These discontinuities are treated
SIMULATING ARTISTIC BRUSHSTROKES USING INTERVAL SPLINES Sara L. Su 1, 2
Su, Sara
SIMULATING ARTISTIC BRUSHSTROKES USING INTERVAL SPLINES Sara L. Su 1, 2 sarasu, we generate artistic strokes that render faster than earlier methods and are also resistant to the artistic form of lettering practiced by Asian and European scholars for centuries. The long, fluid strokes
Ruberti, M.; Averbukh, V. [Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ (United Kingdom); Decleva, P. [Dipartimento di Scienze Chimiche, Universita’ di Trieste, Via Giorgieri 1, I-34127 Trieste (Italy)
2014-10-28
We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters.
Higher-order numerical methods derived from three-point polynomial interpolation
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1976-01-01
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.
Redefining Creativity--Analyzing Definitions, Collocations, and Consequences
ERIC Educational Resources Information Center
Kampylis, Panagiotis G.; Valtanen, Juri
2010-01-01
How holistically is human creativity defined, investigated, and understood? Until recently, most scientific research on creativity has focused on its positive side. However, creativity might not only be a desirable resource but also be a potential threat. In order to redefine creativity we need to analyze and understand definitions, collocations,…
Collocation: Integrating Child Welfare and Substance Abuse Services
Eunju Lee; Nina Esaki; Rose Greene
2009-01-01
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
NASA/CR2003212153 A Stochastic Collocation Algorithm
Mathelin, Lionel
NASA/CRÂ2003Â212153 A Stochastic Collocation Algorithm for Uncertainty Analysis Lionel Mathelin and M. Yousuff Hussaini Florida State University, Tallahassee, Florida February 2003 #12;The NASA STI Program Office . . . in Profile Since its founding, NASA has been dedicated to the advancement
Analytical upstream collocation solution of a quadratically forced
Brill, Stephen H.
", keeping in mind that this is the grid PeÂ´clet number and not the global PeÂ´clet number (the latter of this paper is to present the analytical solution to the Hermite collocation discretization of a quadratically a second-order differential equation (DE) that models physical systems in which a combination of convective
Validation of ocean wind and wave data using triple collocation
S. Caires; A. Sterl
2003-01-01
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
Modelling Of Displacement Washing Of Pulp Bed Using Orthogonal Collocation On Finite Elements
NASA Astrophysics Data System (ADS)
Arora, Shelly; PotÅ¯?ek, František; Dhaliwal, S. S.; Kukreja, V. K.
2009-07-01
Mechanism of displacement washing of packed bed of porous, compressible and cylindrical particles, e.g., fibers is presented with the help of an axial dispersion model involving Peclet number (Pe) and Biot number (Bi). Bulk fluid concentration and intra-pore solute concentration are related by Langmuir adsorption isotherm. Model equations have been solved using orthogonal collocation on finite elements using Lagrangian interpolating polynomials as base functions. Displacement washing has been simulated using a laboratory washing cell and experiments have been performed on pulp beds formed from unbeaten, unbleached kraft fibers. Model predicted values have been compared with experimental values to check the applicability of the method.
Spline-based Motion Recovery for 3D Surfaces Using Nonrigid Shape Properties
Min Li; Chandra Kambhamettu; Maureen Stone
2004-01-01
We present a spline-based nonrigid motion and point correspondence recovery method for 3D surfaces. This method is based on differential geometry. Shape information is used to recover the point correspondences. In contrast to the majority of shape-based methods which assume that shape (unit normal, curvature) changes are minimumafter motion, our method focuses on the nonrigid relationship between before-motion and after-motion
ERIC Educational Resources Information Center
Yamashita, Junko; Jiang, Nan
2010-01-01
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…
Spline-Screw Payload-Fastening System
NASA Technical Reports Server (NTRS)
Vranish, John M.
1994-01-01
Payload handed off securely between robot and vehicle or structure. Spline-screw payload-fastening system includes mating female and male connector mechanisms. Clockwise (or counter-clockwise) rotation of splined male driver on robotic end effector causes connection between robot and payload to tighten (or loosen) and simultaneously causes connection between payload and structure to loosen (or tighten). Includes mechanisms like those described in "Tool-Changing Mechanism for Robot" (GSC-13435) and "Self-Aligning Mechanical and Electrical Coupling" (GSC-13430). Designed for use in outer space, also useful on Earth in applications needed for secure handling and secure mounting of equipment modules during storage, transport, and/or operation. Particularly useful in machine or robotic applications.
Integration by cell algorithm for Slater integrals in a spline basis
Qiu, Y.; Fischer, C.F.
1999-12-10
An algorithm for evaluating Slater integrals in a B-spline basis is introduced. Based on the piecewise property of the B-splines, the algorithm divides the two-dimensional (r{sub 1}, r{sub 2}) region into a number of rectangular cells according to the chosen grid and implements the two-dimensional integration over each individual cell using Gaussian quadrature. Over the off-diagonal cells, the integrands are separable so that each two-dimensional cell-integral is reduced to a product of two one-dimensional integrals. Furthermore, the scaling invariance of the B-splines in the logarithmic region of the chosen grid is fully exploited such that only some of the cell integrations need to be implemented. The values of given Slater integrals are obtained by assembling the cell integrals. This algorithm significantly improves the efficiency and accuracy of the traditional method that relies on the solution of differential equations and renders the B-spline method more effective when applied to multi-electron atomic systems.
Smoothing noisy data with spline functions
Grace Wahba
1975-01-01
It is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m-1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed “white”, and the true curve is assumed to be in the Sobolev spaceW2(2m) of periodic functions with absolutely continuousv-th derivative,v=0, 1, ..., 2m-1 and square integrable 2m-th
Curvilinear bicubic spline fit interpolation scheme
NASA Technical Reports Server (NTRS)
Chi, C.
1973-01-01
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.
Estimation of transition redshift based on Reinsch splines
NASA Astrophysics Data System (ADS)
Lü, Guo-Dong; Liu, De-Zi; Yuan, Shuo; Zhang, Tong-Jie
2015-03-01
Many schemes have been proposed to define a model-independent constraint on cosmological dynamics, such as the nonparametric dark energy equation of state ?(z) or the deceleration parameter q(z). These methods usually contain derivatives with respect to observational data with noise. However, there can be large uncertainties when one estimates values with numerical differentiation, especially when noise is significant. We introduce a global numerical differentiation method, first formulated by Reinsch, which is smoothed by cubic spline functions, and apply it to the estimation of the transition redshift zt with a simulated expansion rate E(z) based on observational Hubble parameter data. We also discuss some deficiencies and limitations of this method. Supported by the National Natural Science Foundation of China.
Forecasting the Hourly Ontario Energy Price by Multivariate Adaptive Regression Splines
CaÃ±izares, Claudio A.
1 Forecasting the Hourly Ontario Energy Price by Multivariate Adaptive Regression Splines H Abstract-- Multivariate adaptive regression splines (MARS) technique is an adaptive non forecasting. Index Terms-- Price forecasting, electricity markets, Multivari- ate Adaptive Regression Splines
A spline-theoretic approach to minimum-energy control
HOWARD L. WEINERT; T. Kailath
1976-01-01
The problem of minimum-energy control of linear systems with linear functional constraints on the output is considered from a spline-theoretic viewpoint. It is shown that constrained minimum-energy control and spline interpolation are dual projection problems: if the given system is driven by the minimum-energy control, the system output will be the spline that interpolates the output constraints. This duality result
Scattered Data Interpolation with Multilevel B-Splines
Seungyong Lee; George Wolberg; Sung Yong Shin
1997-01-01
This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines areintroduced to compute a C2-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofinehierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desiredinterpolation function. Large performance gains are realized by using B-spline refinement
On the spline-based wavelet differentiation matrix
NASA Technical Reports Server (NTRS)
Jameson, Leland
1993-01-01
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.
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
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.
Image inpainting using cubic spline-based edge reconstruction
NASA Astrophysics Data System (ADS)
Voronin, V. V.; Marchuk, V. I.; Sherstobitov, A. I.; Egiazarian, K. O.
2012-03-01
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.
An improved approach to the cubic-spline interpolation
NASA Astrophysics Data System (ADS)
Lin, Tsung-Ching; Hong, Shao-Hua; Truong, Trieu-Kien; Wang, Lin
2013-09-01
Cubic-spline interpolation (CSI) scheme is known to be designed to resample the discrete image data based on the leastsquares method with the cubic convolution interpolation (CCI) function. It is superior in performance to other interpolation functions for digital image processing. In this paper, an improved CSI scheme that combines the leastsquares method with an eight-point cubic interpolation kernel is developed in order to improve the performance of the original CSI scheme. Either the FFT/Winograd DFT or the fast direct computation algorithm can also be used to perform the circular convolution needed in this improved CSI scheme. Furthermore, its correlated image data and auto-correlated filter coefficients are also accurately calculated in this paper. Experimental results indicate that the proposed improved CSI scheme yields a much better quality of reconstructed image than existing interpolation algorithms.
An algebraic spline model of molecular surfaces for energetic computations.
Zhao, Wenqi; Xu, Guoliang; Bajaj, Chandrajit
2011-01-01
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 Protein data bank (PDB). 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. PMID:21519111
NASA Astrophysics Data System (ADS)
Li, Shengquan; Li, Juan; Mo, Yueping; Zhao, Rong
2014-01-01
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.
NASA Technical Reports Server (NTRS)
Jarosch, H. S.
1982-01-01
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.
Free-knot cubic spline modelling in cryogenic thermometer calibration
Patrizia Ciarlini; Daniela Ichim
2006-01-01
In a calibration process of thousands of thermometers, optimization of the experimental design is an important step to save time and costs. In this paper, a modelling procedure is proposed for the construction of a suitable cubic spline approximation of the R–T characteristic of cryogenic thermometers. An iterative algorithm is used to estimate the parameters of a free-knot cubic spline
Smoothing parameter selection in two frameworks for penalized splines
Krivobokova, Tatyana
Introduction Since works of Grace Wahba and co-authors, smoothing splines with the cross-validated smoothing parameter have become an established nonparametric regression tool. One of the attractive features of spline this Courant Research Center "Poverty, equity and growth" and Institute for Mathematical Stochastics, Georg
A multiresolution spline with application to image mosaics
Peter J. Burt; Edward H. Adelson
1983-01-01
We define a multiresolution spline technique for combining two or more images into a larger image mosaic. In this procedure, the images to be splined are first decomposed into a set of band-pass filtered component images. Next, the component images in each spatial frequency hand are assembled into a corresponding bandpass mosaic. In this step, component images are joined using
Flexible smoothing with B-splines and penalties
Paul H. C. Eilers; Brian D. Marx
1996-01-01
B-splines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent B-splines. We show connections
Local Control of Bias and Tension in Beta-splines
Brian A. Barsky; John C. Beatty
1983-01-01
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
[Eco-environmental evaluation and spatial-temporal collocation of regional land consolidation].
Wang, Ailing; Zhao, Genxiang; Wang, Ruiyan; Yuan, Xiangming
2006-08-01
Eco-environmental evaluation and spatial-temporal collocation of land consolidation is the basis of regional land consolidation. Taking Qingzhou County of Shandong Province as an example, this paper established the eco-environmental evaluation index system and evaluation model of land consolidation, based on the systematic analysis of land consolidation characteristics and natural and social conditions of Qingzhou County. The comprehensive score of each evaluation unit was obtained by integrated index evaluation method and GIS techniques, and the spatial-temporal collocation of regional land consolidation was proposed accordingly. The results indicated that in Qingzhou County, the total area of cultivated and un-utilized land was 1446 km2, among which, the land consolidation area in near future mainly distributed in the northwest part of plain region, occupying 15.35% of the total, mid-phase land consolidation area mainly distributed in the northwest and central parts of plain region, occupying 13.58%, land consolidation area in specified future mainly distributed in the north part of plain region, occupying 40.71%, and non-land consolidation area mainly distributed in hilly region, occupying 30.36%. These results could provide scientific instruction for the land consolidation planning and implement in Qingzhou County. PMID:17066707
Adaptive image coding based on cubic-spline interpolation
NASA Astrophysics Data System (ADS)
Jiang, Jian-Xing; Hong, Shao-Hua; Lin, Tsung-Ching; Wang, Lin; Truong, Trieu-Kien
2014-09-01
It has been investigated that at low bit rates, downsampling prior to coding and upsampling after decoding can achieve better compression performance than standard coding algorithms, e.g., JPEG and H. 264/AVC. However, at high bit rates, the sampling-based schemes generate more distortion. Additionally, the maximum bit rate for the sampling-based scheme to outperform the standard algorithm is image-dependent. In this paper, a practical adaptive image coding algorithm based on the cubic-spline interpolation (CSI) is proposed. This proposed algorithm adaptively selects the image coding method from CSI-based modified JPEG and standard JPEG under a given target bit rate utilizing the so called ?-domain analysis. The experimental results indicate that compared with the standard JPEG, the proposed algorithm can show better performance at low bit rates and maintain the same performance at high bit rates.
NASA Astrophysics Data System (ADS)
Jakeman, John D.; Narayan, Akil; Xiu, Dongbin
2013-06-01
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.
Surface mesh to volumetric spline conversion with generalized polycubes.
Li, Bo; Li, Xin; Wang, Kexiang; Qin, Hong
2013-09-01
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
Zhou, Zhongxing; Zhu, Qingzhen; Zhao, Huijuan; Zhang, Lixin; Ma, Wenjuan; Gao, Feng
2014-04-01
To develop an effective curve-fitting algorithm with a regularization term for measuring the modulation transfer function (MTF) of digital radiographic imaging systems, in comparison with representative prior methods, a C-spline regression technique based upon the monotonicity and convex/concave shape restrictions of the edge spread function (ESF) was proposed for ESF estimation in this study. Two types of oversampling techniques and following four curve-fitting algorithms including the C-spline regression technique were considered for ESF estimation. A simulated edge image with a known MTF was used for accuracy determination of algorithms. Experimental edge images from two digital radiography systems were used for statistical evaluation of each curve-fitting algorithm on MTF measurements uncertainties. The simulation results show that the C-spline regression algorithm obtained a minimum MTF measurement error (an average error of 0.12% ± 0.11% and 0.18% ± 0.17% corresponding to two types of oversampling techniques, respectively, up to the cutoff frequency) among all curve-fitting algorithms. In the case of experimental edge images, the C-spline regression algorithm obtained the best uncertainty performance of MTF measurement among four curve-fitting algorithms for both the Pixarray-100 digital specimen radiography system and Hologic full-field digital mammography system. Comparisons among MTF estimates using four curve-fitting algorithms revealed that the proposed C-spline regression technique outperformed other algorithms on MTF measurements accuracy and uncertainty performance. PMID:24658257
Robust real-time segmentation of images and videos using a smooth-spline snake-based algorithm
Frédéric Precioso; Michel Barlaud; Thierry Blu; Michael Unser
2005-01-01
This paper deals with fast image and video seg- mentation using active contours. Region based active contours using level-sets are powerful techniques for video segmentation but they suffer from large computational cost. A parametric active contour method based on B-Spline interpolation has been proposed in (26) to highly reduce the computational cost but this method is sensitive to noise. Here,
Parameter estimation in systems biology models using spline approximation
2011-01-01
Background Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints. Results Two parameter estimation methods of combining spline theory with Linear Programming (LP) and Nonlinear Programming (NLP) are developed. These methods remove the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surfaces used in the two proposed methods are smoother; which can ease the optima searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily. Eight system biology models are used for testing the proposed approaches. Our results confirm that the proposed methods are both efficient and robust. Conclusions The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models. PMID:21255466
Quantitative coronary angiography with deformable spline models.
Klein, A K; Lee, F; Amini, A A
1997-10-01
Although current edge-following schemes can be very efficient in determining coronary boundaries, they may fail when the feature to be followed is disconnected (and the scheme is unable to bridge the discontinuity) or branch points exist where the best path to follow is indeterminate. In this paper, we present new deformable spline algorithms for determining vessel boundaries, and enhancing their centerline features. A bank of even and odd S-Gabor filter pairs of different orientations are convolved with vascular images in order to create an external snake energy field. Each filter pair will give maximum response to the segment of vessel having the same orientation as the filters. The resulting responses across filters of different orientations are combined to create an external energy field for snake optimization. Vessels are represented by B-Spline snakes, and are optimized on filter outputs with dynamic programming. The points of minimal constriction and the percent-diameter stenosis are determined from a computed vessel centerline. The system has been statistically validated using fixed stenosis and flexible-tube phantoms. It has also been validated on 20 coronary lesions with two independent operators, and has been tested for interoperator and intraoperator variability and reproducibility. The system has been found to be specially robust in complex images involving vessel branchings and incomplete contrast filling. PMID:9368103
Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery
Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery Qingzhi Guo, University of South Carolina, Columbia, South Carolina 29208, USA A cubic spline regression model was used of fitting parameters, the cubic spline regression model is more accurate. The cubic spline regression model
Alwan, Aravind; Aluru, N.R.
2013-12-15
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.
NASA Astrophysics Data System (ADS)
Alwan, Aravind; Aluru, N. R.
2013-12-01
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.
Ordered subsets Bayesian tomographic reconstruction using 2-D smoothing splines as priors.
Lee, Soo-Jin
2003-09-01
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
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
Wenping Wang; Helmut Pottmann; Yang Liu
2006-01-01
Computing a curve to approximate data points is a problem encountered frequently in many ap- plications in computer graphics, computer vision, CAD\\/CAM, and image processing. We present a novel and efficient method, calledsquared distance minimization (SDM), for computing a planar B-spline curve, closed or open, to approximate a target shape defined by a point cloud, i.e., a set of unorganized,
3-D knee cartilage segmentation using a smoothing B-Spline active surface
Xian Du; Jérôme Velut; Radu Bolbos; Olivier Beuf; Christophe Odet; Hugues Benoit-cattin
2008-01-01
We present an adaptive solution for guinea pig knee cartilage segmentation using a 3-D smoothing B-Spline active surface. An adaptive parametric combination of edge-based forces and balloon force solves the problem of capture range of external forces. The comparison between the results of the experiments using this method and previous 3-D validated snake segmentation shows that the accuracy and robustness
Fitting B-Spline Curves to Point Clouds by Squared Distance Minimization
Wenping Wang; Helmut Pottmann; Yang Liu
2004-01-01
Computing a curve to approximate data points is a problem encountered frequently in many applications in computer graphics, computer vision, CAD\\/CAM, and image processing. We present a novel and efficient method, calledsquared distance minimization (SDM), for computing a planar B-spline curve, closed or open, to approximate a target shape defined by a point cloud, i.e., a set of unorganized, possibly
The algorithms for rational spline interpolation of surfaces
NASA Technical Reports Server (NTRS)
Schiess, J. R.
1986-01-01
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.
Collocational frameworks in medical research papers: a genre-based study
Maria José Luzon Marco
2000-01-01
Each genre favours some linguistic structures and elements over others. The present paper reveals the usefulness of corpus-based analysis to discover the linguistic patterns selected and favoured by a specific genre. It analyzes the use of collocational frameworks, or discontinuous sequences of words, in a corpus of medical research papers and describes the intermediate words, or collocates, which fill these
On Adaptive Unsymmetric Meshless Collocation Leevan Ling1 and Robert Schaback2
Schaback, Robert
On Adaptive Unsymmetric Meshless Collocation Leevan Ling1 and Robert Schaback2 Summary Though the unsymmetric meshless collocation technique introduced by E. J. Kansa [5],[6] for solving PDE boundary valueÂdependent meshless selection of separated test and trial spaces. Introduction The general idea for solving PDE
Going beyond Patterns: Involving Cognitive Analysis in the Learning of Collocations
ERIC Educational Resources Information Center
Liu, Dilin
2010-01-01
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,…
NASA Technical Reports Server (NTRS)
Lashmet, P. K.; Woodrow, P. T.
1975-01-01
Numerical instabilities often arise in the use of high-ordered collocation approximations for numerically solving parabolic partial differential equations. These problems may be reduced by formulations involving evaluation of collocation polynomials rather than combination of the polynomials into a power series. As an illustration, two formulations using shifted Legendre polynomials of order 26 and less are compared.
Facilitating Non-Collocated Coexistence for WiFi and 4G Wireless Networks
Sahoo, Anirudha
Facilitating Non-Collocated Coexistence for WiFi and 4G Wireless Networks Punit Rathod Department of non- collocated coexistence of WiFi and 4G technologies such as WiMAX and LTE due to adjacent channel.4 GHz ISM band used by WiFi. We show, with measurements on our test-bed and from existing results
English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information
ERIC Educational Resources Information Center
Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji
2012-01-01
We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic…
Grace Wahba
1985-01-01
The partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood (GML) estimate for the smoothing parameter. Then this estimate is compared with the generalized cross validation (GCV) estimate both analytically and by Monte Carlo methods. The comparison is based on a predictive mean square error criteria. It is shown that if
Optimal spline regression utilizing steepest descent
Flora, Eric Shirley
1975-01-01
WEIGHTS FOR DATA C????? ????'???????????????????'?*????????????????'???*??'???????????????? SIGMA=1/FLOAT (K ) KP1=K+I NA=MAXO( Nlr IF I X(LX/10 + ~ 5) ) NN= N4+K P 1 STP=(X(LX)-X(1) )/(N4+I) C????? SET UP N4-K EVFNLY SPACED KNOTS FOR A CLOSE F...-K THAT( I ) =THAT ( I+1) DO 19 JJ=IMK I VD(JJ)=O 0 LHAT=L [F (L. GE I ) LHAT=L+1 JLOW=MAXO(LHATe I)-KM 1 JHIGH=MIND(LHAT rl ) IF( JLOW GT JHIGH) GO TO 43 GET VALUF. OF SPLINE US ING THAT CALL BSPLVN (THAT ~ K, 1yXX ~ LHAT~DUMMY) KMLHAT=K-LHAT DO...
Spline-Locking Screw Fastening Strategy (SLSFS)
NASA Technical Reports Server (NTRS)
Vranish, John M.
1991-01-01
A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotic or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.
Spline-locking screw fastening strategy
NASA Technical Reports Server (NTRS)
Vranish, John M.
1992-01-01
A fastener was developed by NASA Goddard for efficiently performing assembly, maintenance, and equipment replacement functions in space using either robotics or astronaut means. This fastener, the 'Spline Locking Screw' (SLS) would also have significant commercial value in advanced space manufacturing. Commercial (or DoD) products could be manufactured in such a way that their prime subassemblies would be assembled using SLS fasteners. This would permit machines and robots to disconnect and replace these modules/parts with ease, greatly reducing life cycle costs of the products and greatly enhancing the quality, timeliness, and consistency of repairs, upgrades, and remanufacturing. The operation of the basic SLS fastener is detailed, including hardware and test results. Its extension into a comprehensive fastening strategy for NASA use in space is also outlined. Following this, the discussion turns toward potential commercial and government applications and the potential market significance of same.
A stable interface element scheme for the p-adaptive lifting collocation penalty formulation
NASA Astrophysics Data System (ADS)
Cagnone, J. S.; Nadarajah, S. K.
2012-02-01
This paper presents a procedure for adaptive polynomial refinement in the context of the lifting collocation penalty (LCP) formulation. The LCP scheme is a high-order unstructured discretization method unifying the discontinuous Galerkin, spectral volume, and spectral difference schemes in single differential formulation. Due to the differential nature of the scheme, the treatment of inter-cell fluxes for spatially varying polynomial approximations is not straightforward. Specially designed elements are proposed to tackle non-conforming polynomial approximations. These elements are constructed such that a conforming interface between polynomial approximations of different degrees is recovered. The stability and conservation properties of the scheme are analyzed and various inviscid compressible flow calculations are performed to demonstrate the potential of the proposed approach.
Smoothing in occupational cohort studies: an illustration based on penalised splines
Eisen, E; Agalliu, I; Thurston, S; Coull, B; Checkoway, H
2004-01-01
Aims: To illustrate the contribution of smoothing methods to modelling exposure-response data, Cox models with penalised splines were used to reanalyse lung cancer risk in a cohort of workers exposed to silica in California's diatomaceous earth industry. To encourage application of this approach, computer code is provided. Methods: Relying on graphic plots of hazard ratios as smooth functions of exposure, the sensitivity of the curve to amount of smoothing, length of the exposure lag, and the influence of the highest exposures was evaluated. Trimming and data transformations were used to down-weight influential observations. Results: The estimated hazard ratio increased steeply with cumulative silica exposure before flattening and then declining over the sparser regions of exposure. The curve was sensitive to changes in degrees of freedom, but insensitive to the number or location of knots. As the length of lag increased, so did the maximum hazard ratio, but the shape was similar. Deleting the two highest exposed subjects eliminated the top half of the range and allowed the hazard ratio to continue to rise. The shape of the splines suggested a parametric model with log hazard as a linear function of log transformed exposure would fit well. Conclusions: This flexible statistical approach reduces the dependence on a priori assumptions, while pointing to a suitable parametric model if one exists. In the absence of an appropriate parametric form, however, splines can provide exposure-response information useful for aetiological research and public health intervention. PMID:15377772
Noise correction on LANDSAT images using a spline-like algorithm
NASA Technical Reports Server (NTRS)
Vijaykumar, N. L. (principal investigator); Dias, L. A. V.
1985-01-01
Many applications using LANDSAT images face a dilemma: the user needs a certain scene (for example, a flooded region), but that particular image may present interference or noise in form of horizontal stripes. During automatic analysis, this interference or noise may cause false readings of the region of interest. In order to minimize this interference or noise, many solutions are used, for instane, that of using the average (simple or weighted) values of the neighboring vertical points. In the case of high interference (more than one adjacent line lost) the method of averages may not suit the desired purpose. The solution proposed is to use a spline-like algorithm (weighted splines). This type of interpolation is simple to be computer implemented, fast, uses only four points in each interval, and eliminates the necessity of solving a linear equation system. In the normal mode of operation, the first and second derivatives of the solution function are continuous and determined by data points, as in cubic splines. It is possible, however, to impose the values of the first derivatives, in order to account for shapr boundaries, without increasing the computational effort. Some examples using the proposed method are also shown.
Nehorai, Arye
of Two Collocated Orthogonally Oriented Circular Thin-Wire Loops Yikun Huang, Arye Nehorai, Fellow, IEEE, and Gary Friedman Abstract--Coupling between two collocated orthogonal circular thin-wire loops is analyzed. It is also found that coupling for orthogonal collocated loop antennas depends on the relative locations
ERIC Educational Resources Information Center
Chang, Yu-Chia; Chang, Jason S.; Chen, Hao-Jan; Liou, Hsien-Chin
2008-01-01
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…
Construction and properties of non-polynomial spline-curves
NASA Astrophysics Data System (ADS)
Laksâ, Arne
2014-12-01
Bézier curves can be expressed by using De Casteljau's corner cutting algorithm. This can also be formulated using factorization matrices. Each matrix reduce the coefficient vector with 1, and each line in each matrix represent a linear interpolation describing the corner cutting. This matrix formulation may also be used for B-splines. One just have to introduce a linear transformation from the local domains of the basis function, to the interval [0;1]. This leads to a further expansion where the linear transformation is "deformed" by a perturbation function. The result is a non-polynomial spline. We will se that the typical properties of B-splines are preserved or even improved in the nonpolynomial case. Further, we describes the construction of the B-spline, and provide some practical examples.
Planar Spline Trajectory Following for an Autonomous Helicopter
Sukhatme, Gaurav S.
Planar Spline Trajectory Following for an Autonomous Helicopter Kale Harbick, James F. Montgomery helicopter. Results from two flight experiments are presented. The trajec- tory tracking error distur- bances (wind), this is quite reasonable. Keywords: Path planning, Robotic Helicopter, UAV
Modeling terminal ballistics using blending-type spline surfaces
NASA Astrophysics Data System (ADS)
Pedersen, Aleksander; Bratlie, Jostein; Dalmo, Rune
2014-12-01
We explore using GERBS, a blending-type spline construction, to represent deform able thin-plates and model terminal ballistics. Strategies to construct geometry for different scenarios of terminal ballistics are proposed.
A Constrained Spline Estimator of a Hazard Function.
ERIC Educational Resources Information Center
Bloxom, Bruce
1985-01-01
A constrained quadratic spline is proposed as an estimator of the hazard function of a random variable. A maximum penalized likelihood procedure is used to fit the estimator to a sample of psychological response times. (Author/LMO)
Detail view of redwood spline joinery of woodframe section against ...
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
Construction of spline functions in spreadsheets to smooth experimental data
Technology Transfer Automated Retrieval System (TEKTRAN)
A previous manuscript detailed how spreadsheet software can be programmed to smooth experimental data via cubic splines. This addendum corrects a few errors in the previous manuscript and provides additional necessary programming steps. ...
The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points
NASA Technical Reports Server (NTRS)
Don, Wai Sun; Gottlieb, David
1993-01-01
We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.
Polyharmonic smoothing splines and the multidimensional Wiener filtering of fractal-like signals.
Tirosh, Shai; Van De Ville, Dimitri; Unser, Michael
2006-09-01
Motivated by the fractal-like behavior of natural images, we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional was initially introduced by Duchon for the approximation of nonuniformily sampled, multidimensional data. He proved that the general solution is a smoothing spline that is represented by a linear combination of radial basis functions (RBFs). Unfortunately, this is tedious to implement for images because of the poor conditioning of RBFs and their lack of decay. Here, we present a much more efficient method for the special case of a uniform grid. The key idea is to express Duchon's solution in a fractional polyharmonic B-spline basis that spans the same space as the RBFs. This allows us to derive an algorithm where the smoothing is performed by filtering in the Fourier domain. Next, we prove that the above smoothing spline can be optimally tuned to provide the MMSE estimation of a fractional Brownian field corrupted by white noise. This is a strong result that not only yields the best linear filter (Wiener solution), but also the optimal interpolation space, which is not bandlimited. It also suggests a way of using the noisy data to identify the optimal parameters (order of the spline and smoothing strength), which yields a fully automatic smoothing procedure. We evaluate the performance of our algorithm by comparing it against an oracle Wiener filter, which requires the knowledge of the true noiseless power spectrum of the signal. We find that our approach performs almost as well as the oracle solution over a wide range of conditions. PMID:16948307
Converting an unstructured quadrilateral mesh to a standard T-spline surface
NASA Astrophysics Data System (ADS)
Wang, Wenyan; Zhang, Yongjie; Scott, Michael A.; Hughes, Thomas J. R.
2011-10-01
This paper presents a novel method for converting any unstructured quadrilateral mesh to a standard T-spline surface, which is C 2-continuous except for the local region around each extraordinary node. There are two stages in the algorithm: the topology stage and the geometry stage. In the topology stage, we take the input quadrilateral mesh as the initial T-mesh, design templates for each quadrilateral element type, and then standardize the T-mesh by inserting nodes. One of two sufficient conditions is derived to guarantee the generated T-mesh is gap-free around extraordinary nodes. To obtain a standard T-mesh, a second sufficient condition is provided to decide what T-mesh configuration yields a standard T-spline. These two sufficient conditions serve as a theoretical basis for our template development and T-mesh standardization. In the geometry stage, an efficient surface fitting technique is developed to improve the geometric accuracy. In addition, the surface continuity around extraordinary nodes can be improved by adjusting surrounding control nodes. The algorithm can also preserve sharp features in the input mesh, which are common in CAD (Computer Aided Design) models. Finally, a Bézier extraction technique is used to facilitate T-spline based isogeometric analysis. Several examples are tested to show the robustness of the algorithm.
Generalized b-spline subdivision-surface wavelets and lossless compression
Bertram, M; Duchaineau, M A; Hamann, B; Joy, K I
1999-11-24
We present a new construction of wavelets on arbitrary two-manifold topology for geometry compression. The constructed wavelets generalize symmetric tensor product wavelets with associated B-spline scaling functions to irregular polygonal base mesh domains. The wavelets and scaling functions are tensor products almost everywhere, except in the neighborhoods of some extraordinary points (points of valence unequal four) in the base mesh that defines the topology. The compression of arbitrary polygonal meshes representing isosurfaces of scalar-valued trivariate functions is a primary application. The main contribution of this paper is the generalization of lifted symmetric tensor product B-spline wavelets to two-manifold geometries. Surfaces composed of B-spline patches can easily be converted to this scheme. We present a lossless compression method for geometries with or without associated functions like color, texture, or normals. The new wavelet transform is highly efficient and can represent surfaces at any level of resolution with high degrees of continuity, except at a finite number of extraordinary points in the base mesh. In the neighborhoods of these points detail can be added to the surface to approximate any degree of continuity.
Algebraic grid generation using tensor product B-splines. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Saunders, B. V.
1985-01-01
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.
Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2013-01-01
We present a scalable, parallel mechanism for stochastic identification/control for problems constrained by partial differential equations with random input data. Several identification objectives will be discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm, and the distributed parameters/control can both deterministic or stochastic. Given an objective we prove the existence of an optimal solution, establish the validity of the Lagrange multiplier rule and obtain a stochastic optimality system of equations. The modeling process may describe the solution in terms of high dimensional spaces, particularly in the case when the input data (coefficients, forcing terms, boundary conditions, geometry, etc) are affected by a large amount of uncertainty. For higher accuracy, the computer simulation must increase the number of random variables (dimensions), and expend more effort approximating the quantity of interest in each individual dimension. Hence, we introduce a novel stochastic parameter identification algorithm that integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. This allows for decoupled, moderately high dimensional, parameterized computations of the stochastic optimality system, where at each collocation point, deterministic analysis and techniques can be utilized. The advantage of our approach is that it allows for the optimal identification of statistical moments (mean value, variance, covariance, etc.) or even the whole probability distribution of the input random fields, given the probability distribution of some responses of the system (quantities of physical interest). Our rigorously derived error estimates, for the fully discrete problems, will be described and used to compare the efficiency of the method with several other techniques. Numerical examples illustrate the theoretical results and demonstrate the distinctions between the various stochastic identification objectives.
User's guide for Wilson-Fowler spline software: SPLPKG, WFCMPR, WFAPPX - CADCAM-010
Fletcher, S.K.
1985-02-01
The Wilson-Fowler spline is widely used in computer aided manufacturing, but is not available in all commercial CAD/CAM systems. These three programs provide a capability for generating, comparing, and approximating Wilson-Fowler splines. SPLPKG generates a spline passing through given nodes, and computes a piecewise linear approximation to the spline. WFCMPR computes the difference between two splines with common nodes. WFAPPX computes the difference between a spline and a piecewise linear curve. The programs are in Fortran 77 and are machine independent.
Bivariate B-splines and its Applications in Spatial Data Analysis
Pan, Huijun 1987-
2011-08-09
domain. One is the soap smoother and the other is the nite element splines from the applied mathematics. Now we start to review these methods. 3.2.1 Finite element smoother The nite element technique is a sophisticated method in applied mathematics... equations that only involve rst order derivatives. In this way, the problem can be easily solved by nite element method. But the constraints of normal derivatives zero on boundary is arbitrary and may not be satis ed in many cases. 3.2.2 Soap lm...
The Computation of American Option Price Sensitivities using a Monotone Multigrid Method
Bartels, Soeren
Order BÂSpline Discretizations Markus Holtz October 26, 2004 Abstract In this paper a fast solver is presented. The numerical method consists of a finite element discretization with BÂspline ansatz functions problems, linear com- plementary problems, finite elements, cardinal higher order BÂsplines, monotone
BSpline Based Monotone Multigrid Methods, with an Application to the Prizing of American Options
Bartels, Soeren
BÂSpline Based Monotone Multigrid Methods, with an Application to the Prizing of American Options on a BÂspline basis of arbitrary smooth- ness for the efficient numerical solution of elliptic function which are based on BÂspline expansion coefficients. To illustrate the potential of the scheme
NASA Technical Reports Server (NTRS)
Rummel, R.; Sjoeberg, L.; Rapp, R. H.
1978-01-01
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.
3D profile filter algorithm based on parallel generalized B-spline approximating Gaussian
NASA Astrophysics Data System (ADS)
Ren, Zhiying; Gao, Chenghui; Shen, Ding
2015-01-01
Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, these methods are only suitable for the study of one-dimensional filtering, when these methods are used for three-dimensional filtering, it is found that a rounding error and quantization error would be passed to the next in every part. In this paper, a new and high-precision implementation approach for Gaussian filter is described, which is suitable for three-dimensional reference filtering. Based on the theory of generalized B-spline function and the variational principle, the transmission characteristics of a digital filter can be changed through the sensitivity of the parameters ( t 1, t 2), and which can also reduce the rounding error and quantization error by the filter in a parallel form instead of the cascade form. Finally, the approximation filter of Gaussian filter is obtained. In order to verify the feasibility of the new algorithm, the reference extraction of the conventional methods are also used and compared. The experiments are conducted on the measured optical surface, and the results show that the total calculation by the new algorithm only requires 0.07 s for 480×480 data points; the amplitude deviation between the reference of the parallel form filter and the Gaussian filter is smaller; the new method is closer to the characteristic of the Gaussian filter through the analysis of three-dimensional roughness parameters, comparing with the cascade generalized B-spline approximating Gaussian. So the new algorithm is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.
Sun, Weiwei; Huang, Weizhang; Russell, Robert D.
1996-12-01
A technique to construct a low-order finite difference preconditioner for solving orthogonal collocation equations for boundary value problems is presented. It is shown numerically and theoretically that the spectral condition numbers...
NASA Technical Reports Server (NTRS)
Eren, K.
1980-01-01
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.
Fast B-spline Transforms for Continuous Image Representation and Interpolation
Michael Unser; Akram Aldroubi; Murray Eden
1991-01-01
Efficient algorithms for the continuous representation of a discrete signal in terms of B-splines (direct B-spline transform) and for interpolative signal reconstruction (indirect B-spline transform) with an expansion factor m are described. Expressions for the z-transforms of the sampled B-spline functions are determined and a convolution property of these kernels is established. It is shown that both the direct and
NASA Technical Reports Server (NTRS)
Croom, D. R.; Dunham, R. E., Jr.
1975-01-01
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.
NASA Astrophysics Data System (ADS)
Driscoll, Tobin A.
2010-08-01
Automatic Chebyshev spectral collocation methods for Fredholm and Volterra integral and integro-differential equations have been implemented as part of the chebfun software system. This system enables a symbolic syntax to be applied to numerical objects in order to pose and solve problems without explicit references to discretization. The same objects can be used in matrix-free iterative methods in linear algebra, in order to avoid very large dense matrices or allow application to problems with nonsmooth coefficients. As a further application of the ability to implement operator equations, a method of Greengard [1] for the recasting of differential equations as integral equations is generalized to mth order boundary value and generalized eigenvalue problems. In the integral form, large condition numbers associated with differentiation matrices in high-order problems are avoided. The ability to implement the recasting process generally follows from implementation of the operator expressions in chebfun. The integral method also can be extended to first-order systems, although chebfun syntax does not currently allow easy implementation in this case.
Toronto, University of
Shape reconstruction and subsequent deformation of soleus muscle models using B-spline solid to allow simulation of animated muscle tissue. Keywords: deformable models, B-spline solids, soleus, muscle that can be used to create deformable models of muscle shape. B-spline solids can be used to model skeletal
Cardinal spline filters: Stability and convergence to the ideal sinc interpolator
A. Aldroubi; M. Unser; M. Eden
1992-01-01
In this paper, we provide an interpretation of polynomial spline interpolation as a continuous filtering process. We prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all Lfnorms with 1 ~
spline tends to infinity. We provide estimates for the resolution errors and the
On the asymptotic convergence of B-spline wavelets to Gabor functions
Michael Unser; Akram Aldroubi; Murray Eden
1992-01-01
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.
Advanced BEM for potential problems using spline techniques
Bi, Haifen
1992-01-01
. 1 4. 2 4. 3 4. 4 4. 5 4. 6 4. 7 4. 8 4. 9 4. 10 Bdzier net of quadratic vertex spline. . . . . . Two-dimensional cathodic protection problem . Cubic local cardinal spline function . Pipeline with infinite length . The test problem.../288 1f144 1/72 0 -1/72 -7/144 -7/98-7/72-1/9 0 1/9 25/72 41/72 57/72 1 1 -6 -5 -4 -3 -2 -1 0 1 1 57/72 41/72 25/72 1/9 0 -1/9 -7/72 -7/98-7/144 -t/72 0 1/72 1/144 1/288 0 0 0 Fig 3. 3. Bdzier net of cubic cardinal spline This C -cubic local cardinal...
Error bounded conic spline approximation for NC code
NASA Astrophysics Data System (ADS)
Shen, Liyong
2012-01-01
Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed.
Error bounded conic spline approximation for NC code
NASA Astrophysics Data System (ADS)
Shen, Liyong
2011-12-01
Curve fitting is an important preliminary work for data compression and path interpolator in numerical control (NC). The paper gives a simple conic spline approximation algorithm for G01 code. The algorithm is mainly formed by three steps: divide the G01 code to subsets by discrete curvature detection, find the polygon line segment approximation for each subset within a given error and finally, fit each polygon line segment approximation with a conic Bezier spline. Naturally, B-spline curve can be obtained by proper knots selection. The algorithm is designed straightforward and efficient without solving any global equation system or optimal problem. It is complete with the selection of curve's weight. To design the curve more suitable for NC, we present an interval for the weight selection and the error is then computed.
A note on a nonparametric regression test through penalized splines
Chen, Huaihou; Wang, Yuanjia; Li, Runze; Shear, Katherine
2014-01-01
We examine a test of a nonparametric regression function based on penalized spline smoothing. We show that, similarly to a penalized spline estimator, the asymptotic power of the penalized spline test falls into a small- K or a large-K scenarios characterized by the number of knots K and the smoothing parameter. However, the optimal rate of K and the smoothing parameter maximizing power for testing is different from the optimal rate minimizing the mean squared error for estimation. Our investigation reveals that compared to estimation, some under-smoothing may be desirable for the testing problems. Furthermore, we compare the proposed test with the likelihood ratio test (LRT). We show that when the true function is more complicated, containing multiple modes, the test proposed here may have greater power than LRT. Finally, we investigate the properties of the test through simulations and apply it to two data examples. PMID:25076817
Simple spline-function equations for fracture mechanics calculations
NASA Technical Reports Server (NTRS)
Orange, T. W.
1979-01-01
The paper presents simple spline-function equations for fracture mechanics calculations. A spline function is a sequence of piecewise polynomials of degree n greater than 1 whose coefficients are such that the function and its first n-1 derivatives are continuous. Second-degree spline equations are presented for the compact, three point bend, and crack-line wedge-loaded specimens. Some expressions can be used directly, so that for a cyclic crack propagation test using a compact specimen, the equation given allows the cracklength to be calculated from the slope of the load-displacement curve. For an R-curve test, equations allow the crack length and stress intensity factor to be calculated from the displacement and the displacement ratio.
B-spline active rays segmentation of microcalcifications in mammography
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
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.
How to fly an aircraft with control theory and splines
NASA Technical Reports Server (NTRS)
Karlsson, Anders
1994-01-01
When trying to fly an aircraft as smoothly as possible it is a good idea to use the derivatives of the pilot command instead of using the actual control. This idea was implemented with splines and control theory, in a system that tries to model an aircraft. Computer calculations in Matlab show that it is impossible to receive enough smooth control signals by this way. This is due to the fact that the splines not only try to approximate the test function, but also its derivatives. A perfect traction is received but we have to pay in very peaky control signals and accelerations.
Normal type-2 fuzzy interpolating B-spline curve
NASA Astrophysics Data System (ADS)
Zakaria, Rozaimi; Wahab, Abd Fatah; Gobithaasan, R. U.
2014-07-01
This paper discusses about the construction of a normal type-2 fuzzy interpolating B-spline curves. The construction of this model is based on type-2 fuzzy sets theory. This theory defines complex uncertainty data sets which form the type-2 fuzzy control and data points. In addition, the definition of normal type-2 fuzzy control and data points are also explained in this paper. The processes such as the fuzzification, reduction and defuzzification of interpolating B-spline curves and surfaces are explained. The final section illustrates a numerical example on the practicalities of the proposed model.
Comparison of various drag coefficient expansions using polynomials and splines
NASA Technical Reports Server (NTRS)
Sabot, S. M.; Winchenbach, G. L.; Chapman, G. T.
1984-01-01
The longitudinal differential equation of motion has been used to investigate various aerodynamic expansion techniques. The total drag coefficient was expanded using conventional polynomials and splines with and without floating knot locations. This paper discusses the various techniques and approaches, compares results obtained from simultaneously fitting four separate flights (time vs distance measurements) and outlines the potential advantages and/or disadvantages of the various aerodynamic expansion techniques. It is believed that this is the first time splines have been used in the aerodynamic coefficient estimation process and that these results and techniques are germane to other applications.
T. Brage; C. Froese Fischer; G. Miecznik
1992-01-01
A non-variational Galerkin method, completely based on B-spline methods is introduced and applied to calculations of resonance positions and widths in H- and He. The results agree very well with other theories and experiments. Photodetachment in H- and photoionization of He are also considered.
Castillo, Edward; Castillo, Richard; Fuentes, David; Guerrero, Thomas
2014-01-01
Purpose: Block matching is a well-known strategy for estimating corresponding voxel locations between a pair of images according to an image similarity metric. Though robust to issues such as image noise and large magnitude voxel displacements, the estimated point matches are not guaranteed to be spatially accurate. However, the underlying optimization problem solved by the block matching procedure is similar in structure to the class of optimization problem associated with B-spline based registration methods. By exploiting this relationship, the authors derive a numerical method for computing a global minimizer to a constrained B-spline registration problem that incorporates the robustness of block matching with the global smoothness properties inherent to B-spline parameterization. Methods: The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimal l1-perturbation to block match pairs required to produce a B-spline fitting error within a given tolerance. The sparsity pattern of the optimal perturbation then defines a voxel point cloud subset on which the B-spline fit is a global minimizer to a constrained variant of the B-spline registration problem. As opposed to traditional B-spline algorithms, the optimization step involving the actual image data is addressed by block matching. Results: The performance of the method is measured in terms of spatial accuracy using ten inhale/exhale thoracic CT image pairs (available for download at www.dir-lab.com) obtained from the COPDgene dataset and corresponding sets of expert-determined landmark point pairs. The results of the validation procedure demonstrate that the method can achieve a high spatial accuracy on a significantly complex image set. Conclusions: The proposed methodology is demonstrated to achieve a high spatial accuracy and is generalizable in that in can employ any displacement field parameterization described as a least squares fit to block match generated estimates. Thus, the framework allows for a wide range of image similarity block match metric and physical modeling combinations. PMID:24694135
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
NASA Technical Reports Server (NTRS)
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
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.
Cubic Hermite Bezier spline based reconstruction of implanted aortic valve stents from CT images.
Gessat, Michael; Altwegg, Lukas; Frauenfelder, Thomas; Plass, André; Falk, Volkmar
2011-01-01
Mechanical forces and strain induced by transcatheter aortic valve implantation are usually named as origins for postoperative left ventricular arrhythmia associated with the technique. No quantitative data has been published so far to substantiate this common belief. As a first step towards quantitative analysis of the biomechanic situation at the aortic root after transapical aortic valve implantation, we present a spline-based method for reconstruction of the implanted stent from CT images and for locally measuring the deformation of the stent. PMID:22254890
B-Spline Filtering for Automatic Detection of Calcification Lesions in Mammograms
Bueno, G. [E.T.S. Ingenieros Industrials. Universidad de Castilla-La Mancha. Ciudad Real (Spain); Ruiz, M. [Servicio de Patologia Mamaria. Fundacion Rioja Salud (Spain); Sanchez, S
2006-10-04
Breast cancer continues to be an important health problem between women population. Early detection is the only way to improve breast cancer prognosis and significantly reduce women mortality. It is by using CAD systems that radiologist can improve their ability to detect, and classify lesions in mammograms. In this study the usefulness of using B-spline based on a gradient scheme and compared to wavelet and adaptative filtering has been investigated for calcification lesion detection and as part of CAD systems. The technique has been applied to different density tissues. A qualitative validation shows the success of the method.
Splines minimizing rotation-invariant semi-norms in Sobolev spaces
Jean Duchon
1976-01-01
We define a family of semi-norms ???m,s=(??\\u000a n???2s?? Dmu(?)?2 d?)1\\/2 Minimizing such semi-norms, subject to some interpolating conditions, leads to functions of very simple forms, providing\\u000a interpolation methods that: 1°) preserve polynomials of degree?m?1; 2°) commute with similarities as well as translations\\u000a and rotations of ?n; and 3°) converge in Sobolev spaces Hm+s(?).\\u000a \\u000a Typical examples of such splines are: \\
Evaluation of Assumptions in Soil Moisture Triple Collocation Studies
NASA Astrophysics Data System (ADS)
Yilmaz, M.; Crow, W. T.
2013-12-01
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.
Wang, Yuanjia
2011-07-10
Longitudinal data are routinely collected in biomedical research studies. A natural model describing longitudinal data decomposes an individual's outcome as the sum of a population mean function and random subject-specific deviations. When parametric assumptions are too restrictive, methods modeling the population mean function and the random subject-specific functions nonparametrically are in demand. In some applications, it is desirable to estimate a covariance function of random subject-specific deviations. In this work, flexible yet computationally efficient methods are developed for a general class of semiparametric mixed effects models, where the functional forms of the population mean and the subject-specific curves are unspecified. We estimate nonparametric components of the model by penalized spline (P-spline, Biometrics 2001; 57:253-259), and reparameterize the random curve covariance function by a modified Cholesky decomposition (Biometrics 2002; 58:121-128) which allows for unconstrained estimation of a positive-semidefinite matrix. To provide smooth estimates, we penalize roughness of fitted curves and derive closed-form solutions in the maximization step of an EM algorithm. In addition, we present models and methods for longitudinal family data where subjects in a family are correlated and we decompose the covariance function into a subject-level source and observation-level source. We apply these methods to the multi-level Framingham Heart Study data to estimate age-specific heritability of systolic blood pressure nonparametrically. PMID:21491474
A high-order conservative collocation scheme and its application to global shallow-water equations
NASA Astrophysics Data System (ADS)
Chen, C.; Li, X.; Shen, X.; Xiao, F.
2015-02-01
In this paper, an efficient and conservative collocation method is proposed and used to develop a global shallow-water model. Being a nodal type high-order scheme, the present method solves the pointwise values of dependent variables as the unknowns within each control volume. The solution points are arranged as Gauss-Legendre points to achieve high-order accuracy. The time evolution equations to update the unknowns are derived under the flux reconstruction (FR) framework (Huynh, 2007). Constraint conditions used to build the spatial reconstruction for the flux function include the pointwise values of flux function at the solution points, which are computed directly from the dependent variables, as well as the numerical fluxes at the boundaries of the computational element, which are obtained as Riemann solutions between the adjacent elements. Given the reconstructed flux function, the time tendencies of the unknowns can be obtained directly from the governing equations of differential form. The resulting schemes have super convergence and rigorous numerical conservativeness. A three-point scheme of fifth-order accuracy is presented and analyzed in this paper. The proposed scheme is adopted to develop the global shallow-water model on the cubed-sphere grid, where the local high-order reconstruction is very beneficial for the data communications between adjacent patches. We have used the standard benchmark tests to verify the numerical model, which reveals its great potential as a candidate formulation for developing high-performance general circulation models.
Parallel iterative solution of the Hermite Collocation equations on GPUs II
NASA Astrophysics Data System (ADS)
Vilanakis, N.; Mathioudakis, E.
2014-03-01
Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation.
Free-form deformation using lower-order B-spline for nonrigid image registration.
Sun, Wei; Niessen, Wiro J; Klein, Stefan
2014-01-01
In traditional free-form deformation (FFD) based registration, a B-spline basis function is commonly utilized to build the transformation model. As the B-spline order increases, the corresponding B-spline function becomes smoother. However, the higher-order B-spline has a larger support region, which means higher computational cost. For a given D-dimensional nth-order B-spline, an mth-order B-spline where (m < or = n) has (m +1/n + 1)D times lower computational complexity. Generally, the third-order B-spline is regarded as keeping a good balance between smoothness and computation time. A lower-order function is seldom used to construct the deformation field for registration since it is less smooth. In this research, we investigated whether lower-order B-spline functions can be utilized for efficient registration, by using a novel stochastic perturbation technique in combination with a postponed smoothing technique to higher B-spline order. Experiments were performed with 3D lung and brain scans, demonstrating that the lower-order B-spline FFD in combination with the proposed perturbation and postponed smoothing techniques even results in better accuracy and smoothness than the traditional third-order B-spline registration, while substantially reducing computational costs. PMID:25333118
Meshless cubature over the disk by Thin-Plate Splines
Vianello, Marco
Meshless cubature over the disk by Thin-Plate Splines Alessandro Punzi, Alvise Sommariva a,, Marco papers, the construction of meshless interpolatory cubature formulas by Radial Basis Functions has been on scattered samples of small/moderate size over polygons. Here, we discuss the extension to meshless cubature
A Novel Planar Conformal Antenna Designed With Splines
Stavros Koulouridis; John L. Volakis
2009-01-01
A broadband planar dipole, radiating from 280 to 1000 MHz (with Gain > 0 dBi), is considered for shape optimization using splines. It is demonstrated via simulations and measurements that the 0 dBi gain point is shifted to 190 MHz (32% size reduction). The entire optimization amounts to antenna reshaping.
INCREMENTAL ALGORITHMS FOR THE DESIGN OF TRIANGULAR-BASED SPLINE
Gallier, Jean
Fulfillment of the Requirements for the Degree of Doctor of Philosophy. 2002 Professor Jean Gallier Supervisor;ACKNOWLEDGMENTS I would like to thank my advisor Jean Gallier, who made this dissertation a most challenging SURFACES Dianna Xu Professor Jean Gallier Spline surfaces consisting of triangular patches have a number
Planar point set fairing and fitting by arc splines
Xunnian Yang; Guozhao Wang
2001-01-01
We fair and fit planar point sets by minimal-energy arc splines. The fairing process consists of two steps: computing the optimal tangents for curve interpolation and adjusting the point positions by smoothing the discrete curvatures. To fit the point set with minimal-energy arc curve, a simple linear algorithm is given for computing the optimal tangents. The discrete curvatures derived from
Radial Splines Would Prevent Rotation Of Bearing Race
NASA Technical Reports Server (NTRS)
Kaplan, Ronald M.; Chokshi, Jaisukhlal V.
1993-01-01
Interlocking fine-pitch ribs and grooves formed on otherwise flat mating end faces of housing and outer race of rolling-element bearing to be mounted in housing, according to proposal. Splines bear large torque loads and impose minimal distortion on raceway.
Bezier-and B-spline techniques Hartmut Prautzsch
Prautzsch, Hartmut
BÂ´ezier- and B-spline techniques Hartmut Prautzsch Wolfgang Boehm Marco Paluszny March 26, 2002 #12;2 #12;To Paul de Faget de Casteljau #12;#12;Preface Computer-aided modeling techniques have been, thorough and final proofreading. WolfenbÂ¨uttel, Wolfgang Boehm Caracas, Marco Paluszny Karlsruhe, Hartmut
Cubic spline approximation techniques for parameter estimation in distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Crowley, J. M.; Kunisch, K.
1983-01-01
Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.
Interpolating Mean Rainfall Using Thin Plate Smoothing Splines
M. F. Hutchinson
1995-01-01
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
Thin-plate spline quadrature of geodetic integrals
NASA Technical Reports Server (NTRS)
Vangysen, Herman
1989-01-01
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.
B-Spline vs. Lifting Architecture for Neuroprosthetic Devices
K. E. Thomson; T. Shlien; Yasir Suhail; A. Mason; K. G. Oweiss
2006-01-01
Advances in high-density microelectrode arrays has created a need for high level signal processing to cope with the immense data throughput. The discrete wavelet transform (DWT) has been shown to optimally reduce the amount of data throughput, while concisely preserving the information in the data. Two factorizations, lifting and B-spline, have been proposed for implementing the DWT in hardware. A
John E. Lavery
2002-01-01
We investigate C1-smooth univariate curvature-based cubic L1 interpolating splines in Cartesian and polar coordinates. The coefficients of these splines are calculated by minimizing the L1 norm of curvature. We compare these curvature-based cubic L1 splines with second-derivative-based cubic L1 splines and with cubic L2 splines based on the L2 norm of curvature and of the second derivative. In computational experiments
Fast simulation of x-ray projections of spline-based surfaces using an append buffer.
Maier, Andreas; Hofmann, Hannes G; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca
2012-10-01
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. PMID:22975431
Fast Simulation of X-ray Projections of Spline-based Surfaces using an Append Buffer
Maier, Andreas; Hofmann, Hannes G.; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca
2012-01-01
Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector, and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 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. Source code is available at http://conrad.stanford.edu/ PMID:22975431
Evaluation of the spline reconstruction technique for PET
Kastis, George A., E-mail: gkastis@academyofathens.gr; Kyriakopoulou, Dimitra [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece)] [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece); Gaitanis, Anastasios [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece)] [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece); Fernández, Yolanda [Centre d’Imatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain)] [Centre d’Imatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain); Hutton, Brian F. [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom)] [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom); Fokas, Athanasios S. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)] [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)
2014-04-15
Purpose: The spline reconstruction technique (SRT), based on the analytic formula for the inverse Radon transform, has been presented earlier in the literature. In this study, the authors present an improved formulation and numerical implementation of this algorithm and evaluate it in comparison to filtered backprojection (FBP). Methods: The SRT is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of “custom made” cubic splines. By restricting reconstruction only within object pixels and by utilizing certain mathematical symmetries, the authors achieve a reconstruction time comparable to that of FBP. The authors have implemented SRT in STIR and have evaluated this technique using simulated data from a clinical positron emission tomography (PET) system, as well as real data obtained from clinical and preclinical PET scanners. For the simulation studies, the authors have simulated sinograms of a point-source and three digital phantoms. Using these sinograms, the authors have created realizations of Poisson noise at five noise levels. In addition to visual comparisons of the reconstructed images, the authors have determined contrast and bias for different regions of the phantoms as a function of noise level. For the real-data studies, sinograms of an{sup 18}F-FDG injected mouse, a NEMA NU 4-2008 image quality phantom, and a Derenzo phantom have been acquired from a commercial PET system. The authors have determined: (a) coefficient of variations (COV) and contrast from the NEMA phantom, (b) contrast for the various sections of the Derenzo phantom, and (c) line profiles for the Derenzo phantom. Furthermore, the authors have acquired sinograms from a whole-body PET scan of an {sup 18}F-FDG injected cancer patient, using the GE Discovery ST PET/CT system. SRT and FBP reconstructions of the thorax have been visually evaluated. Results: The results indicate an improvement in FWHM and FWTM in both simulated and real point-source studies. In all simulated phantoms, the SRT exhibits higher contrast and lower bias than FBP at all noise levels, by increasing the COV in the reconstructed images. Finally, in real studies, whereas the contrast of the cold chambers are similar for both algorithms, the SRT reconstructed images of the NEMA phantom exhibit slightly higher COV values than those of FBP. In the Derenzo phantom, SRT resolves the 2-mm separated holes slightly better than FBP. The small-animal and human reconstructions via SRT exhibit slightly higher resolution and contrast than the FBP reconstructions. Conclusions: The SRT provides images of higher resolution, higher contrast, and lower bias than FBP, by increasing slightly the noise in the reconstructed images. Furthermore, it eliminates streak artifacts outside the object boundary. Unlike other analytic algorithms, the reconstruction time of SRT is comparable with that of FBP. The source code for SRT will become available in a future release of STIR.
Radecki, Peter P [Los Alamos National Laboratory; Farinholt, Kevin M [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory; Bement, Matthew T [Los Alamos National Laboratory
2008-01-01
The machining process is very important in many engineering applications. In high precision machining, surface finish is strongly correlated with vibrations and the dynamic interactions between the part and the cutting tool. Parameters affecting these vibrations and dynamic interactions, such as spindle speed, cut depth, feed rate, and the part's material properties can vary in real-time, resulting in unexpected or undesirable effects on the surface finish of the machining product. The focus of this research is the development of an improved machining process through the use of active vibration damping. The tool holder employs a high bandwidth piezoelectric actuator with an adaptive positive position feedback control algorithm for vibration and chatter suppression. In addition, instead of using external sensors, the proposed approach investigates the use of a collocated piezoelectric sensor for measuring the dynamic responses from machining processes. The performance of this method is evaluated by comparing the surface finishes obtained with active vibration control versus baseline uncontrolled cuts. Considerable improvement in surface finish (up to 50%) was observed for applications in modern day machining.
Applications of B-spline Methodology to Three-Dimensional Simulations of Flow over a Cylinder
NASA Astrophysics Data System (ADS)
Kravchenko, Arthur; Moin, Parviz; Shariff, Karim
1997-11-01
A numerical method based on B-splines(A.G. Kravchenko, P. Moin, R. Moser, J. Comp. Phys.), 127, 412-423 (1996) is generalized for turbulence simulations on zonal grids in curvilinear coordinates. The performance of the method is assessed in three-dimensional simulations of a flow over a circular cylinder. Numerical simulations at Re=300 show good agreement with the corresponding spectral calculations. Coefficient of drag and Strouhal shedding frequency agree well with the experimental data for this flow. Large eddy simulations at the subcritical Reynolds number, Re=3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the near-wake, all three simulations are in excellent agreement with each other and agree fairly well with the experimental data of Lourenco and Shih. In the far-wake, the results obtained from the B-spline computations are in better agreement with the experimental data of Ong and Wallace than those obtained in upwind and central finite-difference simulations. The influence of numerical resolution and the spanwise domain size on the three-dimensional simulations will be discussed.
Change detection of lung cancer using image registration and thin-plate spline warping
NASA Astrophysics Data System (ADS)
Almasslawi, Dawood M. S.; Kabir, Ehsanollah
2011-06-01
Lung cancer has the lowest survival rate comparing to other types of cancer and determination of the patient's cancer stage is the most vital issue regarding the cancer treatment process. In most cases accurate estimation of the cancer stage is not easy to achieve. The changes in the size of the primary tumor can be detected using image registration techniques. The registration method proposed in this paper uses Normalized Mutual Information metric and Thin-Plate Spline transformation function for the accurate determination of the correspondence between series of the lung cancer Computed Tomography images. The Normalized Mutual Information is used as a metric for the rigid registration of the images to better estimate the global motion of the tissues and the Thin Plate Spline is used to deform the image in a locally supported manner. The Control Points needed for the transformation are extracted semiautomatically. This new approach in change detection of the lung cancer is implemented using the Insight Toolkit. The results from implementing this method on the CT images of 8 patients provided a satisfactory quality for change detection of the lung cancer.
Reuse of B-spline-based shape interrogation tools for triangular mesh models
NASA Astrophysics Data System (ADS)
Kobashi, Yuji; Suzuki, Junya; Joo, Han Kyul; Maekawa, Takashi
2012-06-01
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.
BSR: B-spline atomic R-matrix codes
NASA Astrophysics Data System (ADS)
Zatsarinny, Oleg
2006-02-01
BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian. New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].
Brown, C; Adcock, A; Azevedo, S; Liebman, J; Bond, E
2010-12-28
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, time-varying, 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.
Nilles, M.A.; See, R.B.; Willoughby, T.C.; Gordon, J.D.
1992-01-01
The collocated sampler program was established in 1988 to estimate the overall precision of the precipitation-monitoring system. This estimate of precision includes variability in the data-collection system from the point of sample collection through storage of the data in the NADP/NTN data base. The ongoing collocated sampler program continues to increase the geographic and climatological coverage of the data on sampling precision for the NADP/NTN. The report describes the collocated sampler study, including the location of sites, installation of equipment, and visits to each site included in the study. In addition, estimates of intrasite precision are provided for sites included in the first 2 years of the study.
Temporal gravity field modeling based on least square collocation with short-arc approach
NASA Astrophysics Data System (ADS)
ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet
2014-05-01
After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.
Paris-Sud XI, UniversitÃ© de
1 Abstract-In this paper, collocated antennas for MIMO systems are presented. The structure that the proposed antenna system can replace a classical system based on space diversity. Index Terms-collocated antennas, radiation pattern diversity, MIMO system, channel capacity measurements I. INTRODUCTION ULTIPLE
Amit Goyal; Shailaja Mandapuram; Bozena Michniak; Laurent Simon
2007-01-01
This work focuses on the estimation of model parameters for a two-pathway transdermal drug-delivery system in which molecules are allowed to transfer from one pathway to the other. Orthogonal collocation, implemented in Mathematica® (Wolfram Research Inc.), was used to reduce the original system into a set of ordinary differential equations (ODEs). After selecting the optimum number of internal collocation points,
ERIC Educational Resources Information Center
Krummes, Cedric; Ensslin, Astrid
2015-01-01
Whereas there exists a plethora of research on collocations and formulaic language in English, this article contributes towards a somewhat less developed area: the understanding and teaching of formulaic language in German as a foreign language. It analyses formulaic sequences and collocations in German writing (corpus-driven) and provides modern…
Miniaturized Multi-Band Antenna via Element Collocation
Martin, R. P.
2012-06-01
The resonant frequency of a microstrip patch antenna may be reduced through the addition of slots in the radiating element. Expanding upon this concept in favor of a significant reduction in the tuned width of the radiator, nearly 60% of the antenna metallization is removed, as seen in the top view of the antenna’s radiating element (shown in red, below, left). To facilitate an increase in the gain of the antenna, the radiator is suspended over the ground plane (green) by an air substrate at a height of 0.250? while being mechanically supported by 0.030? thick Rogers RO4003 laminate in the same profile as the element. Although the entire surface of the antenna (red) provides 2.45 GHz operation with insignificant negative effects on performance after material removal, the smaller square microstrip in the middle must be isolated from the additional aperture in order to afford higher frequency operation. A low insertion loss path centered at 2.45 GHz may simultaneously provide considerable attenuation at additional frequencies through the implementation of a series-parallel, resonant reactive path. However, an inductive reactance alone will not permit lower frequency energy to propagate across the intended discontinuity. To mitigate this, a capacitance is introduced in series with the inductor, generating a resonance at 2.45 GHz with minimum forward transmission loss. Four of these reactive pairs are placed between the coplanar elements as shown. Therefore, the aperture of the lower-frequency outer segment includes the smaller radiator while the higher frequency section is isolated from the additional material. In order to avoid cross-polarization losses due to the orientation of a transmitter or receiver in reference to the antenna, circular polarization is realized by a quadrature coupler for each collocated antenna as seen in the bottom view of the antenna (right). To generate electromagnetic radiation concentrically rotating about the direction of propagation, ideally one-half of the power must be delivered to the output of each branch with a phase shift of 90 degrees and identical amplitude. Due to this, each arm of the coupler is spaced ?/4 wavelength apart.
Evaluating techniques for multivariate classification of non-collocated spatial data.
McKenna, Sean Andrew
2004-09-01
Multivariate spatial classification schemes such as regionalized classification or principal components analysis combined with kriging rely on all variables being collocated at the sample locations. In these approaches, classification of the multivariate data into a finite number of groups is done prior to the spatial estimation. However, in some cases, the variables may be sampled at different locations with the extreme case being complete heterotopy of the data set. In these situations, it is necessary to adapt existing techniques to work with non-collocated data. Two approaches are considered: (1) kriging of existing data onto a series of 'collection points' where the classification into groups is completed and a measure of the degree of group membership is kriged to all other locations; and (2) independent kriging of all attributes to all locations after which the classification is done at each location. Calculations are conducted using an existing groundwater chemistry data set in the upper Dakota aquifer in Kansas (USA) and previously examined using regionalized classification (Bohling, 1997). This data set has all variables measured at all locations. To test the ability of the first approach for dealing with non-collocated data, each variable is reestimated at each sample location through a cross-validation process and the reestimated values are then used in the regionalized classification. The second approach for non-collocated data requires independent kriging of each attribute across the entire domain prior to classification. Hierarchical and non-hierarchical classification of all vectors is completed and a computationally less burdensome classification approach, 'sequential discrimination', is developed that constrains the classified vectors to be chosen from those with a minimal multivariate kriging variance. Resulting classification and uncertainty maps are compared between all non-collocated approaches as well as to the original collocated approach. The non-collocated approaches lead to significantly different group definitions compared to the collocated case. To some extent, these differences can be explained by the kriging variance of the estimated variables. Sequential discrimination of locations with a minimum multivariate kriging variance constraint produces slightly improved results relative to the collection point and the non-hierarchical classification of the estimated vectors.
Uncertainty quantification using multiscale methods for porous media flows
Dostert, Paul Francis
2009-05-15
, polynomial chaos methods and sparse grid collocation methods. We apply the proposed methods to uncertainty quantification problems where the goal is to sample porous media properties given an integrated response. We propose several efficient sampling...
Uji, Akihito; Ooto, Sotaro; Hangai, Masanori; Arichika, Shigeta; Yoshimura, Nagahisa
2013-01-01
Purpose To investigate the effect of B-spline-based elastic image registration on adaptive optics scanning laser ophthalmoscopy (AO-SLO)-assisted capillary visualization. Methods AO-SLO videos were acquired from parafoveal areas in the eyes of healthy subjects and patients with various diseases. After nonlinear image registration, the image quality of capillary images constructed from AO-SLO videos using motion contrast enhancement was compared before and after B-spline-based elastic (nonlinear) image registration performed using ImageJ. For objective comparison of image quality, contrast-to-noise ratios (CNRS) for vessel images were calculated. For subjective comparison, experienced ophthalmologists ranked images on a 5-point scale. Results All AO-SLO videos were successfully stabilized by elastic image registration. CNR was significantly higher in capillary images stabilized by elastic image registration than in those stabilized without registration. The average ratio of CNR in images with elastic image registration to CNR in images without elastic image registration was 2.10 ± 1.73, with no significant difference in the ratio between patients and healthy subjects. Improvement of image quality was also supported by expert comparison. Conclusions Use of B-spline-based elastic image registration in AO-SLO-assisted capillary visualization was effective for enhancing image quality both objectively and subjectively. PMID:24265796
Spline function approximation for velocimeter Doppler frequency measurement
NASA Technical Reports Server (NTRS)
Savakis, Andreas E.; Stoughton, John W.; Kanetkar, Sharad V.
1989-01-01
A spline function approximation approach for measuring the Doppler spectral peak frequency in a laser Doppler velocimeter system is presented. The processor is designed for signal bursts with mean Doppler shift frequencies up to 100 MHz, input turbulence up to 20 percent, and photon counts as low as 300. The frequency-domain processor uses a bank of digital bandpass filters for the capture of the energy spectrum of each signal burst. The average values of the filter output energies, as a function of normalized frequency, are modeled as deterministic spline functions which are linearly weighted to evaluate the spectral peak location associated with the Doppler shift. The weighting coefficients are chosen to minimize the mean square error. Performance evaluation by simulation yields average errors in estimating mean Doppler frequencies within 0.5 percent for poor signal-to-noise conditions associated with a low photon count of 300 photons/burst.
Bases of T-meshes and the refinement of hierarchical B-splines
NASA Astrophysics Data System (ADS)
Berdinsky, Dmitry; Kim, Tae-wan; Cho, Durkbin; Bracco, Cesare; Kiatpanichgij, Sutipong
2015-01-01
In this paper we consider spaces of bivariate splines of bi-degree (m, n) with maximal order of smoothness over domains associated to a two-dimensional grid. We define admissible classes of domains for which suitable combinatorial technique allows us to obtain the dimension of such spline spaces and the number of tensor-product B-splines acting effectively on these domains. Following the strategy introduced recently by Giannelli and Juettler, these results enable us to prove that under certain assumptions about the configuration of a hierarchical T-mesh the hierarchical B-splines form a basis of bivariate splines of bi-degree (m, n) with maximal order of smoothness over this hierarchical T-mesh. In addition, we derive a sufficient condition about the configuration of a hierarchical T-mesh that ensures a weighted partition of unity property for hierarchical B-splines with only positive weights.
Convergence of spectral methods for hyperbolic initial-boundary value systems
NASA Technical Reports Server (NTRS)
Gottlieb, D.; Lustman, L.; Tadmor, E.
1986-01-01
A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as Legendre collocation or tau-methods.
Deformation styles for spline-based skeletal animation
Sven Forstmann; Jun Ohya; Artus Krohn-grimberghe; Ryan Mcdougall
2007-01-01
We present a novel skinned skeletal animation system based on spline-aligned deformations for providing high quality and fully designable deformations in real-time. Our ambition is to allow artists the easy creation of ab- stract, pose-dependent deformation behaviors that might directly be assigned to a large variety of target objects simultaneously. To achieve this goal, we introduce the usage of deformation