Improving the Efficiency of Calculating B-splines in parallel Programming Tasks

2021 ◽  
Vol 12 (5) ◽  
pp. 267-273
Author(s):  
P. M. Nikolaev ◽  
Keyword(s):  
Parallel Programming ◽  
Data Exchange ◽  
Limited Resource ◽  
Buffer Size ◽  
B Spline ◽  
B Splines ◽  
Common Solution ◽  
Shared Data ◽  
Multithreaded Programs ◽  
Intermediate Data

The use of parallel computing tools can significantly reduce the execution time of calculations in many engineer­ing tasks. One of the main difficulties in the development of multithreaded programs remains the organization of simultaneous access from different threads to shared data. The most common solution to this problem is to use locking facilities when accessing shared data. There are a number of tasks where data sharing is not needed, but you need to synchronize access to a limited resource, such as a temporary buffer. In such tasks, there is no data exchange between different threads, but there is an object that at a given time can be used by the code of only one thread. One such task is calculating the value of a B-spline. The software implementation of the functions for calculating B-splines, performed according to classical algorithms, requires the use of blocking objects when accessing the common array of intermediate data from different threads. This reduces the degree of parallelism and reduces the efficiency of computational programs using B-splines running on multiprocessor computing systems. The article discusses a way to improve the efficiency of calculating B-splines in parallel programming tasks by eliminating locks when accessing general modified data. A soft­ware implementation is presented in the form of a C++ class template, which provides placement of a temporary array used for calculating a B-spline into a local buffer of a given size with the possibility of increasing it if necessary. Using the developed template in conjunction with the threadlocal qualifier reduces the number of requests for increasing the buffer for high degree B-splines (larger than the initially specified buffer size). It is also possible to implement this scheme using the std::vector template of the C++ STL Standard Library. The results of the application of the developed class when calculating the values of B-splines in a multithreaded environment, showing a reduction in the calculation time in proportion to an increase in the number of computational processors, are presented. The methods of specifying arrays for storing intermediate calculation results considered in this article can be used in other parallel programming tasks.

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

scholarly journals Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
C. H. Garcia-Capulin ◽  
F. J. Cuevas ◽  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez
Keyword(s):  
Genetic Algorithm ◽  
Geometric Modeling ◽  
Data Set ◽  
Surface Approximation ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Surface Dimension ◽  
Hierarchical Genetic Algorithm

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.

scholarly journals Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

2019 ◽  
pp. 1-8
Author(s):  
Kanchan Lata Gupta ◽  
B. Kunwar ◽  
V. K. Singh
Keyword(s):  
Scaling Function ◽  
Simple Procedure ◽  
Smoothness Property ◽  
Vanishing Moments ◽  
B Spline ◽  
B Splines ◽  
Compactly Supported ◽  
Spline Wavelets ◽  
Vanishing Moment ◽  
Rule Order

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

On the Literature of B-Spline Interpolation Functions

2009 ◽  
pp. 214-222
Author(s):  
Carlo Ciulla
Keyword(s):  
Scientific Community ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Spline Functions ◽  
Great Effort ◽  
Formal Definition ◽  
B Spline ◽  
B Splines ◽  
Scientific Disciplines ◽  
Definition Of

This chapter reviews the extensive and comprehensive literature on B-Splines. In the forthcoming text emphasis is given to hierarchy and formal definition of polynomial interpolation with specific focus to the subclass of functions that are called B-Splines. Also, the literature is reviewed with emphasis on methodologies and applications of B-Splines within a wide array of scientific disciplines. The review is conducted with the intent to inform the reader and also to acknowledge the merit of the scientific community for the great effort devoted to B-Splines. The chapter concludes emphasizing on the proposition that the unifying theory presented throughout this book has for what concerns two specific cases of B-Spline functions: univariate quadratic and cubic models.

scholarly journals Bayesian B-spline mapping for dynamic quantitative traits

2012 ◽  
Vol 94 (2) ◽  
pp. 85-95 ◽  
Author(s):  
JUN XING ◽  
JIAHAN LI ◽  
RUNQING YANG ◽  
XIAOJING ZHOU ◽  
SHIZHONG XU
Keyword(s):  
Legendre Polynomial ◽  
Legendre Polynomials ◽  
Simulated Dataset ◽  
Model Parameters ◽  
B Spline ◽  
B Splines ◽  
Bayesian Mapping ◽  
Bayesian Shrinkage ◽  
Dynamic Traits ◽  
Over Time

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

Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
Corinna Harmening ◽  
Hans Neuner
Keyword(s):  
Data Analysis ◽  
Laser Scanner ◽  
Point Clouds ◽  
Optimal Number ◽  
Deformation Analysis ◽  
Control Points ◽  
Trial And Error ◽  
B Spline ◽  
B Splines ◽  
Spline Surfaces

AbstractFreeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis.A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures.In [The present paper continues these investigations. If necessary, the methods proposed in [The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.

Approximation of 3D convection diffusion equation using DQM based on modified cubic trigonometric B-splines

2020 ◽  
pp. 1-10
Author(s):  
Mohammad Tamsir ◽  
Neeraj Dhiman ◽  
F.S. Gill ◽  
Robin
Keyword(s):  
Diffusion Equation ◽  
Numerical Solutions ◽  
Basis Functions ◽  
B Spline ◽  
Convection Diffusion ◽  
B Splines ◽  
Convection Diffusion Equation ◽  
First Order ◽  
The Stability ◽  
Derivatives Of

This paper presents an approximate solution of 3D convection diffusion equation (CDE) using DQM based on modified cubic trigonometric B-spline (CTB) basis functions. The DQM based on CTB basis functions are used to integrate the derivatives of space variables which transformed the CDE into the system of first order ODEs. The resultant system of ODEs is solved using SSPRK (5,4) method. The solutions are approximated numerically and also presented graphically. The accuracy and efficiency of the method is validated by comparing the solutions with existing numerical solutions. The stability analysis of the method is also carried out.

A B-Spline Based Higher-Order Panel Method Applied to Marine Hydrodynamic Problems

2008 ◽  
Author(s):  
Chang-Sup Lee ◽  
Byoung-Kwon Ahn ◽  
Gun-Do Kim ◽  
Hyun Yup Lee ◽  
Do-Chun Hong
Keyword(s):  
Boundary Surface ◽  
Higher Order ◽  
Panel Method ◽  
Floating Bodies ◽  
B Spline ◽  
B Splines ◽  
Marine Propellers ◽  
Panel Methods ◽  
Infinite Extent ◽  
Blade Tip

A B-spline based higher order panel method (hereinafter, HiPan) is developed for the motion of bodies in ideal fluid, either of infinite extent or with free boundary surface. In this method, both the geometry and the potential are represented by B-splines, and it guarantees more accurate results than most potential based panel methods. In the present work, we apply the HiPan, which differs with the works at MIT in evaluating the induction integrals, to two major marine hydrodynamic problems: analysis of propulsive performance of the marine propellers and the motion of the floating bodies on the free surface. The present HiPan is shown superior to the constant panel method (hereinafter, CoPan) in predicting flow quantities in the area of the thin trailing edge and blade tip of the propeller. Numerical results are validated by comparison with experimental measurements.

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