Isogeometric approximation of functions of one variable

Grebennikov, Alexandre

doi:10.1016/0041-5553(82)90095-7

Cited by 15 publications

(11 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…) and S3(xi+2, y) Based on the onevariable cubic spline functions built above, after a certain compression, the following view of the following two-variable interpolation bicubic spline function is formed [4][5][6][7][8]: , y) and S3(xi+2, y) are generated by putting the values of the bicubic spline functions of a variable built above (8) [9,10,11,12,13].…”

Section: Astesj Issn: 2415-6698mentioning

confidence: 99%

Lacol Interpolation Bicubic Spline Method in Digital Processing of Geophysical Signals

Zaynidinov¹,

Bahromov²,

Azimov³

et al. 2021

Adv. sci. technol. eng. syst. j.

View full text Add to dashboard Cite

The paper a cubic spline built through a local base spline and the local interpolation bicubic spline models we offer have been selected. The construction details of the models are given, the two-dimensional local interpolation bicubic spline models considered in this study provide high accuracy in digital processing of signals, which helps experts to make the right decision as a result of digital processing of signals. As an example, the initial values of the geophysical signal were digitally processed and error results were obtained. The error results obtained by digital processing of the geophysical signal of the considered models were compared on the basis of numerical and graphical comparisons.

show abstract

Section: Astesj Issn: 2415-6698mentioning

confidence: 99%

Lacol Interpolation Bicubic Spline Method in Digital Processing of Geophysical Signals

Zaynidinov¹,

Bahromov²,

Azimov³

et al. 2021

Adv. sci. technol. eng. syst. j.

View full text Add to dashboard Cite

show abstract

“…Considering f(x) as a sufficiently smooth function, we assume that It is convenient to rewrite these inequalities as (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) In order for these inequalities to hold and the conditions ^. (0) > 0, 4^.…”

Section: Solution Of the Hermite Interpolation Problem With Constraintsmentioning

confidence: 99%

“…We assume that φ·'(ί) 9 Taking into account the parameter ^ that defines the position of the spline glueing point, the function S(x) has nine parameters. The interpolation and smoothness requirements (2.1) also lead to the system of nine equations.…”

Section: Solution Of the Hermite Interpolation Problem With Constraintsmentioning

confidence: 99%

“…The problem of spline construction with given geometric characteristics seems to be formalized for the first time in the papers by A. I. Grebennikov [9,10], where it was referred to as the problem of isogeometric approximation. In particular, based on the local B-spline approximation methods, it was shown that on a sufficiently detailed mesh the cubic spline retains the geometric properties of the approximated function.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Isogeometric interpolation by generalized splines

Kvasov¹

1996

Russian Journal of Numerical Analysis and Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…This method employs the same basis functions as a technique for describing and analyzing the geometric model, which features the IGA method and CAD-based parameterization of field variables in an isoparametric manner. The first work on isogeometric approximation dates back to 1982 [28]; however, this method is considerably different from the IGA method. Several methods have been devised to help alleviate the difficulties faced by IGA.…”

Section: Introductionmentioning

confidence: 99%

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Wang

Xie

2019

Front. Mech. Eng.

View full text Add to dashboard Cite

Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

show abstract

Isogeometric approximation of functions of one variable

Cited by 15 publications

References 5 publications

Lacol Interpolation Bicubic Spline Method in Digital Processing of Geophysical Signals

Lacol Interpolation Bicubic Spline Method in Digital Processing of Geophysical Signals

Isogeometric interpolation by generalized splines

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Contact Info

Product

Resources

About