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1

One-dimensional fully automatic h-adaptive isogeometric finite element method package

Lipski P., Paszyński M

Computer Science

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2016

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Vol. 17 (4)

439--459

EN

his paper deals with an adaptive finite element method originally developed by Prof. Leszek Demkowicz for hierarchical basis functions. In this paper, we investigate the extension of the adaptive algorithm for isogeometric analysis performed with B-spline basis functions. We restrict ourselves to h-adaptivity, since the polynomial order of approximation must be fixed in the isogeometric case. The classical variant of the adaptive FEM algorithm, as delivered by the group of Prof. Demkowicz, is based on a two-grid paradigm, with coarse and fine grids (the latter utilized as a reference solution). The problem is solved independently over a coarse mesh and a fine mesh. The fine-mesh solution is then utilized as a reference to estimate the relative error of the coarse-mesh solution and to decide which elements to refine. Prof. Demkowicz uses hierarchical basis functions, which (though locally providing Cp−1 continuity) ensure only C0 on the interfaces between elements. The CUDA C library described in this paper switches the basis to B-spline functions and proposes a one-dimensional isogeometric version of the h-adaptive FEM algorithm to achieve global Cp−1 continuity of the solution.

2

Application of the difference equation method to the vibrations analysis of infinite Rayleigh beams by the isogeometric approach

Rakowski J., Wielentejczyk P.

Archives of Civil and Mechanical Engineering

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2015

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Vol. 15, no. 4

1108--1117

EN

An efficient method of vibration investigations of infinite Rayleigh beams applied to the isogeometric analysis called NURBS (non-uniform rational B-splines) is proposed. The research objective is to examine the influence of rotational inertia effects on the dynamic behaviour of the discrete systems approximated by NURBS and compare obtained results with the finite element method (FEM) and exact ones. In NURBS methodology transverse displacements are approximated by quadratic, cubic and quartic B-splines basis functions. For all types of approximations stiffness and consistent mass matrices with rotational inertia effects are found. The equilibrium conditions for an arbitrary interior element are expressed in the form of one difference equation equivalent to the infinite set of equations derived by numerical NURBS formulation for this dynamic problem. The convergence of these equations to the exact differential equations of motion is presented. Assuming the wavy nature of vibration propagation phenomenon the analytical dispersive equations are obtained for various orders of B-spline basis functions. The parametrical analysis of rotational inertia effects on the wave propagation is carried out. The influence of the adopted discretization and the mass distribution is taken into account, as well. The analytical NURBS results are compared with the FEM and exact ones.

3

Application of non-uniform B-Splines of 2-nd order for description vertical distribution of sound speed in water

Makar A.

Hydroacoustics

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2009

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Vol. 12

133-140

EN

Modeling of the vertical distribution of the sound speed in water is useful during determination of the depth on the basis of the acoustic method, modeling refraction phenomena and determination the trajectory of the acoustic wave. For modeling 1D functions (vertical distribution of the sound speed) and 2D (surface of the sea bottom for hydrography) uniform B-Splines was used. In this paper description of uniform B-Splines and description and application of non-uniform B-Splines have been presented.

4

On some application of biorthogonal spline systems to integral equations

Wronicz Z.

Opuscula Mathematica

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2005

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Vol. 25, no. 1

149-160

EN

We consider an operator PN : LP(I) -> Sn(deltaN), such that PN f = f for f mem Sn(deltaN), where Sn(deltaN) is the space of splines of degree n with repect to a given partition deltaN of the interval I. This operator is defined by means of a system of step functions biorthogonal to B-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the aproximation of the solution of this equation are given.

5

B-spline approximation of DSC data of specific heat of NiAl and NiCr alloys

Panas A.

Archives of Thermodynamics

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2003

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Vol. 24, no 4

47-65

EN

B-spline approximation procedures applied to fitting of the high thermal resolution thermophysical data are presented. Both fixed are varied knot algorithms were analysed using DSC (Differential Scanning Calorimetry) data for specific heat of NiAl and NiCr alloys. The tests were performed on specific heat DSC (Differential Scanning Calorimetry) data. The experimental data were selected to show performance of the algorithm in reproducing higher order discontinuity of the approximated thermal characteristics - the experiments were conducted on NiCr alloys within the temperature range from - 20 stopni C to 560 stopni C. The details concerning the measurements are also provided.

6

Neurofuzzy Adaptive B-spline Circuit Performance Modelling Aided by Means of Genetic Algorithm

Horbowski R., Białko M

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2001

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vol. 49, nr 3

445-459

EN

An application of a lattice adaptive neurofuzzy system to circuit performance modelling is presented in the paper. The investigated system makes use of the B-spline membership functions and a structure of the system is determined by means of a genetic algorithm. The presented approach possesses good modelling capabilities and, contrary to non-lattice neurofuzzy approaches, can explore structural dependencies existing in training data supporting us with valuable knowledge about the modelled circuit. This knowledge gives an insight into behaviour of the modelled performance function and makes it possible to reduce a size of the set of circuit variables, to simplify the structure of the model and hence to speed-up its evaluation and identification.