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Article
Publication date: 25 February 2014

Dragan Ribarić and Gordan Jelenić

In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of…

Abstract

Purpose

In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance.

Design/methodology/approach

Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples.

Findings

The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom.

Research limitations/implications

The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples.

Originality/value

A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.

Details

Engineering Computations, vol. 31 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 14 August 2017

Ming-min Liu, L.Z. Li and Jun Zhang

The purpose of this paper is to discuss a data interpolation method of curved surfaces from the point of dimension reduction and manifold learning.

Abstract

Purpose

The purpose of this paper is to discuss a data interpolation method of curved surfaces from the point of dimension reduction and manifold learning.

Design/methodology/approach

Instead of transmitting data of curved surfaces in 3D space directly, the method transmits data by unfolding 3D curved surfaces into 2D planes by manifold learning algorithms. The similarity between surface unfolding and manifold learning is discussed. Projection ability of several manifold learning algorithms is investigated to unfold curved surface. The algorithms’ efficiency and their influences on the accuracy of data transmission are investigated by three examples.

Findings

It is found that the data interpolations using manifold learning algorithms LLE, HLLE and LTSA are efficient and accurate.

Originality/value

The method can improve the accuracies of coupling data interpolation and fluid-structure interaction simulation involving curved surfaces.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 January 1993

W. JOPPICH and R.A. LORENTZ

We develop new high‐order positive, monotone and convex interpolations, which are to be used in the multigrid context. This means that the value of the interpolant is…

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Abstract

We develop new high‐order positive, monotone and convex interpolations, which are to be used in the multigrid context. This means that the value of the interpolant is calculated only at the midpoints lying between the locations of the given values. As a consequence, these interpolants can be calculated very efficiently. They are then tested in a time‐dependent very large scale integration process simulation application.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 12 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 April 1995

B.P. Leonard, A.P. Lock and M.K. Macvean

The NIRVANA project is concerned with the development of anonoscillatory, integrally reconstructed,volume‐averaged numerical advectionscheme. The conservative, flux‐based…

Abstract

The NIRVANA project is concerned with the development of a nonoscillatory, integrally reconstructed, volume‐averaged numerical advection scheme. The conservative, flux‐based finite‐volume algorithm is built on an explicit, single‐step, forward‐in‐time update of the cell‐average variable, without restrictions on the size of the time‐step. There are similarities with semi‐Lagrangian schemes; a major difference is the introduction of a discrete integral variable, guaranteeing conservation. The crucial step is the interpolation of this variable, which is used in the calculation of the fluxes; the (analytic) derivative of the interpolant then gives sub‐cell behaviour of the advected variable. In this paper, basic principles are described, using the simplest possible conditions: pure one‐dimensional advection at constant velocity on a uniform grid. Piecewise Nth‐degree polynomial interpolation of the discrete integral variable leads to an Nth‐order advection scheme, in both space and time. Nonoscillatory results correspond to convexity preservation in the integrated variable, leading naturally to a large‐Δt generalisation of the universal limited. More restrictive TVD constraints are also extended to large Δt. Automatic compressive enhancement of step‐like profiles can be achieved without exciting “stair‐casing”. One‐dimensional simulations are shown for a number of different interpolations. In particular, convexity‐limited cubic‐spline and higher‐order polynomial schemes give very sharp, nonoscillatory results at any Courant number, without clipping of extrema. Some practical generalisations are briefly discussed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 January 1986

Sergio PISSANETZKY

A magnetization table describing the magnetic properties of the material of interest is the primary input for any computer program expected to calculate magnetic fields or…

Abstract

A magnetization table describing the magnetic properties of the material of interest is the primary input for any computer program expected to calculate magnetic fields or other magnetic parameters in a nonlinear case. Magnetization tables, however, consist of discrete points, and the program assumes some interpolation rule to calculate values between them. There exists a variety of interpolation schemes, and some of them can produce very large errors and even unphysical results when the intervals are not narrow enough. Unfortunately, it was found that intervals used in practice are seldom narrow enough. The accurate interpolation of magnetization tables thus becomes a central issue in the numerical solution of nonlinear magnetic problems. We discuss several interpolation schemes used in practice. We propose a new one that is guaranteed to give physical results, and we address the question as to how wide the table invervals can be if a desired accuracy is specified. The discussion is illustrated with many examples.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 5 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 25 May 2021

Miaomiao Yang, Xinkun Du and Yongbin Ge

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate…

Abstract

Purpose

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high wavenumber problems, but also the variable wave number problems.

Design/methodology/approach

In this paper, the authors developed a meshless collocation method by using barycentric Lagrange interpolation basis function based on the Chebyshev nodes to deduce the scheme for solving the three-dimensional Helmholtz equation. First, the spatial variables and their partial derivatives are treated by interpolation basis functions, and the collocation method is established for solving second order differential equations. Then the differential matrix is employed to simplify the differential equations which is on a given test node. Finally, numerical experiments show the accuracy and effectiveness of the proposed method.

Findings

The numerical experiments show the advantages of the present method, such as less number of collocation nodes needed, shorter calculation time, higher precision, smaller error and higher efficiency. What is more, the numerical solutions agree well with the exact solutions.

Research limitations/implications

Compared with finite element method, finite difference method and other traditional numerical methods based on grid solution, meshless method can reduce or eliminate the dependence on grid and make the numerical implementation more flexible.

Practical implications

The Helmholtz equation has a wide application background in many fields, such as physics, mechanics, engineering and so on.

Originality/value

This meshless method is first time applied for solving the 3D Helmholtz equation. What is more the present work not only gives the relationship of interpolation nodes but also the test nodes.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Book part
Publication date: 21 November 2014

Eric Ghysels and J. Isaac Miller

We analyze the sizes of standard cointegration tests applied to data subject to linear interpolation, discovering evidence of substantial size distortions induced by the…

Abstract

We analyze the sizes of standard cointegration tests applied to data subject to linear interpolation, discovering evidence of substantial size distortions induced by the interpolation. We propose modifications to these tests to effectively eliminate size distortions from such tests conducted on data interpolated from end-of-period sampled low-frequency series. Our results generally do not support linear interpolation when alternatives such as aggregation or mixed-frequency-modified tests are possible.

Details

Essays in Honor of Peter C. B. Phillips
Type: Book
ISBN: 978-1-78441-183-1

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Article
Publication date: 2 February 2015

Songhao Shang

The purpose of this paper is to propose a new temporal disaggregation method for time series based on the accumulated and inverse accumulated generating operations in grey…

Abstract

Purpose

The purpose of this paper is to propose a new temporal disaggregation method for time series based on the accumulated and inverse accumulated generating operations in grey modeling and the interpolation method.

Design/methodology/approach

This disaggregation method includes three main steps, including accumulation, interpolation, and differentiation (AID). First, a low frequency flow series is transformed to the corresponding stock series through accumulated generating operation. Then, values of the stock series at unobserved time is estimated through appropriate interpolation method. And finally, the disaggregated stock series is transformed back to high frequency flow series through inverse accumulated generating operation.

Findings

The AID method is tested with a sales series. Results shows that the disaggregated sales data are satisfactory and reliable compared with the original data and disaggregated data using a time series model. The AID method is applicable to both long time series and grey series with insufficient information.

Practical implications

The AID method can be easily used to disaggregate low frequency flow series.

Originality/value

The AID method is a combination of grey modeling technique and interpolation method. Compared with other disaggregation methods, the AID method is simple, and does not require auxiliary information or plausible minimizing criterion required by other disaggregation methods.

Details

Grey Systems: Theory and Application, vol. 5 no. 1
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 1 January 1993

E.A. BADEA and S. PISSANETZKY

The accurate interpolation of magnetization tables is of paramount importance in the design of high‐precision magnets used for particle accelerators or for magnetic…

Abstract

The accurate interpolation of magnetization tables is of paramount importance in the design of high‐precision magnets used for particle accelerators or for magnetic resonance imaging of the human body. Cubic spline interpolation is normally used in combination with the fast converging Newton‐Raphson scheme in the two‐dimensional finite element modelling of such magnets. We compare cubic spline interpolation with experiment, using the magnetization tables as a source of carefully measured experimental data. We show that, in all examined cases, cubic spline interpolation introduces errors large enough to invalidate a design. We also propose a simple solution to the problem, thus combining the best of all worlds: the speed and convergence properties of Newton‐Raphson, the accuracy of a good interpolation scheme, and the convenient mathematical properties of cubic splines. We examine both two‐dimensional and three‐dimensional cases.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 12 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 January 2006

Herbert De Gersem, Mariana Ion, Markus Wilke, Thomas Weiland and Andrzej Demenko

To propose trigonometric interpolation in combination with both sliding‐surface and moving‐band techniques for modelling rotation in finite‐element electrical machine…

Abstract

Purpose

To propose trigonometric interpolation in combination with both sliding‐surface and moving‐band techniques for modelling rotation in finite‐element electrical machine models. To show that trigonometric interpolation is at least as accurate and efficient as standard stator‐rotor coupling schemes.

Design/methodology/approach

Trigonometric interpolation is explained concisely and put in a historical perspective. Characteristic drawbacks of trigonometric interpolation are alleviated one by one. A comparison with the more common locked‐step linear‐interpolation and mortar‐element approaches is carried out.

Findings

Trigonometric interpolation offers a higher accuracy and therefore can outperform standard stator‐rotor coupling techniques when equipped with an appropriate iterative solver incorporating Fast Fourier Transforms to reduce the higher computational cost.

Originality/value

The synthetic interpretation of trigonometric interpolation as a spectral‐element approach in the machine's air gap, the efficient iterative solver combining conjugate gradients with Fast Fourier Transforms. The unified application to both sliding‐surface and moving‐band techniques.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

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