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Article
Publication date: 11 July 2008

Pavel Kus, Pavel Solin and Ivo Dolezel

This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are…

Abstract

Purpose

This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority.

Design/methodology/approach

Adaptive hp‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular.

Findings

Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory.

Originality/value

The paper describes results obtained from an original and innovative implementation of the adaptive hp‐FEM.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 3 May 2013

Pavel Karban, František Mach and Ivo Doležel

The paper presents the principal elements of automatic adaptivity built in our 2D software for monolithic solution of multiphysics problems based on a fully adaptive…

Abstract

Purpose

The paper presents the principal elements of automatic adaptivity built in our 2D software for monolithic solution of multiphysics problems based on a fully adaptive finite element method of higher order of accuracy. The adaptive techniques are illustrated by appropriate examples.

Design/methodology/approach

Presented are algorithms for realization of the hadaptivity, padaptivity, hpadaptivity, creation of curvilinear elements for modelling general boundaries and interfaces. Indicated also is the possibility of combining triangular and quadrilateral elements (both classical and curved).

Findings

The presented higher‐order adaptive processes are reliable, robust and lead to a substantial reduction of the degrees of freedom in comparison with the techniques used in low‐order finite element methods. They allow solving examples that are by classical approaches either unsolvable or solvable at a cost of high memory and time of computation.

Research limitations/implications

The adaptive processes described in the paper are still limited to 2D computations. Their computer implementation is highly nontrivial (every physical field in a multiphysics task is generally solved on a different mesh satisfying its specific features) and in 3D the number of possible adaptive steps is many times higher.

Practical implications

The described adaptive techniques may represent a powerful tool for the monolithic solution of complex multiphysics problems.

Originality/value

The presented higher‐order adaptive approach of solution is shown to provide better results than the schemes implemented in professional codes based on low‐order finite element methods. Obtaining the results, moreover, requires less time and computer memory.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 13 September 2011

Pavel Karban, František Mach, Ivo Dolezel and Jerzy Barglik

The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in…

Abstract

Purpose

The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in static magnetic field produced by appropriately arranged permanent magnets.

Design/methodology/approach

The mathematical model consisting of two partial differential equations describing the distribution of the magnetic and temperature fields are solved by a fully adaptive higher‐order finite element method in the monolithic formulation and selected results are validated experimentally.

Findings

The method of solution realized by own code is very fast, robust and exhibits much more powerful features when compared with classical low‐order numerical methods implemented in existing commercial codes.

Research limitations/implications

For sufficiently long arrangements the method provides good results even for 2D model. The principal limitation consists in problems with determining correct boundary conditions for the temperature field (generalized coefficient of convective heat transfer as a function of the temperature and revolutions).

Practical implications

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and determination of their operation parameters.

Originality/value

The paper is a presentation of the fully adaptive higher‐order finite element and its utilization for a monolithic numerical solution of a relatively complicated coupled problem.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 December 2001

Jaroslav Mackerle

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for…

Abstract

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Details

Engineering Computations, vol. 18 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 6 March 2017

David Pánek, Václav Kotlan, Roman Hamar and Ivo Doležel

This paper aims to present a methodology of finding temperature dependencies of selected physical parameters of metals. The method is based on the combination of…

Abstract

Purpose

This paper aims to present a methodology of finding temperature dependencies of selected physical parameters of metals. The method is based on the combination of measurement of the surface temperature of material during the process of heating and subsequent solution of the inverse problem using multi-parametric optimization.

Design/methodology/approach

The methodology is based on measurements and numerical solution of the forward and inverse problem, taking into account all involved nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). The inverse problem is solved by a genetic algorithm.

Findings

The suggested methodology was successfully verified on several metal materials whose temperature-dependent parameters are known. The calculated and measured results exhibit a very good accordance (the differences do not exceed about 10 per cent for room and higher temperatures).

Research limitations/implications

At this moment, the methodology successfully works when the temperature dependence of just one material parameter is to be found (which means that the temperature dependencies of other parameters are known). The accuracy of results also depends on the correctness of other input data.

Practical implications

This paper provides a relatively easy possibility of finding the temperature dependencies of thermal conductivity or heat capacity of various alloys.

Originality/value

The paper proposes a methodology of finding the temperature dependence of a given material parameter that is not known in advance (which is of great importance in case of alloys).

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 7 September 2012

Pavel Karban, František Mach and Ivo Dolezel

The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is…

Abstract

Purpose

The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is solved by the authors' own software and the results are verified experimentally.

Design/methodology/approach

The mathematical model of the problem given by two partial differential equations describing the distribution of the magnetic and temperature fields in the system is solved by a fully adaptive higher‐order finite element method in the hard‐coupled formulation. All material nonlinearities are taken into account.

Findings

The method of solution realized by the code is reliable and works faster in comparison with the existing low‐order finite element codes.

Research limitations/implications

The method works for 2D arrangements with an extremely high accuracy. Its limitations consist mainly in problems of determining the coefficients of convection and radiation for temperature field in the system (respecting both temperature and revolutions).

Practical implications

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and anticipation of their operation parameters.

Originality/value

The paper presents a fully adaptive higher‐order finite element and its utilization for a hard‐coupled numerical solution of the problem of induction heating.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 31 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 August 1996

Ales Svoboda, Hans‐Åke Häggblad and Mats Näsström

Presents a finite element formulation of hot isostatic pressing (HIP) based on a continuum approach using thermal‐elastoviscoplastic constitutive equations with…

Abstract

Presents a finite element formulation of hot isostatic pressing (HIP) based on a continuum approach using thermal‐elastoviscoplastic constitutive equations with compressibility. The formulation takes into consideration dependence of the viscoplastic part on the porosity. Also takes into account the thermomechanical response, including nonlinear effects in both the thermal and mechanical analyses. Implements the material model in an implicit finite element code. Presents experimental procedures for evaluating the inelastic behaviour of metal powders during densification and experimental data. Chooses the simulation of the dilatometer measurement of a cylindrical component during HIP and manufacturing simulation of a turbine component to near net shape (NNS) as a demonstrator example. Both components are made of a hot isostatically pressed hot‐working martensitic steel. Compares the result of the simulation in the form of the final geometry of the container with the geometry of a real component produced by HIP. Makes a comparison between the calculated and measured deformations during the HIP process for the cylindrical component. Measures the final geometry of the turbine component by means of a computer controlled measuring machine (CMM). Performs the complete process from design and simulation to geometry verification within a computer‐aided concurrent engineering (CACE) system.

Details

Engineering Computations, vol. 13 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 25 June 2019

Václav Kotlan, Roman Hamar, Ivan Alexandrovich Smolyanov and Ivo Doležel

The paper aims to describe the modeling of the induction-assisted laser welding process taking into account the keyhole effect and phase changes in the material.

Abstract

Purpose

The paper aims to describe the modeling of the induction-assisted laser welding process taking into account the keyhole effect and phase changes in the material.

Design/methodology/approach

A sophisticated mathematical model of the above heat treatment process is presented, taking into account the above phenomena and all available nonlinearities of the material. Its numerical solution is carried out using the finite element method incorporating algorithms for the deformation of geometry and solution of the flow field.

Findings

Unlike various simplified models solved in the past, this approach incorporating a sophisticated model of heat transfer and flow of melt is able to reach a very accurate solution, differing only by a small error (not more than 8 per cent) from the experiment.

Research limitations/implications

The presented model does not consider several subtle phenomena related to the evaporation of metal after irradiation of the material by a laser beam. In fact, at the heated spot, all three phases of the material coexist. The evaporated metal forms a capillary leak off and forms a cloud above the spot of irradiation. Due to the absorption of laser power in this cloud, the process of heating decelerates, which leads to a decrease in the process efficiency.

Practical implications

The presented model and methodology of its solution may represent a basis for design of the process of laser welding.

Originality/value

The main value is the proposal of numerical model for solution a complex multiphysical model with respecting several physical phenomena whose results are available in a short time and still with a good agreement with the experimental verification.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 10 April 2007

Marc Schober and Manfred Kasper

This paper aims to show that simple geometry‐based hp‐algorithms using an explicit a posteriori error estimator are efficient in wave propagation computation of complex…

Abstract

Purpose

This paper aims to show that simple geometry‐based hp‐algorithms using an explicit a posteriori error estimator are efficient in wave propagation computation of complex structures containing geometric singularities.

Design/methodology/approach

Four different hp‐algorithms are compared with common h‐ and p‐adaptation in electrostatic and time‐harmonic problems regarding efficiency in number of degrees of freedom and runtime. An explicit a posteriori error estimator in energy norm is used for adaptive algorithms.

Findings

Residual‐based error estimation is sufficient to control the adaptation process. A geometry‐based hp‐algorithm produces the smallest number of degrees of freedom and results in shortest runtime. Predicted error algorithms may choose inappropriate kind of refinement method depending on p‐enrichment threshold value. Achieving exponential error convergence is sensitive to the element‐wise decision on h‐refinement or p‐enrichment.

Research limitations/implications

Initial mesh size must be sufficiently small to confine influence of phase lag error.

Practical implications

Information on implementation of hp‐algorithm and use of explicit error estimator in electromagnetic wave propagation is provided.

Originality/value

The paper is a resource for developing efficient finite element software for high‐frequency electromagnetic field computation providing guaranteed error bound.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 26 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 2 January 2009

Uroš Bohinc, Adnan Ibrahimbegovic and Boštjan Brank

The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most…

Abstract

Purpose

The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable plate model (among available hierarchical plate models) for each particular FE of the selected mesh, that is provided as the final output of the mesh adaptivity procedure.

Design/methodology/approach

The model adaptivity procedure can be seen as an appropriate extension to model adaptivity for linear elastic plates of so‐called equilibrated boundary traction approach error estimates, previously proposed for 2D/3D linear elasticity. Model error indicator is based on a posteriori element‐wise computation of improved (continuous) equilibrated boundary stress resultants, and on a set of hierarchical plate models. The paper illustrates the details of proposed model adaptivity procedure for choosing between two most frequently used plate models: the one of Kirchhoff and the other of Reissner‐Mindlin. The implementation details are provided for a particular case of the discrete Kirchhoff quadrilateral four‐node plate FE and the corresponding Reissner‐Mindlin quadrilateral with the same number of nodes. The key feature for those elements that they both provide the same quality of the discretization space (and thus the same discretization error) is the one which justifies uncoupling of the proposed model adaptivity from the mesh adaptivity.

Findings

Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology in guiding the final choice of the optimal model and mesh in analysis of complex plate structures.

Originality/value

The paper confirms that one can make an automatic selection of the most appropriate plate model for thin and thick plates on the basis of proposed model adaptivity procedure.

Details

Engineering Computations, vol. 26 no. 1/2
Type: Research Article
ISSN: 0264-4401

Keywords

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