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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: 5 March 2018

Xiaogang Wang, Wutao Qin, Yu Wang and Naigang Cui

This paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering…

Abstract

Purpose

This paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering plays an important role in many science and engineering fields for estimating the state of dynamic system, but the existing filtering algorithms are mainly used for solving the problem of Gauss system.

Design/methodology/approach

Under the Bayesian framework, the time update of this filtering is based on solving Fokker–Planck equation, while the measurement update uses the Bayes formula directly. Therefore, this novel algorithm can be applied to nonlinear, non-Gaussian estimation. To reduce the computational complexity due to standard meshing, an adaptive meshing algorithm proposed which includes the coarse meshing, significant domain determination that is generated using extended Kalman filtering and Chebyshev’s inequality theorem, and value assignment for significant domain. Simulations are conducted on a reentry body tracking problem to demonstrate the effectiveness of this novel algorithm.

Findings

In this way, finer grid points can be placed in the regions with high conditional probability density, while the grid points with low conditional probability density can be neglected. The simulation results indicate that the novel algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

Practical implications

A novel Bayesian filtering based on solving the Fokker–Planck equation using adaptive meshing is proposed, and the simulations show that algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

Originality/value

A novel nonlinear filtering based on solving the Fokker–Planck equation is proposed. The novel algorithm is suitable for non-Gauss system, and can achieve similar accuracy compared to the standard meshing with the significant reduction of computational burden.

Details

Aircraft Engineering and Aerospace Technology, vol. 90 no. 2
Type: Research Article
ISSN: 1748-8842

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Article
Publication date: 1 February 1987

Ajay Kela, Mukul Saxena and Renato Perucchio

This paper deals initially with a new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially…

Abstract

This paper deals initially with a new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially addressable quaternary trees (for 2D work) or octal trees (for 3D work). Because such meshes are inherently hierarchical as well as spatially addressable, they permit efficient substructuring techniques to be used for both global analysis and incremental re‐meshing and re‐analysis. The paper summarizes the global and incremental techniques, and presents some results from an experimental closed loop 2D system in which meshing, analysis, error evaluation, and re‐meshing and re‐analysis are done automatically and adaptively. The paper concludes with a progress report on a 3D implementation.

Details

Engineering Computations, vol. 4 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 15 August 2019

Etienne Muller, Dominique Pelletier and André Garon

This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing

Abstract

Purpose

This paper aims to focus on characterization of interactions between hp-adaptive time-integrators based on backward differentiation formulas (BDF) and adaptive meshing based on Zhu and Zienkiewicz error estimation approach. If mesh adaptation only occurs at user-supplied times and results in a completely new mesh, it is necessary to stop the time-integration at these same times. In these conditions, one challenge is to find an efficient and reliable way to restart the time-integration. The authors investigate what impact grid-to-grid interpolation errors have on the relaunch of the computation.

Design/methodology/approach

Two restart strategies of the time-integrator were used: one based on resetting the time-step size h and time-integrator order p to default values (used in the initial startup phase), and another designed to restart with the time-step size h and order p used by the solver prior to remeshing. The authors also investigate the benefits of quadratically interpolate the solution on the new mesh. Both restart strategies were used to solve laminar incompressible Navier–Stokes and the Unsteady Reynolds Averaged Naviers-Stokes (URANS) equations.

Findings

The adaptive features of our time-integrators are excellent tools to quantify errors arising from the data transfer between two grids. The second restart strategy proved to be advantageous only if a quadratic grid-to-grid interpolation is used. Results for turbulent flows also proved that some precautions must be taken to ensure grid convergence at any time of the simulation. Mesh adaptation, if poorly performed, can indeed lead to losing grid convergence in critical regions of the flow.

Originality/value

This study exhibits the benefits and difficulty of assessing both spatial error estimates and local error estimates to enhance the efficiency of unsteady computations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 2003

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 2001

Jaroslav Mackerle

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography…

Abstract

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Details

Engineering Computations, vol. 18 no. 5/6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 18 June 2019

Yiyi Dong, Si Yuan and Qinyan Xing

This study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element…

Abstract

Purpose

This study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy projection (EEP) technique.

Design/methodology/approach

In view of the inflexibility of the existing global dimension-by-dimension (D-by-D) recovery method via EEP technique, in which displacements are recovered through element strips, an improved element D-by-D recovery strategy was proposed, which enables the EEP recovery of super-convergent displacements to be implemented mostly on a single element. Accordingly, a posteriori error estimate in maximum norm was established and an EEP-based adaptive FE strategy of h-version with local mesh refinement was developed.

Findings

Representative numerical examples, including stress concentration and singularity problems, were analyzed; the results of which show that the adaptively generated meshes reasonably reflect the local difficulties inherent in the physical problems and the proposed adaptive analysis can produce FE displacement solutions satisfying the user-specified tolerances in maximum norm with an almost optimal adaptive convergence rate.

Originality/value

The proposed element D-by-D recovery method is a more efficient and flexible displacement recovery method, which is implemented mostly on a single element. The EEP-based adaptive FE analysis can produce displacement solutions satisfying the specified tolerances in maximum norm with an almost optimal convergence rate and thus can be expected to apply to other 2D problems.

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Article
Publication date: 16 November 2018

Soheil Mohajerani, Duruo Huang, Gang Wang, Seyed-Mohammad Esmaeil Jalali and Seyed Rahman Torabi

This study aims to develop an efficient algorithm for generation of conforming mesh for seepage analysis through 3D discrete fracture networks (DFN).

Abstract

Purpose

This study aims to develop an efficient algorithm for generation of conforming mesh for seepage analysis through 3D discrete fracture networks (DFN).

Design/methodology/approach

The algorithm is developed based on a refined conforming Delaunay triangulation scheme, which is then validated using analytical solutions. The algorithm is well able to meet the challenge of meshing complex geometry of DFNs.

Findings

A series of sensitivity analysis have been performed to evaluate the effect of meshing parameters on steady state solution of Darcy flow using a finite element scheme. The results show that an optimized minimum internal angle of meshing elements should be predetermined to guarantee termination of the algorithm.

Originality/value

The developed algorithm is computationally efficient, fast and is of low cost. Furthermore, it never changes the geometrical structure and connectivity pattern of the DFN.

Details

Engineering Computations, vol. 35 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 10 May 2019

Kumar Kaushik Ranjan, Sandeep Kumar, Amit Tyagi and Ambuj Sharma

The real challenge in the solution of contact problems is the lack of an optimal adaptive scheme. As the contact zone is a priori unknown, successive refinement and…

Abstract

Purpose

The real challenge in the solution of contact problems is the lack of an optimal adaptive scheme. As the contact zone is a priori unknown, successive refinement and iterative method are necessary to obtain a high-accuracy solution. The purpose of this paper is to provide an optimal adaptive scheme based on second-generation finite element wavelets for the solution of non-linear variational inequality of the contact problem.

Design/methodology/approach

To generate an elementary multi-resolution mesh, the authors used hierarchical bases (HB) composed of Lagrange finite element interpolation functions. These HB functions are customized using second-generation wavelet techniques for a fast convergence rate. At each step of the algorithm, the active set method along with mesh adaptation is used for solving the constrained minimization problem of contact case. Wavelet coefficients-based error indicators are used, and computation is focused on mesh zones with a high error indication. The authors take advantage of the wavelet transform to develop a parameter-free adaptive scheme to generate an appropriate and optimal mesh.

Findings

Adaptive wavelet Galerkin scheme (AWGS), a newly developed method for multi-scale mesh adaptivity in this work, is a combination of the second-generation wavelet transform and finite element method and significantly improves the accuracy of the results without approximating an additional problem of error estimation equations. A comparative study is performed taking a solution on a highly refined mesh and results are generated using AWGS.

Practical implications

The proposed adaptive technique can be utilized in the simulation of mechanical and biomechanical structures where multiple bodies come into contact with each other. The algorithm of the method is easy to implement and found to be successful in producing a sufficiently accurate solution with relatively less number of mesh nodes.

Originality/value

Although many error estimation techniques have been developed over the past several years to solve contact problems adaptively, because of boundary non-linearity development, a reliable error estimator needs further investigation. The present study attempts to resolve this problem without having to recompute the entire solution on a new mesh.

Details

Engineering Computations, vol. 36 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 21 July 2020

Tadashi Yamaguchi, Yoshihiro Kawase and Shota Ishimura

This paper aims to propose a method to create 3-D finite element meshes automatically using the Delaunay tetrahedralization with the weighted node density technique. Using…

Abstract

Purpose

This paper aims to propose a method to create 3-D finite element meshes automatically using the Delaunay tetrahedralization with the weighted node density technique. Using this method, the adaptive finite element analysis (FEA) was carried out for the calculation of the magnetic field of an eddy current verification model to clarify the usefulness of the method. Moreover, the error evaluation function for the adaptive FEA was also discussed.

Design/methodology/approach

The method to create the 3-D finite element meshes using the Delaunay tetrahedralization is realized by the weighted node density technique, and Zienkiewicz-Zhu’s error estimator is used as the error evaluation function of the adaptive FEA.

Findings

The magnetic flux density vectors on the node in the error evaluation function for the adaptive FEA should be calculated with the weighted average by the reciprocal of the volume of elements.

Originality/value

This paper describes the method to create 3-D finite element meshes and the comparison among calculation methods of the magnetic flux density vectors on the node for the error estimator.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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