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Article
Publication date: 10 May 2019

Rituraj Singh and Krishna Mohan Singh

The purpose of this paper is to assess the performance of the stabilised moving least squares (MLS) scheme in the meshless local Petrov–Galerkin (MLPG) method for heat conduction…

Abstract

Purpose

The purpose of this paper is to assess the performance of the stabilised moving least squares (MLS) scheme in the meshless local Petrov–Galerkin (MLPG) method for heat conduction method.

Design/methodology/approach

In the current work, the authors extend the stabilised MLS approach to the MLPG method for heat conduction problem. Its performance has been compared with the MLPG method based on the standard MLS and local coordinate MLS. The patch tests of MLS and modified MLS schemes have been presented along with the one- and two-dimensional examples for MLPG method of the heat conduction problem.

Findings

In the stabilised MLS, the condition number of moment matrix is independent of the nodal spacing and it is nearly constant in the global domain for all grid sizes. The shifted polynomials based MLS and stabilised MLS approaches are more robust than the standard MLS scheme in the MLPG method analysis of heat conduction problems.

Originality/value

The MLPG method based on the stabilised MLS scheme.

Details

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

Keywords

Article
Publication date: 1 April 2022

Can Ban, Na Na Pu, Yi Fei Zhang and Ma Wentao

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Abstract

Purpose

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

Design/methodology/approach

This paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.

Findings

On the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.

Originality/value

This study provides an accurate and efficient meshfree method for simulating crack growth.

Details

Engineering Computations, vol. 39 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 5 July 2021

Abhishek Kumar Singh and Krishna Mohan Singh

The work presents a novel implementation of the generalized minimum residual (GMRES) solver in conjunction with the interpolating meshless local Petrov–Galerkin (MLPG) method to…

Abstract

Purpose

The work presents a novel implementation of the generalized minimum residual (GMRES) solver in conjunction with the interpolating meshless local Petrov–Galerkin (MLPG) method to solve steady-state heat conduction in 2-D as well as in 3-D domains.

Design/methodology/approach

The restarted version of the GMRES solver (with and without preconditioner) is applied to solve an asymmetric system of equations, arising due to the interpolating MLPG formulation. Its performance is compared with the biconjugate gradient stabilized (BiCGSTAB) solver on the basis of computation time and convergence behaviour. Jacobi and successive over-relaxation (SOR) methods are used as the preconditioners in both the solvers.

Findings

The results show that the GMRES solver outperforms the BiCGSTAB solver in terms of smoothness of convergence behaviour, while performs slightly better than the BiCGSTAB method in terms of Central processing Unit (CPU) time.

Originality/value

MLPG formulation leads to a non-symmetric system of algebraic equations. Iterative methods such as GMRES and BiCGSTAB methods are required for its solution for large-scale problems. This work presents the use of GMRES solver with the MLPG method for the very first time.

Details

Engineering Computations, vol. 39 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 2 May 2017

Grand Roman Joldes, Peter Teakle, Adam Wittek and Karol Miller

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate…

Abstract

Purpose

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate reference solutions.

Design/methodology/approach

An adaptive quadrature algorithm which allows user control over integration accuracy, previously developed for integrating boundary value problems, is adapted to elasticity problems. The algorithm allows the development of a convergence study procedure that takes into account both integration and discretisation errors. The convergence procedure is demonstrated using an elasticity problem which has an analytical solution and is then applied to accurately solve a soft-tissue extension problem involving large deformations.

Findings

The developed convergence procedure, based on the presented adaptive integration scheme, allows the computation of accurate reference solutions for challenging problems which do not have an analytical or finite element solution.

Originality/value

This paper investigates the application of adaptive quadrature to solid mechanics problems in engineering analysis using the element-free Galerkin method to obtain accurate reference solutions. The proposed convergence procedure allows the user to independently examine and control the contribution of integration and discretisation errors to the overall solution error. This allows the computation of reference solutions for very challenging problems which do not have an analytical or even a finite element solution (such as very large deformation problems).

Details

Engineering Computations, vol. 34 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 September 2019

E.J. Sellountos, Jorge Tiago and Adelia Sequeira

This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.

Abstract

Purpose

This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.

Design/methodology/approach

The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.

Findings

The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.

Originality/value

The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 May 2023

Mostafa Abbaszadeh, AliReza Bagheri Salec and Afaq Salman Alwan

This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with…

Abstract

Purpose

This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence.

Design/methodology/approach

In the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix.

Findings

This current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries.

Originality/value

The proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 May 1975

APPLIED Technology, Middle East and European marketing and technical support representative of PF Industries Inc, will exhibit ground support equipment supplied to airlines…

Abstract

APPLIED Technology, Middle East and European marketing and technical support representative of PF Industries Inc, will exhibit ground support equipment supplied to airlines worldwide.

Details

Aircraft Engineering and Aerospace Technology, vol. 47 no. 5
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 28 September 2022

Wei Wang, Junping Shi, Xiaoshan Cao and Yifeng Hu

The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding…

Abstract

Purpose

The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.

Design/methodology/approach

In this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.

Findings

On the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.

Originality/value

The proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.

Details

Engineering Computations, vol. 39 no. 9
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 7 April 2015

Sonam Singh and Rama Bhargava

The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid…

Abstract

Purpose

The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid takes place within a square enclosure in the presence of natural convection.

Design/methodology/approach

The physical problem, described with non-linear partial differential equations, is simulated using a hybrid finite element and element free Galerkin method (FEM/EFGM) approach. In energy conservation equation, the fixed-domain, effective heat capacity method is used to take into account the latent heat of phase change. The governing partial differential equations are solved with a meshfree, EFGM near the phase transition front while in the region away from the front with uniform nodal distribution; problem is simulated with traditional FEM.

Findings

A sensitivity analysis of characteristic dimensionless numbers Rayleigh number (Ra), Prandtl number (Pr), Stefan number (ste) is presented in order to investigate their impact on thermal and flow fields. Typically computational times of EFGM are higher than that of FEM. Therefore, by using EFGM only in that portion of physical problem where phase transition occurs, the hybrid FEM/EFGM strategy employed in present paper could reduce the computational time of EFGM while still retaining its accuracy. Also, the consistent performance of the results obtained with this hybrid approach is validated with those already available in literature for some special cases.

Originality/value

The hybrid methodology adopted in this paper, is quite new for solving such type of phase transition problem.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Book part
Publication date: 29 August 2018

Paul A. Pautler

The Bureau of Economics in the Federal Trade Commission has a three-part role in the Agency and the strength of its functions changed over time depending on the preferences and…

Abstract

The Bureau of Economics in the Federal Trade Commission has a three-part role in the Agency and the strength of its functions changed over time depending on the preferences and ideology of the FTC’s leaders, developments in the field of economics, and the tenor of the times. The over-riding current role is to provide well considered, unbiased economic advice regarding antitrust and consumer protection law enforcement cases to the legal staff and the Commission. The second role, which long ago was primary, is to provide reports on investigations of various industries to the public and public officials. This role was more recently called research or “policy R&D”. A third role is to advocate for competition and markets both domestically and internationally. As a practical matter, the provision of economic advice to the FTC and to the legal staff has required that the economists wear “two hats,” helping the legal staff investigate cases and provide evidence to support law enforcement cases while also providing advice to the legal bureaus and to the Commission on which cases to pursue (thus providing “a second set of eyes” to evaluate cases). There is sometimes a tension in those functions because building a case is not the same as evaluating a case. Economists and the Bureau of Economics have provided such services to the FTC for over 100 years proving that a sub-organization can survive while playing roles that sometimes conflict. Such a life is not, however, always easy or fun.

Details

Healthcare Antitrust, Settlements, and the Federal Trade Commission
Type: Book
ISBN: 978-1-78756-599-9

Keywords

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