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1 – 6 of 6Mehdi Dehghan, Baharak Hooshyarfarzin and Mostafa Abbaszadeh
This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover…
Abstract
Purpose
This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover, this method does not require establishing grids in the computational domain.
Design/methodology/approach
In this study, the authors present a meshfree method based on Pascal polynomial expansion for the numerical solution of the Sobolev equation. In general, Sobolev-type equations have several applications in physics and mechanical engineering.
Findings
The authors use the Crank-Nicolson scheme to discrete the time variable and the Pascal polynomial-based (PPB) method for discretizing the spatial variables. But it is clear that increasing the value of the final time or number of time steps, will bear a lot of costs during numerical simulations. An important purpose of this paper is to reduce the execution time for applying the PPB method. To reach this aim, the proper orthogonal decomposition technique has been combined with the PPB method.
Originality/value
The developed procedure is tested on various examples of one-dimensional, two-dimensional and three-dimensional versions of the governed equation on the rectangular and irregular domains to check its accuracy and validity.
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Keywords
Long Thanh Cung, Nam Hoang Nguyen, Pierre Yves Joubert, Eric Vourch and Pascal Larzabal
The purpose of this paper is to propose an approach, which is easy to implement, for estimating the thickness of the air layer that may separate metallic parts in some…
Abstract
Purpose
The purpose of this paper is to propose an approach, which is easy to implement, for estimating the thickness of the air layer that may separate metallic parts in some aeronautical assemblies, by using the eddy current method.
Design/methodology/approach
Based on an experimental study of the coupling of a magnetic cup core coil sensor with a metallic layered structure (consisting of first metal layer/air layer/second metal layer), which is confirmed by finite element modelling simulations, an inversion technique relying on a polynomial forward model of the coupling is proposed to estimate the air layer thickness. The least squares and the nonnegative least squares algorithms are applied and analysed to obtain the estimation results.
Findings
The choice of an appropriate inversion technique to optimize the estimation results is dependent on the signal-to-noise ratio of measured data. The obtained estimation error is smaller than a few percent, for both simulated and experimental data. The proposed approach can be used to estimate both the air layer thickness and the second metal layer thickness simultaneously/separately.
Originality/value
This model-based approach is easy to implement and available to all types of eddy current sensors.
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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.
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Behrooz Ariannezhad, Shahram Shahrooi and Mohammad Shishesaz
1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO…
Abstract
Purpose
1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.
Design/methodology/approach
Using appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).
Findings
By doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.
Originality/value
The present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].
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Xiaosong Du and Leifur Leifsson
Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is…
Abstract
Purpose
Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models.
Design/methodology/approach
In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels.
Findings
To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent.
Originality/value
The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.
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Christos Salis, Nikolaos V. Kantartzis and Theodoros Zygiridis
The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as…
Abstract
Purpose
The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as simulating the performance of those devices via deterministic approaches may lead to a misinterpretation of the extracted outcomes. This paper aims to present a novel heuristic for the sparse representation of the polynomial chaos (PC) expansion of the output of interest, aiming at calculating the involved coefficients with a small computational cost.
Design/methodology/approach
This paper presents a novel heuristic that aims to develop a sparse PC technique based on anisotropic index sets. Specifically, this study’s approach generates those indices by using the mean elementary effect of each input. Accurate outcomes are extracted in low computational times, by constructing design of experiments (DoE) which satisfy the D-optimality criterion.
Findings
The method proposed in this study is tested on three test problems; the first one involves a transmission line that exhibits several random dielectrics, while the second and the third cases examine the effects of various random design parameters to the transmission coefficient of microwave filters. Comparisons with the Monte Carlo technique and other PC approaches prove that accurate outcomes are obtained in a smaller computational cost, thus the efficiency of the PC scheme is enhanced.
Originality/value
This paper introduces a new sparse PC technique based on anisotropic indices. The proposed method manages to accurately extract the expansion coefficients by locating D-optimal DoE.
Details