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At this work, we propose a local approximation based search method to optimize any function. For this purpose, an approximation method is combined with an estimation filter, and a new local search mechanism is constituted.

RBF network is very efficient interpolation method especially if we have sufficient reference data. Here, reference data refers to the exact value of the objective function at some points. Using this capability of RBFs, we can approximately inspect the vicinity each point in search space. Meanwhile, in order to obtain a smooth, rapid and better trajectory toward the global optimum, the alpha-beta filter can be integrated to this mechanism. For better description and visualization, the operations are defined in 2-dimensional search space; but the outlined procedure can be extended to higher dimensions without loss of generality.

When compared with our previous studies using conventional heuristic methods, approximation based curvilinear local search mechanism provide better minimization performance for almost all benchmark functions. Moreover computational cost of this method too less than heuristics. The number of iteration down to at least 1/10 compared to conventional heuristic algorithm. Additionally, the solution accuracy is very improved for majority of the test cases.

This paper proposes a new search approach to solve optimization problems with less cost. For this purpose, a new local curvilinear search mechanism is built using RBF based approximation technique and alpha-beta estimation filter.

This paper proposes an interpolating approach of the element‐free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non‐homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces.

The authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations.

The local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM‐oriented programs can, thus, be easily extended to provide EFGM approximations.

The robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high‐material discontinuity.

The proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations.

This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well as of a penalty strategy. The resulting formulation provided accurate results including in the case of high‐material discontinuity.

The problems of shear flexible beams are analyzed by the MLPG method based on a locking‐free weak formulation. In order for the weak formulation to be locking‐free, the numerical characteristics of the variational functional for a shear flexible beam, in the thin beam limit, are discussed. Based on these discussions a locking‐free local symmetric weak form is derived by changing the set of two dependent variables in governing equations from that of transverse displacement and total rotation to the set of transverse displacement and transverse shear strain. For the interpolation of the chosen set of dependent variables (i.e. transverse displacement and transverse shear strain) in the locking‐free local symmetric weak form, the recently proposed generalized moving least squares (GMLS) interpolation scheme is utilized, in order to introduce the derivative of the transverse displacement as an additional nodal degree of freedom, independent of the nodal transverse displacement. Through numerical examples, convergence tests are performed. To identify the locking‐free nature of the proposed method, problems of shear flexible beams in the thick beam limit and in the thin beam limit are analyzed, and the numerical results are compared with analytical solutions. The potential of using the truly meshless local Petrov‐Galerkin (MLPG) method is established as a new paradigm in totally locking‐free computational analyses of shear flexible plates and shells.

Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error caused by the meta-model approximation, which leads to the inaccuracy of the optimization results of the reliability evaluation. Taking the local high efficiency of the proxy model, this paper aims to propose a local effective constrained response surface method (LEC-RSM) based on a meta-model.

The operating mechanisms of LEC-RSM is to calculate the index of the local relative importance based on numerical theory and capture the most effective area in the entire design space, as well as selecting important analysis domains for sample changes. To improve the efficiency of the algorithm, the constrained efficient set algorithm (ESA) is introduced, in which the sample point validity is identified based on the reliability information obtained in the previous cycle and then the boundary sampling points that violate the constraint conditions are ignored or eliminated.

The computational power of the proposed method is demonstrated by solving two mathematical problems and the actual engineering optimization problem of a car collision. LEC-RSM makes it easier to achieve the optimal performance, less feature evaluation and fewer algorithm iterations.

This paper proposes a new RSM technology based on proxy model to complete the reliability design. The originality of this paper is to increase the sampling points by identifying the local importance of the analysis domain and introduce the constrained ESA to improve the efficiency of the algorithm.

Integrality of surface mesh is requisite for computational engineering. Nonwatertight meshes with holes can bring inconvenience to applications. Unlike simple modeling or visualization, the downstream industrial application scenarios put forward higher requirements for hole-filling, although many related algorithms have been developed. This study aims at the hole-filling issue in industrial application scenarios.

This algorithm overcomes some inherent weakness of general methods and generates a high-level resulting mesh. Initially, the primitive hole boundary is filled with a more appropriate triangulation which introduces fewer geometric errors. And in order for better performances on shape approximation of the background mesh, the algorithm also refines the initial triangulation with topology optimization. When obtaining the background mesh defining the geometry and size field, spheres on it are packed to determine the vertex configuration and then the resulting high-level mesh is generated.

Through emphasizing geometry recovery and mesh quality, the proposed algorithm works well in hole-filling in industrial application scenarios. Many experimental results demonstrate the reliability and the performance of the algorithm. And the processed meshes are capable of being used for industrial simulation computations directly.

This paper makes input meshes more adaptable for solving programs through local modifications on meshes and perfects the preprocessing technology of finite element analysis (FEA).

This article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).

In the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.

For simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.

The developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.

A new finite volume (FV) method is proposed for the solution of convection‐diffusion equations defined on 2D convex domains of general shape. The domain is approximated by a polygonal region; a structured non‐uniform mesh is defined; the domain is partitioned in control volumes. The conservative form of the problem is solved by imposing the law to be verified on each control volume. The dependent variable is approximated to the second order by means of a quadratic profile. When, for the hyperbolic equation, discontinuities are present, or when the gradient of the solution is very high, a cubic profile is defined in such a way that it enjoys unidirectional monotonicity. Numerical results are given.

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.

The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.

The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.

The current study paves the road for future studies on dynamic and static crack propagation problems.

The purpose of this study is, First, to leverage the limitation of annotated data and to identify the cognitive level of learning objectives efficiently, this study adopts transfer learning by using word2vec and a bidirectional gated recurrent units (GRU) that can fully take into account the context and improves the classification of the model. This study adds a layer based on attention mechanism (AM), which captures the context vector and gives keywords higher weight for text classification. Second, this study explains the authors’ model’s results with local interpretable model-agnostic explanations (LIME).

Bloom's taxonomy levels of cognition are commonly used as a reference standard for identifying e-learning contents. Many action verbs in Bloom's taxonomy, however, overlap at different levels of the hierarchy, causing uncertainty regarding the cognitive level expected. Some studies have looked into the cognitive classification of e-learning content but none has looked into learning objectives. On the other hand, most of these research papers just adopt classical machine learning algorithms. The main constraint of this study is the availability of annotated learning objectives data sets. This study managed to build a data set of 2,400 learning objectives, but this size remains limited.

This study’s experiments show that the proposed model achieves highest scores of accuracy: 90.62%, F1-score and loss. The proposed model succeeds in classifying learning objectives, which contain ambiguous verb from the Bloom’s taxonomy action verbs, while the same model without the attention layer fails. This study’s LIME explainer aids in visualizing the most essential features of the text, which contributes to justifying the final classification.

In this study, the main objective is to propose a model that outperforms the baseline models for learning objectives classification based on the six cognitive levels of Bloom's taxonomy. In this sense, this study builds the bidirectional GRU (BiGRU)-attention model based on the combination of the BiGRU algorithm with the AM. This study feeds the architecture with word2vec embeddings. To prove the effectiveness of the proposed model, this study compares it with four classical machine learning algorithms that are widely used for the cognitive classification of text: Bayes naive, logistic regression, support vector machine and K-nearest neighbors and with GRU. The main constraint related to this study is the absence of annotated data; there is no annotated learning objective data set based on Bloom’s taxonomy's cognitive levels. To overcome this problem, this study seemed to have no choice but to build the data set.