An overview on some Meshless methods, and a Meshless procedure for solving linear convection-diffusion equation in steady state and nonlinear burgear equation in transient are presented in this paper. The approach termed generically the "Element Free Galerkin method" is based on a weighted moving least square (MLS) interpolation of point data for evaluating the approximation integral. EFG Meshless method uses a background mesh to introducing the Guossian points for solution of the integral equation. In this paper we develop EFG Meshless procedure for linear and nonlinear convection-diffusion equation problems in steady and transient forms. A one dimensional example by different values of peclet number is solved using MATLAB, V6.5 programming and the results are compared with the exact solution. The method is tested for shock wave propagation in example no two.

The importance of focusing on the research of viable models to predict the behaviour of structures which may possess in some cases complex geometries is an issue that is growing in different scientific areas, ranging from the civil and mechanical engineering to the architecture or biomedical devices fields. In these cases, the research effort to find an efficient approach to fit laser scanning point clouds, to the desired surface, has been increasing, leading to the possibility of modelling as-built/as-is structures and components’ features. However, combining the task of surface reconstruction and the implementation of a structural analysis model is not a trivial task. Although there are works focusing those different phases in separate, there is still an effective need to find approaches able to interconnect them in an efficient way. Therefore, achieving a representative geometric model able to be subsequently submitted to a structural analysis in a similar based platform is a fundamental step to establish an effective expeditious processing workflow. With the present work, one presents an integrated methodology based on the use of Meshless approaches, to reconstruct shells described by points’ clouds, and to subsequently predict their static behaviour. These methods are highly appropriate ondealing with unstructured points clouds, as they do not need to have any specific spatial or geometric requirement when implemented, depending only on the distance between the points. Details on the formulation, and a set of illustrative examples focusing the reconstruction of cylindrical and double-curvature shells, and its further analysis, are presented.

Interpolation and approximation are the most important parts of partial differential equation solution procedures, which significantly affect the cost and the accuracy of the results. This paper is aimed to exhaustively investigate the interpolation algorithms and trace their chronologically developments. The interpolation methods are classified based on their mathematical representation, and then surveyed separately. An abridgement of calculation steps of methods are presented and for details, the reader is referred by the main references. The usage records in applied science and engineering are included and their numerical dominance, stability and convergence rate are discussed.

In this paper, an adaptive Meshless method of line is applied to distributethe nodes in the spatial domain. In many cases in Meshless methods, it isalso necessary for the chosen nodes to have certain smoothness properties. The set of nodes is also required to satisfy certain constraints. In this paper, one of these constraints is investigated. The aim of this manuscript is theimplementation of an algorithm for selection of the nodes satisfying a givenconstraint, in the Meshless method of line. This algorithm is applied to someillustrative examples to show the e ciency of the algorithm and its ability toincrease the accuracy.

In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a Meshless method, because it is independent of the geom-etry of the domain and it does not require any background interpolation or approximation cells. The error analysis of the method is provided. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method.

Topological aspects of Meshless element free Galerkian method (EFGM) as the nodal connectivity of matrices are studied. Four different graphs are defined for Meshless discretizations of EFGM and their connectivity is investigated. Graphs are used for nodal ordering of Meshless models in order to reduce the bandwidth, profile, maximum front width, and root-mean-square wave front of the corresponding matrices.      

Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a Meshless method is described for solving this integral equation. Error analysis of this method is discussed and then its application and accuracy are illustrated by some case studies.

Automatic topic detection seems unavoidable in social media analysis due to big text data which their users generate. Clustering-based methods are one of the most important and up-to-date categories in topic detection. The goal of this research is to have a wide study on this category. Therefore, this paper aims to study the main components of clustering-based-topic-detection, which are embedding methods, distance metrics, and clustering algorithms. Transfer learning and consequently pretrained language models and word embeddings have been considered in recent years. Regarding the importance of embedding methods, the efficiency of five new embedding methods, from earlier to recent ones, are compared in this paper. To conduct our study, two commonly used distance metrics, in addition to five important clustering algorithms in the field of topic detection, are implemented by the authors. As COVID-19 has turned into a hot trending topic on social networks in recent years, a dataset including one-month tweets collected with COVID-19-related hashtags is used for this study. More than 7500 experiments are performed to determine tunable parameters. Then all combinations of embedding methods, distance metrics and clustering algorithms (50 combinations) are evaluated using Silhouette metric. Results show that T5 strongly outperforms other embedding methods, cosine distance is weakly better than other distance metrics, and DBSCAN is superior to other clustering algorithms.