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.

In this paper we use radial basis functions to solve multivariable integral equations. We use collocation Method for implementation. Numerical experiments show the accuracy of the Method.

In this paper, a computational technique is presented based on the natural element Method (NEM) for large plastic deformation simulation of the metal forming problems. NEM is a numerical technique in the field of computational mechanics and can be considered as a Meshless Method. The selected process is backward extrusion for circular shape hollow components from round billets. The punch stroke value is divided into sub-steps, whereas a new set of nodes become active at the end of each sub-step of deformation. Solutions are obtained for different area reductions under friction condition. Hollman-Ludwik law is selected to explain the material behavior after the yielding point. The experiments are carried out with fully annealed commercial aluminum alloy billets at room temperature, using various punch sizes. A set of die and punches are designed and constructed for experimental works. The validity of the proposed Method is verified by comparing the results from deformed geometry, contours of equivalent strain and forming loads with those obtained from finite element simulation and experimental measurements. It is concluded that the results obtained by NEM are in good agreement with those from FEM and experiments and therefore, the Meshless natural element Method is capable of handling large plastic deformation.

The objective of this research is to study the ability of a Meshless Method, called finite point Method, in solving incompressible fluid flow problems using two stabilization schemes. The main goal of Meshless Methods is to reduce or remove the cost of grid generation. This issue is implemented using the satisfaction of governing differential equations on a regular or irregular set of nodes by interpolation functions, based on special least-squares approximations. In this research, the finite point Method is used to solve the Stokes and the Navier-Stokes equations by employing two different stabilization schemes. In addition, the effects of least-squares approximations are studied

This paper goals to expand a Meshless Method using the collocated discrete least squares Meshless (CDLSM) approach for mathematical modeling of a category of time fractional diffusion-wave equation (TFDWE). First, moving least squares (MLS) Method used to construct the shape function is brie y described. Then, using the shape function generated by the least squares Method, the discrete shape of the TFDWE is received in the strong form. Two-dimensional test problems with different nodes and collocations distributions are studied to validate and look at the accuracy and performance of proposed Method.

Introduction: In order to avoid meshing and its difficulties and costs, Multiquadric Radial Basis Function (MQ-RBF) Method has been developed (Kansa, 1990) and has been examined for different types of physical phenomena. In this regard, the present study develops this Meshless Method for analysis of dam break problem. MQ is more convenient and accurate than other RBF Methods for solving partial differential equations (Fallah et al., 2019). This Meshless Method have advantages such as; 1) creating a continuous response function all over the computational domain, 2) no need to discretize the entire domain with optimal usability in large-scale problems, 3) high capability in modelling irregular and complex geometries, 4) high ability to simulate discontinuities of responses, 5) easy generalization to 3D problems, and etc. Both the accuracy and the convergence rate of MQ depend strongly on its shape parameter (Koushki et al., 2019). So far, researchers have been working on many Methods for determining the optimal shape parameter but a comprehensive Method has not been developed yet (Babaee et al., 2019). In this study, the commonly previous Methods have been considered for determining the optimal shape parameter and a novel idea has been presented for analyzing the flood flow caused by dam break. The efficiency and accuracy of the present approach compared to other solutions have been examined through three examples. Methodology: The governing PDEs of dam break problem consist of the continuity equation and two momentum equations in two dimensions. MQ approximates solution of 2D equations system using an estimation function in which the unknown coefficients have to be determined for each unknown variable of the PDE, i. e. the velocities in two directions and the pressure. In one hand, for definition of the estimation function, the RBF Methods need N center points inside the domain or on the boundaries which leads to N unknown coefficients. On the other hand, the governing PDEs and their boundary conditions again have to be satisfied on N collocation points inside the domain and on the boundaries, respectively, which leads to N algebraic equations to be solved for the mentioned unknown coefficients. A critical parameter, namely, the shape parameter strongly affects the precision of the estimation function which may be considered constant or variable from point to point for each estimation function. Determining the optimal value of the shape parameter has always been a challenge in using MQ and other RBF Methods. In this study it has been shown that the shape parameter in all time steps can be considered the same and a new high-speed approach is proposed to determine its optimal value. In this approach, the initial conditions of the problem will be estimated using MQ function and it has been shown that the optimal value of the shape parameter in the initial conditions is also the optimal value of the shape parameter for the next time steps and there is no need to be optimized for all next time steps. Therefore, the computational cost will be considerably reduced. Also for discretizing the time dependent terms, the forward finite difference Method is used and it was shown that for discretizing the local terms, a semiimplicit Method could be used by substituting MQ function, to be led to a linear system of algebraic equations. Consequently, the presented approach becomes more stable than the explicit Methods. In order to verify and validate the proposed approach, four numerical examples are presented. In two of examples with 1D and 2D behaviors, discontinuities in initial conditions and run times are different. Sharp discontinuities highlight the capabilities of the approach while in long run time show stability. Besides, results of the proposed approach have been compared with those of other numerical and analytical Methods. Also, in this research, inefficiency of previously common Methods for determining the optimal shape parameter in solving the dam-break problem was shown (Golbabai et al., 2015). In verification, the RMSE error criterion has been considered which results in errors less than 5 percent. In the third and fourth examples capability of the numerical model has been demonstrated by a two-dimensional dam break flow in symmetric and asymmetric conditions, respectively. Conclusion: Using the MQ-RBF, the disadvantages of mesh-based Methods including: high cost of meshing, need to fundamental solution, dependence on the conditions of each problem, singularity, continuous discretization of domain and need to a regular mesh will be eliminated.

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.

1. Introduction Concrete is the most widely used construction material in the world for many decades. Old existing structures are deteriorated and needed inspection and repair. Electrical Methods, which are inexpensive and easy to handle, are well known as non-destructive inspection Methods. They can give information about the position, size, and orientation of inclusions like bar and fiber, condition of corrosion, state of humidity and probable corrosive ions, and the degree of cracking in concrete. Both alternate and direct currents (AC & DC) can be used in electrical resistance measurement (ERT). A major problem of the DC Method is the measurement error produced by a polarization of the specimen. In AC Methods the frequency should be kept as low as possible to avoid the inductance effects of long connecting cables and also the frequency has to be high enough to avoid electrode polarization effects. In ERT, electric current is injected through electrodes, and the voltage produced on the object surface is recorded using several electrode pairs. Then an estimate of the spatial distribution of conductivity is mapped (Karhunen et al., 2010)...