Purpose – In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues. Design/methodology/approach – In space domain, the fields at the collocation points are expanded into a series of new Shepard’s functions which ha...

A two-phase DLSM model is proposed to model transverse isotropic materials, in which the layer structure of the anisotropic materials is explicitly represented. Equations are derived to obtain elastic parameters of the two phase model from the elastic modules in parallel to the bedding planes and that in normal direction of the bedding planes. Then, the mechanical properties of the two-phase DL...

ii Preface Radial Basis Function (RBF) methods have become the primary tool for interpolating multidimensional scattered data. RBF methods also have become important tools for solving Partial Differential Equations (PDEs) in complexly shaped domains. Classical methods for the numerical solution of PDEs (finite difference, finite element, finite volume, and pseudospectral methods) are based on p...

We use the global collocation method, the first and the third-order shear deformation plate theories, the Mori–Tanaka technique to homogenize material properties, and approximate the trial solution with multiquadric radial basis functions to analyze free vibrations of functionally graded plates. Frequencies computed by the present method are found to agree well with those from the analytical so...

In this article, we present an efficient local meshless method for the numerical treatment of 3-D convection-diffusion PDE. The demand techniques increment because its nature and simplicity usage in higher dimensions. This technique approximates solution on set uniform scattered nodes. space derivatives models are discretized by proposed procedure though time fractional part is Liouville-Caputo...

Development of a new meshless technique is described that presents certain advantages over conventional meshless schemes due to unique weights that force alignment of the derivative approximation. The method is completelymeshless, yet retains the low storage and simple fluxdistribution technique that are characteristic of finite volumemethods. The newmethod is based on thewell-knownTaylor serie...

In this paper, we explore the effect of numerical integration on the meshless method used to approximate the solution of an elliptic partial differential equation with non-constant coefficients with Neumann boundary conditions. We considered meshless methods with shape functions that reproduce polynomials of degree k ≥ 1. We have obtained an estimate for the energy norm of the error in the appr...

In this paper, the two-dimensional Stokes problem is analyzed by the modified collocation Trefftz method (MCTM) and the Laplacian decomposition. The coupled Stokes equations are converted to three Laplace equations by utilizing the Laplacian decomposition and then the boundary-type meshless MCTM is adopted to solve the resultant Laplace equations. The MCTM, free from mesh and numerical quadratu...

We present a new approach to simultaneously denoise and parameterize unorganized point cloud data. This is achieved by minimizing an appropriate energy function defined on the point cloud and its parameterization. An iterative algorithm to minimize the energy is described. The key ingredient of our approach is an “as-rigid-as-possible” meshless parameterization to map a point cloud with disk to...

A general framework for proving error bounds and convergence of a large class of unsymmetric meshless numerical methods for solving well-posed linear operator equations is presented. The results provide optimal convergence rates, if the test and trial spaces satisfy a stability condition. Operators need not be elliptic, and the problems can be posed in weak or strong form without changing the t...