Abstract The complicated behavior of groundwater system in an arid aquifer is generally studied by solving the governing equations using either analytical or numerical methods. In this regard, methods are just for some aquifers with regular boundaries. Numerical used aim finite difference (FDM) and element (FEM) which engaged simple aquifers. Using them complex cases irregular boundaries has sh...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

Title of dissertation: MESHLESS COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUED PROBLEMS AND THE ROTATIONAL SHALLOW WATER EQUATIONS ON THE SPHERE Christopher D. Blakely, Doctor of Philosophy, 2009 Dissertation directed by: Professor John Osborn Department of Mathematics Professor Ferdinand Baer Department of Atmospheric and Oceanic Science This dissertation thesis has...

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen...

This work concerns the development of a highly accurate and efficient meshless flow solver for inviscid flow in two dimensions. Novel aspects of this work include the application of mesh-based reconstruction, diffusion, and convergence acceleration schemes within an edge-based meshless framework. Most notably, “multicloud,” a meshless counterpart to multigrid, has been implemented. Multicloud d...

The root of this study, comes from the lack of regularity where exists in shape function selection in meshless methods. Up to now, shape functions in meshless methods were being established by basis functions. In other words, there was no predictable rule by which the shape functions be predetermined, without any need to basis functions. In presented approach, the authors are going to establish...

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...