Solving Poisson’s Equations By The
Discrete Least Square Meshless Method
Author(s)
H. Arzani & M. H. Afshar
Abstract
A meshless method is proposed in this paper for the solution of two-dimensional
elliptic problems. The proposed method does not require any mesh so it is truly a
meshless method. The approach termed generically the \“Discrete Least Square
meshless method” is applied to discrete the governing differential equations in
inner and boundary nodes. A functional is defined as the sum of the squared
residual of the governing differential equation and the boundary conditions at the
nodal points. Moving least-square (MLS) interpolation is used to construct the
shape function’s values, which have high continuity in the problem domain. To
evaluate the accuracy of the method as an alternative meshless method the
development and theory of this new approach is presented in the context of the
solution of 2D elliptic equations. Numerical results show that the method
possesses high accuracy with low computational effort.
Keywords: meshless method, Discrete Least Square, elliptic problems.
1 Introduction
The idea of using finite difference simplicity and finite element capability of
handling complex geometries are the subject of many researches. This is mainly
because the mesh generation part of the solution has shown to be a very time
consuming challenge especially in finite element applications. The idea of
developing methods requiring no mesh has led to the emerging of a new class of
the so-called ‘meshless’ methods. Many of the meshless methods developed so
far require background mesh to carry out numerical integration. The integration
cells, however, need not be compatible with nodes and thus they can be
generated more easily than the FEM meshes. The existing meshless methods can
Keywords
meshless method, Discrete Least Square, elliptic problems.
Related Book
Other papers in this volume
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