TY - JOUR

T1 - Arbitrary placement of secondary nodes, and error control, in the meshless local Petrov-Galerkin (MLPG) method

AU - Kim, H. G.

AU - Atluri, S. N.

PY - 2000

Y1 - 2000

N2 - The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.

AB - The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.

KW - Local symmetric weak form

KW - MLPG method

KW - MLS

KW - Meshless method

KW - Primary node

KW - Secondary node

UR - http://www.scopus.com/inward/record.url?scp=0040518647&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040518647

SN - 1526-1492

VL - 1

SP - 10

EP - 30

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

IS - 3

ER -