This is a pre-publication version of our paper:
Liszka, T.J., Duarte, C.A.M. and Tworzydlo, W. W. "hp-Meshless
Cloud Medhod'', Comp. Meth. Appl. Mech. Eng., 139, pp. 263-288,
1996.
hp-Meshless
Cloud Method
Liszka, T.J., Duarte, C.A.M. and Tworzydlo,
W. W.
Abstract
A methodology to build discrete
models of boundary-value problems (BVP) is presented. The method is applicable
to arbirtrary domains and employs only a scattered set of nodes to build
approximate solutions to BVPs. A version of moving least square interpolation
and the collocation method are used to discretize BVP equations, which
results in a truly meshless method (i.e. without a background mesh of integration
points). h-and p-adaptive strategies are tested and very good convergence
of the method was observed. The improvements in the methodology, in particular
the introduction of spectral degrees of freedom, result in a fast and accurate
method, significantly more efficient than the Finite Element Method or
Element Free Galerkin Method. Several practical applications of the method
to solve various engineering problems are presented.
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