Abstract
In this paper, an adaptive numerical integration scheme, which does not need non-overlapping and contiguous integration meshes, is proposed for the MLPG (Meshless Local Petrov-Galerkin) method. In the proposed algorithm, the integration points are located between the neighboring nodes to properly consider the irregular nodal distribution, and the nodal points are also included as integration points. For numerical integration without well-defined meshes, the Shepard shape function is adopted to approximate the integrand in the local symmetric weak form, by the values of the integrand at the integration points. This procedure makes it possible to integrate the local symmetric weak form without any integration meshes (non-overlapping and contiguous integration domains). The convergence tests are performed, to investigate the present scheme and several numerical examples are analyzed by using the proposed scheme.
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Cho, J.Y., Jee, Y.B. An adaptive mesh-independent numerical integration for meshless local petrov-galerkin method. KSME International Journal 17, 986–998 (2003). https://doi.org/10.1007/BF02982983
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DOI: https://doi.org/10.1007/BF02982983