A Simple Sub-domain Collocation Method as the Generalization of the Finite Point Method

A new mesh-less method based on a sub-domain collocation approach is proposed. Sub-domains are defined around each node and the equilibrium equations are weakly satisfied. The method can be regarded as an advanced version of the Finite Point Method (FPM). One of the important features of the method is that a set of closed form integrals are taken on the sub-domain boundaries. This leads to reduction of the computational cost in comparison with other integral based mesh-less methods. Moreover, it will be shown that the order of differentiation needed in the new method is less than that of the conventional FPM. Since the accuracy of the procedure depends on the size of the sub-domains, the optimal sizes are found by a series of patch tests. The final results of the patch tests and the optimization procedure are presented in a series of tables for further use. The efficiency of the method in the solution of two dimensional elastic problems is shown by presenting the results for several benchmark problems while comparison is made with the results of other methods such as the finite element and finite point methods.

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Keywords Mesh less ، sub domain ، collocation ، finite point method.