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Radial point interpolation based finite difference method for mechanics problems. (English) Zbl 1129.74049
Summary: We propose a radial point interpolation based finite difference method (RFDM). In this novel method, radial point interpolation using local irregular nodes is employed together with the conventional finite difference procedure to achieve both the adaptivity to irregular domain and the stability in the solution that is often encountered in collocation methods. A least-square technique is adopted, which leads to a system matrix with good properties such as symmetry and positive definiteness. Several numerical examples are presented to demonstrate the accuracy and stability of the RFDM for problems with complex shapes and regular and extremely irregular nodes. The results are examined in detail in comparison with other numerical approaches such as the radial point collocation method that uses local nodes, conventional finite difference and finite element methods.

MSC:
74S20 Finite difference methods applied to problems in solid mechanics
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