Improved integration scheme for the second-order consistent element-free Galerkin method. (English) Zbl 1404.65280
Summary: Consistent element-free Galerkin (CEFG) methods have improved the accuracy, efficiency and convergence of high-order EFG methods remarkably by developing integration schemes using less sampling points and corrected derivatives of nodal shape functions. However, the computation of these derivatives still takes considerable CPU time because it involves the evaluation of shape functions at relatively more points and the solution of equations. To reduce the evaluation of these functions substantially, an improved integration scheme is proposed for the second-order CEFG method. Moreover, these corrected derivatives are explicitly formulated in terms of the shape functions. In consequence, the computational efficiency of second-order CEFG method is further improved by this scheme. Furthermore, the high accuracy and convergence of the CEFG method is still maintained. Numerical results of elastic examples show that this improved CEFG method is evidently faster than the original and its efficiency approaches that of nesting sub-domains gradient smoothing (NSGS), which was developed recently for second-order meshfree Galerkin methods. An extension to small-strain elastoplasticity is also presented where the proposed method is demonstrated to perform much better than NSGS in elastoplastic computations.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
element-free Galerkin; meshfree/meshless; numerical integration; computational efficiency; patch testReferences:
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