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A Smooth Discretization Bridging Finite Element and Mesh-free Methods Using Polynomial Reproducing Simplex Splines

Devaraj, G and Narayan, Shashi and Roy, Debasish (2014) A Smooth Discretization Bridging Finite Element and Mesh-free Methods Using Polynomial Reproducing Simplex Splines. In: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 102 (1). pp. 1-54.

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Official URL: http://dx.doi.org/10.3970/cmes.2014.102.001


This work sets forth a `hybrid' discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing scheme constructed over a conventional Finite Element Method (FEM)-like domain discretization based on Delaunay triangulation. Careful construction of the simplex spline knotset ensures the success of the polynomial reproduction procedure at all points in the domain of interest, a significant advancement over its precursor, the DMS-FEM. The shape functions in the proposed method inherit the global continuity (Cp-1) and local supports of the simplex splines of degree p. In the proposed scheme, the triangles comprising the domain discretization also serve as background cells for numerical integration which here are near-aligned to the supports of the shape functions (and their intersections), thus considerably ameliorating an oft-cited source of inaccuracy in the numerical integration of mesh-free (MF) schemes. Numerical experiments show the proposed method requires lower order quadrature rules for accurate evaluation of integrals in the Galerkin weak form. Numerical demonstrations of optimal convergence rates for a few test cases are given and the method is also implemented to compute crack-tip fields in a gradient-enhanced elasticity model.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the TECH SCIENCE PRESS, 6825 JIMMY CARTER BLVD, STE 1850, NORCROSS, GA 30071 USA
Keywords: globally smooth shape function; hybrid method; polynomial reproduction; bivariate simplex splines; knot construction; moment matrix invertibility
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 21 Apr 2015 07:24
Last Modified: 06 May 2015 09:23
URI: http://eprints.iisc.ac.in/id/eprint/51331

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