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Conservative Taylor least squares reconstruction with application to material point methods
Author(s) -
Wobbes Elizaveta,
Möller Matthias,
Galavi Vahid,
Vuik Cornelis
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5956
Subject(s) - taylor series , basis function , spline (mechanical) , algorithm , grid , mathematics , quadrature (astronomy) , point cloud , least squares function approximation , mathematical optimization , computer science , mathematical analysis , geometry , artificial intelligence , physics , statistics , estimator , optics , thermodynamics
Summary Within the standard material point method (MPM), the spatial errors are partially caused by the direct mapping of material‐point data to the background grid. In order to reduce these errors, we introduced a novel technique that combines the least squares method with the Taylor basis functions, called the Taylor least squares (TLS), to reconstruct functions from scattered data while preserving their integrals. The TLS technique locally approximates quantities of interest such as stress and density, and when used with a suitable quadrature rule, it conserves the total mass and linear momentum after transferring the material‐point information to the grid. The integration of the technique into MPM, dual domain MPM, and B‐spline MPM significantly improves the results of these methods. For the considered examples, the TLS function reconstruction technique resembles the approximation properties of highly accurate spline reconstruction while preserving the physical properties of the standard algorithm.