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Multiscale enrichment based on partition of unity. (English) Zbl 1078.74637
Summary: A new multiscale enrichment method based on the partition of unity (MEPU) method is presented. It is a synthesis of mathematical homogenization theory and the partition of unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. MEPU is perfectly suited for enriching the coarse scale continuum descriptions (PDEs) with fine scale features and the quasi-continuum formulations with relevant atomistic data. Numerical results show that it provides a considerable improvement over classical mathematical homogenization theory and quasi-continuum formulations.

MSC:
74Q05 Homogenization in equilibrium problems of solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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