Multiscale enrichment based on partition of unity
J. Fish and Z. Yuan
International Journal for Numerical Methods in Engineering, 62, 1341-1359 (2005).

ABSTRACT
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.