Mathematics

We introduce and discuss some results related to unfitted finite element methods for parameterized  partial  differential  equations enhanced  by  a  reduced  order  method construction.  A model order reduction technique is proposed to integrate the embedded boundary finite element methods.  Results are validated numerically. This methodology which extracts an unfitted mesh Nitsche finite element method in reduced order proper orthogonal decomposition method is based on a background mesh and stationary Stokes flow systems are examined.  This approach achievements are twofold.  Firstly, we reduce much computational effort since the unfitted mesh method allows us to avoid remeshing when updating the parametric domain.  Secondly, the proposed reduced order model technique gives implementation advantage considering geometrical parametrization.  Computational are even exploited more efficiently since mesh is computed once and the transformation of each geometry to a reference geometry is not required.  These combined advantages allow to solve many PDE  problems  more  efficiently,  and  to provide  the  capability  to  find  solutions  in cases that could not be resolved in the past.