Reduced basis approach for PDE problems with parametric geometry for embedded finite element methods


Wednesday, 10 October, 2018 - 14:00

Title: A Reduced Basis Approach for PDE problems with Parametric  
Geometry for Embedded Finite Element Methods

Speaker: Dr. Efthymios Karatzas (SISSA mathLab)

Time and Venue: 14:00 - SISSA main building room 133

Abstract: 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.