PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Kris Jenssen, Yuxi Zheng.

Abstract:
Title:	A Generalized Finite Element Method for Multiscale Simulations
Seminar:	Computational and Applied Mathematics Colloquium
Speaker:	C. Armando Duarte, University of Illinois at Urbana-Champaign
This presentation focuses on a novel computational method for multiscale phenomena. The methodology is based on the Generalized FEM (GFEM) and can be applied to a broad class of multiscale problems. It involves the solution of interdependent global (structuralscale) and localscale problems. The local problems focus on the resolution of finescale features of the solution in the vicinity of, e.g., three dimensional cracks or regions with sharp thermal gradients, while the global problem addresses the macro scale structural behavior. The boundary conditions for the local problems are provided by the coarse scale solution and can of Dirichlet, Neumann or Cauchy type. The local solutions are embedded into the global solution space using the partition of unity concept. This enables a twoway information transfer between scales and leads to a robust and accurate methodology. We show that this GFEM provides convergent solutions even when classical globallocal analysis fails due to numerical pollution of the FEM solution. Numerical examples demonstrating the application and robustness of the procedure to three dimensional fracture mechanics, heat transfer problems and discontinuous gradients fields are presented.