CSAR Noon Seminar
Armando Duarte,
University of Sao Paulo, Brazil
DATE: Monday, March 17, 2003
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
TITLE: An Overview of Partition of Unity and Generalized Finite
Element Methods
Abstract
Several new computational methods proposed in recent years can be cast
as a partition of unity method. The key feature of these methods is
the use of a partition of unity to build the approximation space.
This partition of unity framework has several powerful properties such
as the ability to produce seamless hp approximations, the ability to
develop customized approximations for specific applications like
dynamic crack propagation, the ability to build p-orthotropic
approximations on tetrahedral finite element meshes, etc.
In this talk, several applications of partition of unity methods and,
in particular, of the generalized finite element method (GFEM) to the
solution of solid mechanics problems are shown. In the GFEM, the
partition of unity is provided by low order Lagrangian finite element
shape functions, linear combinations of these functions or the
so-called Shepard functions. In the context of crack simulation, for
example, the GFEM method allows for modeling of arbitrary dynamic crack
propagation without continuous remeshings or mappings of solutions
between consecutive meshes as the crack propagates.
Several numerical examples demonstrating the main features and
computational efficiency of the GFEM are presented.