Colloquium October 6
Date: Friday October 6
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Mike Parks of Sandia National Laboratories
Title: Relating Atomistic-to-Continuum Coupling and Domain Decomposition
Abstract
The deformation and failure of many engineering materials are
inherently multiscale processes. Models for such processes frequently
call for decomposition of the material domain into atomistic and
continuum subdomains, where the continuum subdomain is modeled via a
finite element analysis. The treatment of the boundary between these
subdomains, or "handshake region", is frequently what distinguishes
one atomistic-to-continuum coupling method from another. A formal
theory of this transition region does not yet exist. Instead, current
coupling schemes employ ad hoc approximations, such as treating finite
element nodes as atoms, or vice-versa, to accommodate the
incompatibility between a non-local atomistic description and a local
finite element description at the atomistic/continuum boundary. There
currently exists little rigorous analysis of these schemes.
The atomistic-to-continuum coupling problem has similarities with the
classical continuum-to-continuum domain decomposition problem. We will
explore some of these similarities and address the extent to which
both problems can be placed within the same mathematical and
algorithmic framework. We will address domain decomposition methods
that can be harnessed when solving the atomistic-to-continuum coupling
problem, and for a particular coupling scheme, provide a convergence
theory giving guidance about when the scheme will produce a
satisfactory answer.
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