TY - JOUR
T1 - Unified embedded parallel finite element computations via software-based Frechet differentiation
AU - Long, Katharine
AU - Kirby, Robert
AU - Waanders, Bart van Bloemen
PY - 2010/11/17
Y1 - 2010/11/17
N2 - Computational analysis of systems governed by partial differential
equations requires not only the calcuation of a solution, but
the extraction of additional information such as the sensitivity of
that solution with respect to input parameters or the inversion of the
system in an optimization or design loop. Moving beyond the
automation of discretization of PDE by finite element methods, we present a
mathematical framework that unifies the discretization of PDE with
these additional analysis requirements. In particular,
Fr\'echet differentiation on a class of functionals together
with a high-performance finite element framework have led to a code,
called Sundance, that provides high-level programming abstractions for
the automatic, efficient evaluation of finite variational forms together with the
derived operators required by engineering analysis.
AB - Computational analysis of systems governed by partial differential
equations requires not only the calcuation of a solution, but
the extraction of additional information such as the sensitivity of
that solution with respect to input parameters or the inversion of the
system in an optimization or design loop. Moving beyond the
automation of discretization of PDE by finite element methods, we present a
mathematical framework that unifies the discretization of PDE with
these additional analysis requirements. In particular,
Fr\'echet differentiation on a class of functionals together
with a high-performance finite element framework have led to a code,
called Sundance, that provides high-level programming abstractions for
the automatic, efficient evaluation of finite variational forms together with the
derived operators required by engineering analysis.
U2 - 10.1137/09076920X
DO - 10.1137/09076920X
M3 - Article
SP - 3323
EP - 3351
JO - SIAM J. Scientific Computing
JF - SIAM J. Scientific Computing
SN - 1064-8275
ER -