Computational Physics GroupKarel Matous |
||||||||||
|
Asynchronous Space-Time Domain Decomposition Method with Localized Uncertainty QuantificationW. Subber1 and K. Matous1,2 1Center for Shock Wave-processing of Advanced Reactive Materials, 2Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA. Abstract The
computational cost associated with uncertainty
quantification of engineering problems featuring
localized phenomenon can be reduced by confining the
random variability of the model parameters within a
region of interest. In this case, a localized
treatment of mesh and time resolutions is required to
capture the effect of the confined material
uncertainty on the global response. We present a
computational approach for localized uncertainty
quantification with the capability of asynchronous
treatment of mesh and time resolutions. In particular,
we allow each subdomain to have its local uncertainty
representation and the corresponding mesh and time
resolutions. As a result, computing resources can be
directed toward a small region of interest where a
model with high spatial and temporal resolutions is
required. To verify the numerical implementation, we
consider elastic wave propagation in an axially loaded
beam. Moreover, we perform convergence studies with
respect to the spatial and temporal discretizations as
well as the size of an uncertain subdomain. A
projectile impacting a composite sandwich plate is
considered as an engineering application for the
proposed method.
Conclusions
We have developed an
asynchronous space and time computational algorithm with
localized uncertainty quantification. The framework is
based on the recently proposed PASTA-DDM algorithm in
conjunction with the intrusive polynomial chaos
expansion for the stochastic representation that can be
efficiently localized to selected subdomains. The
proposed algorithm is customized to reduce the
computational cost of uncertainty quantification in
problems featuring localized phenomenon and described by
stochastic PDE's (i.e., PDE's with random coefficients).
In the region of interest, a rich stochastic model with
high mesh and time resolutions is used, while a low
dimensional stochastic representation with coarse
spatial and temporal resolutions are allowed apart from
the region of interest. We verify our algorithm with the
traditional Monte-Carlo sampling technique and study
different scenarios to reduce the computational cost of
uncertainty quantification. For the elastic wave
propagation problem, the algorithm shows second order
convergence in the mean and standard deviation of both
the displacement and velocity with respect to mesh size
and time increment. Furthermore, the first order
convergence rate is achieved with respect to the
localization length. The application of PASTA-DDM-UQ to
an impact problem shows that localizing the random
variability of the material parameters under the impact
zone gives the closest results to the case when
uncertainty is considered in the entire domain.
Acknowledgment This work has been supported by the
Department of Energy, National Nuclear Security
Administration, under the Award No. DE-NA0002377 as part
of the Predictive Science Academic Alliance Program II. (c) 2017 Notre
Dame and Dr. Karel Matous
|