TY - JOUR
T1 - Randomized residual-based error estimators for the proper generalized decomposition approximation of parametrized problems
AU - Smetana, Kathrin
AU - Zahm, Olivier
N1 - Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.
PY - 2020/12/15
Y1 - 2020/12/15
N2 - This article introduces a novel error estimator for the proper generalized decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: it builds on concentration inequalities of Gaussian maps and an adjoint problem with random right-hand side, which we approximate using the PGD. The effectivity of this randomized error estimator can be arbitrarily close to unity with high probability, allowing the estimation of the error with respect to any user-defined norm as well as the error in some quantity of interest. The performance of the error estimator is demonstrated and compared with some existing error estimators for the PGD for a parametrized time-harmonic elastodynamics problem and the parametrized equations of linear elasticity with a high-dimensional parameter space.
AB - This article introduces a novel error estimator for the proper generalized decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: it builds on concentration inequalities of Gaussian maps and an adjoint problem with random right-hand side, which we approximate using the PGD. The effectivity of this randomized error estimator can be arbitrarily close to unity with high probability, allowing the estimation of the error with respect to any user-defined norm as well as the error in some quantity of interest. The performance of the error estimator is demonstrated and compared with some existing error estimators for the PGD for a parametrized time-harmonic elastodynamics problem and the parametrized equations of linear elasticity with a high-dimensional parameter space.
KW - Monte-Carlo estimator
KW - a posteriori error estimation
KW - concentration phenomenon
KW - goal-oriented error estimation
KW - parametrized equations
KW - proper generalized decomposition
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U2 - 10.1002/nme.6339
DO - 10.1002/nme.6339
M3 - Article
AN - SCOPUS:85081953015
SN - 0029-5981
VL - 121
SP - 5153
EP - 5177
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
IS - 23
ER -