Space and chaos-expansion Galerkin proper orthogonal decomposition low-order discretization of partial differential equations for uncertainty quantification. (English) Zbl 07772232
Summary: The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexity of the model. In this work, we propose a multidimensional Galerkin proper orthogonal decomposition that optimally reduces each dimension of a tensorized product space. We provide the analytical framework and results that define and quantify the low-dimensional approximation. We illustrate its application for uncertainty modeling with polynomial chaos expansions and show its efficiency in a numerical example.
{© 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}
{© 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}
MSC:
| 65-XX | Numerical analysis |
Keywords:
model reduction; proper orthogonal decomposition; tensor spaces; uncertainty quantificationReferences:
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