تقرير
Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity
| العنوان: | Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity |
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| المؤلفون: | Fischer, Hendrik, Roth, Julian, Chamoin, Ludovic, Fau, Amelie, Wheeler, Mary F., Wick, Thomas |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem. Comment: 33 pages, 9 figures, 3 tables |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.08907 |
| رقم الأكسشن: | edsarx.2311.08907 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |