Discrete empirical interpolation for hyper‐reduction of hydro‐mechanical problems in groundwater flow through soil

Abstract

The recent surge in the availability of sensor data and computational resources has fostered the development of technologies for optimization, control and monitoring of large infrastructures, integrating data and numerical modeling. The major bottleneck in this type of technologies is the model response time, since repetitive solutions are typically required. To reduce the computational time, Reduced Order Models (ROMs) are used as surrogates for expensive Finite Element (FE) simulations enabling the use of complex models in this type of applications. In this work, ROMs are explored for the solution of the fully coupled hydro-mechanical system of equations that governs the water flow through partially saturated soil. The POD-based Reduced Basis method and the Discrete Empirical Interpolation Method (DEIM), as well as its localized version (LDEIM), are examined in solving a parametrized problem simulating the mechanical loading of an embankment dam. Hydraulic and mechanical soil properties are considered as parameters. It is shown that the combination of these methods results in simulations that require 1/10 to 1/100 of the FE response time. Moreover, the method is shown to yield scaling efficiency gains with increasing problem size.

Model order reduction of nonlinear thermo-hydro-mechanical systems by means of elastic and plastic domain sub-structuring

“…A local level iterative procedure is used to solve the constitutive model equations, where the stresses and internal variables are iteratively sought based on a total strain state furnished by the equilibrium iteration until convergence is reached. In Algorithm 1, the global iteration is implemented inside the while loop (line [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The local iteration involved in finding the plastic state variables is implemented inside a nested loop (lines [13][14][15][16][17][18][19].…”

“…In Algorithm 1, the global iteration is implemented inside the while loop (line [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The local iteration involved in finding the plastic state variables is implemented inside a nested loop (lines [13][14][15][16][17][18][19]. Although the local level constitutive model integration could also be performed explicitly, an implicit technique is used in this study.…”

“…The coefficients are obtained from interpolation based on nonlinear functions sampled at a much smaller number of points [16,17]. The exploitation of DEIM allowed significant speed-up for Hydro-Mechanical (HM) nonlinear problems involving partial saturation in groundwater flow problems [18]. Gappy Proper Orthogonal Decomposition (POD) is implemented using a similar approach to DEIM and differs mainly by replacing the interpolation procedure with linear regression [19].…”

Assessment of tailings dams using Model Order Reduction

“…In this presentation we describe the results presented in [1] and [2], where model order reduction techniques are applied in the context of data assimilation to learn about the state of tailing dams. A transient nonlinear hydro-mechanical model describing the groundwater flow in unsaturated soil conditions is solved using Reduced Basis method [1].…”

“…A transient nonlinear hydro-mechanical model describing the groundwater flow in unsaturated soil conditions is solved using Reduced Basis method [1]. Hyper-reduction techniques (DEIM, LDEM) are tested and show time gains up to 1/100 with respect to standard finite element methods [2].…”