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

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.