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Abstract

Because of the highly heterogeneous character of the earth's subsurface, the complex coupling of thermal, hydrological, mechanical, and chemical processes, and the limited accessibility geoscientific applications have a high-dimensional character. Hence, the usage of automated calibration algorithms with a reasonable number of iterations is often prohibitively expansive using the standard finite element (FE) method. Therefore, we using the reduced basis (RB) method, being a model order reduction (MOR) technique, that constructs low-order approximations to, for instance, the FE space. We use the RB method to address this computationally challenging simulations because this method significantly reduces the degrees of freedom. The RB method is based on a decomposable implementation of an offline and online stage. This allows performing all the expensive pre-computations beforehand to get real-time results during the online stage, which can be, for instance, directly used during field measurements. Generally, the RB approach is most beneficial in the many-query and real-time context. We will illustrate the advantages of the RB method by applying it to the Upper Rhine Graben. For the forward simulation of the Upper Rhine Graben model we are considering a geothermal conduction problem demonstrating the implementation of the RB method, within the DwarfElephant package, for a steady-state case. We will not only compare the runtimes for both the FE and the RB simulations but also evaluate the quality of the RB approximation. We will emphasize the advantages of this method for repetitive simulations by performing a parameter study for the Upper Rhine Graben model. Here, we are going to emphasize especially the speed-up that is gained by using the RB instead of the FE method. Furthermore, we will demonstrate how the used implementation is usable in high-performance computing (HPC) infrastructures.