In OPTIMA one of the objectives is to develop the industrial use cases and the libraries using the programming environments of the OPTIMA framework so as to take full advantage of the underlying novel HPC system. The 4 industrial use cases from 3 distinct different application areas are:
- Robotics Simulations
- MESHFREE: particle-based computational fluid dynamics
- Underground analysis using Finite Element Methods (FEM)
- SAILFISH-CFD: Lattice-Boltzmann particle-based computational fluid dynamics
In this post we will explain the application of Finite Element Method for Underground Analysis:
The Underground analysis mainly consists of simulations of the withdrawal/injection of subsurface resources (water, CO2, oil, gas, etc.) to understand and evaluate the impact on the environment. The main applications are:
- the evaluation of the induced and/or triggered seismicity due to fault reactivation and/or fracture generation caused by reservoir activities;
- the prediction of the flow field in variably-saturated or multi-aquifer systems both at the well and at the basin scale;
- the evaluation of the aquifer artificial recharge by superficial basins and wells.

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M3E has developed proprietary state-of-the-art Finite Element (FE) software simulators for underground analysis: ATLAS and GWS, for geomechanics and groundwater, respectively.
When it comes to the solution of extreme-size FE models, it is well-known that, for large models, the most time-consuming task (up to 95% of the total computational time) consists of solving the arising linear systems of equations. Both ATLAS and GWS take full advantage of Chronos, a proprietary collection of sparse linear algebra kernels designed for HPC. The library implements best-in-class preconditioners to accelerate the convergence, it can solve systems with hundreds of millions (or even billions) of unknowns.
Within the OPTIMA project, the focus is laid on Chronos. In particular, the main kernels for the preconditioner computation and the linear solver application will be ported and optimized to the FPGA-based HPC systems.

Plan view of the surface above an underground water basin.
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