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Fast and robust flow simulations in discrete fracture networks with GPGPUs

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Abstract

A new approach for flow simulation in very complex discrete fracture networks based on PDE-constrained optimization has been recently proposed in Berrone et al. (SIAM J Sci Comput 35(2):B487–B510, 2013b; J Comput Phys 256:838–853, 2014) with the aim of improving robustness with respect to geometrical complexities. This is an essential issue, in particular for applications requiring simulations on geometries automatically generated like the ones used for uncertainty quantification analyses and hydro-mechanical simulations. In this paper, implementation of this approach in order to exploit Nvidia Compute Unified Device Architecture is discussed with the main focus to speed up the linear algebra operations required by the approach, being this task the most computational demanding part of the approach. Furthermore, two different approaches for linear algebra operations and two storage formats for sparse matrices are compared in terms of computational efficiency and memory constraints.

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  1. Dipartimento di Scienze Matematiche, Politecnico di Torino, Turin, Italy

    S. Berrone, A. D’Auria & F. Vicini

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  1. S. Berrone
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  2. A. D’Auria
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  3. F. Vicini
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Correspondence to S. Berrone.

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This research has been partially supported by INdAM-GNCS Projects 2017 and 2018, and by the MIUR Project “Dipartimenti di Eccellenza 2018–2022”. Computational resources were partially provided by HPC@POLITO (http://hpc.polito.it) and by CINECA Project IsC58 HP10CDFLWH.

Authors are members of the INdAM research group GNCS.

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Berrone, S., D’Auria, A. & Vicini, F. Fast and robust flow simulations in discrete fracture networks with GPGPUs. Int J Geomath 10, 8 (2019). https://doi.org/10.1007/s13137-019-0121-y

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