Abstract
This paper is on a multi-GPU simulation of a petroleum reservoir using a 3D structured grid, where each point is represented by its state. Using the Darcy model for porous media, each grid point is related to its six neighbors by a linear relation. The system equation is a sparse linear system AX = b, where A is a hepta-diagonal matrix, b is model parameters, and X is a state vector. The simulation repeatedly computes (1) A and b given X and (2) X given A and b, which is the focus of this paper. The BiCG-Stab is an iterative procedure for solving AX = b for X. This work focuses on developing a scalable multi-GPU approach for solving large sparse systems Ax = b using BiCG-Stab. We extend a previously developed storage scheme for blocked hepta-diagonal matrices to minimize storage and computing overheads of the sparse matrix–vector multiply (SpMV) used in BiCG-Stab. To honor data dependencies in BiCG-Stab tasks we propose a hierarchical multi-GPUs synchronization scheme that reduces the polling, combines barriers, termination BiCG-Stab iteration, and assembles the solution X. We present a multi-GPU implementation of BiCG-Stab by distribution operations overall units within a GPU and overall GPUs. Reduce-add operations are orchestrated by assembling partial results across all units and all GPUs. Since the cuSparse library works only on a single GPU, we present an SpMV for multi-GPU. In the evaluation, we present the testing of the pinned/paged memory to implement multi-GPU synchronization and communication. The scalability of the multi-GPU implementation of BiCG-Stab is presented showing a smooth increase in the computational load when the problem size grows to a billion, which is useful for developing scalable petroleum reservoir simulation on a clusterof GPUs.
Original language | English |
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Pages (from-to) | 23563-23597 |
Number of pages | 35 |
Journal | Multimedia Tools and Applications |
Volume | 83 |
Issue number | 8 |
DOIs | |
State | Accepted/In press - 2023 |
Bibliographical note
Funding Information:This research was funded through a research project by the National Plan for Science, Technology, and Innovation (MAARIFAH) King Abdulaziz City for Science and Technology through the Science & Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM) the Kingdom of Saudi Arabia, award number (12-INF3008-04). Thanks to King Fahd University of Petroleum & Minerals (KFUPM) for computing support.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- BiCG-Stab solver
- Multi-GPUs
- Numerical Simulation
- Scalable SpMV
ASJC Scopus subject areas
- Software
- Media Technology
- Hardware and Architecture
- Computer Networks and Communications