Matrix-Free Finite Volume Kernels on a Dataflow Architecture
Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO 2 containment as a climate change mitigation strategy. These simulations involve solving numerous large and complex linear systems arising from the implicit Fin...
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| Published in: | SC24: International Conference for High Performance Computing, Networking, Storage and Analysis pp. 1 - 11 |
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IEEE
17.11.2024
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| Abstract | Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO 2 containment as a climate change mitigation strategy. These simulations involve solving numerous large and complex linear systems arising from the implicit Finite Volume (FV) discretization of PDEs governing subsurface fluid flow. Compounded with highly detailed geomodels, solving linear systems is computationally and memory expensive, and accounts for the majority of the simulation time. Modern memory hierarchies are insufficient to meet the latency and bandwidth needs of large-scale numerical simulations. Therefore, exploring algorithms that can leverage alternative and balanced paradigms such as dataflow and in-memory computing is crucial. This work introduces a matrix-free algorithm to solve FV-based linear systems using a dataflow architecture to significantly minimize memory latency and bandwidth bottlenecks. Our implementation achieves two orders of magnitude speedup compared to a GPGPU-based reference implementation, and up to 1.2 PFlops on a single dataflow device. |
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| AbstractList | Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO 2 containment as a climate change mitigation strategy. These simulations involve solving numerous large and complex linear systems arising from the implicit Finite Volume (FV) discretization of PDEs governing subsurface fluid flow. Compounded with highly detailed geomodels, solving linear systems is computationally and memory expensive, and accounts for the majority of the simulation time. Modern memory hierarchies are insufficient to meet the latency and bandwidth needs of large-scale numerical simulations. Therefore, exploring algorithms that can leverage alternative and balanced paradigms such as dataflow and in-memory computing is crucial. This work introduces a matrix-free algorithm to solve FV-based linear systems using a dataflow architecture to significantly minimize memory latency and bandwidth bottlenecks. Our implementation achieves two orders of magnitude speedup compared to a GPGPU-based reference implementation, and up to 1.2 PFlops on a single dataflow device. |
| Author | Sai, Ryuichi Mellor-Crummey, John Hamon, Francois P. Araya-Polo, Mauricio |
| Author_xml | – sequence: 1 givenname: Ryuichi surname: Sai fullname: Sai, Ryuichi email: ryuichi@alumni.rice.edu organization: Rice University,Houston,TX,USA – sequence: 2 givenname: Francois P. surname: Hamon fullname: Hamon, Francois P. email: francois.hamon@totalenergies.com organization: TotalEnergies EP Research & Technology US, LLC.,Houston,TX,USA – sequence: 3 givenname: John surname: Mellor-Crummey fullname: Mellor-Crummey, John email: johnmc@rice.edu organization: Rice University,Houston,TX,USA – sequence: 4 givenname: Mauricio surname: Araya-Polo fullname: Araya-Polo, Mauricio email: mauricio.araya@totalenergies.com organization: TotalEnergies EP Research & Technology US, LLC.,Houston,TX,USA |
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| Snippet | Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO 2 containment as a... |
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| SubjectTerms | Bandwidth Climate change Computational modeling dataflow architecture distributed memory energy finite-volume high-performance computing In-memory computing Linear systems matrix-free linear solver Numerical models Numerical simulation Prevention and mitigation Solid modeling wafer-scale engine |
| Title | Matrix-Free Finite Volume Kernels on a Dataflow Architecture |
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