Scalable Adaptive PDE Solvers in Arbitrary Domains
Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a �...
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| Vydané v: | SC21: International Conference for High Performance Computing, Networking, Storage and Analysis s. 01 - 18 |
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| Hlavní autori: | , , , , , , , , |
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| Jazyk: | English |
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ACM
14.11.2021
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| ISSN: | 2167-4337 |
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| Abstract | Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a 'good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an incomplete octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on incomplete octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers (0(1-10 6 )) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms. |
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| AbstractList | Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a 'good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an incomplete octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on incomplete octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers (0(1-10 6 )) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms. |
| Author | Kumar, Saurabh Ganapathysubramanian, Baskar Sundar, Hari Fernando, Milinda Tan, Kendrick Hsu, Ming-Chen Krishnamurthy, Adarsh Gao, Boshun Ishii, Masado |
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| Snippet | Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of... |
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| SubjectTerms | Computational modeling distributed memory parallelism finite element method Fluids Geometry High performance computing Incomplete octrees matrix-free Octrees Partial differential equations Three-dimensional displays |
| Title | Scalable Adaptive PDE Solvers in Arbitrary Domains |
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