Scalable Adaptive PDE Solvers in Arbitrary Domains

Authors: Kumar Saurabh (Iowa State University); Masado Ishii and Milinda Fernando (University of Utah); Boshun Gao, Kendrick Tan, Ming-Chen Hsu, and Adarsh Krishnamurthy (Iowa State University); Hari Sundar (University of Utah); and Baskar Ganapathysubramanian (Iowa State University)

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 (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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