Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 `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 $\textit{incomplete}$ octree. We develop efficient top-down and
bottom-up traversal methods to perform finite element computations on
$\textit{incomplete}$ 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 ($\mathcal{O}(1-10^6)$)
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.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga