Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The aggregated unfitted finite element method on parallel tree-based
  adaptive meshes   In this work, we present an adaptive unfitted finite element scheme that
combines the aggregated finite element method with parallel adaptive mesh
refinement. We introduce a novel scalable distributed-memory implementation of
the resulting scheme on locally-adapted Cartesian forest-of-trees meshes. We
propose a two-step algorithm to construct the finite element space at hand by
means of a discrete extension operator that carefully mixes aggregation
constraints of problematic degrees of freedom, which get rid of the small cut
cell problem, and standard hanging degree of freedom constraints, which ensure
trace continuity on non-conforming meshes. Following this approach, we derive a
finite element space that can be expressed as the original one plus
well-defined linear constraints. Moreover, it requires minimum parallelization
effort, using standard functionality available in existing large-scale finite
element codes. Numerical experiments demonstrate its optimal mesh adaptation
capability, robustness to cut location and parallel efficiency, on classical
Poisson $hp$-adaptivity benchmarks. Our work opens the path to functional and
geometrical error-driven dynamic mesh adaptation with the aggregated finite
element method in large-scale realistic scenarios. Likewise, it can offer
guidance for bridging other scalable unfitted methods and parallel adaptive
mesh refinement.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex