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@PHDTHESIS{Fehling:878206,
author = {Fehling, Marc},
title = {{A}lgorithms for massively parallel generic hp-adaptive
finite element methods},
volume = {43},
school = {Universität Wuppertal},
type = {Dissertation},
address = {Jülich},
publisher = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
reportid = {FZJ-2020-02694},
isbn = {978-3-95806-486-7},
series = {Schriften des Forschungszentrums Jülich. IAS Series},
pages = {vii, 78 S.},
year = {2020},
note = {Universität Wuppertal, 2020},
abstract = {Efficient algorithms for the numerical solution of partial
differential equations are required to solve problems on an
economically viable timescale. In general, this is achieved
by adapting the resolution of the discretization to the
investigated problem, as well as exploiting hardware
specifications. For the latter category, parallelization
plays a major role for modern multi-core and multi-node
architectures, especially in the context of high-performance
computing. Using finite element methods, solutions are
approximated by discretizing the function space of the
problem with piecewise polynomials. With
$\textit{hp}$-adaptive methods, the polynomial degrees of
these basis functions may vary on locally refined meshes. We
present algorithms and data structures required for generic
hp-adaptive finite element software applicable for both
continuous and discontinuous Galerkin methods on distributed
memory systems. Both function space and mesh may be adapted
dynamically during the solution process. We cover details
concerning the unique enumeration of degrees of freedom with
continuous Galerkin methods, the communication of variable
size data, and load balancing. Furthermore, we present
strategies to determine the type of adaptation based on
error estimation and prediction as well as smoothness
estimation via the decay rate of coefficients of Fourier and
Legendre series expansions. Both refinement and coarsening
are considered. A reference implementation in the
open-source library deal. II$^{1}$ is provided and applied
to the Laplace problem on a domain with a reentrant corner
which invokes a singularity. With this example, we
demonstrate the benefits of the $\textit{hp}$-adaptive
methods in terms of error convergence and show that our
algorithm scales up to 49,152 MPI processes.},
cin = {IAS-7},
cid = {I:(DE-Juel1)IAS-7-20180321},
pnm = {511 - Computational Science and Mathematical Methods
(POF3-511) / ORPHEUS - Optimierung der Rauchableitung und
Personenführung in U-Bahnhöfen: Experimente und
Simulationen (BMBF-13N13266) / PhD no Grant - Doktorand ohne
besondere Förderung (PHD-NO-GRANT-20170405)},
pid = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)BMBF-13N13266 /
G:(DE-Juel1)PHD-NO-GRANT-20170405},
typ = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
urn = {urn:nbn:de:0001-2020071402},
url = {https://juser.fz-juelich.de/record/878206},
}