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@PHDTHESIS{Moser:847903,
author = {Moser, Dieter},
title = {{A} multigrid perspective on the parallel full
approximation scheme in space and time},
volume = {36},
school = {Universität Kassel},
type = {Dr.},
address = {Jülich},
publisher = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
reportid = {FZJ-2018-03225},
isbn = {978-3-95806-315-0},
series = {Schriften des Forschungszentrums Jülich Reihe. IAS Series},
pages = {vi, 131 S.},
year = {2018},
note = {Universität Kassel, Diss., 2017},
abstract = {From careful observations, scientists derive rules to
describe phenomena in nature. These rules are implemented in
form of algorithms in order to simulate these phenomena.
Nowadays, simulations are a vital element of numerous
research fields, which study not only natural phenomena, but
also societal or macro-economical systems. For simulations
of a certain size and complexity, an adequate amount of
computing power is required. Such simulations are found in
fields like molecular dynamics or material science, where
sometimes billions of atoms need to be simulated to observe
emergent structures. Other fields, which employ such
simulations, include weather and climate sciences, where the
degrees of freedom simply surpass the capacities of a
personal computer. For these simulations a high performance
computing approach is required. A more complete list of such
fields and their current state of research is found in [1].
The task of the mathematician is to study the stability,
accuracy, and cost of computation of the numerical methods
used in these simulations. In the last decades, the rapid
increase of processors per machine created a need for
concurrent computation. This resulted in the reformulation
of the existing algorithms and development of new
algorithms, which in turn also need to be studied. Most of
the fields mentioned above model their problems in the form
of partial differential equations. For this class of
equations many effective parallel methods already exist.
Independent of the method chosen, the model of nature has to
be transformed into a model that may be processed by a
computer. Since computers are only able to process and store
a finite number of quantities with a limited precision, the
newly transformed model has to represent nature with this
finite number of quantities. One way to do so is to
decompose the computational domain of the problem into a
finite grid. Imagine, for example, a simulation of the wing
of an airplane. The computational domain consists of the
wing itself and the floating air around it. A system of
partial differential equations describes how the pressure,
the temperature, and the speed of the air interact with the
mechanical forces of the wing at every point in this
computational domain. When we decompose this domain, we are
only interested in the physical quantities on a finite
number of grid points. With, for example, the finite
difference scheme, we derive a set of rules from the partial
differential equations. These rules describe how the values
on [...]},
cin = {JSC},
cid = {I:(DE-Juel1)JSC-20090406},
pnm = {511 - Computational Science and Mathematical Methods
(POF3-511) / PhD no Grant - Doktorand ohne besondere
Förderung (PHD-NO-GRANT-20170405)},
pid = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)PHD-NO-GRANT-20170405},
typ = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
urn = {urn:nbn:de:0001-2018031401},
url = {https://juser.fz-juelich.de/record/847903},
}