% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@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},
}