@phdthesis{Vu2022,
  author    = {Vu, Nils Leif},
  title     = {A task-based parallel elliptic solver for numerical relativity with discontinuous Galerkin methods},
  doi       = {10.25932/publishup-56226},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-562265},
  school      = {Universit{\"a}t Potsdam},
  pages     = {172},
  year      = {2022},
  abstract  = {Elliptic partial differential equations are ubiquitous in physics. In numerical relativity---the study of computational solutions to the Einstein field equations of general relativity---elliptic equations govern the initial data that seed every simulation of merging black holes and neutron stars. In the quest to produce detailed numerical simulations of these most cataclysmic astrophysical events in our Universe, numerical relativists resort to the vast computing power offered by current and future supercomputers. To leverage these computational resources, numerical codes for the time evolution of general-relativistic initial value problems are being developed with a renewed focus on parallelization and computational efficiency. Their capability to solve elliptic problems for accurate initial data must keep pace with the increasing detail of the simulations, but elliptic problems are traditionally hard to parallelize effectively. In this thesis, I develop new numerical methods to solve elliptic partial differential equations on computing clusters, with a focus on initial data for orbiting black holes and neutron stars. I develop a discontinuous Galerkin scheme for a wide range of elliptic equations, and a stack of task-based parallel algorithms for their iterative solution. The resulting multigrid-Schwarz preconditioned Newton-Krylov elliptic solver proves capable of parallelizing over 200 million degrees of freedom to at least a few thousand cores, and already solves initial data for a black hole binary about ten times faster than the numerical relativity code SpEC. I also demonstrate the applicability of the new elliptic solver across physical disciplines, simulating the thermal noise in thin mirror coatings of interferometric gravitational-wave detectors to unprecedented accuracy. The elliptic solver is implemented in the new open-source SpECTRE numerical relativity code, and set up to support simulations of astrophysical scenarios for the emerging era of gravitational-wave and multimessenger astronomy.},
  language  = {en}
}
@phdthesis{Koppitz2004,
  author    = {Koppitz, Michael},
  title     = {Numerical studies of Black Hole initial data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0001245},
  school      = {Universit{\"a}t Potsdam},
  year      = {2004},
  abstract  = {Diese Doktorarbeit behandelt neue Methoden der numerischen Evolution von Systemen mit bin{\"a}ren Schwarzen L{\"o}chern. Wir analysieren und vergleichen Evolutionen von verschiedenen physikalisch motivierten Anfangsdaten und zeigen Resultate der ersten Evolution von so genannten 'Thin Sandwich' Daten, die von der Gruppe in Meudon entwickelt wurden. Zum ersten Mal wurden zwei verschiedene Anfangsdaten anhand von dreidimensionalen Evolutionen verglichen: die Puncture-Daten und die Thin-Sandwich Daten. Diese zwei Datentypen wurden im Hinblick auf die physikalischen Eigenschaften w{\"a}hrend der Evolution verglichen. Die Evolutionen zeigen, dass die Meudon Daten im Vergleich zu Puncture Daten wesentlich mehr Zeit ben{\"o}tigen bevor sie kollidieren. Dies deutet auf eine bessere Absch{\"a}tzung der Parameter hin. Die Kollisionszeiten der numerischen Evolutionen sind konsistent mit unabh{\"a}ngigen Sch{\"a}tzungen basierend auf Post-Newtonschen N{\"a}herungen die vorhersagen, dass die Schwarzen L{\"o}cher ca. 60\% eines Orbits rotieren bevor sie kollidieren.},
  language  = {en}
}