@article{Schweitzer.Ziegenhagel:2018,
  author="Schweitzer, Marc Alexander
  and Ziegenhagel, Albert",
  title="Multilevel preconditioners for embedded enriched partition of unity approximations",
  journal="Advanced Modeling and Simulation in Engineering Sciences",
  year="2018",
  month="May",
  day="18",
  volume="5",
  number="1",
  pages="13",
  abstract = {In this paper we are concerned with the non-invasive
		  embedding of enriched partition of unity approximations in
		  classical finite element simulations and the efficient
		  solutionof the resulting linear systems. The employed
		  embedding is based on the partition ofunity approach
		  introduced in Schweitzer and Ziegenhagel (Embedding
		  enrichedpartition of unity approximations in finite element
		  simulations. In: Griebel M, SchweitzerMA, editors. Meshfree
		  methods for partial differential equations VIII. Lecture
		  notes inscience and engineering, Cham, Springer
		  International Publishing; 195–204,2017)which is
		  applicable to any finite element implementation and thus
		  allows for a stableenrichment of e.g. commercial finite
		  element software to improve the quality of itsapproximation
		  properties in a non-invasive fashion. The major remaining
		  challenge isthe efficient solution of the arising linear
		  systems. To this end, we apply classical subspace
		  correction techniques to design non-invasive efficient
		  multilevel solvers byblending a non-invasive algebraic
		  multigrid method (applied to the finite elementcomponents)
		  with a (geometric) multilevel solver (Griebel and
		  Schweitzer in SIAM J SciComput 24:377–409,2002;
		  Schweitzer in Numer Math 118:307–28,2011) (applied tothe
		  enriched embedded components). We present first numerical
		  results in two andthree space dimensions which clearly show
		  the (close to) optimal performance of theproposed solver.},
  doi = {10.1186/s40323-018-0107-6},
  url = {https://amses-journal.springeropen.com/articles/10.1186/s40323-018-0107-6},
  annote = {refereed article,ag-schweitzer}
}