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DTSTART;TZID=America/Toronto:20251114T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-sander-rhebergen
SUMMARY:Tutte Colloquium - Sander Rhebergen
CLASS:PUBLIC
DESCRIPTION:TITLE: Parameter robust preconditioning\n\nSPEAKER:\n Sander R
 hebergen\n\nAFFILIATION:\n University of Waterloo\n\nLOCATION:\n MC 5501\n
 \nABSTRACT: The discretization of a partial differential equation (PDE)\n
 results in a linear system and iterative solvers are typically used to\nso
 lve these linear systems\, especially if these linear systems are\nlarge. 
 Krylov subspace methods are an important class of iterative\nmethods but f
 or these methods to be effective they must be combined\nwith a preconditio
 ner. However\, finding a good preconditioner for a\ngiven discretization o
 f a PDE is a nontrivial task and so in the first\npart of this talk I will
  summarize some useful results from the\nliterature that use a Functional 
 Analysis framework to identify\npreconditioners for symmetric PDEs.\n\n  
    Many PDEs depend on parameters such as viscosity\,\npermeability\, a 
 discrete time-step\, etc. and these parameters can have\na large effect on
  the convergence of preconditioned Krylov subspace\nmethods if they are no
 t properly accounted for by the preconditioner.\nIn the second part of thi
 s talk I will show how the Functional\nAnalysis framework is used to ident
 ify preconditioners such that the\nconvergence of a preconditioned Krylov 
 subspace method is robust with\nrespect to these parameters. \n     In 
 the final part of this talk I will discuss discretizations\nthat allow for
  static condensation. Static condensation is the process\nof eliminating c
 ertain degrees of freedom from the linear system with\nthe purpose of redu
 cing the size of the linear system. The main\nquestion I will answer is: I
 f one has a parameter robust\npreconditioner for a linear system before st
 atic condensation\, is the\npreconditioner still parameter robust after st
 atic condensation?
DTSTAMP:20260402T162136Z
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