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UID:news219@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T175418
DTSTART;TZID=Europe/Zurich:20180427T110000
SUMMARY:Seminar in Numerical Analysis: Pierre-Henri Tournier (UPMC - Univer
 sity Pierre and Marie Curie)
DESCRIPTION:This work deals with preconditioning the time-harmonic Maxwell 
 equations with absorption\, where the preconditioner is constructed using 
 two-level overlapping Additive Schwarz Domain Decomposition\, and the PDE 
 is discretised using finite-element methods of fixed\, arbitrary order. Th
 e theory shows that if the absorption is large enough\, and if the subdoma
 in and coarse mesh diameters are chosen appropriately\, then classical two
 -level overlapping Additive Schwarz Domain Decomposition preconditioning p
 erforms optimally – in the sense that GMRES converges in a wavenumber-in
 dependent number of iterations – for the problem with absorption. This w
 ork is an extension of the theory proposed in [1] for the Helmholtz equati
 on. Numerical experiments illustrate this theoretical result and also (i) 
 explore replacing the PEC boundary conditions on the subdomains by impedan
 ce boundary conditions\, and (ii) show that the preconditioner for the pro
 blem with absorption is also an effective preconditioner for the problem w
 ith no absorption. The numerical results include examples arising from app
 lications: a problem with absorption arising from medical imaging shows th
 e robustness of the preconditioner against heterogeneity\, and a scatterin
 g problem by the COBRA cavity shows good scalability of the preconditioner
  with up to 3000 processors. Finally\, additional numerical results for th
 e elastic wave equation are presented for benchmarks in seismic inversion.
 \\r\\n[1] I. G. Graham\, E. A. Spence\, and E. Vainikko. Domain decomposit
 ion preconditioning for high-frequency Helmholtz problems with absorption.
  Mathematics of Computation\, 86(307):2089–2127\, 2017.
X-ALT-DESC:This work deals with preconditioning the time-harmonic Maxwell e
 quations with absorption\, where the preconditioner is constructed using t
 wo-level overlapping Additive Schwarz Domain Decomposition\, and the PDE i
 s discretised using finite-element methods of fixed\, arbitrary order. The
  theory shows that if the absorption is large enough\, and if the subdomai
 n and coarse mesh diameters are chosen appropriately\, then classical two-
 level overlapping Additive Schwarz Domain Decomposition preconditioning pe
 rforms optimally – in the sense that GMRES converges in a wavenumber-ind
 ependent number of iterations – for the problem with absorption. This wo
 rk is an extension of the theory proposed in [1] for the Helmholtz equatio
 n. Numerical experiments illustrate this theoretical result and also (i) e
 xplore replacing the PEC boundary conditions on the subdomains by impedanc
 e boundary conditions\, and (ii) show that the preconditioner for the prob
 lem with absorption is also an effective preconditioner for the problem wi
 th no absorption. The numerical results include examples arising from appl
 ications: a problem with absorption arising from medical imaging shows the
  robustness of the preconditioner against heterogeneity\, and a scattering
  problem by the COBRA cavity shows good scalability of the preconditioner 
 with up to 3000 processors. Finally\, additional numerical results for the
  elastic wave equation are presented for benchmarks in seismic inversion.\
 n[1] I. G. Graham\, E. A. Spence\, and E. Vainikko. Domain decomposition p
 reconditioning for high-frequency Helmholtz problems with absorption. Math
 ematics of Computation\, 86(307):2089–2127\, 2017. 
DTEND;TZID=Europe/Zurich:20180427T120000
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