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UID:news289@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T234846
DTSTART;TZID=Europe/Zurich:20120420T090000
SUMMARY:Seminar in Numerical Analysis: Ilario Mazzieri (MOX - Politecnico d
 i Milano)
DESCRIPTION:The study and development of spectral element (SE) methods for 
  simulating elastic wave propagation in seismic regions has been  subjecte
 d to a tremendous growth\, occurred in the past ten years. SE  methods are
  based on high-order Lagrangian interpolants sampled at the  Gauss-Legendr
 e-Lobatto quadrature points\, and combine the flexibility of  finite eleme
 nts with the accuracy of spectral techniques. Since they  are based on the
  weak formulation of the elastodynamics equations\, they  handle naturally
  both interface continuity and free boundary conditions\,  allowing very a
 ccurate resolutions of evanescent interface and surface  waves. Moreover\,
  SE methods retain a high level parallel structure\, thus  are well suited
  for massively parallel computations. The main drawback  of SE methods is 
 that they usually require a uniform polynomial order on  the whole computa
 tional domain\, and this can lead to an unreasonably  large computational 
 effort\, in particular in regions where a fine mesh  grid is needed alread
 y to describe accurately the domain geometry.\\r\\nHere\,  we consider a D
 iscontinuous Galerkin (DGSE) and a Mortar (MSE) spectral  element methods 
 coupled with the leap-frog time integration scheme to  simulate seismic wa
 ve propagations in two and three dimensional  heterogeneous media. The mai
 n advantage with respect to conforming  discretizations\, as SE method\, i
 s that DGSE and MSE discretizations can  accommodate discontinuities\, not
  only in the parameters\, but also in the  wavefield\, while preserving th
 e energy. The domain of interest Ω is  assumed to be union of polygonal s
 ubdomain Ωi. We allow this subdomain decomposition to be geometrically no
 n-conforming. Inside each subdomain Ωi\, a conforming high order finite e
 lement space associated to a partition Thi(Ωi)  is introduced. We conside
 r different polynomial approximation degrees  within different subdomains.
  To handle non-conforming meshes and  non-uniform polynomial degrees acros
 s ∂Ωi \, a DG or a Mortar discretization is considered.\\r\\nApplicatio
 ns of the DGSE and MSE methods to simulate realistic seismic wave propagat
 ion problems are presented.\\r\\nJoint work with: P.F. Antonietti\, A. Qua
 rteroni and F. Rapetti.
X-ALT-DESC:The study and development of spectral element (SE) methods for  
 simulating elastic wave propagation in seismic regions has been  subjected
  to a tremendous growth\, occurred in the past ten years. SE  methods are 
 based on high-order Lagrangian interpolants sampled at the  Gauss-Legendre
 -Lobatto quadrature points\, and combine the flexibility of  finite elemen
 ts with the accuracy of spectral techniques. Since they  are based on the 
 weak formulation of the elastodynamics equations\, they  handle naturally 
 both interface continuity and free boundary conditions\,  allowing very ac
 curate resolutions of evanescent interface and surface  waves. Moreover\, 
 SE methods retain a high level parallel structure\, thus  are well suited 
 for massively parallel computations. The main drawback  of SE methods is t
 hat they usually require a uniform polynomial order on  the whole computat
 ional domain\, and this can lead to an unreasonably  large computational e
 ffort\, in particular in regions where a fine mesh  grid is needed already
  to describe accurately the domain geometry.\nHere\,  we consider a Discon
 tinuous Galerkin (DGSE) and a Mortar (MSE) spectral  element methods coupl
 ed with the leap-frog time integration scheme to  simulate seismic wave pr
 opagations in two and three dimensional  heterogeneous media. The main adv
 antage with respect to conforming  discretizations\, as SE method\, is tha
 t DGSE and MSE discretizations can  accommodate discontinuities\, not only
  in the parameters\, but also in the  wavefield\, while preserving the ene
 rgy. The domain of interest Ω is  assumed to be union of polygonal subdom
 ain Ω<sub>i</sub>. We allow this subdomain decomposition to be geometrica
 lly non-conforming. Inside each subdomain Ω<sub>i</sub>\, a conforming hi
 gh order finite element space associated to a partition <i>T</i><sub>hi</s
 ub>(Ω<sub>i</sub>)  is introduced. We consider different polynomial appro
 ximation degrees  within different subdomains. To handle non-conforming me
 shes and  non-uniform polynomial degrees across ∂Ω<sub>i</sub> \, a DG 
 or a Mortar discretization is considered.\nApplications of the DGSE and MS
 E methods to simulate realistic seismic wave propagation problems are pres
 ented.\nJoint work with: P.F. Antonietti\, A. Quarteroni and F. Rapetti. 
DTEND;TZID=Europe/Zurich:20120420T100000
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