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UID:news350@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181023T144703
DTSTART;TZID=Europe/Zurich:20181102T110000
SUMMARY:Seminar in Numerical Analysis: Maryna Kachanovska (ENSTA ParisTech)
DESCRIPTION:In  this work we consider the problem of the sound propagation 
 in a  bronchial network. Asymptotically\, this phenomenon can be modelled 
 by a  weighted wave equation posed on a fractal (i.e. self-similar) 1D tre
 e.  The  principal difficulty for the numerical resolution of the problem 
 is the  'infiniteness' of the geometry. To deal with this issue\, we will 
  present  transparent boundary conditions\, used to truncate the computati
 onal  domain to a finite subtree.\\r\\nThe  construction of such transpare
 nt conditions relies on the approximation  of the Dirichlet-to-Neumann (Dt
 N) operator\, whose symbol is a  meromorphic function that  satisfies a ce
 rtain non-linear functional  equation. We present two approaches to approx
 imate the DtN in the time  domain\, alternative to the low-order absorbing
  boundary conditions\, which appear inefficient in this case.\\r\\n The  f
 irst approach stems from the use of the convolution quadrature (cf.  [Lubi
 ch 1988]\, [Banjai\, Lubich\, Sayas 2016])\, which consists in  constructi
 ng an exact DtN for a semi-discretized in time problem. In  this case the 
 combination of the explicit leapfrog method for the  volumic terms and the
  implicit trapezoid rule for the boundary terms  leads to a second-order s
 cheme stable under the classical CFL condition.\\r\\nThe  second approach 
 is motivated by the Engquist-Majda ABCs (cf. [Engquist\,  Majda 1977])\, a
 nd consists in approximating the DtN by local operators\, obtained from th
 e truncation of the  meromorphic series which represents the symbol of the
  DtN. We show how  the respective error can be controlled and provide some
  complexity  estimates.\\r\\nThis is a joint work with Patrick Joly (INRIA
 \, France) and Adrien Semin (TU Darmstadt\, Germany). \\r\\nFor further in
 formation about the seminar\, please visit this webpage.
X-ALT-DESC: In  this work we consider the problem of the sound propagation 
 in a  bronchial network. Asymptotically\, this phenomenon can be modelled 
 by a  weighted wave equation posed on a fractal (i.e. self-similar) 1D tre
 e.  The  principal difficulty for the numerical resolution of the problem 
 is the  'infiniteness' of the geometry. To deal with this issue\, we will 
  present  transparent boundary conditions\, used to truncate the computati
 onal  domain to a finite subtree.\nThe  construction of such transparent c
 onditions relies on the approximation  of the Dirichlet-to-Neumann (DtN) o
 perator\, whose symbol is a  meromorphic function that  satisfies a certai
 n non-linear functional  equation. We present two approaches to approximat
 e the DtN in the time  domain\, alternative to the low-order absorbing bou
 ndary conditions\, which appear inefficient in this case.\n The  first app
 roach stems from the use of the convolution quadrature (cf.  [Lubich 1988]
 \, [Banjai\, Lubich\, Sayas 2016])\, which consists in  constructing an ex
 act DtN for a semi-discretized in time problem. In  this case the combinat
 ion of the explicit leapfrog method for the  volumic terms and the implici
 t trapezoid rule for the boundary terms  leads to a second-order scheme st
 able under the classical CFL condition.\nThe  second approach is motivated
  by the Engquist-Majda ABCs (cf. [Engquist\,  Majda 1977])\, and consists 
 in approximating the DtN by local operators\, obtained from the truncation
  of the  meromorphic series which represents the symbol of the DtN. We sho
 w how  the respective error can be controlled and provide some complexity 
  estimates.\nThis is a joint work with Patrick Joly (INRIA\, France) and A
 drien Semin (TU Darmstadt\, Germany). \nFor further information about the 
 seminar\, please visit this <link de/forschung/mathematik/seminar-in-numer
 ical-analysis/ - - "Opens internal link in current window">webpage</link>.
DTEND;TZID=Europe/Zurich:20181102T120000
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