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SUMMARY:Efficient high-order accurate  boundary integral solvers for  comp
 licated three dimensional geometries - Manas Rachh (Simons Foundation)
DTSTART:20230420T100000Z
DTEND:20230420T104500Z
UID:TALK198745@talks.cam.ac.uk
DESCRIPTION:The numerical simulation of the Helmholtz and Maxwell equation
 s play&nbsp\;a critical role in chip and antennadesign\, radar cross secti
 on determination\, speaker design\,&nbsp\;biomedical imaging\, wireless co
 mmunications\, and the development of new meta-materials and better wavegu
 ides to name a few. In order to enable design by simulation for problems a
 rising&nbsp\;in these applications\,&nbsp\;automatically adaptive solvers 
 which resolve the complexity of the geometry&nbsp\;and the input data play
  a critical role.&nbsp\;In two dimensions\, this has been made possible th
 rough the development of high-order integral equation based solvers which 
 rely on well-conditioned integral representations\, efficient quadrature f
 ormulas\, and coupling to fast multipole methods/fast direct solvers.&nbsp
 \;However\, much is still to desired of these solvers&nbsp\;in three dimen
 sions (both in terms of their efficiency and accuracy)\,&nbsp\;particularl
 y in the context of enabling automatic adaptivity&nbsp\;in complex geometr
 ies. In this talk\, I will present efficient high-order accurate solvers f
 or solving&nbsp\;boundary integral equations in complex three dimensional 
 geometries with focus on the following two issues --- quadrature methods f
 or computing singular integrals on high order meshes surfaces\, and a loca
 lly corrected quadrature framework for fast multipole accelerated iterativ
 e solvers and strong skeletonization based direct solvers.
LOCATION:Seminar Room 1\, Newton Institute
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