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SUMMARY:Computing periodic conformal mappings - Peter Baddoo (Imperial Col
 lege London)
DTSTART:20191213T150000Z
DTEND:20191213T153000Z
UID:TALK135703@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Conformal mappings are used to model a range of phenomena in t
 he physical sciences. Although the Riemann mapping theorem guarantees the 
 existence of a mapping between two conformally equivalent domains\, actual
 ly constructing these mappings is extremely challenging. Moreover\, even w
 hen the mapping is known in principle\, an efficient representation is not
  always available. Accordingly\, we present techniques for rapidly computi
 ng the conformal mapping from a multiply connected canonical circular doma
 in to a periodic array of polygons. The boundary correspondence function i
 s found by solving the parameter problem for a new periodic Schwarz--Chris
 toffel formula. We then represent the mapping using rational function appr
 oximation. To this end\, we present a periodic analogue of the adaptive An
 toulas--Anderson (AAA) algorithm to obtain the relevant support points and
  weights. The procedure is extremely fast\; evaluating the mappings typica
 lly takes around 10 microseconds. Finally\, we leverage the new algorithms
  to solve problems in fluid mechanics in periodic domains.
LOCATION:Seminar Room 1\, Newton Institute
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