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SUMMARY:Pollution in Helmholtz boundary integral methods - Jeffrey Galkows
 ki (University College London)
DTSTART:20260417T104500Z
DTEND:20260417T114500Z
UID:TALK244051@talks.cam.ac.uk
DESCRIPTION:We consider solving the acoustic scattering problem for the He
 lmholtz equation (-\\Delta-k^2)u=0 with constant wave speed and bounded Di
 richlet or Neumann scatterer using the standard second-kind BIEs. We discu
 ss various methods (including Galerkin\, Collocation\, and Nystrom) for th
 e numerical approximation solutions of these BIEs\;&nbsp\; addressing the 
 fundamental question: how quickly must N\, the dimension of the approximat
 ion space\, grow with k to maintain accuracy as k &rarr\;\\infty? We give 
 sufficient conditions on N to maintain accuracy as k\\to \\infty. Strikini
 ngly\, we show that these conditions are optimal for the Galerkin method w
 ith piecewise polynomials\, and hence that\, despite the common belief to 
 the contrary\, the boundary element method suffers from the pollution effe
 ct in many geometries&nbsp\;(i.e. N growing like k^{d-1} is&nbsp\;not&nbsp
 \;sufficient to maintain accuracy).&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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