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SUMMARY:Recent advances on preconditioning for BEM on complex geometries. 
 - Carolina   Urzúa-Torres (Delft University of Technology)
DTSTART:20230420T084500Z
DTEND:20230420T093000Z
UID:TALK198742@talks.cam.ac.uk
DESCRIPTION:We are interested in the numerical solution of time-harmonic s
 cattering by complex geometries. We will first consider so-called multi-sc
 reens\, which are geometries composed of panels meeting at junction lines.
  This is modelled via first kind integral equations using the framework pr
 oposed by Claeys and Hiptmair. The key realisation is that solutions of th
 e related boundary integral equations belong to jump spaces\, that can be 
 represented as the quotient-space of a multi-trace space and a single trac
 e space. As shown in previous work\, the corresponding Galerkin discretiza
 tion via quotient-space boundary element methods is up to the task. Howeve
 r\, it does not address the ill-conditioning of the arising Galerkin matri
 ces and the performance of iterative solvers deteriorates significantly wh
 en increasing the mesh refinement.\nAs a remedy\, we introduce a Calder\\'
 on-type preconditioner and discuss two possible multi-trace discretization
 s. First\, we work with the full multi-trace discrete space\, which contai
 ns many more degrees of freedom (DoFs) than strictly required. Then\, we p
 ropose a representation of the quotient-space that reduces significantly t
 he number of degrees of freedom while still allowing for efficient Calder\
 \'on preconditioning. For this\, we exploit the fact that the solution to 
 the scattering problem is determined only up to a function in the single t
 race space. This implies that if we modify the single trace subspace of th
 e multi-trace discrete space\, the solution\, as an element of the quotien
 t-space\, is unaffected.&nbsp\;\n&nbsp\;\nFinally\, we will also consider 
 time-harmonic scattering by composite structures including multiple domain
 s and metallic coatings that can contain junctions. This is achieved by co
 mbining the global multi-trace method with the quotient space discretisati
 on of the multi-screen boundary integral equation.&nbsp\;\n&nbsp\;\nThis i
 s joint work with Kristof Cools.
LOCATION:Seminar Room 1\, Newton Institute
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