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math.NA2023★ 1 cited
Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner
Martin Averseng, Xavier Claeys, Ralf Hiptmair
We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a -dimensional triangulated…
math.AP2023
Skeleton Integral Equations for Acoustic Transmission Problems with Varying Coefficients
Francesco Florian, Ralf Hiptmair, Stefan A. Sauter
In this paper we will derive an non-local (``integral'') equation which transforms a three-dimensional acoustic transmission problem with \emph{variable} coefficients, non-zero abs…
math.NA2023
Semi-Lagrangian Finite-Element Exterior Calculus for Incompressible Flows
Wouter Tonnon, Ralf Hiptmair
We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport p…