49 citations · 119 across the 18 of their papers we have counts for
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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…
Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem
Ralf Hiptmair, Andrea Moiola, Euan A. Spence
We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and the standard associated direct boundary integral equations. For certain coefficien…
First-Kind Boundary Integral Equations for the Dirac Operator in 3D Lipschitz Domains
Erick Schulz, Ralf Hiptmair
We develop novel first-kind boundary integral equations for Euclidean Dirac operators in 3D Lipschitz domains comprising square-integrable potentials and involving only weakly sing…
Spurious Resonances in Coupled Domain-Boundary Variational Formulations of Transmission Problems in Electromagnetism and Acoustics
Erick Schulz, Ralf Hiptmair
We develop a framework shedding light on common features of coupled variational formulations arising in electromagnetic scattering and acoustics. We show that spurious resonances h…
Coupled Domain-Boundary Variational Formulations For Hodge-Helmholtz Operators
Erick Schulz, Ralf Hiptmair
We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boun…
Closed-Form Exact Inverses of the Weakly Singular and Hypersingular Operators On Disks
Ralf Hiptmair, Carlos Jerez-Hanckes, Carolina Urzua-Torres
We introduce new boundary integral operators which are the exact inverses of the weakly singular and hypersingular operators for the Laplacian on flat disks. Moreover, we provide e…