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math.NA2019
Pseudo-differential analysis of the Helmholtz layer potentials on open curves
Martin Averseng
We introduce two new classes of pseudo-differential operators on open curves. They correspond via a change of variables to subclasses of the periodic pseudo-differential operators,…
math.NA2019
New preconditioners for Laplace and Helmholtz integral equations on open curves: Analytical framework and Numerical results
François Alouges, Martin Averseng
The Helmholtz wave scattering problem by screens in 2D can be recast into first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introd…