A non-conforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator

摘要

We present and analyze a non-conforming domain decomposition approximationfor a hypersingular operator governed by the Helmholtz equation in threedimensions. This operator appears when considering the corresponding Neumannproblem in unbounded domains exterior to open surfaces. We consider small wavenumbers and low-order approximations with Nitsche coupling across interfaces.Under appropriate assumptions on mapping properties of the weakly singular andhypersingular operators with Helmholtz kernel, we prove that this methodconverges almost quasi-optimally. Numerical experiments confirm our errorestimate.