A non-conforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator
It provides a theoretical and numerical framework for solving Neumann problems on open surfaces in unbounded domains, which is relevant for computational acoustics and electromagnetics.
The paper presents a non-conforming domain decomposition method for the hypersingular Helmholtz operator on screens, proving almost quasi-optimal convergence for small wave numbers and low-order approximations, with numerical validation.
We present and analyze a non-conforming domain decomposition approximation for a hypersingular operator governed by the Helmholtz equation in three dimensions. This operator appears when considering the corresponding Neumann problem in unbounded domains exterior to open surfaces. We consider small wave numbers and low-order approximations with Nitsche coupling across interfaces. Under appropriate assumptions on mapping properties of the weakly singular and hypersingular operators with Helmholtz kernel, we prove that this method converges almost quasi-optimally. Numerical experiments confirm our error estimate.