Quantitative bounds on impedance-to-impedance operators with applications to fast direct solvers for PDEs
Quantitative bounds on impedance-to-impedance operators with applications to fast direct solvers for PDEs
We prove quantitative norm bounds for a family of operators involving impedance boundary conditions on convex, polygonal domains. A robust numerical construction of Helmholtz scattering solutions in variable media via the Dirichlet-to-Neumann operator involves a decomposition of the domain into a sequence of rectangles of varying scales and constructing impedance-to-impedance …