Data‐sparse numerical models for SNOM tips

Summary We propose a compressed non-local surface-impedance-type boundary condition for the efficient numerical modeling of large geometrically persistent parts in multi-scale electromagnetic simulations. The underlying compressed model is an approximate Schur complement of finite element Galerkin matrix. Our approach relies on local low-rank representation in the framework of the -matrix storage format. We discuss two ways to build -matrix approximations of Schur-complement matrices: adaptive cross approximation and -arithmetics. Profound numerical tests and studies of accuracy are carried out for an axisymmetric setting, employing the open source library AHMED by M. Bebendorf. To demonstrate the use of our method, we build the compressed model for an axisymmetric scanning near-field optical microscopy tip. The model can be embedded in three-dimensional tip-sample simulations. Copyright © 2016 John Wiley & Sons, Ltd.