Spatial sampling and interpolation techniques in computational electromagnetics and beyond

The spatial sampling and interpolation approach, facilitating construction of fast algorithms, for a variety of computational problems of computational electromagnetics and acoustics, is reviewed. Efficient sampling techniques for static and dynamic fields in near and far zones are presented and employed to construct pertinent fast field evaluation algorithms. The algorithms are based on hierarchical source domain decomposition and multilevel interpolation over a series of uniform and non-uniform grids (NGs). These algorithms are useful in high-frequency scattering and radiation problems and for iterative solution of integral equations. Development of fast direct solvers employing the NG sampling grids is also outlined. The proposed approach is shown to facilitate the construction of fast algorithms for synthetic aperture radar and sonar imaging as well as for computer tomography.