Solution box: SOLBOX-11

In computational electromagnetics, nonuniform discretizations with a large variety in the sizes of the discretization elements have always been challenging to handle. Such problems are inherently multi-scale, where different regimes coexist, as small elements are used to model tiny details while large elements are used on suitable parts comparable to the wavelength. When the variety in the element size is large, conventional implementations often suffer from inaccuracy, instability, and/or inefficiency issues due to numerical breakdowns in the context of discretization, expansion, and/or matrix solution. As a natural consequence, there is an enormous collective effort in the literature [1–9] to develop accurate, stable, and efficient numerical solvers for multi-scale problems involving nonuniform discretizations.