Top-down extended meshing algorithm and its applications to Green's tensor nano-optics calculations

We present a computational algorithm which speeds up Green's tensor nano-optics calculations by means of optimizing the mesh that represents the system we want to investigate. The algorithm automates the process of creating a variable-size mesh that describes an arbitrary nanostructure. The total number of elements of this mesh is smaller than that of a regular mesh representing the same structure, and thus the Green's tensor calculations can be performed faster. Precision, however, is kept at a similar level than for the regular mesh. Typically, the algorithm yields a mesh that speeds up Green's tensor calculations by a factor of 4, while giving a maximum error in the field magnitude of about 5%. The speed-up factor makes it very suitable for otherwise lengthy calculations, and the error should be acceptable for most applications.