Methods for streamlining expensive function calls

The focus of this thesis has been developing and validating new methods of streamlining expensive function calls. These new methods of streamlining are applied to the problem of modeling electrodynamic response in in nite two-dimensional nanoparticle (NP) arrays. Using these methods, an exact analytical solution for electromagnetic interaction with two-dimensional spherical periodic in nite arrays has been developed. The new solution o ers fundamental insight into the singularities responsible for dramatic sensitivity in- creases seen in sensory applications. The new analytical solution also provides increased computational time with 60x improvement demonstrated in this work. In addition, a new electroless deposition method followed by thermal annealing was developed by Ahn et al. for spherical Au array fabrication. To complement the model and fabrication technique, additional improvements in NP array sample analysis have been adapted and developed. Algorithms for NP particle density, size, and shape analysis are described using Atomic Force Microscope (AFM) and Scanning Electron Microscope (SEM) with a comparison between the two microscopy methods. Using fabrication and analysis, the methods of streamlining expensive function calls can be tested and improved.