Light-matter interaction is among the most enduring interests of the physical sciences. Theunderstanding and control of this physics is of paramount importance to the design of myriadtechnologies ranging from stained glass, to molecular sensing and characterization techniques,to quantum computers. The development of complex engineered systems that exploit thisphysics is predicated at least partially upon in silico design and optimization that properlycapture the light-matter coupling. In this thesis, the details of computational frameworksthat enable this type of analysis, based upon both Integral Equation and DiscontinuousGalerkin formulations will be explored. There will be a primary focus on the developmentof efficient and accurate software, with results corroborating both. The secondary focus willbe on the use of these tools in the analysis of a number of exemplary systems.
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