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: This project dealt with the theory, implementation, and application of simulations of light-matter interactions characterized by four attributes: i) Extreme temporal dynamics and super-broad spectra, ii) Strong reshaping of pulsed waveforms, iii) Interaction with matter over long distances, and iv) Structured geometry. The goal of this project was to create A) Theoretical basis, and B) Practical implementation in software. Both of these objectives were achieved in what is the first practical framework to deal with these difficult-to-model situations. The theory is realized in the generalized unidirectional pulse propagation equations (gUPPE), which marries techniques of extreme nonlinear optics with a whole class of beam-propagation methods for waveguides. New methods were implemented that facilitate modeling on realistic scales in situations which until now required approximate approaches. An important product of this effort is a freely available software, called gUPPEcore. This is complemented by the gUPPElab, which helps new users to adopt the techniques developed in this project. Through collaboration with several research groups, gUPPEcore and lab has been designed and tested in applications to a number of problems in nonlinear optics. Dedicated website was created to serve new users.

Simulation Methods for Optics and Electromagnetics in Complex Geometries and Extreme Nonlinear Regimes with Disparate Scales