A hypothetical smuggling of material suitable for a nuclear weapon is known as a threat scenario. There is a considerable effort by the U.S. government to reduce this threat by placing radiation detectors at key interdiction points around the world. These detectors provide deterrence and defense against smuggling attempts by scanning vehicles, ships, and pedestrians for threat objects. Formulating deployment strategies for these detectors within the global transportation network requires an understanding of the complex interactions between the attributes of a smuggler and the detection systems. These strategies are rooted in the continued development of novel detection systems and alarm algorithms. Radiation transport simulation provides a means for characterizing detection system response to threat scenarios. However, this task is computationally expensive with existing radiation transport codes. Furthermore, the degrees of freedom in smuggler and threat scenario attributes create a large, constantly evolving problem space. Previous research has demonstrated that decomposing the scenario into independently simulated components using Green's functions can simulate photon detector signals with coarse energy resolution. This dissertation presents a general form of this approach, applicable to a wide range of threat scenarios through physics enhancements and numerical treatments for high energy resolution photon transport, neutron transport, and time dependent transport. While each Green's function implicitly captures the full transport phase-space within each component, these new methods ensure that this information is preserved between components. As a result, detector signals produced from full forward transport simulations can be replicated within 20% while requiring multiple orders of magnitude less computation time. This capability is presented as a general threat scenario simulation platform which can efficiently model a large problem space while preserving the full radiation transport phase-space. / text