The numerical characterization of a 10 kWe Xenon arc high flux solar simulator is thoroughly presented via two approaches: a forward Monte Carlo ray tracing method, and an inverse ray tracing method. An in-house Monte Carlo ray tracing code was used to determine the shape of the Xenon arc to custom model the simulator radiative map. It was determined that an isotropic volumetric source consisting of a hemisphere of 1 mm radius that is attached to a cylinder of 1 mm in radius and 10 mm in length explicitly describes the experimental results obtained. The in-house code was then used to generate heat flux maps similar to that obtained experimentally and to determine the intensity at the focal plane. Accuracy of the model was verified via inverse ray tracing method where the intensity interpolation schemes of the zeroth and the first-order were examined in addition to different solution strategies. It is shown that the first order interpolation scheme adds an unnecessary complications to the inverse problem leading to larger errors. Lastly, a new approach is proposed by constraining the formulated system of equations with an equality constraint that works by eliminating the intensity values that are not tracing back to the ellipsoidal reflector. This new approach provided intensity values with more accuracy by reducing the percentage errors.