The numerical characterization of a 10 kWe xenon arc high flux solar simulator is thoroughly presented and performed using two approaches: a forward Monte Carlo ray tracing (MCRT) method and an inverse ray tracing method. Experimental characterization was previously performed for the solar simulator using an indirect flux mapping technique, where the experimental heat flux distribution was obtained at the focal plane and additional 12 planes away from the simulator. For the first numerical characterization method, an in-house MCRT code was used to determine the shape of the xenon arc to best model the simulator. 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 well described the experimental results obtained. The in-house code was then used to generate heat flux maps similar to that obtained experimentally and determine the intensity at the focal plane to be used by the inverse ray tracing method presented for its validation. For the inverse method, intensity interpolation schemes of zeroth and first-order were examined in addition to different solution strategies. It is shown that a first-order interpolation scheme unnecessary complicates the inverse problem, leading to larger errors. In addition, a new approach of constraining the formulated system of equations with an equality constraint that works by eliminating intensity values not tracing back to the ellipsoidal reflector is proposed. This new approach provided intensity values with reduced percentage errors.