Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars

The Galerkin method is used to numerically solve the exterior boundary value problem for the radiosity equation for the spherical quatrefoil. The radiosity equation is a mathematical model for the brightness of a collection of one or more surfaces when their reflectivity and emissivity are given. On planet Mars the surface emissivity is closely related to its surface temperature. The radiosity of a surface is the rate at which the energy leaves that surface; it includes the energy emitted by a surface as well as the energy reflected from other surfaces.