Fast hierarchical low-rank view factor matrices for thermal irradiance on planetary surfaces

We present an algorithm for compressing the radiosity view factor model commonly used in radiation heat transfer and computer graphics. use a format inspired by hierarchical off-diagonal low rank format, where elements are recursively partitioned using quadtree or octree blocks compressed sparse singular value decomposition—the matrix is assembled dynamic programming. The motivating application time-dependent thermal modeling on vast planetary surfaces, with focus permanently shadowed craters which receive energy through indirect irradiance. In this setting, shape models comprised of large number triangular facets conform to rough surface. At each time step, quadratic triangle-to-triangle scattered fluxes must be summed; that is, as sun moves sky, we solve same system equations potentially unlimited time-varying righthand sides. first conduct numerical experiments synthetic spherical cap-shaped crater, equilibrium temperature analytically available. also test our implementation triangle meshes surfaces derived from digital elevation recovered orbiting spacecrafts. Our results indicate can time, comparable it takes assemble full itself. Memory requirements during assembly reduced factor. Finally, range compression tolerances, size speed resulting vector product both scale linearly (as opposed quadratically matrix), orders magnitude savings processing memory space.