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In a recent article the authors showed that the radiative Transfer equationswith multiple frequencies and scattering can be formulated as a nonlinearintegral system. In the present article, the formulation is extended to handlereflective boundary conditions. The fixed point method to solve the system isshown to be monotone. The discretization is done with a $P^1$ Finite ElementMethod. The convolution integrals are precomputed at every vertices of the meshand stored in compressed hierarchical matrices, using Partially PivotedAdaptive Cross-Approximation. Then the fixed point iterations involve onlymatrix vector products. The method is $O(N\sqrt[3]{N}\ln N)$, with respect tothe number of vertices, when everything is smooth. A numerical implementationis proposed and tested on two examples. As there are some analogies with raytracing the programming is complex.

Reflective Conditions for Radiative Transfer in Integral Form with H-Matrices