Time evolution of photon-pulse propagation in scattering and absorbing   media: The dynamic radiative transfer system
  A new dynamic system approach to the problem of radiative transfer inside scattering and absorbing media is presented, directly based on firsthand physical principles. This method, the Dynamic Radiative Transfer System (DRTS), calculates accurately the time evolution of photon propagation in media of complex structure and shape. DRTS employs a dynamical system formality using a global sparse matrix which characterizes the physical, optical and geometrical properties of the material volume of interest. The new system state vector is generated by the above time-independent matrix, using simple matrix vector multiplication addition for each subsequent time step. DRTS simulation results are presented for 3D light propagation in different optical media, demonstrating greatly reduced computational cost and resource requirements compared to other methods. Flexibility of the method allows the integration of time-dependent sources, boundary conditions, different media and several optical phenomena like reflection and refraction in a unified and consistent way. 
Anastasios Georgakopoulos, Konstantinos Politopoulos and Efstratios   Georgiou
cond-mat.stat-mech physics.comp-ph