Numerical codes for the time-dependent radiative transfer equation by FDM-DOM

Published: 1 July 2020| Version 2 | DOI: 10.17632/gb892bxd5j.2
Hiroyuki Fujii


The numerical codes provide the calculation of the time-dependent radiative transfer equation (RTE) using the Galerkin quadrature method with the 6th order level-symmetric even quadrature set based on the finite difference and discrete ordinates methods for highly forward scattering media under the non-reentry boundary condition. 【Numerical schemes for the RTE-calculations】 ・3rd order weighted essentially non oscillatory scheme (spatial discretization) ・3rd order total variation diminishing-Runge-Kutta method (temporal discretization) ・Galerkin quadrature method (angular discretization) 【The medium geometry and optical properties (default)】 ・Rectangular medium with the source-detector distance of 0.4 cm ・Spatial grid size: 0.02 cm and timestep: 0.5 ps ・Absorption coefficient: 0.2 cm-1 ・Scattering coefficient: 100 cm-1 ・Anisotropic factor: 0.9 ・Refractive index: 1.4


Steps to reproduce

【Compiling and execution】 The program language for the source code is C++ and the code uses OpenMP for parallel computing and "Eigen" and "vector" libraries, so that before execution of the source code, please prepare those libraries. For compiling the code, please type the below command in the command prompt: user $ make -f makefile_C++_linux.txt Then, please run the executable file "all.out" in the command prompt: user $ ./all.out 【Output files】 ・condition.txt: run time, measurement setup, etc ・phi_det.txt: temporal profile of the fluence rate using the RTE ・time.txt: timesteps ・omega.txt: a vector of discrete angular direction with a weight ・P.txt: a matrix of the phase function


Applied Sciences, Radiative Transfer, Near Infrared Spectroscopy, Biomedical Optics, Light Scattering