StaRMAP (Staggered grid Radiation Moment Approximation) is a simple method to solve spherical harmonics moment systems, such as the the time-dependent PN and SPN equations, of radiative transfer. The approach works for arbitrary moment order N, making use of the specific coupling between the moments in the PN equations. The method allows for an efficient implementation in Matlab. The StaRMAP project is reproducible research: all program and example files can be downloaded below.
|Current version (03/13/2015): 1.9|
|StaRMAP_ver1p9.zip||Zip file of all project files (given below)|
|ChangeLog.txt||List of changes from previous version|
|README.txt||A brief documentation|
|starmap_closure_pn.m||Creates PN moment matrices|
|starmap_closure_spn.m||Creates SPN moment matrices|
|starmap_create_beam.m||Creates example file starmap_ex_beam_auto.m, beam in void and medium|
|starmap_create_hemisphere_filter_convergence.m||Creates example file starmap_ex_hemisphere_filter_convergence_auto.m, FPN convergence for hemisphere test|
|starmap_create_mms.m||Creates example file starmap_ex_mms_auto.m, manufactured solution|
|starmap_ex_boxes.m||Example file: boxes test case|
|starmap_ex_controlrod.m||Example file: control rod test|
|starmap_ex_gauss_filter_convergence.m||Example file: FPN convergence for Gauss test|
|starmap_ex_homogeneous.m||Example file: comparison of various closures for spreading initial hump|
|starmap_ex_lattice.m||Example file: lattice/checkerboard test|
|starmap_ex_lattice_diffusion.m||Example file: lattice/checkerboard test with various diffusive closures|
|starmap_ex_lattice_filter.m||Example file: lattice/checkerboard test with filtering|
|starmap_ex_lattice_filter_convergence.m||Example file: FPN convergence for lattice/checkerboard test|
|starmap_ex_linesource.m||Example file: line source test|
|starmap_ex_linesource_filter.m||Example file: line source test with filtering|
|starmap_ex_linesource_filter_reconstruction.m||Example file: line source test with angular reconstruction in a point|
|starmap_ex_l2norm.m||Example file: evolution of L2 norm of numerical solution|
|starmap_solver.m||The computational code|
|Old Version (10/10/2014): 1.5|
|StaRMAP_ver1p5.zip||Zip file of all project files|
|StaRMAP_ver1p5_create_figures.zip||Zip file of files used to create the figures and tables for the paper|
[Frank, Hauck, Kuepper, Convergence of filtered spherical harmonic equations for radiation transport (2014)]
|Old Version (07/14/2013): 1.1|
|StaRMAP_ver1p1.zip||Zip file of all project files|
|Old Version (11/11/2012): 1.0|
|StaRMAP_ver1p0.zip||Zip file of all project files|
Authors: Benjamin Seibold, Martin Frank
Contributors: Edgar Olbrant (v1.0), Kerstin Küpper (v1.5)
Numerical convergence analysis using a manufactured solution.
Temporal evolution of discrete L2 norm of numerical solution.
Checkerboard test case with various moment orders (P3, P5, P15, and P39).
Line source test case, computed with P19 and P39.
Beam that starts in void and hits forward scattering medium, computed with P9 and P39.
Control rod test case, computed with SP3.
Boxes test, demonstrating the equivalence of PN and SPN under the given assumptions.
October 2014: Talk by Benjamin Seibold at the
|B. Seibold, M. Frank, StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer, ACM Trans. Math. Software, Vol. 41, No. 1, 2014.|
|E. Olbrant, E. W. Larsen, M. Frank, B. Seibold, Asymptotic derivation and numerical investigation of time-dependent simplified PN equations, J. Comput. Phys., Vol. 238, 2013, pp. 315-336.|