StaRMAP (Staggered grid Radiation Moment Approximation) is a simple method to solve spherical harmonics moment systems, such as the the time-dependent P_{N} and SP_{N} equations, of radiative transfer. The approach works for arbitrary moment order N, making use of the specific coupling between the moments in the P_{N} 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 | |
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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 P_{N} moment matrices |
starmap_closure_spn.m | Creates SP_{N} 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, FP_{N} 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: FP_{N} 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: FP_{N} 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 (P_{3}, P_{5}, P_{15}, and P_{39}).
Line source test case, computed with P_{19} and P_{39}.
Beam that starts in void and hits forward scattering medium, computed with P_{9} and P_{39}.
Control rod test case, computed with SP_{3}.
Boxes test, demonstrating the equivalence of P_{N} and SP_{N} under the given assumptions.
October 2014: Talk by Benjamin Seibold at the Workshop on Moment Methods in Kinetic Theory II, Fields Institute, Toronto, StaRMAP - A staggered grid moment approach and its asymptotic preserving properties
(video of talk:
interactive and
static)
October 2014: Talk by Martin Frank at the Workshop on Moment Methods in Kinetic Theory II, Fields Institute, Toronto, Convergence of filtered spherical Harmonic equations for radiation transport
(video of talk:
interactive and
static)
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 P_{N} equations, J. Comput. Phys., Vol. 238, 2013, pp. 315-336. |