I n t r o d u c t o r y n o t e s

Approach  Applicability range  Speed  Accuracy  Source and dust configurations  Polarized radiation 

Single scattering approximation (tau<<1)  tau < 0.10.5 (depends on albedo, g)  very fast (depends on albedo, g or scatterer shape?)  may be not accurate  any 3D configuration  yes 
Double scattering approximation  tau<1 (depends on albebo, g?)  rather fast  not very accurate  any 3D configuration  yes 
Lambdaiteration mathod (generalization of 1,2,...scattering approximations)  tau_{max} ~ albedo, g?  quick (if number scattering is small)  depends on the numbers of itarations and scatterings?  any 3D configuration  yes 
Numerical methods developed for a given geometry  any tau  not fast  not very exact?  usually 1D configurations  no 
Gridpoint methods  ?  very slow  ?  3D configurations  yes 
Monte Carlo method  tau about 1100?  not fast (depends on tau and configuration)  not very accurate  any 3D configuration  yes 
Author(s)  Method  Particles  Geometry  Output  Applications 
Leung [1976]  MoM, quasidiffusion approximation  homogeneous and coated spheres  1D (sphere)  intensity, SED  dust clouds with central source, CS shells 
Witt [1977]  MC  spheres, HG phase function  planeparallel layer  intensity  RN 
White [1979]  Doubling method  MRN mixture  homogeneous layer (optically thick but geometrically thin)  intensity, polarization  RN 
Daniel [1980]  MC  single size spheres  homogeneous sphere  polarization  cool stars 
Yorke [1980]  MoM  single size spheres  1D (sphere), isotropic scattering  SED  cocoon stars 
RowanRobinson [1980]  Ray tracing method  single size homogeneous and coated spheres  1D (inhomogeneous sphere), isotropic scattering  SED, intensity profiles  hotcentred interstellar clouds, M giants and supergiants 
Lefevre et al. [1982]  MC  graphite and silicate spheres  inhomogeneous sphere, anisotropic scattering  SED  latetype stars 
Lefevre et al. [1983]  MC  graphite and silicate spheres  homogeneous ellipsoid, anisotropic scattering  SED,images  young and latetype stars 
WarrenSmith [1983]  MC  spheres of different sizes  plane layers  surface brightness, polarization  RN 
Spagna and Leung [1983]  NewtonRaphson iterative scheme  spheres (up to 5 constituents)  1D (homogeneous sphere)  SED  CS shells, clouds 
Rogers and Martin [1986]  Halfrange MoM  spheres  1D (sphere) with power density distribution  SED  CS shells (IRC +10 216) 
Chini et al. [1986]  MoM  MRN mixture  1D (sphere) with power density distribution  SED  CS shells 
Wolfire and Cassinelli [1986]  Modified MoM  MRN mixture  1D (sphere) with power density distribution  SED  protostars 
Spagna and Leung [1987]  MoM, quasidiffusion approximation  homogeneous and coated spheres  2D (disks)  intensity, SED  disk dust clouds, CS disks, disk galaxies 
Bastien and Menard [1988]  MC  spheres  3D, arbitrary geometry, inhomogeneous density distribution  images, polarization maps  YSO, CS shells 
Egan et al. [1988]  Updated and comprehensive versions of codes of Leung [1976] and Spagna and Leung [1983] for onedimensional geometries (sphere, planeparallel, cylindrical)  
Efstathiou and RowanRobinson [1990]  Ray tracing method  single and multicomponent mixtures of spheres  2D axisymmetric inhomogeneous configurations (disks, ellipsoids, tori)  SED  late type stars, AGN 
Hoefflich [1991]  MC  Thomson scattering  axisymmetric photospheres  polarization  SN 1987A 
Collison and Fix [1991]  Iterative scheme  single size silicate spheres  2D axisymmetric inhomogeneous shells, isotropic scattering  SED, images  CS shells 
Whitney and Hartmann [1992]  MC  spheres, HG phase function  3D (disks)  images, polarization maps  PMS objects 
Pier and Krolik [1992]  Multidimensional NewtonRaphson technique  MRN mixture  2D (homogeneous torus)  SED  AGN, Seyfert galaxies 
Bosma [1993a], [1993b]  New iterative scheme in MoM  anisotropic scattering, randomly oriented particles  1D (sphere)  intensity and polarization  
Fischer [1993]  MC  MRN mixture  3D, arbitrary geometry, inhomogeneous density distribution  images, polarization maps  protostellar sources 
Groenewegen [1993]  Iterative scheme  spheres  1D (sphere) with power density distribution, isotropic scattering, determination of inner radius as dust condensation boundary  SED  shells around AGB stars 
Voshchinnikov and Karjukin [1994]  MC, method of symmetrized trajectories  spheres (Rayleigh, MRN mixture)  2D (inhomogeneous spheroid)  intensity, polarization  CS shells around young stars 
Code and Whitney [1995]  MC  electrons, spherical particles  3D (illuminated spherical blobs)  intensity, polarization  supergiants, RCB stars, DGL, RN 
Sonnhalter et al. [1995]  Frequency dependent fluxlimited diffusion approximation  mixture of carbon, silicate and silicateice spheres  2D axiallysymmetric dusty disks with different density distribution  intensities, images at different wavelengths  
Lopez et al. [1996]  MC  carbon spheres  inhomogeneous axisymmetric shell, anisotropic scattering  SED, images  AGB stars, Red Rectangle 
Steinacker and Henning [1996]^{1}  Direct solution to discretized radiative transfer equation  spheres  3D arbitrary configuration  SED, images  CS shells, YSO 
Men'shchikov and Henning [1997]  MoM  spheres of different sizes and materials  2D axiallysymmetric CS disks with arbitrary density distribution  SED, images  CS shells, YSO 
Ivezic and Elitzur [1997]  Numerical integration  spheres (6 types of materials and 2 size distributions)  1D (sphere and planeparallel slab)  SED  CS shells, clouds, YSO 
Varosi and Dwek [1999]  Analytical approximation and MC  spheres  sphericallysymmetric twophase clumpy medium  fluxes  starforming regions, starburst galaxies 
Wolf and Henning [2000]  MC including calculations of dust temperature  spheres of different sizes and materials  3D, arbitrary number, shape and geometrical configuration of illuminating sources and dust density distribution  SED, images, polarization maps  CS shells, YSO, AGN 
Gordon et al. [2001] and Misselt et al. [2001]  MC  mixture of carbonaceous and silicate grains, polycyclic aromatic hydrocarbons (PAHs)  3D, arbitrary distribution of stars and dust  SED, images, polarization maps  RN, clusters of stars, galaxies 
Wolf et al. [2002] ^{1}  Dissemination of MC code of Wolf and Henning [2000] on nonspherical particles 
Notes: 1. First results only. 2. All notations are explained in the text above the table. 