1. Simple Radiative Transfer in Decomposed Domains Tobi Heinemann Åke Nordlund Axel Brandenburg Wolfgang Dobler

2. 2 The Pencil Code High order finite difference code for MHD –6 th order in space, 3 rd order in time –Memory and cache efficient Typical applications –MHD turbulence –Convection –Accretion discs Massive parallelization with MPI (Message Passing Interface)

3. 3 Radiative Transfer in Decomposed Domains RT important for optically thin media Diffusion approximation(s) deficient RT is a highly non-local problem Difficult to reconcile with domain decomposition

4. 4 The Transfer Equation & Parallelization Analytic Solution: Processors

5. The Transfer Equation & Parallelization Analytic Solution: Ray direction Intrinsic Calculation Processors

6. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

7. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

8. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

9. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

10. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

11. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

12. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

13. The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

14. The Transfer Equation & Parallelization Analytic Solution: Ray direction Processors Intrinsic Calculation

15. 15 Details about the implementation Plasma composed of H and He Only hydrogen ionization Only H - opacity, calculated analytically No need for look-up tables Ray directions determined by grid geometry No interpolation is needed

16. 16 Preliminary Results 2D model of surface convection –Started from uniform initial state

17. 17 Preliminary Results 3D model of sunspot –Started from Nordlund-Stein snapshot –Uniform initial magnetic field added

18. 18 Preliminary Results 3D model of sunspot BottomSurface

19. 19 Timing results With 6 rays, and with ionization: 42.7  s/pt/st With 2 rays, and with ionization: 37.6  s/pt/st No radiation, but with ionization: 19.6  s/pt/st No radiation, and no ionization: 8.7  s/pt/st Ionization 2.3 times slower! Radiation either 1.9 or 2.2 times slower.

20. 20 Conclusions The method is conceptually simple is robust (analytic expressions, not limited by table bounds) has the potential to scale well in parallel environments