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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
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Simple Radiative Transfer in Simple Radiative Transfer in Decomposed DomainsDecomposed Domains
Tobi HeinemannÅke Nordlund
Axel Brandenburg
Wolfgang Dobler
2
The Pencil CodeThe Pencil Code
• High order finite difference code for MHD– 6th order in space, 3rd order in time– Memory and cache efficient
• Typical applications– MHD turbulence– Convection– Accretion discs
• Massive parallelization with MPI (Message Passing Interface)
3
Radiative Transfer in Radiative Transfer in Decomposed DomainsDecomposed 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
The Transfer Equation & The Transfer Equation & ParallelizationParallelization
Analytic Solution:Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Intrinsic Calculation
Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParParaallelizationllelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParallelizationParallelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParallelizationParallelization
Analytic Solution:
Ray direction
Communication
Processors
The Transfer Equation & The Transfer Equation & ParallelizationParallelization
Analytic Solution:
Ray direction
Processors
Intrinsic Calculation
15
Details about the Details about the implementationimplementation
• 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
Preliminary ResultsPreliminary Results• 2D model of surface convection
– Started from uniform initial state
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Preliminary ResultsPreliminary Results
• 3D model of sunspot– Started from Nordlund-Stein snapshot– Uniform initial magnetic field added
18
Preliminary ResultsPreliminary Results
• 3D model of sunspot
Bottom Surface
19
Timing resultsTiming 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
ConclusionsConclusions
The method• is conceptually simple• is robust (analytic expressions, not limited
by table bounds)• has the potential to scale well in parallel
environments