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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
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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)
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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
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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
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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
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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
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Preliminary ResultsPreliminary Results
• 3D model of sunspot
Bottom Surface
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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.
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ConclusionsConclusions
The method• is conceptually simple• is robust (analytic expressions, not limited
by table bounds)• has the potential to scale well in parallel
environments
