simple radiative transfer in decomposed domains
DESCRIPTION
Simple Radiative Transfer in Decomposed Domains. Tobi Heinemann Åke Nordlund Axel Brandenburg Wolfgang Dobler. 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 - PowerPoint PPT PresentationTRANSCRIPT
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)
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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