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

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

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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