FLASH and Self Gravity March 23, 2005

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FLASH and Self GravityMarch 23, 2005

• Anshu Dubey

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Gravity Algorithms in FLASH

• Externally imposed fields
• Constant field (g constant)
• Point mass (g -GMr/r 3)
• Plane-parallel (g -GMx/r 3)
• Self-gravity Poisson equation
• Multipole
• Nearly spherically symmetric problems
• Multigrid
• Arbitrary source fields

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The Multi-pole Solver

• Isolated boundary conditions
• Supported geometries
• 3-D cartesian
• 2-D cylindrical
• 1 and 2-D spherical
• Compute moment integrals for a given source field
• Use moment integrals to calculate the potential
• Source and potential are zone averaged with
  varying zone sizes
• Refinement criterion to maximally refine the
  block containing the center of mass.

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The Multipole Solver Future plans

• The algorithm is O(n2) with number of poles
• Use of a monopole get inaccurate with loss in
  symmetry.
• Increasing the number of poles makes the
  algorithm too expensive
• Investigating FMM implementations
• Collaboration with tree-code groups

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The Multigrid Algorithm
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AMR Multigrid
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Multigrid Steps

• Compute residual of the source equation on all
  leaf blocks
• Residual operation uses flux conservation at
  fine-coarse boundaries
• V-cycle
• a) Zero the correction on level lmax.
• b) For i lmax down to 2
• ii. Zero correction on level i-1.
• iii. Relax correction equation on level i.
  
• iv. Add correction to the solution on level i.
  
• v. Compute residual of the correction equation
  on all blocks (leaf or not) on level i. Restrict
  this residual to level i-1.
• vi. Compute the residual of the source equation
  on all leaf blocks of level i-1.
• c) Solve correction equation on level 1.
• d) Correct the solution on this level.

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Gravity in the FLASH Source Tree
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Methods supplied by Gravity module

• Usage
• use Gravity, ONLY ltlist of gravity methods to
  importgt
• Types of sub-modules in FLASH
• - Compute acceleration natively
• - Compute potential, then difference to get
  acceleration
• Methods generic to all gravity sub-modules (not
  called by user modules)
• - InitGravity()
• Initialize the gravity module (called by
  init_flash())
• - GravityTimestep(dt_grav, dt_minloc, block)
• Compute any timestep restrictions imposed by
  gravity module (called by timestep())

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Methods supplied by Gravity F90 module

• Methods oriented toward computing gravitational
  acceleration
• No mesh variables generically defined declared
  by physics FLASH modules
• - GravAccelAllBlocks(pot_var, acc_var, component)
  
• Compute a component of the acceleration on all
  blocks.
• - GravAccelOneBlock(pot_var, acc_var, component,
  block)
• Compute a component of the acceleration on a
  single block.
• - GravAccelOneLevel(pot_var, acc_var, component,
  level)
• Compute a component of the acceleration on all
  blocks at a single level of refinement.
• - GravAccelOneRow(j, k, direction, block,
  pot_var, g, n)
• Compute a component of the acceleration along a
  single row of a single block return as an array
  (g).
• - GravAccelOneZone(x, y, z, g)
• Compute all components of the acceleration at a
  single position in space.

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Methods supplied by Gravity module

• Methods oriented toward computing gravitational
  potential
• Generically defined mesh variables gpot, gpol
• - GravPotentialAllBlocks(pot_var)
• Compute potential on the entire mesh.
• - GravPotentialOneBlock(pot_var, block)
• (Planned) return potential on a single block.
• - GravPotentialOneLevel(pot_var, level)
• (Planned) return potential on all blocks at a
  given level of refinement.

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Multigrid vs. Multipole
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Multigrid Future

• The multigrid in FLASH is known to be slow
• FLASH 2.5 release has somewhat faster multigrid.
• In house investigation of better multigrid
  algorithm/implementation

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• Questions and discussion