ESMF Regridding Update

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ESMF Regridding Update

• Robert Oehmke Ryan OKuinghttons Amik St. Cyr

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ESMF Regridding

• This overview describes ESMF 4.0.0r which came
  out in October
• Methods of accessing regridding
• Online
• Subroutine calls which calculate weights during
  run
• Can get weights or feed directly into ESMF Sparse
  Mat. Mult.
• Requires LAPACK if higher order interpolation is
  used
• Offline
• Application which generates a netCDF weight file
  from two netCDF grid files
• Requires pnetCDF and LAPACK
• Computation of weights
• Parallel
• Have tested scaling up to 2048 procs.
• Requires MPI library
• Serial
• New faster tree-based search (order of magnitude
  faster than old search)

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Online Regridding Supports

• Regridding between any combination of
• 2D Meshes composed of triangles and
  quadrilaterals
• 2D logically rectangular Grids composed of a
  single patch
• Regridding between any combination of
• 3D Meshes composed of hexahedrons
• 3D logically rectangular Grids composed of a
  single patch
• Regridding between a pair of 2D Grids mapped to a
  sphere
• One pole option pole value is average of all
  source points around pole
• Interpolation Types
• Bilinear
• Higher order (patch recovery, a finite element
  method, described later)
• Masking
• Source
• Destination

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Online Regridding Testing

• Regression testing
• Mostly sanity tests
• Source Field set to simple linear function (e.g.
  xy20)
• After interpolation check that dest. Field is
  point wise close to function (e.g. within .0001)
• Bilinear interpolation between these cases
  regression tested
• Pair of 2D Grids mapped to sphere
• Pair of 3D structured Grids
• Pair of 2D Grids with destination masks
• Pair of 2D Grids with source masks (Also higher
  order interpolation)
• Pair of 2D Grids mapped to sphere with source
  masks (Also higher order interpolation)
• 2D Mesh (triangles and quadrilaterals) to Grid
• 2D Grid to Mesh (triangles and quadrilaterals)
• Pair of 2D Mesh (triangles and quadrilaterals)
• 3D Mesh (triangles and quadrilaterals) to Grid
• Manual testing
• More in depth tests
• Source Field set to range of functions (e.g.
  (1-xy)sin(3px)cos(2py)2 )

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Offline Regridding

• Offline application can be automatically built as
  part of ESMF
• Regridding between a pair of 2D Grids mapped to a
  sphere
• Pole options (for spherical grids)
• Full circle average artificial pole is average
  of all source points next to pole
• N-point average artificial pole is average of n
  top source neighbors of dest point
• No pole error if destination point lies above
  top row of source points
• Interpolation Types
• Higher order (patch recovery, a finite element
  method, described later)
• Masking
• Destination

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Offline Regridding Testing

• Interior regridding functionality is tested along
  with online regridding
• Offline testing is testing higher order
  interpolation
• Manual testing
• Performed using the SCRIP weight testing
  application
• Application scrip_test which comes packaged with
  SCRIP weight generation application
• See Section 2.3 in the SCRIP users guide for
  more information
• Mostly using source field set to 2cos2?cos(2?)
  (Field option 2 in scrip_test)
• Mostly focused on a few cases provided by CCSM
• T62 CAM grid to a 1-degree POP ocean grid
• Fv1.9x2.5 grid to a 1-degree POP ocean grid
• Single and multiple processor cases
• Average and max error checked to ensure they
  havent degraded after changes

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Higher Order Interpolation

• Based on patch recovery used in finite element
  modeling
• Typically results in better approx. to values and
  derivatives than bilinear interpolation
• A patch is a 2nd order n-D polynomial
  representing source data
• Patches generated for each corner of source cell
• Each patch created by least-square fit through
  source data in cells surrounding corner
• Destination value is weighted average of patch
  values
• Longer description in ESMF v4.0.0r Reference
  Manual
• References at end of talk

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Future work

• Coming soon (within a couple of months)
• Extrapolation generating values for points
  outside unmasked source region
• More regression testing
• More regridding options
• Regional Grid with Grid mapped to a sphere
• Tetrahedral unstructured Meshes
• Unifying capabilities of offline and online
• Mostly just a matter of interfaces, internal
  functionality is available
• Conservative interpolation parallel, no
  derivatives needed
• Longer term
• Shortcuts for additional grids
• Tripole
• Multi-tile (e.g . Cube sphere)
• Note both can be done now via unstructured grids

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References

• Patch Interpolation
• Khoei S.A., Gharehbaghi A. R. The superconvergent
  patch recovery technique and data transfer
  operators in 3d plasticity problems. Finite
  Elements in Analysis and Design, 43(8), 2007.
• Hung K.C, Gu H., Zong Z. A modified
  superconvergent patch recovery method and its
  application to large deformation problems. Finite
  Elements in Analysis and Design, 40(5-6), 2004.
• Questions?