Elliptic Solvers in Cactus

1
Elliptic Solvers in Cactus

• Gerd Lanfermann
• Albert Einstein Institute
• lanfer_at_aei-potsdam.mpg.de

2
CactusElliptic

• Infrastructure and Solvers
• EllBase provides an interface to elliptic solvers
  ...
• and a registration mechanism to expand the solver
  and elliptic equation classes
• Comes with two solvers SOR, PETSc
• Comes with 4 elliptic equation classes
• Includes a test suite

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EllBase Elliptic Equation Classes

• Elliptic equation classes that come with Cactus
• Standard elliptic equation
• LinFlat Standard 3D Cartesian
• LinMetric Laplacian by metric
• LinConfMetric Laplacian by metricconformal
• Generic Provides 27 grid functions (33)
• to be loaded by user
• Each class requires different arguments and has a
  unique/fixed interface!

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EllBase Using the Interface

• Defines an elliptic (problem) class, e.g.
• Using the interface for the standard Cartesian
  Laplacian
• AbsTol(1) 1.0d5 AbsTol(2,3) -1
  
• RelTol(1,2,3) -1
• call CCTK_VarIndex(phi_idx, "elltestphi_gf")
• call CCTK_VarIndex(M_idx, "elltestM_gf")
• N_idx -1
• call Ell_LinFlat(ierr, cctkGH, phi_idx, M_idx,
  N_idx,
• AbsTol, RelTol, "sor")

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EllBase Expanding the Interfaces

• EllBase is needed for any elliptic solve using
  the CactusElliptic package and provides some
  basic problem classes.
• I have a different problem and need a different
  interface !?
• The registration mechanism allows any thorn to
  register its own elliptic class and to provide a
  interface for it. Your are independent of all
  thorns but EllBase!
• Then add one or more solvers that understand your
  problem class.

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EllSOR / EllPETSc Elliptic Solvers

• Currently two parallel elliptic solvers
• Successive overrelaxation (SOR)
• PETSc Portable, Extensible Toolkit for
  Scientific Computations. Very sophisticated, free
  software by Argonne National Lab, co-authored by
  Lois Curfman McInnes
• Supported boundary conditions
• Dirichlet BC, constant BC, Robin BC (dev).

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EllTest

• EllTest provides some test and demo routines for
  the elliptic solvers.
• Use EllTest to develop / incorporate your own
  solvers.