This is old DOUG wiki, please go to http://www.dougdevel.org/trac/wiki

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DOUG - Domain Decomposition on Unstructured Grids

DOUG (University of Bath, University of Tartu) 1997 - 2006

Fast parallel "black box" solver

• Parallel implementation based on:
  • MPI
  • UMFPACK
  • METIS
  • BLAS

The first version of DOUG is available at: http://www.maths.bath.ac.uk/~parsoft/doug

• Current development (pre-beta vers.) of DOUG overview
  • Large linear system solver
  • automatic parallelisation and load-balancing
  • Block-structured matrices (systems of PDEs)
  • 2D & 3D problems
  • 2-level Additive Schwarz method
  • 2-level partitioning of the domain
  • Automatic Coarse Grid generation
  • Adaptive refinement of the coarse grid
  • Different input-types for linear systems
  • Web service interface
  • New coarsening strategies based on aggregation
  • Completely rewritten code in Fortran95 (Intel Fortran, g95, gfortran)

• Overview of DOUG strategies
  • Iterative solver based on Krylov subspace methods PCG, MINRES, BiCGstab, 2-layered FPGMRES with left or right preconditioning.
  • Non-blocking communication where at all possible (Ax-operation, coarse grid vector distribution,...)
  • Preconditioner based on Domain Decomposition with 2-level solvers
  • Subproblems are solved with a direct, sparse multifrontal solver (UMFPACK)

Ongoing work based on aggregaton

For coarse grid problem: 2 strategies

• Aggregating strongly connected nodes together to forma basis for simple (constant) interpolation

DOUG & aggregation

Aggregation-based DD methods We are:

• making use of strong connections
• Second aggregation for creating subdomains, or
• using rough aggregation before graph partitioner
• Major progress - development of the theory: sharper bounds
  • R. Scheichl and E. Vainikko, Robust Aggregation-Based Coarsening for Additive Schwarz in the Case of Highly Variable Coefficients, Proceddings of the European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2006 (P. Wesseling, E. ONate, J. Periaux, Eds.), TU Delft, 2006. [1]
  • R. Scheichl and E. Vainikko, Additive Schwarz and Aggregation-Based Coarsening for Elliptic Problems with Highly Variable Coefficients, (submitted), 2006.[2]

• Parallel implementation - on the way

Aggregation

Key issues:

• how to find good aggregates?
• Smoothing step(s) for restriction and interpolation operators

Four (often conflicting) aims:

• follow adequatly underlying physial properties of the domain
• try to retain optimal aggregate size
• keep the shape of aggregates regular
• reduce communication => develop aggregates with smooth boundaries

Overview of DOUG communication

• DOUG Communication