Sundance rapid prototyping tool for parallel PDE optimization. High-performance algorithms for partial differential equation (PDE)-constrained optimization often require application of operators and solution of systems of equations that are different from those used in a single solution of the PDE; consequently, exploration of a research idea entails startup costs for modification to the PDE solver. A software tool to enable rapid development of parallel codes for large-scale complex PDEs on realistic problems would be a useful aid to research in this area. As part of Sandia’s research efforts in PDE-constrained optimization, we are developing Sundance, an environment in which a parallel PDE solver is accessed via a high-level problem description, using abstract concepts such as functions, operators, and regions. With this high-level problem description, it is possible to specify a variational formulation of a PDE and its discretization method in a small amount of user-level code. It is then straightforward to obtain operators such as Jacobians and Hessians for use in optimization algorithms.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Howle, Victoria E.; Kirby, Robert C.; Dillon, Geoffrey: Block preconditioners for coupled physics problems (2013)
  2. Notz, Patrick K.; Pawlowski, Roger P.; Sutherland, James C.: Graph-based software design for managing complexity and enabling concurrency in multiphysics PDE software (2012)
  3. Prud’homme, Christophe; Chabannes, Vincent; Doyeux, Vincent; Ismail, Mourad; Samake, Abdoulaye: Feel++: a computational framework for Galerkin methods and advanced numerical methods (2012)
  4. Bungartz, Hans-Joachim; Mehl, Miriam; Neckel, Tobias; Weinzierl, Tobias: The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids (2010)
  5. Bungartz, H.-J.; Benk, J.; Gatzhammer, B.; Mehl, M.; Neckel, T.: Partitioned simulation of fluid-structure interaction on Cartesian grids (2010)
  6. Kirby, Robert C.: From functional analysis to iterative methods (2010)
  7. Terrel, A.R.; Scott, L.R.; Knepley, M.G.; Kirby, R.C.: Automated FEM discretizations for the Stokes equation (2008)
  8. Logg, Anders: Automating the finite element method (2007)
  9. Kirby, Robert C.; Logg, Anders; Scott, L.Ridgway; Terrel, Andy R.: Topological optimization of the evaluation of finite element matrices (2006)
  10. Kirby, Robert C.; Knepley, Matthew; Logg, Anders; Scott, L.Ridgway: Optimizing the evaluation of finite element matrices (2005)
  11. Long, Kevin R.: Sundance rapid prototyping tool for parallel PDE optimization (2003)