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 19 articles , 1 standard article )

Showing results 1 to 19 of 19.
Sorted by year (citations)

  1. Renard, Yves; Poulios, Konstantinos: GetFEM. Automated FE modeling of multiphysics problems based on a generic weak form language (2021)
  2. Boggs, Paul T.; Byrd, Richard H.: Adaptive, limited-memory BFGS algorithms for unconstrained optimization (2019)
  3. Kirby, Robert C.; Mitchell, Lawrence: Solver composition across the PDE/linear algebra barrier (2018)
  4. Thomas H. Gibson, Lawrence Mitchell, David A. Ham, Colin J. Cotter: Slate: extending Firedrake’s domain-specific abstraction to hybridized solvers for geoscience and beyond (2018) arXiv
  5. Ruthotto, Lars; Treister, Eran; Haber, Eldad: jInv -- a flexible Julia package for PDE parameter estimation (2017)
  6. Simon, Moritz; Ulbrich, Michael: Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO(_2) sequestration in underground reservoirs (2015)
  7. Howle, Victoria E.; Kirby, Robert C.; Dillon, Geoffrey: Block preconditioners for coupled physics problems (2013)
  8. Notz, Patrick K.; Pawlowski, Roger P.; Sutherland, James C.: Graph-based software design for managing complexity and enabling concurrency in multiphysics PDE software (2012)
  9. Prud’homme, Christophe; Chabannes, Vincent; Doyeux, Vincent; Ismail, Mourad; Samake, Abdoulaye: \textttFeel++: a computational framework for Galerkin methods and advanced numerical methods (2012)
  10. Alnæs, Martin Sandve; Mardal, Kent-André: On the efficiency of symbolic computations combined with code generation for finite element methods (2010)
  11. 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)
  12. Bungartz, H.-J.; Benk, J.; Gatzhammer, B.; Mehl, M.; Neckel, T.: Partitioned simulation of fluid-structure interaction on Cartesian grids (2010)
  13. Kirby, Robert C.: From functional analysis to iterative methods (2010)
  14. Logg, Anders; Wells, Garth N.: DOLFIN: automated finite element computing (2010)
  15. Terrel, A. R.; Scott, L. R.; Knepley, M. G.; Kirby, R. C.: Automated FEM discretizations for the Stokes equation (2008)
  16. Logg, Anders: Automating the finite element method (2007)
  17. Kirby, Robert C.; Logg, Anders; Scott, L. Ridgway; Terrel, Andy R.: Topological optimization of the evaluation of finite element matrices (2006)
  18. Kirby, Robert C.; Knepley, Matthew; Logg, Anders; Scott, L. Ridgway: Optimizing the evaluation of finite element matrices (2005)
  19. Long, Kevin R.: Sundance rapid prototyping tool for parallel PDE optimization (2003)