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Kaskade 7


Introduction


Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations. The library is written in C++ and is based on the DUNE-Interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. The library is under active development, features are implemented as needed in other projects.


Implemented features


Spatial Discretization


  • Continuous and discontinuous, scalar and vectorial Lagrange and hierarchical elements of arbitrary order on simplices, up to second order on quadrilaterals. First order edge elements.
  • Adaptive mesh refinement and coarsening with hierarchical, embedded, and residual error estimators.
  • Multithreaded assembly.


Time Discretization


  • Extrapolated linearly implicit Euler.
  • Adaptive time step selection.


Solvers


  • Interface to UMFPACK, MUMPS, SuperLU, and Pardiso.
  • Iterative Krylov solvers, Block-Jacobi, ILU and HB preconditioners, preconditioning by lower order FE.
  • Hierarchical basis preconditioner
  • Preconditioned Uzawa.


I/O



Authors: 



with contributions from



Papers:


  • Peter Deuflhard, Martin Weiser:
    Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen,
    de Gruyter, 2011.
  • Peter Deuflhard, Martin Weiser:
    Adaptive numerical solution of PDEs,
    de Gruyter,  2012.
  • Olaf Schenk, Andreas Wächter, Martin Weiser:
    Inertia revealing preconditioning for large-scale nonconvex constrained optimization,
    SIAM J. Sci. Comp. 31(2): 939-960(2008).
  • Martin Weiser:
    Optimization and Identification in Regional Hyperthermia,
    Int. J. Appl. Electromagn. and Mech. 30: 265-275(2009).
  • Martin Weiser:
    Pointwise Nonlinear Scaling for Reaction-Diffusion Equations,
    Appl. Num. Math. 59 (8): 1858-1869(2009).
  • Anton Schiela, Andreas Günther:
    An interior point algorithm with inexact step computation in function space for state constrained optimal control,
    Num. Math. 119(2): 373-407(2011), see also ZIB Report 09-01 (2009).
  • Martin Weiser:
    On goal–oriented adaptivity for elliptic optimal control problems,
    to appear in Opt. Meth. Softw., see also ZIB-Report 09-08 (2009).
  • Anton Schiela, Martin Weiser:
    Barrier methods for a control problem from hyperthermia treatment planning,
    in M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (eds.): Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009), 419-428(2010),
    Springer, see also ZIB-Report 09-36 (2009).
  • Martin Weiser, Sebastian Götschel:
    State trajectory compression for optimal control with parabolic PDEs,
    SIAM J. Sci. Comp., 34(1):A161-A184(2012), see also ZIB Report 10-05 (2010).
  • Sebastian Götschel, Martin Weiser, Anton Schiela:
    Solving optimal control problems with the Kaskade7 Finite Element Toolbox,
    in Dedner, Flemisch, Klöfkorn (Eds.) Advances in DUNE, 101-112(2012), Springer, see also ZIB Report 10-25 (2010).
  • Lars Lubkoll:
    Optimal control in implant shape design,
    thesis, TU Berlin 2011.
  • Peter Deuflhard, Anton Schiela, Martin Weiser:
    Mathematical cancer therapy planning in deep regional hyperthermia,
    Acta Numerica 21: 307-378(2012), see also ZIB-Report 11-39 (2011).
  • Lars Lubkoll, Anton Schiela, Martin Weiser:
    An optimal control problem in polyconvex hyperelasticity,
    ZIB-Report 12-08 (2012).

Documentation:


 Research code available on request (license) from M. Weiser.