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.

Kaskade 7 has been used for generating numerical results in a number of publications, listed below.

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, Morley elements.

Adaptive mesh refinement and coarsening with hierarchical, embedded, and residual error estimators.

Multithreaded, NUMA-aware assembly.

Time Discretization

Extrapolated linearly implicit Euler, spectral deferred correction methods.

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. NUMA-aware matrix-vector products. Dual and augmented Lagrangian QP solvers.

Geometric multigrid, multiplicative and additive, for P1 and for higher order elements. 

Preconditioned Uzawa.

I/O

Input from Amira, VTK, and Triangle files.

Output to Amira and VTK files.

Lossy compression of trajectories 

Authors

Martin Weiser, Anton Schiela, Sebastian Götschel

with contributions from

Felix Baumann, Fatemeh Chegini, Bodo Erdmann, Lars Lubkoll, Marian Moldenhauer, Rainer Roitzsch, Jakob Schneck, Phillip Semler, Julia Ulrich, Lutz Weimann

Distribution

The Kaskade 7 distribution page provides a recent development snapshot of the source code, the online Doxygen documentation and the Programmer's Manual. The distribution includes installer scripts for downloading and installing required third-party libraries.

Attention: Use this software at your own risk. These are development snapshots which might or might not work (usually they do, we run a test suite regularly). Please read the license before using the code.

Publications

2023
Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model SIAM Journal on Scientific Computing, 45(6), pp. A2836-A2857, 2023 Ngoc Huynh, Fatemeh Chegini, Luca Pavarino, Martin Weiser, Simone Scacchi BibTeX
arXiv
Kaskade7 Finite Element Toolbox
The impact of anatomy variation on temperature based time of death estimation International Journal of Legal Medicine, Vol.137, pp. 1615-1627, 2023 Julia Ullrich, Martin Weiser, Jayant Subramaniam, Sebastian Schenkl, Holger Muggenthaler, Michael Hubig, Gita Mall BibTeX
DOI
Kaskade7 Finite Element Toolbox
2022
Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering, pp. 528-531, 2022 Martin Weiser, Fatemeh Chegini BibTeX
Kaskade7 Finite Element Toolbox
Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods 2022 (under review) Fatemeh Chegini, Thomas Steinke, Martin Weiser BibTeX
arXiv
Kaskade7 Finite Element Toolbox
Higher-order time integration using spectral deferred correction method (SDC) in a cell by cell discretization of cardiac excitation 2022 Martin Weiser, Fatemeh Chegini BibTeX
DOI
Kaskade7 Finite Element Toolbox
2021
A primal dual projection algorithm for efficient constraint preconditioning SIAM Journal on Scientific Computing, 43(6), pp. A4095-A4120, 2021 Anton Schiela, Matthias Stöcklein, Martin Weiser BibTeX
DOI
Kaskade7 Finite Element Toolbox
Impact of mixed precision and storage layout on additive Schwarz smoothers Numerical Linear Algebra with Applications, 28(4), 2021 (preprint available as ZIB-Report 18-62) Jakob Schneck, Martin Weiser, Florian Wende PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
Kaskade 7 - a Flexible Finite Element Toolbox Computers and Mathematics with Applications, Vol.81, pp. 444-458, 2021 (preprint available as ZIB-Report 19-48) Sebastian Götschel, Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
Multilevel augmented Lagrangian solvers for overconstrained contact formulations ESAIM: ProcS, pp. 175-184, Vol.71, 2021 Rolf Krause, Martin Weiser BibTeX
DOI
Kaskade7 Finite Element Toolbox
Numerical treatment of radiative heat transfer on cooling process Master's thesis, Freie Universität Berlin, Martin Weiser (Advisor), 2021 Maria Mathew BibTeX
Kaskade7 Finite Element Toolbox
2020
Impact of Contact Surfaces on the Death Estimation Master's thesis, Technische Universität Berlin, Konstantin Fackeldey, Martin Weiser (Advisors), 2020 Felix Baumann BibTeX
Kaskade7 Finite Element Toolbox
Mixed finite elements in cloth simulation Master's thesis, Beuth Hochschule für Technik Berlin, Martin Weiser, Frank Haußer (Advisors), 2020 Phillip Semler BibTeX
Kaskade7 Finite Element Toolbox
Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen de Gruyter, 2, 2020, ISBN: 978-3-11-069168-9 Peter Deuflhard, Martin Weiser BibTeX
DOI
Kaskade7 Finite Element Toolbox
2019
Compression Challenges in Large Scale Partial Differential Equation Solvers Algorithms, 12(9), p. 197, 2019 (preprint available as ZIB-Report 19-32) Sebastian Götschel, Martin Weiser PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
2018
Lossy data compression reduces communication time in hybrid time-parallel integrators Comput. Vis. Sci., 19(1), pp. 19-30, 2018 (preprint available as ) Lisa Fischer, Sebastian Götschel, Martin Weiser BibTeX
DOI
Kaskade7 Finite Element Toolbox
Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine ZIB-Report 18-08 (Inverse Problems 34, 125005, 2018. DOI 10.1088/1361-6420/aae7a5) Martin Weiser, Yvonne Freytag, Bodo Erdmann, Michael Hubig, Gita Mall PDF
BibTeX
URN
Kaskade7 Finite Element Toolbox
Uncertainty in Temperature-Based Determination of Time of Death Heat and Mass Transfer, 54(9), pp. 2815-2826, 2018 (preprint available as ) Martin Weiser, Bodo Erdmann, Sebastian Schenkl, Holger Muggenthaler, Michael Hubig, Gita Mall, Stefan Zachow BibTeX
DOI
Kaskade7 Finite Element Toolbox
2017
Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis International Journal of Legal Medicine, 131(3), pp. 699-712, 2017 Sebastian Schenkl, Holger Muggenthaler, Michael Hubig, Bodo Erdmann, Martin Weiser, Stefan Zachow, Andreas Heinrich, Felix Victor Güttler, Ulf Teichgräber, Gita Mall BibTeX
DOI
Kaskade7 Finite Element Toolbox
Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography AIP Conference Proceedings, Vol.1806, 2017 Jan Müller, Sebastian Götschel, Christiane Maierhofer, Martin Weiser BibTeX
DOI
Kaskade7 Finite Element Toolbox
Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014, pp. 321-328, 2017 (preprint available as ZIB-Report 14-22) Martin Weiser, Simone Scacchi PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
Thermografie mit optimierter Anregung für die quantitative Untersuchung von Delaminationen in kohlenstofffaserverstärkten Kunststoffen NDT.net Proc. DGZfP 2017, 2017 Jan Müller, Sebastian Götschel, Martin Weiser, Christiane Maierhofer BibTeX
Kaskade7 Finite Element Toolbox
2016
Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology Master's thesis, Freie Universität Berlin, Martin Weiser (Advisor), 2016 (preprint available as ZIB-Report 16-50) Adrian Sali PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Inside Finite Elements De Gruyter, 2016 Martin Weiser BibTeX
Kaskade7 Finite Element Toolbox
Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites ZIB-Report 16-13 (Appeared in: Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)) Sebastian Götschel, Christiane Maierhofer, Jan P. Müller, Nick Rothbart, Martin Weiser PDF
BibTeX
URN
Kaskade7 Finite Element Toolbox
2015
Adaptive Lossy Trajectory Compression for Optimal Control of Parabolic PDEs Doctoral thesis, Freie Universität Berlin, Peter Deuflhard (Advisor), 2015 Sebastian Götschel BibTeX
Kaskade7 Finite Element Toolbox
Lossy Compression for PDE-constrained Optimization: Adaptive Error Control Comput. Optim. Appl., 62(1), pp. 131-155, 2015 (preprint available as ZIB-Report 13-27) Sebastian Götschel, Martin Weiser PDF
PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Reducing Memory Requirements in Scientific Computing and Optimal Control Multiple Shooting and Time Domain Decomposition Methods, T. Carraro, M. Geiger, S. Koerkel, R. Rannacher (Eds.), pp. 263-287, 2015 Sebastian Götschel, Christoph von Tycowicz, Konrad Polthier, Martin Weiser PDF
BibTeX
Kaskade7 Finite Element Toolbox
Zielorientierte Fehlerschätzer für die Topologieoptimierung Master's thesis, Technische Universität Berlin, Martin Weiser (Advisor), 2015 Jakob Schneck PDF
BibTeX
URN
Kaskade7 Finite Element Toolbox
2014
An optimal control problem in polyconvex hyperelasticity SIAM J. Control Opt., 52(3), pp. 1403-1422, 2014 (preprint available as ZIB-Report 12-08) Lars Lubkoll, Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
Lossy Compression in Optimal Control of Cardiac Defibrillation J. Sci. Comput., 60(1), pp. 35-59, 2014 (preprint available as ZIB-Report 13-26) Sebastian Götschel, Chamakuri Nagaiah, Karl Kunisch, Martin Weiser PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
Mathematics cures virtual patients MATHEON-Mathematics for Key Technologies, Vol.1, pp. 7-25, Peter Deuflhard, Martin Grötschel, Dietmar Hömberg, Ulrich Horst, Jürg Kramer, Volker Mehrmann, Konrad Polthier, Frank Schmidt, Christof Schütte, Martin Skutella, Jürgen Sprekels (Eds.), European Mathematical Society, 2014 Peter Deuflhard, Ralf Kornhuber, Oliver Sander, Anton Schiela, Martin Weiser BibTeX
Kaskade7 Finite Element Toolbox
2013
On goal-oriented adaptivity for elliptic optimal control problems Opt. Meth. Softw., 28(13), pp. 969-992, 2013 (preprint available as ZIB-Report 09-08) Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Reducing Memory Requirements in Scientific Computing and Optimal Control ZIB-Report 13-64 (submitted to "Multiple Shooting and Time Domain Decomposition Methods", Springer Series "Contributions in Mathematical and Computational Sciences") Sebastian Götschel, Christoph von Tycowicz, Konrad Polthier, Martin Weiser PDF
BibTeX
URN
Kaskade7 Finite Element Toolbox
2012
Adaptive numerical solution of PDEs de Gruyter: Berlin, 2012 Peter Deuflhard, Martin Weiser BibTeX
Kaskade7 Finite Element Toolbox
Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia Acta Numerica, Vol.21, pp. 307-378, 2012 (preprint available as ZIB-Report 11-39) Peter Deuflhard, Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox Advances in DUNE, pp. 101-112, A. Dedner, B. Flemisch, R. Klöfkorn (Eds.), Springer, 2012 (preprint available as ZIB-Report 10-25) Sebastian Götschel, Martin Weiser, Anton Schiela PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
State Trajectory Compression for Optimal Control with Parabolic PDEs SIAM J. Sci. Comput., 34(1), pp. A161-A184, 2012 (preprint available as ZIB-Report 10-05) Martin Weiser, Sebastian Götschel PDF (ZIB-Report)
BibTeX
DOI
Kaskade7 Finite Element Toolbox
2011
Numerische Mathematik 3 de Gruyter, Berlin, 2011 Peter Deuflhard, Martin Weiser BibTeX
Kaskade7 Finite Element Toolbox
2010
Barrier methods for a control problem from hyperthermia treatment planning Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009), pp. 419-428, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (Eds.), Springer, 2010 (preprint available as ZIB-Report 09-36) Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Delayed Residual Compensation for Bidomain Equations AIP Conference Proceedings, Vol.1281, pp. 419-422, 2010 Martin Weiser BibTeX
DOI
Kaskade7 Finite Element Toolbox
2009
Optimization and Identification in Regional Hyperthermia Int. J. Appl. Electromagn. and Mech., Vol.30, pp. 265-275, 2009 (preprint available as ZIB-Report 08-40) Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Pointwise Nonlinear Scaling for Reaction-Diffusion Equations Appl. Num. Math., 59(8), pp. 1858-1869, 2009 (preprint available as ZIB-Report 07-45) Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
2008
A control reduced primal interior point method for a class of control constrained optimal control problems Comput. Optim. Appl., 41(1), pp. 127-145, 2008 (preprint available as ZIB-Report 04-38) Martin Weiser, Tobias Gänzler, Anton Schiela PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization SIAM J. Sci. Comp., 31(2), pp. 939-960, 2008 (preprint available as ZIB-Report 07-32) O. Schenk, Andreas Wächter, Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox
Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization Computational Optimization and Applications, 39(3), pp. 369-393, 2008 (preprint available as ZIB-Report 05-15) Anton Schiela, Martin Weiser PDF (ZIB-Report)
BibTeX
Kaskade7 Finite Element Toolbox