Kardos - Introduction

A Software Package for Solving Nonlinear Parabolic Systems

Jens Lang - Peter Deuflhard - Bodo Erdmann - Rainer Roitzsch

The code KARDOS was developed for the solution of nonlinear systems of parabolic equations in one, two, and three space dimensions. Only the 1D-version can be downloaded. If you are interested in the 2D- or 3D-code, please contact one of the authors. Please read our sample license agreement for more details.

The underlying algorithm is a Rothe method, enabling adaptivity both in space and time. We first discretize in time using linearly implicit one-step methods of Rosenbrock type possibly of high order. In each time step only linear elliptic problems have to be solved. This is the main structural advantage of Rosenbrock type methods because it avoids an explicit use of Newton iterations. By embedding techniques we get an estimation of the temporal discretization error which is used to control the time step.

The elliptic subproblems are discretized by a finite element method comprising a posteriori error estimation, local mesh refinement, and multilevel preconditioning. This provides solution procedures of optimal computational complexity.

The code KARDOS is written in ANSI style C based on the modules of the KASKADE toolbox.

Questions or any comments should be forwarded to the authors at the Konrad-Zuse-Zentrum (ZIB), e-mail address


Last update: December, 2011
© 2007-2011 by Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)