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A general object-oriented framework for discretizing nonlinear evolution equations. (English) Zbl 1310.76113

Shokin, Yuri (ed.) et al., Advances in high performance computing and computational sciences. The 1st Kazakh-German advanced research workshop, Almaty, Kazakhstan, September 25 – October 1, 2005. Berlin: Springer (ISBN 3-540-33864-0/hbk). Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) 93, 69-87 (2006).
Summary: For a large class of nonlinear evolution problems we derive an abstract formulation that is based on writing the original model as a system of first-order partial differential equations. Starting from this reformulation, a set of interface classes are derived that allow a problem-independent implementation of various temporal and spacial discretization schemes. In particular, the abstract framework is very well suited for discretizing evolution equations with the Local Discontinuous Galerkin ansatz. The implementation of the proposed framework is done within the Distributed and Unified Numerics Environment DUNE.
For the entire collection see [Zbl 1097.76004].

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76T30 Three or more component flows
68N19 Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)

Software:

DUNE
PDFBibTeX XMLCite
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