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83 lines
4.3 KiB
TeX
83 lines
4.3 KiB
TeX
\chapter{Introduction}
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\Dumux aims to be a generic framework for simulation of multiphase
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fluid flow and transport processes in porous media using contiuum
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mechanical approaches. At the same time, \Dumux aims to deliver
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top-notch computational performance, high flexibility, a sound
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software architecture and the ability to run on anything from single
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processor systems to highly parallel supercomputers with specialized
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hardware architectures.
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The means to achieve these somewhat contradictory goals are the
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thorough use of object oriented design in conjunction with template
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programming. These requirements lead to C++ as the implementation
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language.
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One of the more complex issues when dealing with parallel continuum
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models is managing the grids used for the spatial discretization of
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the physical model. To date, no generic and efficient approach exists
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for all possible cases, so \Dumux is build on top of DUNE, the
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\textbf{D}istributed and \textbf{U}nified \textbf{N}umerics
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\textbf{E}nvironment~\cite{DUNE-HP}. DUNE provides a generic interface
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to many existing grid management libraries such as UG~\cite{UG-HP},
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ALBERTA~\cite{ALBERTA-HP}, ALU-Grid~\cite{ALUGRID-HP} and a few
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more. DUNE also extensively uses template programming in order to
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achieve minimal overhead when accessing the underlying grid
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libraries\footnote{In fact, the performance penalty resulting from the
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use of DUNE's grid interface is usually
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negligible~\cite{BURRI2006}.}.
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\begin{figure}[hbt]
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\centering
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\includegraphics[width=.5\linewidth, keepaspectratio]{EPS/dunedesign}
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\caption{
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\label{fig:dune-design}
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A high-level overview on DUNE's design as available on the project's
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web site~\cite{DUNE-HP}.
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}
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\end{figure}
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DUNE's grid interface is independent of the spatial dimension of the
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underlying grid. For this purpose, it uses the concept of
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co-dimensional entities. Roughly speaking, an entity of co-dimension
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$0$ constitutes a cell, co-dimension $1$ entities are faces between
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cells, co-dimension $1$ are edges, and so on until co-dimension $n$
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which are the cell's vertices. The DUNE grid interface generally
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assumes that all entities are convex polytopes, which means that it
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must be possible to express each entity as the convex hull of a set of
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vertices. For efficiency, all entities are further expressed in terms
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of so-called reference elements which are transformed to the actual
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spatial incarnation within the grid by a so-called geometry
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function\footnote{The same approach is also used by \texttt{dune-disc} for
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finite element shape functions.}. Here, a reference element for an
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entity can be thought of as a prototype for the actual grid
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entity. For example, if we used a grid that used hexahedrons as cells,
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the reference element for each cell would be the unit cube $[0, 1]^3$
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and the geometry function would scale and translate the cube so that
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it matches the grid's cell. For a more thorough description of DUNE's
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grid definition, see~\cite{BASTIAN2008}.
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In addition to the grid interface, DUNE also provides quite a few
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additional modules, of which the \texttt{dune-pdelab},
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\texttt{dune-localfunctions} and \texttt{dune-istl} modules are the
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most relevant in the context of this handbook. \texttt{dune-pdelab}
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provides a toolbox for discretization and includes matrix assemblers
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for translating local stiffness matrices into a global linear system
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of equations and much more, while \texttt{dune-localfunctions}
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provides a set of generic finite element shape
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functions. \texttt{dune-istl} is the \textbf{I}terative
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\textbf{S}olver \textbf{T}emplate \textbf{L}ibrary and provides
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generic, highly optimized linear algebra routines for solving the
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generated systems.
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\Dumux comes in form of an additional module \texttt{dumux}.
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It depends on the DUNE core modules
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\texttt{dune-common}, \texttt{dune-grid}, \texttt{dune-istl}, \texttt{dune-localfunctions}, as well as from
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the discretization module \texttt{dune-pdelab}.
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The main intention of \Dumux is to provide a framework for easy and efficient
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implementation of new physical models for porous media flow problems,
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ranging from problem formulation, the selection of
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spatial and temporal discretization schemes, as well as nonlinear solvers,
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up to general concepts for model coupling.
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Moreover, \Dumux includes ready to use numerical models and a few example applications.
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