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有限元学习研究用源代码(老外的),供科研人员参考

<h3>Abstract</h3>

We introduce a new concept for the geometry description called
contravariant geometry description (or shortly cogeometry). This concept
is dual to the standard way to describe the geometry. It is based on
functions which compute intersections with boundary segments. We
consider different algorithms which allow to create and modify
cogeometries for arbitrary space dimension.  We consider also problems
of grid generation for diffusion-reaction equations. We consider the
connection between optimal grids and discretization and remark that
for finite volume discretization (in contrast to FEM) the Delaunay
grid is optimal even in 3D. We emphasize the necessity of anisotropic
grids. We consider the problems related with anisotropic Delaunay grid
generation and the usage of the contravariant geometry description. We
describe a combined octree/Delaunay method for grid generation which
allows to solve most of the problems.  The concept has been
implemented in the grid generation and geometry description package
IBG. We show some examples for an application of IBG.

<h1>Preface</h1>

The aim of the thesis is to derive a concept for geometry description
and grid generation which allows to meet the (very high) requirements
of the simulation of semiconductor technology. We hope, that these
algorithms may be applied in a wide range of other applications.  They
have been implemented in the general purpose grid generation and
geometry description package IBG, which will be also described here.

  <p>This thesis consists of two main parts --- a geometry description
and a grid generation part.  In an introduction we describe our
motivation to consider these two questions. We describe our reference
application --- the simulation of semiconductor technology --- and
list the resulting requirements for grid generation and geometry
description.

  <p>In the geometry description part we introduce a new concept of
geometry description which is dual to the usual concept. In this
concept, the geometry description consists of a set of functions.
The first function allows to find the region containing a point, the
other allow to compute intersections of simplices with boundary
segments.
  <p>We show that this concept allows to create and modify geometry
descriptions in a much more natural way than the standard geometry
description based on a cell complex. Because of the natural functional
behaviour of this alternative geometry description we call it
contravariant geometry description or (shortly) cogeometry. The concept
may be used for arbitrary space dimension.

  <p> In the grid generation part we consider different questions
connected with 3D grid generation. We give a short overview over usual
grid generation techniques, consider the requirements connected with
the discretization of partial differential equations and the problems
connected with anisotropy. Then we describe in detail the grid
generation algorithm used in the package IBG.


  <p>At last, we consider the results of some example applications of the
IBG package. They especially show the simplicity of creating complicate
geometries using the contravariant geometry description.