A mesh with the minimum possible number of elements that captures
all relevant features of the investigated geometry is desired in order
to support methods for fast numerical analysis as well as an accurate
description of the geometry. This in particular aids the
discretization of partial differential equations used for the solution
in a reasonable amount of time, computer resources, and minimal manual
interaction.
The increase in geometrical feature complexity and number of elements
requires a modern software design approach for the actual mesh
generation and adaptation codes. Especially regarding the coupling of modeling,
mesh generation, and error estimation, mesh adaptation pushes the
currently available methods beyond their limits. Programming paradigms
with support for orthogonality, reusability, and modularity that still
maintain reasonable performance are required. A shift to real
three-dimensional devices in the current research can be observed
clearly, which obviously requires three-dimensional structure
modeling. The three-dimensional mesh generation and adaptation process
is therefore becoming essential for successful spatial discretization
techniques and any manual interaction for adaptation of the mesh
elements by the user can no longer be demanded. Three-dimensional
structures lack an intuitive view of user interaction. Therefore
assisted or fully automatic mesh generation coupled with error
estimation techniques (a-priori and a-posteriori) for the used PDE is
required in order to control the mesh adaptation process. Error
estimation techniques have shown, that a-priori estimation techniques,
such as condition estimations, can be used as a basic guide for the
mesh generation, whereas a-posteriori techniques can be used as
control instance for adaptation techniques.
The automation and coupling of mesh generation and mesh adaptation
driven by control mechanisms, e.g., error estimation (considering the applied
partial differential equation's discretization technique and the
subsequent properties of the equation system) were investigated.
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