In some of the previous tutorial programs (step-1, step-3, step-5, step-6 and
step-49 among others) we have learned how to use the mesh refinement methods
provided in deal.II. These tutorials have shown how to employ such tools to
-produce a fine grid for a single simulation, as done in step-3; or to start
-from a coarse grid and carry out a series of simulations on adaptively refined
-grids, as is the case of step-6. Regardless of which approach is taken, the
-mesh refinement requires a suitable geometrical description of the
-computational domain boundary in order to place, at each refinement, the new
-mesh nodes onto the boundary surface. For instance, step-5 shows how to assign
-a circular shape to the boundary of the computational domain, so that the
-faces lying on the boundary are refined onto the circle. step-53 shows how to
-do this with a boundary defined by experimentally obtained data. But, at
-least as far as elementary boundary shapes are concerned, deal.II really only
-provides circles, spheres, boxes and various combinations. In this tutorial,
-we will show how to use a set of classes developed to import arbitrary CAD
-geometries, assign them to the desired boundary of the computational domain,
+produce a fine grid for a single simulation, as done in step-3; or to start from
+a coarse grid and carry out a series of simulations on adaptively refined grids,
+as is the case of step-6. Regardless of which approach is taken, the mesh
+refinement requires a suitable geometrical description of the computational
+domain boundary in order to place, at each refinement, the new mesh nodes onto
+the boundary surface. For instance, step-5 shows how creating a circular grid
+automatically attaches a circular manifold object to the computational domain,
+so that the faces lying on the boundary are refined onto the circle. step-53
+shows how to do this with a Manifold defined by experimentally obtained data.
+But, at least as far as elementary boundary shapes are concerned, deal.II really
+only provides circles, spheres, boxes and other elementary combinations. In this
+tutorial, we will show how to use a set of classes developed to import arbitrary
+CAD geometries, assign them to the desired boundary of the computational domain,
and refine a computational grid on such complex shapes.
Exchange Representation (IGES) neutral file format, which is used in this
example.
-<h3> The boundary projector classes </h3>
+<h3> The CAD boundary projector classes </h3>
-To import and interrogate CAD models, the deal.II library contains a series of
-wrapper functions for the OpenCASCADE open source library for CAD
-modeling. These functions allow to import IGES files into OpenCASCADE native
-objects, and wrap them inside a series of Manifold classes.
+To import and interrogate CAD models, the deal.II library implements a series of
+wrapper functions for the OpenCASCADE open source library for CAD modeling.
+These functions allow to import IGES files into OpenCASCADE native objects, and
+wrap them inside a series of Manifold classes.
Once imported from an IGES file, the model is stored in a
<code>TopoDS_Shape</code>, which is the generic topological entity defined in
-the OpenCASCADE framework. From a <code>TopoDS_Shape</code>, it is then
-possible to access all the sub-shapes (such as vertices, edges and faces)
-composing it, along with their geometrical description. In the deal.II
-framework, the topological entities composing a shape are used to create
-a corresponding Manifold representation. In Step-6 we saw how to build a
-SphericalManifold and assign it to a set of faces (or cells, for co-dimension
-1) of a Triangulation, to have cells and faces refined on a sphere or circle.
-The functions of the CAD modeling interface have been designed to retain the
-same structure, allowing the user to build a projector object using the
-imported CAD shapes, maintaining the very same procedure we use with
-SphericalManifold, i.e., assigning such projector object to cells, faces or
-edges of a coarse mesh. At each refinement cycle, the new mesh nodes will be
-then automatically generated by projecting a midpoint of an existing object
-onto the specified geometry.
+the OpenCASCADE framework. From a <code>TopoDS_Shape</code>, it is then possible
+to access all the sub-shapes (such as vertices, edges and faces) composing it,
+along with their geometrical description. In the deal.II framework, the
+topological entities composing a shape are used to create a corresponding
+Manifold representation. In step-6 we saw how to build a hyper sphere, which is
+automatically assigned a SphericalManifold to its boundary faces, to have them
+refined on a sphere or on a circle. The functions of the CAD modeling interface
+have been designed to retain the same structure, allowing the user to build a
+projector object using the imported CAD shapes, maintaining the same procedure
+we used in other tutorial programs, i.e., assigning such projector object to
+cells, faces or edges of a coarse mesh. At each refinement cycle, the new mesh
+nodes will be then automatically generated by projecting a midpoint of an
+existing object onto the specified geometry.
Differently from a spherical or circular boundary, a boundary with a complex
geometry poses problems as to where it is best to place the new nodes created
projects / dealii.git / commitdiff