Regions in Three Dimensions

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Regions in Three Dimensions

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The concept of a REGION in 3D domains retains the same character as for 2D domains.


The REGION is a partition of the 2D projection of the figure, and is extruded into the third dimension according to the EXTRUSION specification.


A material compartment in 3D is uniquely defined by the REGION of the projection which bounds it, and the LAYER of the extrusion in which it resides.


Extrusion of each 2D REGION therefore creates a stack of layers above it, each with possibly unique material properties.


A question then arises as to when a component that exists in a given layer of the domain must be divided into multiple regions.  The rule can be stated as follows:


Rule:  When two points in the projection plane see different stacks of materials above them in the extrusion direction, then these two points must reside in different REGIONS of the domain layout.


In the presence of LIMITED REGIONS, the above rule can be interpreted to consider only the two layers adjoining a given extrusion surface.  If the materials above and below the surface differ between two points, then there must be a REGION boundary separating the two points in the subject extrusion surface. REGION boundaries are induced in surfaces by the presence of a REGION boundary in either adjoining LAYER (subject to the overlay rule).


See the User Guide chapter Using FlexPDE in Three-Dimensional Problems for further discussion of the construction of 3D domains.