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# Mapping the Domain

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# Mapping the Domain

Two-Dimensional Domain Description

A two-dimensional problem domain is described in the BOUNDARIES section, and is made up of REGIONS, each assumed to contain unique material properties.  A REGION may contain many closed loops or islands, but they are all assumed to have the same material properties.

 • A REGION specification begins with the statement REGION  (or REGION "name") and all loops following the header are included in the region.

 • REGIONs occurring later in the script overlay and cover up parts of earlier REGIONs.

 • The first REGION should contain the entire domain.  This is an unenforced convention that makes the attachment of boundary conditions easier.

Region shapes are described by walking the perimeter, stepping from one joint to another with LINE, SPLINE, ARC or CURVE segments.  Each segment assumes that it will continue from the end of the previous segment, and the START clause gets things rolling.  You can make a segment return to the beginning with the word CLOSE (or TO CLOSE).

 • A rectangular region, for example, is made up of four line segments:

START(x1,y1)

LINE TO(x2,y1)

TO (x2,y2)

TO (x1,y2)

TO CLOSE

(Of course, any quadrilateral figure can be made with the same structure, merely by changing the coordinates.  And any polygonal figure can be constructed by adding more points.)

 • Arcs can be built in several ways, the simplest of which is by specifying a center and an angle:

START(r,0)

ARC(CENTER=0,0) ANGLE=360

 • Arcs can also be built by specifying a center and an end point:

START(r,0)

ARC(CENTER=0,0) TO (0,r)        { a 90 degree arc }

An elliptical arc will be built if the distance from the center to the endpoint is different than the distance from the center to the beginning point.  The axes of the ellipse will extend along the horizontal and vertical coordinate axes.  The axes can be rotated with the ROTATE=degrees command.

 • Curves can be built by specifying a start point and an expression for the curve:

START(r,0)

CURVE(x^2+y^2=r^2) BY (+X) TO (0,r)        { a 90 degree arc }

A curve.

 • Loops can be named for use in later references, as in:

START "Name" (…)

The prototype form of The BOUNDARIES section is then:

BOUNDARIES

REGION 1

<closed loops around the domain>

REGION 2

<closed loops around overlays of the second material>

You can build your domain a little at a time, using the "domain review" menu button to preview a drawing of what you have created so far.

The "Save" and "Save_As" menu buttons allow you to frequently save your work, just in case.