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{ 3D_PYRAMID.PDE
This problem considers the flow of heat in a pyramidshaped body.
It demonstrates the use of FlexPDE in 3D problems with nonplanar
extrusion surfaces.
Note that FEATURE paths are used to delineate discontinuities in the
extrusion surfaces.
The outer edge is used as a heat source, so it is clipped to form an edge wall.
}
title '3D Test  Pyramid'
coordinates cartesian3
select regrid=off ngrid=5 { reduce mesh size for example }
variables u
definitions k = 0.1 heat = 4
equations U: div(K*grad(u)) + heat = 0
extrusion surface z = 0 surface z = min(1.1 abs(x),1.1abs(y))

boundaries
{ implicit natural(u) = 0 on top and bottom faces }
Region 1
start(1,1)
value(u) = 0 { Fixed value on short vertical sides }
line to (1,1) to (1,1) to (1,1) to close
{ Features delineate hidden discontinuities in surface slope.
This forces gridding nodes along break lines. }
feature start(1,1) line to (1,1)
feature start(1,1) line to (1,1)
plots
contour(u) on x=0 as "YZ plane intersects peak"
contour(u) on y=0 as "XZ plane intersects peak"
contour(u) on z=0.1 as "XY plane intersects full outline"
contour(u) on x=0.51 as "YZ plane near midpoint of side slope"
contour(u) on x+y=0.51 as "Oblique plane cuts corner"
contour(u) on z=0.8 as "XY plane near tip"
contour(u) on z=0.8 zoom as "XY plane near tip  zoomed"
end