{
This example shows the use of FlexPDE in applications with two-way periodic boundaries.
FlexPDE cannot support multiple periodic images of a single point, so straightforward
request for periodicity in both X nad Y will not work.
If a small boundary segment is introduced at the corner point, however, then no point
is imaged twice, and the specification will be accepted.
The default boundary condition on the small non-periodic segment will be natural()=0, which
is not strictly correct, but if the segment is short and located in a region of relative
inactivity, the distortion should not be significant.
Alternatively, the "tautological" boundary condition may be used. This condition merely
supplies the surface terms required by the definition of the natural BC. In the diffusion
equation used in this example it is simply Natural()=normal(K*grad(u)).
}
title 'TWO-WAY PERIODIC BOUNDARY TEST'
Variables
u
definitions
k = 0.1
h=0
x0=0.5 y0=-0.2
x1=1.0 y1 = 0.2
x2=-0.5 x3=0.0
equations
div(K*grad(u)) + h = 0
boundaries
Region 1
{ Periodic bottom boundary }
start(-1,-1)
periodic(x,y+2) line to(0.95,-1)
{ New "line" spec breaks periocity }
! optional: natural(u) = normal(K*grad(u))
line to (1,-1)
{ Periodic right boundary }
periodic(x-2,y) arc(center=-1,0) to (1,1)
{ Images of non-periodic stub and periodic bottom boundry }
line to (0.95,1) to (-1,1)
{ Image of periodic right boundary }
arc(center= -3,0) to close
{ off-center hot box }
value(u)=1
start(x0,y0) line to (x1,y0) to (x1,y1) to (x0,y1) to close
{ off-center cold box }
value(u)=-1
start(x2,y0) line to (x3,y0) to (x3,y1) to (x2,y1) to close
monitors
grid(x,y)
contour(u)
plots
grid(x,y)
contour(u)
end