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{ SAVE.PDE
This example illustrates use of the SAVE function.
SAVE(F) computes the value of F at each mesh node, and returns interpolated
values for any position within a cell.
If F is very expensive to compute, the use of SAVE can reduce the overall cost
of a simulation.
SAVE also hides the complexity of F from differentiation in forming the coupling
matrix, and may therefore avoid numerical difficulties encountered in computing
the derivatives of pathological functions.
}
title 'SAVE test'
select
ngrid=20
contourgrid=100 { use a very dense plot grid to show data structure }
Variables
u,v
definitions
k = 2
u0 = 1+x^2+y^2
s = cos(20*x)*cos(20*y)
save_s = save(s) { Used in a definition }
Initial values
u = 1
equations
U: u - div(K*grad(u)) = s
V: v - div(K*grad(v)) = save_s
boundaries
region 1
start(-1,-1)
value(u)=u0 value(v)=u0
line to (1,-1) to (1,1) to (-1,1) to close
region 2
k=4
start(-1,-1) line to (0,-1) to (0,0) to (-1,0) to close
plots
grid(x,y)
contour(u)
contour(v)
contour(s)
contour(save_s)
elevation(s, save_s) from(-1,0) to (1,0)
end