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# constraint

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# constraint   {  CONSTRAINT.PDE

This problem shows the use of CONSTRAINTS to resolve an ill-posed problem.

There are no value boundary conditions in any of the three equations, so

there are infinitely many solutions that satisfy the PDE's.  The constraints

select from the family of solutions those which have a mean value of 1.

}

title 'Constraint Test'

variables

u1 u2 u3

equations

constraints

integral(u1) = integral(1)

integral(u2) = integral(1)

integral(u3) = integral(1)

boundaries

Region 1

start(-1,-1) line to (1,-1) to (1,1) to (-1,1) to close

monitors

contour(u1)

contour(u2)

contour(u3)

plots

contour(u1) report(integral(u1)/integral(1)) as "Average"

contour(u2) report(integral(u2)/integral(1)) as "Average"

contour(u3) report(integral(u3)/integral(1)) as "Average"

surface(u1) report(integral(u1)/integral(1)) as "Average"

surface(u2) report(integral(u2)/integral(1)) as "Average"

surface(u3) report(integral(u3)/integral(1)) as "Average"

end