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Imposing zero mean value
Posted May 4, 2010, 1:17 p.m. EDT 1 Reply
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Does anybody know if there is a standard way of imposing that the solution of a PDE has zero mean value on the domain of definition of the equation?
I am thinking of the Laplace equation with pure Neumann boundary conditions.
The solution is well defined up to a constant and I need to impose that the solution has zero mean value (integral of u over the domain of definition of the problem = 0) in order to fix the constant.
I am thinking of the Laplace equation with pure Neumann boundary conditions.
The solution is well defined up to a constant and I need to impose that the solution has zero mean value (integral of u over the domain of definition of the problem = 0) in order to fix the constant.
1 Reply Last Post May 4, 2010, 3:30 p.m. EDT
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Posted:
1 decade ago
Hi
If I understand you right you want to tweak a parameter (in a least square sens) or a BC (boundary condition)value ,such that the average of let's say "u" is "0" over a sub-domain (or boundary).
Assume you are in 2D, I would then define two coupling integration subdomain values over the subdomain of interest:
Area = 1
U = u/Area
where Area is the total area of the subdomain, and U is the average value of "u". For 3D adapt accordingly, as well if it's on an edge, replace Area by Length ...
then, I would define the BC value on the desired BC' conditions, let us say the variable name is "BC", this is not yet defined, so then we must add a global equation with:
name: BC , equation: U
which means implicitely search BC such that U=0
I hope this helps on the way
Have fun Comsoling
Ivar
If I understand you right you want to tweak a parameter (in a least square sens) or a BC (boundary condition)value ,such that the average of let's say "u" is "0" over a sub-domain (or boundary).
Assume you are in 2D, I would then define two coupling integration subdomain values over the subdomain of interest:
Area = 1
U = u/Area
where Area is the total area of the subdomain, and U is the average value of "u". For 3D adapt accordingly, as well if it's on an edge, replace Area by Length ...
then, I would define the BC value on the desired BC' conditions, let us say the variable name is "BC", this is not yet defined, so then we must add a global equation with:
name: BC , equation: U
which means implicitely search BC such that U=0
I hope this helps on the way
Have fun Comsoling
Ivar