griffgruff

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15 years, 79 days

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These are replies submitted by griffgruff

@Kitonum Thank you for your reply which provides the answer I need.

On inspection, it appears that the first code example can be simplified to:

V:=Del(u(x,y));
n:=Normalize(V,2); 
bcN := simplify(DotProduct(n,V));

 

@Rouben Rostamian  Thank you for your replies.

The function u(x,y) is the solution to a PDE (elliptical) which represents a 2D surface over its domain. The point (xo,yo) lies on the bounday of the domain. I wish to calculate the Neumann boundary condition (the normal derivative) at (xo,yo), i.e. du/dnn . del(u) . I may have confused the issue by showing u in 'bold'. Actually, u is a scalar function not a vector function.

The boundary does not need to be a level curve (although it can be); for example, the solution to a well posed Laplace equation with a Dirichlet boundary whose value varies over its length. This could represent (at equilibrium) the Heat equation with different temperatures imposed along the boundary.

@Rouben Rostamian  Just to clarify, n and u are related. If u(x,y) represents a 2D surface and n the unit normal at point (xo,yo) on the boundary, then

     n . del(u)

represents the Neumann boundary condition for a PDE with solution u(x,y) at point (xo,yo).

Apologies for any confusion.

Sorry for any confusion due to the spelling mistake in the subject heading.
Thanks very much. Your suggestion works fine. Regards, Graham
Thanks very much. Your suggestion works fine. Regards, Graham
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