Re: [Getfem-users] How to impose radiation boundary condition of heterogeneous Helmholtz equation

[Yves Renard]

Dear Tsai,

I do not have access to the content of the paper, so I am not able to see the 
difficulty it represents to make the assembly of this radiation condition.

One of the key point is of course the weak formulation and the eventual 
integration by part along the boundary to reduce the order. Getfem++ allows to 
compute up to order 2 derivatives. It is usually sufficient for up to order 4 
pde problems.




On mardi 23 août 2011, you wrote:
> Dear All,
> 
> We appreciate the innovation of GetFem++.
> 
> Recently, we tried to apply the GetFem++ to a problem governed
> by heterogeneous Helmholtz equation. We can find the system matrix by
> the generic assembly procedures. However, we don't known how to  impose
> radiation boundary condition which involves high-order mixed derivatives
> (see http://cedb.asce.org/cgi/WWWdisplay.cgi?138489 for details). We will
> be very glad to have your suggestions.
> 
> On the other hand, If we have a function on grid points, what is the
> easiest way to interpolate it and get its derivatives? Do we need to
> establish a mesh and then interpolate it?

This is a way (define a regular mesh, your mesh and call the interpolation 
procedure). This is not necessarily the more stable way of course. L2 or H1 
projection could be better in some situations.

Yves. 




-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
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  http://math.univ-lyon1.fr/~renard

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