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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