extreme points problem
 

Hello, everyone Now here is a difficult for me and hope to be helped out. I have got scalar data at every grid point in a Cartesian coordinate and also found the positions of extreme points. The criteria for extreme points is

[S(i)-S(i+1)]*[S(i)-S(i-1)]>0, where i will be in x, y and z 3 directions.

But we want to know more precisely the positions of extreme points so I tried to do interpolation and found some extreme points will dispear with the same criteria. This is due to the effect from no-adjencent points. For example, S(0,0,0) is extreme, then S(1,1,0), S(1,1,1),S(1,-1,0) are no-adjencent.

So I wonder should I also consider these no-adjencent points, or only adjent points(totally they are S(0,0,1),S(0,0,-1),S(1,0,0),S(-1,0,0),S(0,1,0),S(0,-1,0)) for interpolation? Of course, more points considered, more reasonable. But more negative effect will destroy the criteria. How do you think about it?

Great thanks

Re: extreme points problem
 

The extrema may not coincide with any of the grid points. You can try to set up a finite-element interpolation and solve for grad(u)=0 to locate the extrema.

Re: extreme points problem
 

thanks a lot. The finite element interpolation you mentioned is for irregular gird? Because the mesh I used is Cartesian coordinate grid,FE interpolation is still good? How about it if compared with other kind of interpolation, like polynomial, B-spline etc? Thanks