I am facing a problem performing replacement of certain terms of a long sum by non zero values. I have posted a similar question ( Having problem with using Replace in Do-loop) but I was trying to replace with zero the out of bound terms. Well the sum is
`BM = 0;
For[ i = 1, i <= ndof1, i++,
For[ j = 1, j <= ndof2, j++,
If[ Mod[ i + j, 2] == 0,
BM = BM +
VM[u[i, j, 1], u[i, j, 2], u[i, j + 1, 1], u[i, j + 1, 2]] +
VM[u[i, j, 1], u[i, j, 2], u[i - 1, j, 1], u[i - 1, j, 2]] +
VM[ u[i, j, 1], u[i, j, 2], u[i, j - 1, 1], u[i, j - 1, 2]];
Print[ "In even : " <> ToString[i + j]] ;(*
Check the way the code is taking the sum *)
]
If[ Mod[ i + j, 2] == 1,
BM = BM +
VM[u[i, j, 1], u[i, j, 2], u[i, j + 1, 1], u[i, j + 1, 2]] +
VM[u[i, j, 1], u[i, j, 2], u[i + 1, j, 1], u[i + 1, j, 2]] +
VM[ u[i, j, 1], u[i, j, 2], u[i, j - 1, 1], u[i, j - 1, 2]];
Print[ "In odd : " <> ToString[i + j]] ; (*
Check the way the code is taking the sum *)
]
]
]
BM = BM /2;`
Where VM is a function defined on this way:
r[x1_ , y1_ , x2_ , y2_] := Sqrt[(x2 - x1)^2 + (y2 - y1)^2]
VM[xi_, yi_, xo_, yo_] := D*(Exp[-a* (r[xi, yi, xo, yo] - r0)] -
1)^2'
I want to replace out of bound terms with in in-bound terms for instance
u[i, 0, 1] -> u[i, ndof2, 1]
(periodic boundaries conditions)
Hence, I do in my code (for instance)
`Do[ u[i, 0, 1] = u[i, ndof2, 1], {i, -ndof1, ndof1 + 1}]
ruleIO1 = Table[u[i, 0, 1] -> u[i, ndof2, 1], {i, -ndof1, ndof1 + 1}]
BMNew = BM /. ruleIO1;`
which seems to work fine. But when I perform the derivative of BMNew with respect to one of the removed variables says
D[BMNew, u[5, 0, 1]]
I get a result!!!! Meaning that I don't do it properly.
Can some one help me to do it properly.
Thanks
