First I would like to remark that with the ti's you gave above you don't cover the whole (square) region where your function may be defined. The ti's form something like a "diagonal" region.
Second I would really like to know what an "unstructured grid " is.
But perhaps you can get what you want by a modified approach.
Let n be the exponent (of 10) of your highest number. Then define for example
n = 3;
elim = Range[0, n]
f[x_, y_] := x^2/5 + Sqrt[y]
and
values[i_, j_] := Module[{a, b, x, y},
a = 10^i;
b = 10^j;
Flatten[
Table[{{x = a (1 + 9 u), y = b (1 + 9 v)}, f[x, y]}, {u, 0, 1, .2}, {v, 0, 1, .2}], 1]
]
For more datapoints you should change the .2 to .1 in the iterators.
Then
intpol = Table[
Interpolation[values[i, j]],
{i, 1, Length[elim]}, {j, 1, Length[elim]}];
and
func[x_, y_] :=
intpol[[IntegerPart[Log[10, x]], IntegerPart[Log[10, y]]]][x, y]
will call the appropriate interpolation-function
