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

Thank you! This indeed work for these simplest cases, as there is a single table of values with the same spacing. However, I would be still interested in knowing if there is a way to actually interpolate by joining different tables of the same function with different spacings in different intervals, or whether this is really not possible in Mathematica. Thank you again, Best Fabrizio