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[Dag Lindbo <dag@xxxxxxxxxx>]

As per request, I ran some 2d tests of evaluation of a P1-function 
(Laplace demo C++, UnitSquare mesh) at a set of random points (cost of 
randomization small fraction of runtime).

Almost only initialization:
Elapsed time: 0.010000   Points: 1       Mesh 64 x 64
Elapsed time: 0.070000   Points: 1       Mesh 128 x 128
Elapsed time: 0.340000   Points: 1       Mesh 256 x 256
Elapsed time: 1.460000   Points: 1       Mesh 512 x 512

The first 10000 evaluations are almost free:
Elapsed time: 0.040000   Points: 10000   Mesh 64 x 64
Elapsed time: 0.110000   Points: 10000   Mesh 128 x 128
Elapsed time: 0.400000   Points: 10000   Mesh 256 x 256
Elapsed time: 1.540000   Points: 10000   Mesh 512 x 512

Here the cost of initialization is reasonably amortized:
Elapsed time: 2.850000   Points: 1000000         Mesh 64 x 64
Elapsed time: 3.610000   Points: 1000000         Mesh 128 x 128
Elapsed time: 4.780000   Points: 1000000         Mesh 256 x 256
Elapsed time: 6.610000   Points: 1000000         Mesh 512 x 512

From 1e6 to 4e6 evaulation the scaling is linear:
Elapsed time: 11.77000   Points: 4000000         Mesh 64 x 64
Elapsed time: 14.21000   Points: 4000000         Mesh 128 x 128
Elapsed time: 18.21000   Points: 4000000         Mesh 256 x 256
Elapsed time: 22.17000   Points: 4000000         Mesh 512 x 512

Another conclusion:
Initialization does not scale so well with mesh size (as expected). 
Finding some points, however, does scale well with bigger meshes.

/Dag
PS. And some valgrinding confirms that there is no memory leaking.
(Use G_SLICE=always-malloc to supress "errors" from GLib).