Return internal information for future use

[juliamath]

Return internal information for future use

[stevengj]

The best way to share points between similar integrals is probably to integrate a vector-valued integrand. (Use StaticArrays.jl for the integrand so that you don't need to allocate lots of temporary vectors on the heap.)

Also, I'm skeptical that the savings from saving/re-using cubature regions would be that great — because it's a geometric series of points, you waste at most a factor of two in the number of integrand evaluations during adaptivity.

[jwscook]

It's going to be quite a challenge to create a vector valued integrand because the integral bounds are different for each quantity that would be in the vector, or so it's been written. It's for a least squares finite element method where I'm integrating over the intersection of at least two multi-dimensional basis functions of compact supports. Also the problem isn't in general translationally invariant because of spatially dependent factors in the integrand.

I wasn't very clear before. When I said saving intervals, I meant it in a relative sense:

Let's say that in the course of the first integral over the interval [a,b), normalised to [-1, 1), there are N subdivisions e.g. [-1, -0.75), [-0.75, 0.25) [0.25, 0.5) and [0.25, 1). It is then possible to start with the same subdivision, relatively speaking, but over the interval of the next integral [a', b')?

I assume not because it sounds difficult.

[jwscook]

Also, a factor of 2 sounds good! I'll take what I can get.

[stevengj]

It is then possible to start with the same subdivision, relatively speaking, …

If that is what you want, you could use a vector-valued integrand with a coordinate transformation to map all of your integrands to the same domain.

[jwscook]

A coordinate transformation will be rather challenging because I'm working with non-orthogonal coordinate systems.

Having vectorised it, and storing the vector result with vector of inputs as a dictionary has made re-evaluations redundant.