Fast computation of bilinear forms

General Discussion
1

Hi,

I have the bilinear form q that can be represented as q(f, g) = int2d(Th)( b * ( dx(uf) * dx(ug) + dy(uf) * dy(ug) ) ) where b is a fixed function, uf and ug solve a given BVP (details of the specific problem are not important) with Neumann boundary conditions f and g, respectively.

I also have a collection of functions f1,...,fn and I want to compute the matrix B given by B_jk=q[fj,fk] for all pairs j,k.

The question is, what is the fastest way to do it?

Using the expression for q each time is extremely slow, so what I am doing now is to compute the matrix A = q(Vh, Vh) and computing the inner products <A * f[], g[]> whenever I want to compute q(f, g).

Thanks in advace!

2

How many js and ks do you have? Most often, you do not want to store this explicitly, and want to deal with this in a matrix-free fashion, or with another representation, like Kronecker product.

3

Give or take 40, I don’t think they are the problem. This algorithm fits into a larger process where this has be done a lot of times for different bs since this is an optimization algorithm for q.