On 11/19/18 1:18 AM, 'Maxi Miller' via deal.II User Group wrote:
> I would like to implement Broyden's method, to speed up the assembly of the
> jacobian when solving a nonlinear system, which results in an equation
> containing the difference of the residual, the difference of the solution and
> the current jacobian matrix, i.e.
> J_{n+1}=J_n+\frac{\Delta f_n-J_n\Delta x_n}{\vert\vert \Delta
> x_n\vert\vert^2}\Delta x_n^T
> Now I am not entirely sure how to implement that into the code, especially
> the
> matrix creation due to the multiplication of a row- and a column-vector, such
> that I get the same structure as the original jacobian matrix. If I
> understand
> it correctly I can use the same approach as shown in the matrix-free methods,
> f.ex. step-37, where I create the elements cell-wise, and distribute them
> afterwards. Is that correct, or are there better ways to implement Broyden's
> method?
You don't actually generate the matrix. Instead, you store the two types of
vectors and represent the matrix only through its *action*, not by computing
and storing its elements. That's because the outer product of two dense
vectors is in general a dense matrix.
In other words, you'll have to implement a class that stores these vectors and
implements a vmult function.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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