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?
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