Currently,I have the stiffness matrix A an density vector v.
If I know the constructing process of cell matrix in code,how should I
calculate the derivative of stiffness matrix with density?
A is a 4131*4131 matrix,v is 1024*1 vector. After derivative calculation
the result is a 4131*4131*1024 matrix and a Jacobin matrix,if I am wrong
,please provide your suggestions.
This is conceptually correct, but it is not how you would store things.
That's because while you could probably store 1024 matrices of size
4131x4131, you definitely can't do that any more if you refine once or
twice more.
But in practice, you also don't have to do that. The density on cell k
only affects the matrix entries (i,j) for degrees of freedom i,j that
are located on cell k. As a consequence, the (i,j,k) entries of the
4131x4131x1024 object is only going to be nonzero if i,j,k all live on
the same cell. In other words, the resulting object is going to be
*very* sparse.
Of course, this only tells you what *not* to do, but you want to know
what to do. This depends on what you need this derivative for. You only
tell us *that* you need the derivative, but not why. Can you outline
what it is you really want to do? In other words, what do you need the
derivative for?
Best
W.
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