Question: Calling UMFPACK sparsedirect linearsolver using only sparse entries

@acer,
In the past, you had shown how to use take a given sparse A matrix and store the LU components and use the same factorization for multiple backsolves at https://www.mapleprimes.com/posts/41191-Solving-Sparse-Linear-Systems-In-Maple#comment200817

When PDEs are solved, we are calling the A matrix at every time step (with some discretizations in x) and the factorization is done and stored at every time step (this is time-consuming and memory-consuming). Is it possible to call UMFPACK using only the sparse storage and entries? The main routine seems to provide the option 

https://people.sc.fsu.edu/~jburkardt/f77_src/umfpack/umfpack.html

This would mean that the pattern is found only once for the Jacobian at t= 0, then only the non-zero sparse entries (vector/row, not a matrix) are updated at every time step.

To be clear, what I am asking for is create a random sparse matrix (say 4x4 or 10x10)
create a b Vector.

Solve AZ =b with method = SparseDirect. (This should internally create and store R, CC, X as at https://people.sc.fsu.edu/~jburkardt/f77_src/umfpack/umfpack.html)

Store R, CC, X and update only X for a different A matrix with the same sparsity pattern and solve for Z using stored (R, CC), and updated X.