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Currently when I try to solve a linear algebra system of the form of $A x =b$ I use the algebraic multigrid method. The algebraic multigrid method uses a Galerkin product to form the coarse grid matrix ($A_c = RA_fP$). Where $R$ is the restriction operator, $P$ the prolongation operator, $A_c$ the coarse grid matrix and $A_f$ the fine grid matrix.
In the current state of my implementation I perform the matrix multiplication to form the coarse grid. This step is quite expensive and I was asking myself if there is a way to use the restriction and prolongation operators directly in combination with the fine grid matrix instead of calculating the coarse grid matrix.
The first problem I was facing is to form the strong connection matrix from the fine grid matrix $A_f$, the restriction operator $R$ and the prolongation operator $P$.
Is there any available algebraic multigrid package that is not calculating the coarse grid matrix but using the operators?

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