hecmw_precond_saamg_prolongation Module Reference

Smoothed Aggregation AMG preconditioner : prolongation. More...

Functions/Subroutines
subroutine, public	hecmw_saamg_tentative (bfine, n, m, nb, aggr, naggr, phat, bcoarse)
	Build P-hat (n x naggr*m block-CSR) and B_coarse (naggr*m x m) from B_fine. More...
subroutine, public	hecmw_saamg_smooth_prolongator (A, D, omega, phat, p)
	Smoothed prolongator P = P-hat - omega * D^{-1} (A P-hat), via SpGEMM. Computes A*P-hat once as a sparse product (instead of one full A-matvec per coarse column, which is O(ncoarse * nnz_A)), applies the block-diagonal D^{-1} row-wise, then forms the sparse difference by summing triplets. More...

Detailed Description

Smoothed Aggregation AMG preconditioner : prolongation.

Two operations:

• tentative prolongator P-hat and coarse near-kernel B via per-aggregate thin Householder QR (LAPACK dgeqrf/dorgqr): B_k = Q_k R_k, Q_k -> P-hat block column k, R_k -> B_coarse block row k. By construction P-hat * B_coarse = B_fine and P-hat^T P-hat = I.
• prolongator smoothing P = (I - omega D^{-1} A) P-hat, computed column by column reusing the tested matvec and block-diagonal solve (a SpGEMM-based path is a later optimization).

Coarse layout: aggregate k becomes coarse node k with m dofs; coarse dof (k-1)*m + c. Excluded nodes (aggr=0) get an all-zero P-hat row.

Function/Subroutine Documentation

hecmw_saamg_smooth_prolongator()

subroutine, public hecmw_precond_saamg_prolongation::hecmw_saamg_smooth_prolongator	(	type(hecmwst_saamg_bcsr), intent(in)	A,
		type(hecmwst_saamg_blockdiag), intent(in)	D,
		real(kind=kreal), intent(in)	omega,
		type(hecmwst_saamg_bcsr), intent(in)	phat,
		type(hecmwst_saamg_bcsr), intent(out)	p
	)

Smoothed prolongator P = P-hat - omega * D^{-1} (A P-hat), via SpGEMM. Computes A*P-hat once as a sparse product (instead of one full A-matvec per coarse column, which is O(ncoarse * nnz_A)), applies the block-diagonal D^{-1} row-wise, then forms the sparse difference by summing triplets.

Definition at line 146 of file hecmw_precond_SAAMG_prolongation.F90.

Here is the call graph for this function:

Here is the caller graph for this function:

hecmw_saamg_tentative()

subroutine, public hecmw_precond_saamg_prolongation::hecmw_saamg_tentative	(	real(kind=kreal), dimension(n, m), intent(in)	bfine,
		integer(kind=kint), intent(in)	n,
		integer(kind=kint), intent(in)	m,
		integer(kind=kint), intent(in)	nb,
		integer(kind=kint), dimension(:), intent(in)	aggr,
		integer(kind=kint), intent(in)	naggr,
		type(hecmwst_saamg_bcsr), intent(out)	phat,
		real(kind=kreal), dimension(:,:), intent(out), allocatable	bcoarse
	)

Build P-hat (n x naggr*m block-CSR) and B_coarse (naggr*m x m) from B_fine.

Definition at line 32 of file hecmw_precond_SAAMG_prolongation.F90.

Here is the call graph for this function:

Here is the caller graph for this function: