From f986cf585ee8dd05d78e497d3b2a24b6f9fd3e73 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Tue, 19 Jul 2011 09:28:09 +0000 Subject: [PATCH] mld2p4-2: mlprec/mld_cmlprec_aply.f90 mlprec/mld_dmlprec_aply.f90 mlprec/mld_smlprec_aply.f90 mlprec/mld_zmlprec_aply.f90 Fix description of algorithms. --- mlprec/mld_cmlprec_aply.f90 | 137 +++++++++++++++++------------------ mlprec/mld_dmlprec_aply.f90 | 133 +++++++++++++++++----------------- mlprec/mld_smlprec_aply.f90 | 138 +++++++++++++++++------------------ mlprec/mld_zmlprec_aply.f90 | 139 +++++++++++++++++------------------- 4 files changed, 263 insertions(+), 284 deletions(-) diff --git a/mlprec/mld_cmlprec_aply.f90 b/mlprec/mld_cmlprec_aply.f90 index 7f3296c1..58cd2771 100644 --- a/mlprec/mld_cmlprec_aply.f90 +++ b/mlprec/mld_cmlprec_aply.f90 @@ -173,9 +173,7 @@ ! ! Additive multilevel ! -! This is additive both within the levels and among levels. -! -! For details on the additive multilevel Schwarz preconditioner see the +! For details on the additive multilevel Schwarz preconditioner, see ! Algorithm 3.1.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial @@ -185,130 +183,127 @@ ! ilev-1, while PT(ilev) denotes its transpose, i.e. the corresponding ! restriction operator from level ilev-1 to level ilev). ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel ! a. Call recursively itself -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! -! Hybrid multiplicative, pre-smoothing only +! Hybrid multiplicative---pre-smoothing ! ! The preconditioner M is hybrid in the sense that it is multiplicative through the ! levels and additive inside a level. ! ! For details on the pre-smoothed hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.1 in the book: +! preconditioner, see Algorithm 3.2.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev >1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the ! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) + +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) -! +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! -! Hybrid multiplicative, post-smoothing only ! +! Hybrid multiplicative, post-smoothing variant ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! ! 2. If ilev < nlev -! ! a. Call recursively itself passing -! r(ilev) for transfer to the next level -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! c. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 3. Apply the base preconditioner at the current level to the residual +! x(ilev) for transfer to the next level +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = P(ilev+1)*y(ilev+1) +! c. Compute the residual: +! x(ilev) = x(ilev) - A(ilev)*y(ilev) +! d. Apply the base preconditioner to the residual at the current level: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*x(ilev) +! Else +! Apply the base preconditioner to the residual at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! -! -! 4. if ilev == 1 Transfer the inner Y to the external +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) +! +! 4. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! ! ! Hybrid multiplicative, pre- and post-smoothing (two-side) variant ! -! ! For details on the symmetrized hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.2 of the book: +! preconditioner, see Algorithm 3.2.2 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! d. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 4. Apply the base preconditioner at the current level to the residual -! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) +! d. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) +! e. Apply the base preconditioner at the current level to the residual: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) ! -! 5. if ilev == 1 Transfer the inner Y to the external +! 5. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! diff --git a/mlprec/mld_dmlprec_aply.f90 b/mlprec/mld_dmlprec_aply.f90 index 370c159b..b07c55de 100644 --- a/mlprec/mld_dmlprec_aply.f90 +++ b/mlprec/mld_dmlprec_aply.f90 @@ -173,7 +173,7 @@ ! Additive multilevel ! This is additive both within the levels and among levels. ! -! For details on the additive multilevel Schwarz preconditioner see the +! For details on the additive multilevel Schwarz preconditioner, see ! Algorithm 3.1.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial @@ -183,23 +183,23 @@ ! ilev-1, while PT(ilev) denotes its transpose, i.e. the corresponding ! restriction operator from level ilev-1 to level ilev). ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel ! a. Call recursively itself -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! @@ -209,109 +209,104 @@ ! levels and additive inside a level. ! ! For details on the pre-smoothed hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.1 in the book: +! preconditioner, see Algorithm 3.2.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev >1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the ! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) + +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! ! Hybrid multiplicative, post-smoothing variant ! -! -! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! ! 2. If ilev < nlev -! ! a. Call recursively itself passing -! r(ilev) for transfer to the next level -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! c. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 3. Apply the base preconditioner at the current level to the residual +! x(ilev) for transfer to the next level +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = P(ilev+1)*y(ilev+1) +! c. Compute the residual: +! x(ilev) = x(ilev) - A(ilev)*y(ilev) +! d. Apply the base preconditioner to the residual at the current level: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*x(ilev) +! Else +! Apply the base preconditioner to the residual at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! -! -! 4. if ilev == 1 Transfer the inner Y to the external +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) +! +! 4. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! ! ! Hybrid multiplicative, pre- and post-smoothing (two-side) variant ! -! ! For details on the symmetrized hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.2 of the book: +! preconditioner, see Algorithm 3.2.2 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! d. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 4. Apply the base preconditioner at the current level to the residual -! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) +! d. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) +! e. Apply the base preconditioner at the current level to the residual: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) ! -! 5. if ilev == 1 Transfer the inner Y to the external +! 5. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! -! subroutine mld_dmlprec_aply(alpha,p,x,beta,y,desc_data,trans,work,info) use psb_base_mod diff --git a/mlprec/mld_smlprec_aply.f90 b/mlprec/mld_smlprec_aply.f90 index e21c39df..c13111f0 100644 --- a/mlprec/mld_smlprec_aply.f90 +++ b/mlprec/mld_smlprec_aply.f90 @@ -171,10 +171,9 @@ ! ! ! Additive multilevel +! This is additive both within the levels and among levels. ! -! This is additive both within the levels and among levels. -! -! For details on the additive multilevel Schwarz preconditioner see the +! For details on the additive multilevel Schwarz preconditioner, see ! Algorithm 3.1.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial @@ -184,135 +183,130 @@ ! ilev-1, while PT(ilev) denotes its transpose, i.e. the corresponding ! restriction operator from level ilev-1 to level ilev). ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel ! a. Call recursively itself -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! -! Hybrid multiplicative, pre-smoothing only +! Hybrid multiplicative---pre-smoothing ! ! The preconditioner M is hybrid in the sense that it is multiplicative through the ! levels and additive inside a level. ! ! For details on the pre-smoothed hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.1 in the book: +! preconditioner, see Algorithm 3.2.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev >1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the ! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) + +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! ! Hybrid multiplicative, post-smoothing variant ! -! -! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! ! 2. If ilev < nlev -! ! a. Call recursively itself passing -! r(ilev) for transfer to the next level -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! c. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 3. Apply the base preconditioner at the current level to the residual +! x(ilev) for transfer to the next level +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = P(ilev+1)*y(ilev+1) +! c. Compute the residual: +! x(ilev) = x(ilev) - A(ilev)*y(ilev) +! d. Apply the base preconditioner to the residual at the current level: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*x(ilev) +! Else +! Apply the base preconditioner to the residual at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! -! -! 4. if ilev == 1 Transfer the inner Y to the external +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) +! +! 4. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! ! ! Hybrid multiplicative, pre- and post-smoothing (two-side) variant ! -! ! For details on the symmetrized hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.2 of the book: +! preconditioner, see Algorithm 3.2.2 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! d. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 4. Apply the base preconditioner at the current level to the residual -! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) +! d. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) +! e. Apply the base preconditioner at the current level to the residual: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) ! -! 5. if ilev == 1 Transfer the inner Y to the external +! 5. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! -! subroutine mld_smlprec_aply(alpha,p,x,beta,y,desc_data,trans,work,info) use psb_base_mod diff --git a/mlprec/mld_zmlprec_aply.f90 b/mlprec/mld_zmlprec_aply.f90 index 74549a89..517c8dd7 100644 --- a/mlprec/mld_zmlprec_aply.f90 +++ b/mlprec/mld_zmlprec_aply.f90 @@ -170,12 +170,10 @@ ! level 1 is the finest level and A(1) is the matrix A. ! ! -! ! Additive multilevel +! This is additive both within the levels and among levels. ! -! This is additive both within the levels and among levels. -! -! For details on the additive multilevel Schwarz preconditioner see the +! For details on the additive multilevel Schwarz preconditioner, see ! Algorithm 3.1.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial @@ -185,130 +183,127 @@ ! ilev-1, while PT(ilev) denotes its transpose, i.e. the corresponding ! restriction operator from level ilev-1 to level ilev). ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel ! a. Call recursively itself -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! -! Hybrid multiplicative, pre-smoothing only +! Hybrid multiplicative---pre-smoothing ! ! The preconditioner M is hybrid in the sense that it is multiplicative through the ! levels and additive inside a level. ! ! For details on the pre-smoothed hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.1 in the book: +! preconditioner, see Algorithm 3.2.1 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev >1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the ! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) + +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) ! -! 4. if ilev == 1 Transfer the inner Y to the external -! Yext = beta*Yext + alpha*Y(1) +! 4. if ilev == 1 Transfer the inner y to the external: +! Yext = beta*Yext + alpha*y(1) ! ! ! -! Hybrid multiplicative, post-smoothing only +! Hybrid multiplicative, post-smoothing variant ! -! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! ! 2. If ilev < nlev -! ! a. Call recursively itself passing -! r(ilev) for transfer to the next level -! b. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! c. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 3. Apply the base preconditioner at the current level to the residual +! x(ilev) for transfer to the next level +! b. Transfer y(ilev+1) to the current level: +! y(ilev) = P(ilev+1)*y(ilev+1) +! c. Compute the residual: +! x(ilev) = x(ilev) - A(ilev)*y(ilev) +! d. Apply the base preconditioner to the residual at the current level: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*x(ilev) +! Else +! Apply the base preconditioner to the residual at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! -! -! 4. if ilev == 1 Transfer the inner Y to the external +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) +! +! 4. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! ! ! ! Hybrid multiplicative, pre- and post-smoothing (two-side) variant ! -! ! For details on the symmetrized hybrid multiplicative multilevel Schwarz -! preconditioner, see the Algorithm 3.2.2 of the book: +! preconditioner, see Algorithm 3.2.2 in the book: ! B.F. Smith, P.E. Bjorstad & W.D. Gropp, ! Domain decomposition: parallel multilevel methods for elliptic partial ! differential equations, Cambridge University Press, 1996. ! ! -! 0. Transfer the outer vector Xest to X(1) (inner X at level 1). +! 0. Transfer the outer vector Xest to x(1) (inner X at level 1) ! -! 1. If ilev >1 Transfer X(ilev-1) to the current level. -! X(ilev) = PT(ilev)*X(ilev-1) +! 1. If ilev > 1 Transfer x(ilev-1) to the current level: +! x(ilev) = PT(ilev)*x(ilev-1) ! -! 2. Apply the base preconditioner at the current level. +! 2. Apply the base preconditioner at the current level: ! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = (K(ilev)^(-1))*X(ilev) +! ! application of K(ilev) +! y(ilev) = (K(ilev)^(-1))*x(ilev) ! ! 3. If ilev < nlevel -! a. Compute the residula -! r(ilev) = y(ilev) - A(ilev)*x(ilev) +! a. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) ! b. Call recursively itself passing -! r(ilev) for transfer to the next level -! -! c. Transfer Y(ilev+1) to the current level. -! Y(ilev) = Y(ilev) + P(ilev+1)*Y(ilev+1) -! -! d. Compute the residual -! r(ilev) = y(ilev) - A(ilev)*x(ilev) -! -! 4. Apply the base preconditioner at the current level to the residual -! ! The sum over the subdomains is carried out in the -! ! application of K(ilev). -! Y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) -! +! r(ilev) for transfer to the next level +! (r(ilev) matches x(ilev-1) in step 1) +! c. Transfer y(ilev+1) to the current level: +! y(ilev) = y(ilev) + P(ilev+1)*y(ilev+1) +! d. Compute the residual: +! r(ilev) = x(ilev) - A(ilev)*y(ilev) +! e. Apply the base preconditioner at the current level to the residual: +! ! The sum over the subdomains is carried out in the +! ! application of K(ilev) +! y(ilev) = y(ilev) + (K(ilev)^(-1))*r(ilev) ! -! 5. if ilev == 1 Transfer the inner Y to the external +! 5. if ilev == 1 Transfer the inner Y to the external: ! Yext = beta*Yext + alpha*Y(1) ! !