[petsc-users] Questions Regarding PETSc and Solving Constrained Structural Mechanics Problems
hexioafeng
hexiaofeng at buaa.edu.cn
Thu Jun 19 20:18:34 CDT 2025
Hello,
Here are the outputs with svd:
0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00
Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
Linear fieldsplit_1_ solve did not converge due to DIVERGED_PC_FAILED iterations 0
PC failed due to SUBPC_ERROR
Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0
PC failed due to SUBPC_ERROR
KSP Object: 1 MPI processes
type: cg
maximum iterations=200, initial guess is zero
tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30
left preconditioning
using UNPRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
type: fieldsplit
FieldSplit with Schur preconditioner, blocksize = 1, factorization FULL
Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's diagonal's inverse
Split info:
Split number 0 Defined by IS
Split number 1 Defined by IS
KSP solver for A00 block
KSP Object: (fieldsplit_0_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_) 1 MPI processes
type: gamg
type is MULTIPLICATIVE, levels=2 cycles=v
Cycles per PCApply=1
Using externally compute Galerkin coarse grid matrices
GAMG specific options
Threshold for dropping small values in graph on each level =
Threshold scaling factor for each level not specified = 1.
AGG specific options
Symmetric graph false
Number of levels to square graph 1
Number smoothing steps 1
Complexity: grid = 1.00222
Coarse grid solver -- level -------------------------------
KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
type: bjacobi
number of blocks = 1
Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
type: svd
All singular values smaller than 1e-12 treated as zero
Provided essential rank of the matrix 0 (all other eigenvalues are zeroed)
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=8, cols=8
total: nonzeros=56, allocated nonzeros=56
total number of mallocs used during MatSetValues calls=0
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=8, cols=8
total: nonzeros=56, allocated nonzeros=56
total number of mallocs used during MatSetValues calls=0
using nonscalable MatPtAP() implementation
using I-node (on process 0) routines: found 3 nodes, limit used is 5
Down solver (pre-smoother) on level 1 -------------------------------
KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
type: chebyshev
eigenvalue estimates used: min = 0.0998145, max = 1.09796
eigenvalues estimate via gmres min 0.00156735, max 0.998145
eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes
type: gmres
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
happy breakdown tolerance 1e-30
maximum iterations=10, initial guess is zero
tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
left preconditioning
using PRECONDITIONED norm type for convergence test
estimating eigenvalues using noisy right hand side
maximum iterations=2, nonzero initial guess
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
type: sor
type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
linear system matrix = precond matrix:
Mat Object: (fieldsplit_0_) 1 MPI processes
type: mpiaij
rows=480, cols=480
total: nonzeros=25200, allocated nonzeros=25200
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 160 nodes, limit used is 5
Up solver (post-smoother) same as down solver (pre-smoother)
linear system matrix = precond matrix:
Mat Object: (fieldsplit_0_) 1 MPI processes
type: mpiaij
rows=480, cols=480
total: nonzeros=25200, allocated nonzeros=25200
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 160 nodes, limit used is 5
KSP solver for S = A11 - A10 inv(A00) A01
KSP Object: (fieldsplit_1_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_1_) 1 MPI processes
type: bjacobi
number of blocks = 1
Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
KSP Object: (fieldsplit_1_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_1_sub_) 1 MPI processes
type: bjacobi
number of blocks = 1
Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
KSP Object: (fieldsplit_1_sub_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_1_sub_sub_) 1 MPI processes
type: ilu
out-of-place factorization
0 levels of fill
tolerance for zero pivot 2.22045e-14
matrix ordering: natural
factor fill ratio given 1., needed 1.
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqaij
rows=144, cols=144
package used to perform factorization: petsc
total: nonzeros=240, allocated nonzeros=240
not using I-node routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=144, cols=144
total: nonzeros=240, allocated nonzeros=240
total number of mallocs used during MatSetValues calls=0
not using I-node routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=144, cols=144
total: nonzeros=240, allocated nonzeros=240
total number of mallocs used during MatSetValues calls=0
not using I-node (on process 0) routines
linear system matrix followed by preconditioner matrix:
Mat Object: (fieldsplit_1_) 1 MPI processes
type: schurcomplement
rows=144, cols=144
Schur complement A11 - A10 inv(A00) A01
A11
Mat Object: (fieldsplit_1_) 1 MPI processes
type: mpiaij
rows=144, cols=144
total: nonzeros=240, allocated nonzeros=240
total number of mallocs used during MatSetValues calls=0
not using I-node (on process 0) routines
A10
Mat Object: 1 MPI processes
type: mpiaij
rows=144, cols=480
total: nonzeros=48, allocated nonzeros=48
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 74 nodes, limit used is 5
KSP of A00
KSP Object: (fieldsplit_0_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_) 1 MPI processes
type: gamg
type is MULTIPLICATIVE, levels=2 cycles=v
Cycles per PCApply=1
Using externally compute Galerkin coarse grid matrices
GAMG specific options
Threshold for dropping small values in graph on each level =
Threshold scaling factor for each level not specified = 1.
AGG specific options
Symmetric graph false
Number of levels to square graph 1
Number smoothing steps 1
Complexity: grid = 1.00222
Coarse grid solver -- level -------------------------------
KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
type: bjacobi
number of blocks = 1
Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
type: svd
All singular values smaller than 1e-12 treated as zero
Provided essential rank of the matrix 0 (all other eigenvalues are zeroed)
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=8, cols=8
total: nonzeros=56, allocated nonzeros=56
total number of mallocs used during MatSetValues calls=0
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=8, cols=8
total: nonzeros=56, allocated nonzeros=56
total number of mallocs used during MatSetValues calls=0
using nonscalable MatPtAP() implementation
using I-node (on process 0) routines: found 3 nodes, limit used is 5
Down solver (pre-smoother) on level 1 -------------------------------
KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
type: chebyshev
eigenvalue estimates used: min = 0.0998145, max = 1.09796
eigenvalues estimate via gmres min 0.00156735, max 0.998145
eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes
type: gmres
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
happy breakdown tolerance 1e-30
maximum iterations=10, initial guess is zero
tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
left preconditioning
using PRECONDITIONED norm type for convergence test
estimating eigenvalues using noisy right hand side
maximum iterations=2, nonzero initial guess
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
type: sor
type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
linear system matrix = precond matrix:
Mat Object: (fieldsplit_0_) 1 MPI processes
type: mpiaij
rows=480, cols=480
total: nonzeros=25200, allocated nonzeros=25200
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 160 nodes, limit used is 5
Up solver (post-smoother) same as down solver (pre-smoother)
linear system matrix = precond matrix:
Mat Object: (fieldsplit_0_) 1 MPI processes
type: mpiaij
rows=480, cols=480
total: nonzeros=25200, allocated nonzeros=25200
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 160 nodes, limit used is 5
A01
Mat Object: 1 MPI processes
type: mpiaij
rows=480, cols=144
total: nonzeros=48, allocated nonzeros=48
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 135 nodes, limit used is 5
Mat Object: 1 MPI processes
type: mpiaij
rows=144, cols=144
total: nonzeros=240, allocated nonzeros=240
total number of mallocs used during MatSetValues calls=0
not using I-node (on process 0) routines
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=624, cols=624
total: nonzeros=25536, allocated nonzeros=25536
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 336 nodes, limit used is 5
Thanks,
Xiaofeng
> On Jun 20, 2025, at 00:56, Mark Adams <mfadams at lbl.gov> wrote:
>
> This is what Matt is looking at:
>
> PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
> type: lu
>
> This should be svd, not lu
>
> If you had used -options_left you would have caught this mistake(s)
>
> On Thu, Jun 19, 2025 at 8:06 AM Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>> On Thu, Jun 19, 2025 at 7:59 AM hexioafeng <hexiaofeng at buaa.edu.cn <mailto:hexiaofeng at buaa.edu.cn>> wrote:
>>> Hello sir,
>>>
>>> I remove the duplicated "_type", and get the same error and output.
>>
>> The output cannot be the same. Please send it.
>>
>> Thanks,
>>
>> Matt
>>
>>> Best regards,
>>> Xiaofeng
>>>
>>>
>>>> On Jun 19, 2025, at 19:45, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>>>>
>>>> This options is wrong
>>>>
>>>> -fieldsplit_0_mg_coarse_sub_pc_type_type svd
>>>>
>>>> Notice that "_type" is repeated.
>>>>
>>>> Thanks,
>>>>
>>>> Matt
>>>>
>>>> On Thu, Jun 19, 2025 at 7:10 AM hexioafeng <hexiaofeng at buaa.edu.cn <mailto:hexiaofeng at buaa.edu.cn>> wrote:
>>>>> Dear authors,
>>>>>
>>>>> Here are the options passed with fieldsplit preconditioner:
>>>>>
>>>>> -ksp_type cg -pc_type fieldsplit -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly -fieldsplit_0_pc_type gamg -fieldsplit_0_mg_coarse_sub_pc_type_type svd -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual -fieldsplit_0_mg_levels_ksp_converged_reason -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason
>>>>>
>>>>> and the output:
>>>>>
>>>>> 0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00
>>>>> Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
>>>>> Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
>>>>> Linear fieldsplit_1_ solve did not converge due to DIVERGED_PC_FAILED iterations 0
>>>>> PC failed due to SUBPC_ERROR
>>>>> Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
>>>>> Linear fieldsplit_0_mg_levels_1_ solve converged due to CONVERGED_ITS iterations 2
>>>>> Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0
>>>>> PC failed due to SUBPC_ERROR
>>>>> KSP Object: 1 MPI processes
>>>>> type: cg
>>>>> maximum iterations=200, initial guess is zero
>>>>> tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30
>>>>> left preconditioning
>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>> PC Object: 1 MPI processes
>>>>> type: fieldsplit
>>>>> FieldSplit with Schur preconditioner, blocksize = 1, factorization FULL
>>>>> Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's diagonal's inverse
>>>>> Split info:
>>>>> Split number 0 Defined by IS
>>>>> Split number 1 Defined by IS
>>>>> KSP solver for A00 block
>>>>> KSP Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: gamg
>>>>> type is MULTIPLICATIVE, levels=2 cycles=v
>>>>> Cycles per PCApply=1
>>>>> Using externally compute Galerkin coarse grid matrices
>>>>> GAMG specific options
>>>>> Threshold for dropping small values in graph on each level =
>>>>> Threshold scaling factor for each level not specified = 1.
>>>>> AGG specific options
>>>>> Symmetric graph false
>>>>> Number of levels to square graph 1
>>>>> Number smoothing steps 1
>>>>> Complexity: grid = 1.00222
>>>>> Coarse grid solver -- level -------------------------------
>>>>> KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
>>>>> type: bjacobi
>>>>> number of blocks = 1
>>>>> Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
>>>>> KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=1, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
>>>>> type: lu
>>>>> out-of-place factorization
>>>>> tolerance for zero pivot 2.22045e-14
>>>>> using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
>>>>> matrix ordering: nd
>>>>> factor fill ratio given 5., needed 1.
>>>>> Factored matrix follows:
>>>>> Mat Object: 1 MPI processes
>>>>> type: seqaij
>>>>> rows=8, cols=8
>>>>> package used to perform factorization: petsc
>>>>> total: nonzeros=56, allocated nonzeros=56
>>>>> using I-node routines: found 3 nodes, limit used is 5
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: seqaij
>>>>> rows=8, cols=8
>>>>> total: nonzeros=56, allocated nonzeros=56
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node routines: found 3 nodes, limit used is 5
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=8, cols=8
>>>>> total: nonzeros=56, allocated nonzeros=56
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using nonscalable MatPtAP() implementation
>>>>> using I-node (on process 0) routines: found 3 nodes, limit used is 5
>>>>> Down solver (pre-smoother) on level 1 -------------------------------
>>>>> KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
>>>>> type: chebyshev
>>>>> eigenvalue estimates used: min = 0.0998145, max = 1.09796
>>>>> eigenvalues estimate via gmres min 0.00156735, max 0.998145
>>>>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>>>>> KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes
>>>>> type: gmres
>>>>> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
>>>>> happy breakdown tolerance 1e-30
>>>>> maximum iterations=10, initial guess is zero
>>>>> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using PRECONDITIONED norm type for convergence test
>>>>> estimating eigenvalues using noisy right hand side
>>>>> maximum iterations=2, nonzero initial guess
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
>>>>> type: sor
>>>>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=480, cols=480
>>>>> total: nonzeros=25200, allocated nonzeros=25200
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 160 nodes, limit used is 5
>>>>> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=480, cols=480
>>>>> total: nonzeros=25200, allocated nonzeros=25200
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 160 nodes, limit used is 5
>>>>> KSP solver for S = A11 - A10 inv(A00) A01
>>>>> KSP Object: (fieldsplit_1_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_1_) 1 MPI processes
>>>>> type: bjacobi
>>>>> number of blocks = 1
>>>>> Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
>>>>> KSP Object: (fieldsplit_1_sub_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_1_sub_) 1 MPI processes
>>>>> type: bjacobi
>>>>> number of blocks = 1
>>>>> Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
>>>>> KSP Object: (fieldsplit_1_sub_sub_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_1_sub_sub_) 1 MPI processes
>>>>> type: ilu
>>>>> out-of-place factorization
>>>>> 0 levels of fill
>>>>> tolerance for zero pivot 2.22045e-14
>>>>> matrix ordering: natural
>>>>> factor fill ratio given 1., needed 1.
>>>>> Factored matrix follows:
>>>>> Mat Object: 1 MPI processes
>>>>> type: seqaij
>>>>> rows=144, cols=144
>>>>> package used to perform factorization: petsc
>>>>> total: nonzeros=240, allocated nonzeros=240
>>>>> not using I-node routines
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: seqaij
>>>>> rows=144, cols=144
>>>>> total: nonzeros=240, allocated nonzeros=240
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> not using I-node routines
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=144, cols=144
>>>>> total: nonzeros=240, allocated nonzeros=240
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> not using I-node (on process 0) routines
>>>>> linear system matrix followed by preconditioner matrix:
>>>>> Mat Object: (fieldsplit_1_) 1 MPI processes
>>>>> type: schurcomplement
>>>>> rows=144, cols=144
>>>>> Schur complement A11 - A10 inv(A00) A01
>>>>> A11
>>>>> Mat Object: (fieldsplit_1_) 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=144, cols=144
>>>>> total: nonzeros=240, allocated nonzeros=240
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> not using I-node (on process 0) routines
>>>>> A10
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=144, cols=480
>>>>> total: nonzeros=48, allocated nonzeros=48
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 74 nodes, limit used is 5
>>>>> KSP of A00
>>>>> KSP Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: gamg
>>>>> type is MULTIPLICATIVE, levels=2 cycles=v
>>>>> Cycles per PCApply=1
>>>>> Using externally compute Galerkin coarse grid matrices
>>>>> GAMG specific options
>>>>> Threshold for dropping small values in graph on each level =
>>>>> Threshold scaling factor for each level not specified = 1.
>>>>> AGG specific options
>>>>> Symmetric graph false
>>>>> Number of levels to square graph 1
>>>>> Number smoothing steps 1
>>>>> Complexity: grid = 1.00222
>>>>> Coarse grid solver -- level -------------------------------
>>>>> KSP Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=10000, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_mg_coarse_) 1 MPI processes
>>>>> type: bjacobi
>>>>> number of blocks = 1
>>>>> Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
>>>>> KSP Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
>>>>> type: preonly
>>>>> maximum iterations=1, initial guess is zero
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_mg_coarse_sub_) 1 MPI processes
>>>>> type: lu
>>>>> out-of-place factorization
>>>>> tolerance for zero pivot 2.22045e-14
>>>>> using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
>>>>> matrix ordering: nd
>>>>> factor fill ratio given 5., needed 1.
>>>>> Factored matrix follows:
>>>>> Mat Object: 1 MPI processes
>>>>> type: seqaij
>>>>> rows=8, cols=8
>>>>> package used to perform factorization: petsc
>>>>> total: nonzeros=56, allocated nonzeros=56
>>>>> using I-node routines: found 3 nodes, limit used is 5
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: seqaij
>>>>> rows=8, cols=8
>>>>> total: nonzeros=56, allocated nonzeros=56
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node routines: found 3 nodes, limit used is 5
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=8, cols=8
>>>>> total: nonzeros=56, allocated nonzeros=56
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using nonscalable MatPtAP() implementation
>>>>> using I-node (on process 0) routines: found 3 nodes, limit used is 5
>>>>> Down solver (pre-smoother) on level 1 -------------------------------
>>>>> KSP Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
>>>>> type: chebyshev
>>>>> eigenvalue estimates used: min = 0.0998145, max = 1.09796
>>>>> eigenvalues estimate via gmres min 0.00156735, max 0.998145
>>>>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>>>>> KSP Object: (fieldsplit_0_mg_levels_1_esteig_) 1 MPI processes
>>>>> type: gmres
>>>>> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
>>>>> happy breakdown tolerance 1e-30
>>>>> maximum iterations=10, initial guess is zero
>>>>> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using PRECONDITIONED norm type for convergence test
>>>>> estimating eigenvalues using noisy right hand side
>>>>> maximum iterations=2, nonzero initial guess
>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>> left preconditioning
>>>>> using NONE norm type for convergence test
>>>>> PC Object: (fieldsplit_0_mg_levels_1_) 1 MPI processes
>>>>> type: sor
>>>>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=480, cols=480
>>>>> total: nonzeros=25200, allocated nonzeros=25200
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 160 nodes, limit used is 5
>>>>> Up solver (post-smoother) same as down solver (pre-smoother)
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: (fieldsplit_0_) 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=480, cols=480
>>>>> total: nonzeros=25200, allocated nonzeros=25200
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 160 nodes, limit used is 5
>>>>> A01
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=480, cols=144
>>>>> total: nonzeros=48, allocated nonzeros=48
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 135 nodes, limit used is 5
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=144, cols=144
>>>>> total: nonzeros=240, allocated nonzeros=240
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> not using I-node (on process 0) routines
>>>>> linear system matrix = precond matrix:
>>>>> Mat Object: 1 MPI processes
>>>>> type: mpiaij
>>>>> rows=624, cols=624
>>>>> total: nonzeros=25536, allocated nonzeros=25536
>>>>> total number of mallocs used during MatSetValues calls=0
>>>>> using I-node (on process 0) routines: found 336 nodes, limit used is 5
>>>>>
>>>>>
>>>>> Thanks,
>>>>> Xiaofeng
>>>>>
>>>>>
>>>>>
>>>>>> On Jun 17, 2025, at 19:05, Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>> wrote:
>>>>>>
>>>>>> And don't use -pc_gamg_parallel_coarse_grid_solver
>>>>>> You can use that in production but for debugging use -mg_coarse_pc_type svd
>>>>>> Also, use -options_left and remove anything that is not used.
>>>>>> (I am puzzled, I see -pc_type gamg not -pc_type fieldsplit)
>>>>>>
>>>>>> Mark
>>>>>>
>>>>>>
>>>>>> On Mon, Jun 16, 2025 at 6:40 AM Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>>>>>>> On Sun, Jun 15, 2025 at 9:46 PM hexioafeng <hexiaofeng at buaa.edu.cn <mailto:hexiaofeng at buaa.edu.cn>> wrote:
>>>>>>>> Hello,
>>>>>>>>
>>>>>>>> Here are the options and outputs:
>>>>>>>>
>>>>>>>> options:
>>>>>>>>
>>>>>>>> -ksp_type cg -pc_type gamg -pc_gamg_parallel_coarse_grid_solver -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp -fieldsplit_1_mat_schur_complement_ainv_type lump -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly -fieldsplit_0_pc_type gamg -fieldsplit_0_mg_coarse_pc_type_type svd -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi -fieldsplit_1_sub_pc_type sor -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual -fieldsplit_0_mg_levels_ksp_converged_reason -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason
>>>>>>>
>>>>>>> This option was wrong:
>>>>>>>
>>>>>>> -fieldsplit_0_mg_coarse_pc_type_type svd
>>>>>>>
>>>>>>> from the output, we can see that it should have been
>>>>>>>
>>>>>>> -fieldsplit_0_mg_coarse_sub_pc_type_type svd
>>>>>>>
>>>>>>> THanks,
>>>>>>>
>>>>>>> Matt
>>>>>>>
>>>>>>>> output:
>>>>>>>>
>>>>>>>> 0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>>> Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0
>>>>>>>> PC failed due to SUBPC_ERROR
>>>>>>>> KSP Object: 1 MPI processes
>>>>>>>> type: cg
>>>>>>>> maximum iterations=200, initial guess is zero
>>>>>>>> tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30
>>>>>>>> left preconditioning
>>>>>>>> using UNPRECONDITIONED norm type for convergence test
>>>>>>>> PC Object: 1 MPI processes
>>>>>>>> type: gamg
>>>>>>>> type is MULTIPLICATIVE, levels=2 cycles=v
>>>>>>>> Cycles per PCApply=1
>>>>>>>> Using externally compute Galerkin coarse grid matrices
>>>>>>>> GAMG specific options
>>>>>>>> Threshold for dropping small values in graph on each level =
>>>>>>>> Threshold scaling factor for each level not specified = 1.
>>>>>>>> AGG specific options
>>>>>>>> Symmetric graph false
>>>>>>>> Number of levels to square graph 1
>>>>>>>> Number smoothing steps 1
>>>>>>>> Complexity: grid = 1.00176
>>>>>>>> Coarse grid solver -- level -------------------------------
>>>>>>>> KSP Object: (mg_coarse_) 1 MPI processes
>>>>>>>> type: preonly
>>>>>>>> maximum iterations=10000, initial guess is zero
>>>>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>>>>> left preconditioning
>>>>>>>> using NONE norm type for convergence test
>>>>>>>> PC Object: (mg_coarse_) 1 MPI processes
>>>>>>>> type: bjacobi
>>>>>>>> number of blocks = 1
>>>>>>>> Local solver is the same for all blocks, as in the following KSP and PC objects on rank 0:
>>>>>>>> KSP Object: (mg_coarse_sub_) 1 MPI processes
>>>>>>>> type: preonly
>>>>>>>> maximum iterations=1, initial guess is zero
>>>>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>>>>> left preconditioning
>>>>>>>> using NONE norm type for convergence test
>>>>>>>> PC Object: (mg_coarse_sub_) 1 MPI processes
>>>>>>>> type: lu
>>>>>>>> out-of-place factorization
>>>>>>>> tolerance for zero pivot 2.22045e-14
>>>>>>>> using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
>>>>>>>> matrix ordering: nd
>>>>>>>> factor fill ratio given 5., needed 1.
>>>>>>>> Factored matrix follows:
>>>>>>>> Mat Object: 1 MPI processes
>>>>>>>> type: seqaij
>>>>>>>> rows=7, cols=7
>>>>>>>> package used to perform factorization: petsc
>>>>>>>> total: nonzeros=45, allocated nonzeros=45
>>>>>>>> using I-node routines: found 3 nodes, limit used is 5
>>>>>>>> linear system matrix = precond matrix:
>>>>>>>> Mat Object: 1 MPI processes
>>>>>>>> type: seqaij
>>>>>>>> rows=7, cols=7
>>>>>>>> total: nonzeros=45, allocated nonzeros=45
>>>>>>>> total number of mallocs used during MatSetValues calls=0
>>>>>>>> using I-node routines: found 3 nodes, limit used is 5
>>>>>>>> linear system matrix = precond matrix:
>>>>>>>> Mat Object: 1 MPI processes
>>>>>>>> type: mpiaij
>>>>>>>> rows=7, cols=7
>>>>>>>> total: nonzeros=45, allocated nonzeros=45
>>>>>>>> total number of mallocs used during MatSetValues calls=0
>>>>>>>> using nonscalable MatPtAP() implementation
>>>>>>>> using I-node (on process 0) routines: found 3 nodes, limit used is 5
>>>>>>>> Down solver (pre-smoother) on level 1 -------------------------------
>>>>>>>> KSP Object: (mg_levels_1_) 1 MPI processes
>>>>>>>> type: chebyshev
>>>>>>>> eigenvalue estimates used: min = 0., max = 0.
>>>>>>>> eigenvalues estimate via gmres min 0., max 0.
>>>>>>>> eigenvalues estimated using gmres with translations [0. 0.1; 0. 1.1]
>>>>>>>> KSP Object: (mg_levels_1_esteig_) 1 MPI processes
>>>>>>>> type: gmres
>>>>>>>> restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
>>>>>>>> happy breakdown tolerance 1e-30
>>>>>>>> maximum iterations=10, initial guess is zero
>>>>>>>> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
>>>>>>>> left preconditioning
>>>>>>>> using PRECONDITIONED norm type for convergence test
>>>>>>>> PC Object: (mg_levels_1_) 1 MPI processes
>>>>>>>> type: sor
>>>>>>>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1.
>>>>>>>> linear system matrix = precond matrix:
>>>>>>>> Mat Object: 1 MPI processes
>>>>>>>> type: mpiaij
>>>>>>>> rows=624, cols=624
>>>>>>>> total: nonzeros=25536, allocated nonzeros=25536
>>>>>>>> total number of mallocs used during MatSetValues calls=0
>>>>>>>> using I-node (on process 0) routines: found 336 nodes, limit used is 5
>>>>>>>> estimating eigenvalues using noisy right hand side
>>>>>>>> maximum iterations=2, nonzero initial guess
>>>>>>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>>>>>>>> left preconditioning
>>>>>>>> using NONE norm type for convergence test
>>>>>>>> PC Object: (mg_levels_1_) 1 MPI processes
>>>>>>>> type: sor
>>>>>>>> type = local_symmetric, iterations = 1, local iterations = 1, omega = 1. linear system matrix = precond matrix:
>>>>>>>> Mat Object: 1 MPI processes
>>>>>>>> type: mpiaij
>>>>>>>> rows=624, cols=624
>>>>>>>> total: nonzeros=25536, allocated nonzeros=25536
>>>>>>>> total number of mallocs used during MatSetValues calls=0
>>>>>>>> using I-node (on process 0) routines: found 336 nodes, limit used is 5 Up solver (post-smoother) same as down solver (pre-smoother)
>>>>>>>> linear system matrix = precond matrix:
>>>>>>>> Mat Object: 1 MPI processes
>>>>>>>> type: mpiaij
>>>>>>>> rows=624, cols=624
>>>>>>>> total: nonzeros=25536, allocated nonzeros=25536
>>>>>>>> total number of mallocs used during MatSetValues calls=0
>>>>>>>> using I-node (on process 0) routines: found 336 nodes, limit used is 5
>>>>>>>>
>>>>>>>>
>>>>>>>> Best regards,
>>>>>>>>
>>>>>>>> Xiaofeng
>>>>>>>>
>>>>>>>>
>>>>>>>>> On Jun 14, 2025, at 07:28, Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>> wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Matt,
>>>>>>>>>
>>>>>>>>> Perhaps we should add options -ksp_monitor_debug and -snes_monitor_debug that turn on all possible monitoring for the (possibly) nested solvers and all of their converged reasons also? Note this is not completely trivial because each preconditioner will have to supply its list based on the current solver options for it.
>>>>>>>>>
>>>>>>>>> Then we won't need to constantly list a big string of problem specific monitor options to ask the user to use.
>>>>>>>>>
>>>>>>>>> Barry
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> On Jun 13, 2025, at 9:09 AM, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>>>>>>>>>>
>>>>>>>>>> On Thu, Jun 12, 2025 at 10:55 PM hexioafeng <hexiaofeng at buaa.edu.cn <mailto:hexiaofeng at buaa.edu.cn>> wrote:
>>>>>>>>>>> Dear authors,
>>>>>>>>>>>
>>>>>>>>>>> I tried -pc_type game -pc_gamg_parallel_coarse_grid_solver and -pc_type field split -pc_fieldsplit_detect_saddle_point -fieldsplit_0_ksp_type pronely -fieldsplit_0_pc_type game -fieldsplit_0_mg_coarse_pc_type sad -fieldsplit_1_ksp_type pronely -fieldsplit_1_pc_type Jacobi _fieldsplit_1_sub_pc_type for , both options got the KSP_DIVERGE_PC_FAILED error.
>>>>>>>>>>
>>>>>>>>>> With any question about convergence, we need to see the output of
>>>>>>>>>>
>>>>>>>>>> -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual -fieldsplit_0_mg_levels_ksp_converged_reason -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason
>>>>>>>>>>
>>>>>>>>>> and all the error output.
>>>>>>>>>>
>>>>>>>>>> Thanks,
>>>>>>>>>>
>>>>>>>>>> Matt
>>>>>>>>>>
>>>>>>>>>>> Thanks,
>>>>>>>>>>>
>>>>>>>>>>> Xiaofeng
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>> On Jun 12, 2025, at 20:50, Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> On Thu, Jun 12, 2025 at 8:44 AM Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>>>>>>>>>>>>> On Thu, Jun 12, 2025 at 4:58 AM Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>> wrote:
>>>>>>>>>>>>>> Adding this to the PETSc mailing list,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On Thu, Jun 12, 2025 at 3:43 AM hexioafeng <hexiaofeng at buaa.edu.cn <mailto:hexiaofeng at buaa.edu.cn>> wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Dear Professor,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I hope this message finds you well.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I am an employee at a CAE company and a heavy user of the PETSc library. I would like to thank you for your contributions to PETSc and express my deep appreciation for your work.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Recently, I encountered some difficulties when using PETSc to solve structural mechanics problems with Lagrange multiplier constraints. After searching extensively online and reviewing several papers, I found your previous paper titled "Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics" seems to be the most relevant and helpful.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The stiffness matrix I'm working with, K, is a block saddle-point matrix of the form (A00 A01; A10 0), where A00 is singular—just as described in your paper, and different from many other articles . I have a few questions regarding your work and would greatly appreciate your insights:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 1. Is the AMG/KKT method presented in your paper available in PETSc? I tried using CG+GAMG directly but received a KSP_DIVERGED_PC_FAILED error. I also attempted to use CG+PCFIELDSPLIT with the following options:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> No
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> -pc_type fieldsplit -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly -fieldsplit_0_pc_type gamg -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Unfortunately, this also resulted in a KSP_DIVERGED_PC_FAILED error. Do you have any suggestions?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 2. In your paper, you compare the method with Uzawa-type approaches. To my understanding, Uzawa methods typically require A00 to be invertible. How did you handle the singularity of A00 to construct an M-matrix that is invertible?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You add a regularization term like A01 * A10 (like springs). See the paper or any reference to augmented lagrange or Uzawa
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 3. Can i implement the AMG/KKT method in your paper using existing AMG APIs? Implementing a production-level AMG solver from scratch would be quite challenging for me, so I’m hoping to utilize existing AMG interfaces within PETSc or other packages.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You can do Uzawa and make the regularization matrix with matrix-matrix products. Just use AMG for the A00 block.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 4. For saddle-point systems where A00 is singular, can you recommend any more robust or efficient solutions? Alternatively, are you aware of any open-source software packages that can handle such cases out-of-the-box?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> No, and I don't think PETSc can do this out-of-the-box, but others may be able to give you a better idea of what PETSc can do.
>>>>>>>>>>>>>> I think PETSc can do Uzawa or other similar algorithms but it will not do the regularization automatically (it is a bit more complicated than just A01 * A10)
>>>>>>>>>>>>>
>>>>>>>>>>>>> One other trick you can use is to have
>>>>>>>>>>>>>
>>>>>>>>>>>>> -fieldsplit_0_mg_coarse_pc_type svd
>>>>>>>>>>>>>
>>>>>>>>>>>>> This will use SVD on the coarse grid of GAMG, which can handle the null space in A00 as long as the prolongation does not put it back in. I have used this for the Laplacian with Neumann conditions and for freely floating elastic problems.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Good point.
>>>>>>>>>>>> You can also use -pc_gamg_parallel_coarse_grid_solver to get GAMG to use a on level iterative solver for the coarse grid.
>>>>>>>>>>>>
>>>>>>>>>>>>> Thanks,
>>>>>>>>>>>>>
>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks,
>>>>>>>>>>>>>> Mark
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Thank you very much for taking the time to read my email. Looking forward to hearing from you.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Sincerely,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Xiaofeng He
>>>>>>>>>>>>>>> -----------------------------------------------------
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Research Engineer
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Internet Based Engineering, Beijing, China
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> --
>>>>>>>>>>>>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>>>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T_PyxNcNQ$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!f-YJSzthRa7atIa1xs1GPHW53hGIqSenvp1eO2kDsSyf4jv1_Vp0kL9Lg8pyyPeG8al4Im8XlLqGRHw1FxYh$>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>
>>>>>>>>>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T_PyxNcNQ$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!f-YJSzthRa7atIa1xs1GPHW53hGIqSenvp1eO2kDsSyf4jv1_Vp0kL9Lg8pyyPeG8al4Im8XlLqGRHw1FxYh$>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>>>>>>> -- Norbert Wiener
>>>>>>>
>>>>>>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T_PyxNcNQ$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!dYETsi-moODALE1tmLrk5pxFKF9l552nNiC0cBgsCQ9ebugJWHtsNYa0QBS5Gmws9J_VC_Iec3Nx0c1FgNl1$>
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T_PyxNcNQ$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T9NU14KKw$ >
>>>
>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>> -- Norbert Wiener
>>
>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T_PyxNcNQ$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!aDVdbJudFjso7jHS1DFJhOOh76fS5qSwrvzSb1t5hCFZ2rdj3XFfsHLlDjne7FWFjeweHRXBAbd-5KPlb0st3T9NU14KKw$ >
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