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Add block-diagonal PDE-control preconditioner

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nested_matrix_type
jalmerol 2 days ago
parent 9e77b53c06
commit 157d5ea6ce
2 changed files with 117 additions and 1 deletions
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100
prec/psb_d_nestedprec.f90
Unescape Escape View File

@ -64,6 +64,7 @@ module psb_d_nestedprec
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_upper_ = 6
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_full_ = 7
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_pde_control_ = 8
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_pde_control_diag_ = 9
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_a22_ = 1
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_mf_ = 2
integer(psb_ipk_), parameter, private :: psb_d_nested_schur_selfp_ = 3
@ -144,6 +145,7 @@ module psb_d_nestedprec
& psb_d_nested_clear_built, psb_d_nested_valid_block_solve, &
& psb_d_nested_get_field_block_ptype, psb_d_nested_field_solve, &
& psb_d_nested_apply_schur, psb_d_nested_apply_pde_control_schur, &
& psb_d_nested_apply_pde_control_diag, &
& psb_d_nested_replay_field_options, &
& psb_d_nested_append_iopt, psb_d_nested_append_ropt, &
& psb_d_nested_append_copt, psb_d_nested_schur_action, &
@ -325,6 +327,12 @@ contains
prec%composition_name = 'SCHUR_PDE_CONTROL'
prec%schur_solve = psb_d_nested_schur_mf_
prec%schur_solve_name = 'MATRIX_FREE'
case ('SCHUR_PDE_CONTROL_DIAG','PDE_CONTROL_DIAG', &
& 'BLOCK_DIAG_SCHUR','SCHUR_BLOCK_DIAG')
prec%composition = psb_d_nested_schur_pde_control_diag_
prec%composition_name = 'SCHUR_PDE_CONTROL_DIAG'
prec%schur_solve = psb_d_nested_schur_mf_
prec%schur_solve_name = 'MATRIX_FREE'
case default
info = psb_err_invalid_input_
end select
@ -942,6 +950,8 @@ contains
call psb_d_nested_apply_schur(prec, x, z, desc_data, info)
case (psb_d_nested_schur_pde_control_)
call psb_d_nested_apply_pde_control_schur(prec, x, z, desc_data, info)
case (psb_d_nested_schur_pde_control_diag_)
call psb_d_nested_apply_pde_control_diag(prec, x, z, desc_data, info)
case default
info = psb_err_invalid_input_
call psb_errpush(info, name, a_err='unknown composition')
@ -2079,6 +2089,96 @@ contains
deallocate(q, r, zc, p, ap)
end subroutine psb_d_nested_pde_control_schur_solve
! Apply the block-diagonal three-field PDE-control preconditioner
!
! diag(B1, B2, BS),
!
! where B1 and B2 are the configured field solves and BS is the configured
! field-3 Schur solve. Unlike SCHUR_PDE_CONTROL, this composition performs
! no lower or upper coupling corrections. The composition is therefore
! structurally symmetric; MINRES additionally requires B1, B2, and BS to be
! fixed symmetric positive-definite operators.
subroutine psb_d_nested_apply_pde_control_diag(prec, x, z, desc_data, info)
class(psb_d_nested_prec_type), intent(inout) :: prec
real(psb_dpk_), intent(in) :: x(:)
real(psb_dpk_), intent(inout) :: z(:)
type(psb_desc_type), intent(in) :: desc_data
integer(psb_ipk_), intent(out) :: info
real(psb_dpk_), allocatable :: rhs1(:), rhs2(:), rhs3(:), &
& sol1(:), sol2(:), sol3(:), gwork(:)
type(psb_desc_type), pointer :: desc1, desc2, desc3
integer(psb_ipk_) :: ncol1, ncol2, ncol3
info = psb_success_
z(:) = dzero
if (prec%nfields /= 3) then
info = psb_err_invalid_input_
call psb_errpush(info, 'd_nested_apply_pde_diag', &
& a_err='PDE-control block diagonal requires three fields')
return
end if
desc1 => psb_d_nest_get_field_desc(prec%nest_op, 1)
desc2 => psb_d_nest_get_field_desc(prec%nest_op, 2)
desc3 => psb_d_nest_get_field_desc(prec%nest_op, 3)
if ((.not. associated(desc1)) .or. ( .not. associated(desc2)) .or. &
& (.not. associated(desc3))) then
info = psb_err_invalid_mat_state_
call psb_errpush(info, 'd_nested_apply_pde_diag', &
& a_err='missing field descriptor')
return
end if
ncol1 = desc1%get_local_cols()
ncol2 = desc2%get_local_cols()
ncol3 = desc3%get_local_cols()
allocate(rhs1(ncol1), rhs2(ncol2), rhs3(ncol3), sol1(ncol1), &
& sol2(ncol2), sol3(ncol3), gwork(size(z)), stat=info)
if (info /= 0) then
info = psb_err_alloc_dealloc_
call psb_errpush(info, 'd_nested_apply_pde_diag', a_err='field vectors')
return
end if
rhs1(:) = dzero
rhs2(:) = dzero
rhs3(:) = dzero
sol1(:) = dzero
sol2(:) = dzero
sol3(:) = dzero
gwork(:) = dzero
call psb_d_nest_restrict_field(prec%nest_op, 1, x, rhs1, info)
if (info /= psb_success_) goto 100
call psb_d_nest_restrict_field(prec%nest_op, 2, x, rhs2, info)
if (info /= psb_success_) goto 100
call psb_d_nest_restrict_field(prec%nest_op, 3, x, rhs3, info)
if (info /= psb_success_) goto 100
call psb_d_nested_field_solve(prec, 1, rhs1, sol1, info)
if (info /= psb_success_) goto 100
call psb_d_nested_field_solve(prec, 2, rhs2, sol2, info)
if (info /= psb_success_) goto 100
call psb_d_nested_pde_control_schur_solve(prec, rhs3, sol3, gwork, &
& desc_data, info)
if (info /= psb_success_) goto 100
! The factorization path solves T*x3=-r3 because its KKT Schur block is
! -T. A positive-definite block-diagonal preconditioner needs +T^{-1},
! so reverse that sign here.
sol3(:) = -sol3(:)
call psb_d_nest_prolong_field(prec%nest_op, 1, sol1, z, info)
if (info /= psb_success_) goto 100
call psb_d_nest_prolong_field(prec%nest_op, 2, sol2, z, info)
if (info /= psb_success_) goto 100
call psb_d_nest_prolong_field(prec%nest_op, 3, sol3, z, info)
100 continue
deallocate(rhs1, rhs2, rhs3, sol1, sol2, sol3, gwork)
end subroutine psb_d_nested_apply_pde_control_diag
! Apply a three-field PDE-control Schur preconditioner.
! Fields 1 and 2 are grouped into the leading block D=diag(A11,A22);
! field 3 is the Schur field.

18
test/nested/Nested_Preconditioner_Report.md
Unescape Escape View File

@ -848,6 +848,22 @@ For a standard distributed-control KKT matrix such as
this operator is `T = -S`, where `S` is the field-3 KKT Schur complement. `psb_d_nested_pde_control_schur_solve` solves `T x_3 = -r_3` with a matrix-free CG iteration controlled by `SCHUR_MAXIT` and `SCHUR_TOL`. This is important when `A_33 = 0`: the old field-3 diagonal-block approximation cannot precondition the Schur complement, but the matrix-free CG path can still use the actual Schur action.
The `SCHUR_PDE_CONTROL_DIAG` composition applies the block-diagonal action
```text
z_1 = B_1 r_1, z_2 = B_2 r_2, z_3 = B_S r_3.
```
It reuses the PDE-control Schur solver for field 3 but reverses the KKT Schur
sign so that the third block approximates the positive operator `T^{-1}`.
Unlike `SCHUR_PDE_CONTROL`, it performs no lower or upper coupling corrections.
The composition is therefore structurally symmetric. MINRES also requires
each selected block action to be fixed and SPD; in particular, the
residual-dependent inner CG used by `SCHUR_SOLVE=MATRIX_FREE` is not a fixed
linear preconditioner. A fixed SPD field-3 solve such as the `A33`/identity
fallback is MINRES-compatible, while a future explicit SPD Schur
preconditioner can be attached through the same block-diagonal composition.
## Public Options
The nested preconditioner exposes integer option keys in `psb_d_nestedprec`:
@ -869,7 +885,7 @@ The user-facing string options routed by `psb_d_prec_type_impl.f90` are:
| Option | Type | Values | Scope |
| --- | --- | --- | --- |
| `COMPOSITION`, `NEST_COMPOSITION` | character | `ADDITIVE`, `DIAGONAL`, `MULTIPLICATIVE`, `SYMMETRIC_MULTIPLICATIVE`, `SCHUR_LOWER`, `SCHUR_UPPER`, `SCHUR_FULL`, `SCHUR_PDE_CONTROL` | global |
| `COMPOSITION`, `NEST_COMPOSITION` | character | `ADDITIVE`, `DIAGONAL`, `MULTIPLICATIVE`, `SYMMETRIC_MULTIPLICATIVE`, `SCHUR_LOWER`, `SCHUR_UPPER`, `SCHUR_FULL`, `SCHUR_PDE_CONTROL`, `SCHUR_PDE_CONTROL_DIAG` | global |
| `BLOCK_SOLVE`, `NEST_BLOCK_SOLVE` | character | `DIAG`, `BJAC`, `NONE` | global or `idx` field |
| `SCHUR_SOLVE`, `NEST_SCHUR_SOLVE` | character | `A22`, `A33`, `MATRIX_FREE`, `SELFP`, `SELF` | global |
| `SCHUR_MAXIT`, `NEST_SCHUR_MAXIT` | integer | nonnegative iteration count | global |

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