7.3.3. Tpetra Preconditioners

7.3.3.1. Expert Teko Preconditioner

Scope: Expert Belos Solver, Flexible Gmres Solver, Gmres Solver
Summary: Use a teko preconditioner with parameters specified in an XML file.

begin Expert Teko Preconditioner

   Define Matrix Subblock Number = number Dof = dof name

   Inverse Method {=} value

   Xml File {=} value

end Expert Teko Preconditioner

7.3.3.1.1. Line Commands

Define Matrix Subblock

Syntax: Define Matrix Subblock Number = number Dof = dof name
Summary: Define the dof associated with a matrix subblock for block preconditioning.
Description: Define the matrix subblock number and the equation to apply to that subblock. Please see https://trilinos.github.io/teko.html for more details

Parameter	Value	Default
number	integer	–
dof name	string	–

Inverse Method

Syntax: Inverse Method {=} value
Summary: Supply the name of the inverse method.
Description: The name of the inverse method must correspond to the name of a parameter list specified in the teko XML file. Please see https://trilinos.github.io/teko.html for more details

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	string	–

Xml File

Syntax: Xml File {=} value
Summary: Supply the name of an XML file containing a teko parameter list.
Description: The supplied XML file must contain a ParameterList with a valid teko parameter list. Please see https://trilinos.github.io/teko.html for more details

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	string	–

7.3.3.2. Teko Preconditioner

Scope: Expert Belos Solver, Flexible Gmres Solver, Gmres Solver, Teko Block Preconditioner
Summary: Use a teko preconditioner with parameters specified through the input deck.

begin Teko Preconditioner

   Define Matrix Subblock Number = number Dof = dof name

   begin Block Gauss-Seidel Solver
   end

   begin Block Jacobi Solver
   end

   begin Hierarchical Block Gauss-Seidel Solver
   end

   begin Simple Solver
   end

   begin Teko Block Preconditioner Solver Name
   end

   begin Teko Block Solver Solver Name
   end

   begin Teko Subblock Preconditioner Solver Name
   end

   begin Teko Subblock Solver Solver Name
   end

end Teko Preconditioner

7.3.3.2.1. Line Commands

Define Matrix Subblock

Syntax: Define Matrix Subblock Number = number Dof = dof name
Summary: Define the dof associated with a matrix subblock for block preconditioning.
Description: Define the matrix subblock number and the equation to apply to that subblock. Please see https://trilinos.github.io/teko.html for more details

Parameter	Value	Default
number	integer	–
dof name	string	–

7.3.3.3. Teko Subblock Solver

Scope: Teko Preconditioner
Summary: Define a solver to be used for one or more subblock(s)

begin Teko Subblock Solver Solver Name

   begin Bicgstab Solver
   end

   begin Cg Solver
   end

   begin Expert Belos Solver
   end

   begin Flexible Gmres Solver
   end

   begin Gcrodr Solver
   end

   begin Gmres Solver
   end

   begin Klu2 Solver
   end

   begin Poly Solver
   end

   begin Preset Solver
   end

   begin Superlu Solver
   end

   begin Umfpack Solver
   end

end Teko Subblock Solver Solver Name

7.3.3.4. Teko Subblock Preconditioner

Scope: Teko Preconditioner
Summary: Define a preconditioner to be used to approximate the inverse of one or more subblock(s)

begin Teko Subblock Preconditioner Solver Name

   begin Dd-Ilu Preconditioner
   end

   begin Dd-Ilut Preconditioner
   end

   begin Dd-Parilut Preconditioner
   end

   begin Expert Ifpack2 Preconditioner
   end

   begin Fastilu Preconditioner
   end

   begin Jacobi Preconditioner
   end

   begin Muelu Preconditioner
   end

   begin Preset Preconditioner
   end

   begin Sgs Preconditioner
   end

   begin Sgs2 Preconditioner
   end

end Teko Subblock Preconditioner Solver Name

7.3.3.5. Teko Block Solver

Scope: Teko Preconditioner
Summary: Define a solver to be used to approximate the inverse of a set of subblocks in a hierarchical block Gauss-Seidel scheme.

begin Teko Block Solver Solver Name

   begin Expert Belos Solver
   end

   begin Flexible Gmres Solver
   end

   begin Gmres Solver
   end

end Teko Block Solver Solver Name

7.3.3.6. Teko Block Preconditioner

Scope: Teko Preconditioner
Summary: Define a preconditioner to be used to approximate the inverse of a set of subblocks in a hierarchical block Gauss-Seidel scheme.

begin Teko Block Preconditioner Solver Name

   begin Teko Preconditioner
   end

end Teko Block Preconditioner Solver Name

7.3.3.7. Hierarchical Block Gauss-Seidel Solver

Scope: Teko Preconditioner
Summary: Use a Hierarchical Block Gauss-Seidel solver inside a Teko preconditioner.

begin Hierarchical Block Gauss-Seidel Solver

   Use Block Inverse block inverse For Hierarchical Block number

   Use Subblocks subblocks... For Hierarchical Block number

   Use Upper Triangle {=} {false | true}

end Hierarchical Block Gauss-Seidel Solver

7.3.3.7.1. Line Commands

Use Block Inverse

Syntax: Use Block Inverse block inverse For Hierarchical Block number
Summary: Define the block solver to be used for a given hierarchical block.

Parameter	Value	Default
block inverse	string	–
number	integer	–

Use Subblocks

Syntax: Use Subblocks subblocks… For Hierarchical Block number
Summary: Map subblock(s) to a hierarchical block, which is a set containing one or more blocks.

Parameter	Value	Default
subblocks	integer…	–
number	integer	–

Use Upper Triangle

Syntax: Use Upper Triangle {=} {false | true}
Summary: Define whether to use upper triangular hierarchical block Gauss-Seidel

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{false \| true}	FALSE

7.3.3.8. Muelu Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a MueLu preconditioner.

begin Muelu Preconditioner

   Xml File {=} value

end Muelu Preconditioner

7.3.3.8.1. Line Commands

Xml File

Syntax: Xml File {=} value
Summary: Supply the name of an XML file containing a MueLu parameter list.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	string	–

7.3.3.9. Jacobi Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a Jacobi preconditioner.

begin Jacobi Preconditioner

   Damping Factor {=} value

   Number Of Sweeps {=} value

end Jacobi Preconditioner

7.3.3.9.1. Line Commands

Damping Factor

Syntax: Damping Factor {=} value
Summary: Set the relaxation damping factor.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	1

Number Of Sweeps

Syntax: Number Of Sweeps {=} value
Summary: Set the number of relaxation sweeps to perform.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	3

7.3.3.10. Sgs2 Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a Two-stage symmetric Gauss-Seidel preconditioner.

begin Sgs2 Preconditioner

   Damping Factor {=} value

   Number Of Sweeps {=} value

end Sgs2 Preconditioner

7.3.3.10.1. Line Commands

Damping Factor

Syntax: Damping Factor {=} value
Summary: Set the relaxation damping factor.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	1

Number Of Sweeps

Syntax: Number Of Sweeps {=} value
Summary: Set the number of relaxation sweeps to perform.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	3

7.3.3.11. Sgs Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a symmetric Gauss-Seidel preconditioner.

begin Sgs Preconditioner

   Damping Factor {=} value

   Number Of Sweeps {=} value

end Sgs Preconditioner

7.3.3.11.1. Line Commands

Damping Factor

Syntax: Damping Factor {=} value
Summary: Set the relaxation damping factor.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	1

Number Of Sweeps

Syntax: Number Of Sweeps {=} value
Summary: Set the number of relaxation sweeps to perform.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	3

7.3.3.12. Dd-Ilu Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a domain-decomposition ILU(k) preconditioner.

begin Dd-Ilu Preconditioner

   Fill Level {=} value

   Number Of Gpu Streams {=} value

   Reordering {=} {metis | off | on | rcm}

   Subdomain Overlap Level {=} value

   Use Thread Parallel Implementation {=} {off | on}

end Dd-Ilu Preconditioner

7.3.3.12.1. Line Commands

Fill Level

Syntax: Fill Level {=} value
Summary: Set the level of fill, k, for ILU(k).

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

Number Of Gpu Streams

Syntax: Number Of Gpu Streams {=} value
Summary: DEVELOPER COMMAND: Set the number of GPU streams to use in GPU builds.
Description: On each MPI rank the local matrix will be further decomposed into this number of diagonal sub-matrices and the ILU preconditioner will be applied to each diagonal sub-matrix in parallel using GPU streams.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

Reordering

Syntax: Reordering {=} {metis | off | on | rcm}
Summary: Choose the reordering method to apply to the local matrices.
Description: By default reordering is ON which corresponds to the reordering method that typically performs best. In CPU builds the default reorder method is RCM, but in GPU builds it is METIS. METIS usually requires slightly higher iteration counts than RCM, but provides more parallelism for ILU on the GPU and usually runs faster on those machines as a result. If necessary REORDERING = RCM|METIS can be used to ensure the same reordering method is used regardless of machine type.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{metis \| off \| on \| rcm}	ON

Subdomain Overlap Level

Syntax: Subdomain Overlap Level {=} value
Summary: Set the level of subdomain overlap used in constructing the preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

Use Thread Parallel Implementation

Syntax: Use Thread Parallel Implementation {=} {off | on}
Summary: Control whether or not to use the thread parallel ILU implementation from Kokkos-Kernels.
Description: This will default to the appropriate value based on the platform Aria is built for, but in rare cases it may be helpful to disable the thread parallel implementation in a GPU build for debugging purposes.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{off \| on}	ON

7.3.3.13. Dd-Ilut Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a domain-decomposition ILUT preconditioner.

begin Dd-Ilut Preconditioner

   Drop Tolerance {=} value

   Fill Fraction {=} value

   Reordering {=} {metis | off | on | rcm}

   Subdomain Overlap Level {=} value

end Dd-Ilut Preconditioner

7.3.3.13.1. Line Commands

Drop Tolerance

Syntax: Drop Tolerance {=} value
Summary: Set the drop tolerance for ilut.
Description: Off-diagonal entries of the incomplete factorization smaller than the specified tolerance will be dropped.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	0

Fill Fraction

Syntax: Fill Fraction {=} value
Summary: Set the fill fraction for ilut.
Description: This parameter controls the number of nonzero entries that are kept in each row of the incomplete factorization. Larger values will use more memory and runtime, but may result in a more effective preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	1

Reordering

Syntax: Reordering {=} {metis | off | on | rcm}
Summary: Choose the reordering method to apply to the local matrices.
Description: By default reordering is ON which corresponds to the reordering method that typically performs best. In CPU builds the default reorder method is RCM, but in GPU builds it is METIS. METIS usually requires slightly higher iteration counts than RCM, but provides more parallelism for ILU on the GPU and usually runs faster on those machines as a result. If necessary REORDERING = RCM|METIS can be used to ensure the same reordering method is used regardless of machine type.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{metis \| off \| on \| rcm}	ON

Subdomain Overlap Level

Syntax: Subdomain Overlap Level {=} value
Summary: Set the level of subdomain overlap used in constructing the preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

7.3.3.14. Dd-Parilut Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a domain-decomposition ParILUT preconditioner.
Description: ParILUT is similar to ILUT, but uses an iterative approach to compute the approximate L and U factors in order to enable fine grained parallelism that can improve performance on GPUs.

begin Dd-Parilut Preconditioner

   Fill Fraction {=} value

   Maximum Iterations {=} value

   Reordering {=} {metis | off | on | rcm}

   Subdomain Overlap Level {=} value

end Dd-Parilut Preconditioner

7.3.3.14.1. Line Commands

Fill Fraction

Syntax: Fill Fraction {=} value
Summary: Set the fill level for par_ilut.
Description: This parameter controls the number of nonzero entries that are kept in each row of the incomplete factorization. Larger values will use more memory and runtime, but may result in a more effective preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	1

Maximum Iterations

Syntax: Maximum Iterations {=} value
Summary: Set the maximum number of iterations of the par_ilut algorithm.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	5

Reordering

Syntax: Reordering {=} {metis | off | on | rcm}
Summary: Choose the reordering method to apply to the local matrices.
Description: By default reordering is ON which corresponds to the reordering method that typically performs best. In CPU builds the default reorder method is RCM, but in GPU builds it is METIS. METIS usually requires slightly higher iteration counts than RCM, but provides more parallelism for ILU on the GPU and usually runs faster on those machines as a result. If necessary REORDERING = RCM|METIS can be used to ensure the same reordering method is used regardless of machine type.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{metis \| off \| on \| rcm}	ON

Subdomain Overlap Level

Syntax: Subdomain Overlap Level {=} value
Summary: Set the level of subdomain overlap used in constructing the preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

7.3.3.15. Fastilu Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a domain-decomposition FastILU(k) preconditioner.
Description: FastILU is a beta preconditioner that uses an iterative approximation to the standard DD-ILU preconditioner in order to expose more parallelism for potentially better performance on GPUs.

begin Fastilu Preconditioner

   Damping Factor {=} value

   Fill Level {=} value

   Reordering {=} {metis | off | on | rcm}

   Subdomain Overlap Level {=} value

   Sweeps {=} value

   Triangular Solver Type {=} {fast | standard}

end Fastilu Preconditioner

7.3.3.15.1. Line Commands

Damping Factor

Syntax: Damping Factor {=} value
Summary: Set the damping factor for the FastILU algorithm.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	0.2

Fill Level

Syntax: Fill Level {=} value
Summary: Set the level of fill, k, for FastILU(k).

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

Reordering

Syntax: Reordering {=} {metis | off | on | rcm}
Summary: Choose the reordering method to apply to the local matrices.
Description: By default reordering is ON which corresponds to the reordering method that typically performs best. In CPU builds the default reorder method is RCM, but in GPU builds it is METIS. METIS usually requires slightly higher iteration counts than RCM, but provides more parallelism for ILU on the GPU and usually runs faster on those machines as a result. If necessary REORDERING = RCM|METIS can be used to ensure the same reordering method is used regardless of machine type.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{metis \| off \| on \| rcm}	ON

Subdomain Overlap Level

Syntax: Subdomain Overlap Level {=} value
Summary: Set the level of subdomain overlap used in constructing the preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	0

Sweeps

Syntax: Sweeps {=} value
Summary: Set the number of sweeps for iteratively computing the ILU approximation via the FastILU algorithm.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	integer	5

Triangular Solver Type

Syntax: Triangular Solver Type {=} {fast | standard}
Summary: Set the triangular solver type for FastILU

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{fast \| standard}	Fast

7.3.3.16. Expert Ifpack2 Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use an Ifpack2 preconditioner with parameters specified in an XML file.

begin Expert Ifpack2 Preconditioner

   Xml File {=} value

end Expert Ifpack2 Preconditioner

7.3.3.16.1. Line Commands

Xml File

Syntax: Xml File {=} value
Summary: Supply the name of an XML file containing an Ifpack2 parameter list.
Description: The supplied XML file must contain a ParameterList with a “preconditioner type:” string parameter corresponding to the desired type of Ifpack2 preconditioner as well as any additional parameters for that preconditioner.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	string	–

7.3.3.17. Preset Preconditioner

Scope: Bicgstab Solver, Cg Solver, Expert Belos Solver, Flexible Gmres Solver, Gcrodr Solver, Gmres Solver, Poly Solver, Teko Subblock Preconditioner
Summary: Use a preset preconditioner for a specific linear system type.
Description: The preset preconditioner for a given linear system type is intended to provide reasonable behavior for many problems of that type. If this proves to be insufficient, the user must provide more fine-grained control over preconditioner settings. The equivalent command which produces the preconditioner will be output to the log file, and this may be used as a starting point from which changes for robustness may be made (i.e. increasing Chebyshev degree in a MueLu preconditioner).

begin Preset Preconditioner

   Preconditioner Type {=} {continuity | high_aspect_continuity | multiphysics | scalar_transport | thermal | thermal_multigrid}

end Preset Preconditioner

7.3.3.17.1. Line Commands

Preconditioner Type

Syntax: Preconditioner Type {=} {continuity | high_aspect_continuity | multiphysics | scalar_transport | thermal | thermal_multigrid}
Summary: Set the preset preconditioner type

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{continuity \| high_aspect_continuity \| multiphysics \| scalar_transport \| thermal \| thermal_multigrid}	–

7.3.3.18. Block Gauss-Seidel Solver

Scope: Teko Preconditioner
Summary: Use a Block Gauss-Seidel solver inside a Teko preconditioner.

begin Block Gauss-Seidel Solver

   Use Default Inverse subblock inverse For Subblocks

   Use Inverse subblock inverse For Subblock number

   Use Upper Triangle {=} {false | true}

end Block Gauss-Seidel Solver

7.3.3.18.1. Line Commands

Use Default Inverse

Syntax: Use Default Inverse subblock inverse For Subblocks
Summary: Define a default solver/preconditioner to be used for across subblocks.

Parameter	Value	Default
subblock inverse	string	–

Use Inverse

Syntax: Use Inverse subblock inverse For Subblock number
Summary: Define the solver/preconditioner to be used for a given subblock.

Parameter	Value	Default
subblock inverse	string	–
number	integer	–

Use Upper Triangle

Syntax: Use Upper Triangle {=} {false | true}
Summary: Define whether to use upper triangular block Gauss-Seidel

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{false \| true}	FALSE

7.3.3.19. Block Jacobi Solver

Scope: Teko Preconditioner
Summary: Use a Block Jacobi solver inside a Teko preconditioner.

begin Block Jacobi Solver

   Use Default Inverse subblock inverse For Subblocks

   Use Inverse subblock inverse For Subblock number

end Block Jacobi Solver

7.3.3.19.1. Line Commands

Use Default Inverse

Syntax: Use Default Inverse subblock inverse For Subblocks
Summary: Define a default solver/preconditioner to be used for across subblocks.

Parameter	Value	Default
subblock inverse	string	–

Use Inverse

Syntax: Use Inverse subblock inverse For Subblock number
Summary: Define the solver/preconditioner to be used for a given subblock.

Parameter	Value	Default
subblock inverse	string	–
number	integer	–

7.3.3.20. Simple Solver

Scope: Teko Preconditioner
Summary: Use a SIMPLE/SIMPLEC solver inside a Teko preconditioner.

begin Simple Solver

   Alpha {=} value

   Explicit Velocity Inverse Type {=} {absrowsum | diagonal | lumped}

   Use Default Inverse subblock inverse For Subblocks

   Use Inverse subblock inverse For Subblock number

end Simple Solver

7.3.3.20.1. Line Commands

Alpha

Syntax: Alpha {=} value
Summary: Set alpha value in SIMPLE block decomposition.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	real	1

Explicit Velocity Inverse Type

Syntax: Explicit Velocity Inverse Type {=} {absrowsum | diagonal | lumped}
Summary: Set inverse type used for velocity term when forming the Pressure Schur complement operator.

Parameter	Value	Default
{=}	{= \| are \| is}	–
value	{absrowsum \| diagonal \| lumped}	ABSROWSUM

Use Default Inverse

Syntax: Use Default Inverse subblock inverse For Subblocks
Summary: Define a default solver/preconditioner to be used for across subblocks.

Parameter	Value	Default
subblock inverse	string	–

Use Inverse

Syntax: Use Inverse subblock inverse For Subblock number
Summary: Define the solver/preconditioner to be used for a given subblock.

Parameter	Value	Default
subblock inverse	string	–
number	integer	–