KokkosLinearFVDiffusion

This is the Kokkos version of LinearFVDiffusion.

note

KokkosLinearFVDiffusion does not support nonorthogonal correction yet

Example Syntax

  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
  []

Input Parameters

diffusion_coeffThe diffusion coefficient.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The diffusion coefficient.
variableThe name of the variable whose linear system this object contributes to
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable whose linear system this object contributes to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Options:rhs, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator

Advanced Parameters

Input Files

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-neumann.i)
(test/tests/kokkos/fe-fv-interplay/aux-read-from-fv.i)
(test/tests/kokkos/linearfvkernels/diffusion/match-non-kokkos.i)
(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-internal-neumann.i)
(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-1d-radial.i)
(test/tests/kokkos/linearfvkernels/advection-diffusion/kokkos_advection_diffusion-1d.i)
(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d.i)
(test/tests/kokkos/fe-fv-interplay/multisystem.i)

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 1
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dir]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = "left right top bottom"
    functor = analytic_solution_kokkos
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2*(1.5-y*y) + 2*x*y*(1.5-y*y) + 2*(1.5-x*x) + 2*x*y*(1.5-x*x)'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-neumann.i)

# 2D diffusion MMS test with mixed Dirichlet (left/right) and Neumann (top/bottom) BCs.
# Exact solution:  u = (1.5 - x^2)(1.5 - y^2)
# Diffusion coeff: D = 1 + 0.5*x*y
# Neumann normal gradient on bottom (n = -y): -du/dy|_{y=0} = 0  (du/dy = 0 at y=0)
# Neumann normal gradient on top   (n = +y):  du/dy|_{y=ymax}

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dirichlet_lr]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = 'left right'
    functor = analytic_solution_kokkos
  []
  [neumann_bottom]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = 'bottom'
    functor = neumann_bottom_gradient
  []
  [neumann_top]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = 'top'
    functor = neumann_top_gradient
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2*(1.5-y*y) + 2*x*y*(1.5-y*y) + 2*(1.5-x*x) + 2*x*y*(1.5-x*x)'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  # Outward normal gradient on bottom (n = -y): -du/dy|_{y=0} = 0
  [neumann_bottom_gradient]
    type = KokkosParsedFunction
    expression = 0.0
  []
  # Outward normal gradient on top (n = +y): du/dy|_{y=ymax}
  # du/dy = (1.5-x^2)*(-2*ymax)
  [neumann_top_gradient]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(-2.0*0.5)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/fe-fv-interplay/aux-read-from-fv.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 2
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[AuxVariables]
  [v]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [v]
    type = KokkosCopyValueAux
    source = u
    variable = v
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = 'unity'
  []
[]

[LinearFVBCs]
  [left]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = "left"
    functor = 'zero'
  []
  [right]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = "right"
    functor = 'unity'
  []
[]

[Functions]
  [zero]
    type = KokkosParsedFunction
    expression = '0'
  []
  [unity]
    type = KokkosParsedFunction
    expression = '1'
  []
[]

[Postprocessors]
  [kokkos_avg]
    type = KokkosElementAverageValue
    variable = v
    execute_on = FINAL
  []
  [linear_fv_avg]
    type = ElementAverageFunctorPostprocessor
    functor = 'u'
    execute_on = FINAL
    evaluation_type = CELL_AVERAGE
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_on = FINAL
  []
[]

(test/tests/kokkos/linearfvkernels/diffusion/match-non-kokkos.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 10
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 1.0
  []
[]

[AuxVariables]
  [v_volume]
    type = MooseLinearVariableFVReal
    initial_condition = 50
  []
  [v_functor]
    type = MooseLinearVariableFVReal
    initial_condition = 25
  []
  [v_parsed]
    type = MooseLinearVariableFVReal
    initial_condition = 12.5
  []
[]

[AuxKernels]
  [volume]
    type = VolumeAux
    variable = v_volume
  []
  [functor]
    type = FunctorAux
    variable = v_functor
    functor = u
  []
  [parsed]
    type = ParsedAux
    variable = v_parsed
    coupled_variables = 'v_volume v_functor'
    expression = '0.5*v_volume+0.5*v_functor'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dir]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = "left right"
    functor = analytic_solution
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = '1'
  []
  [coeff_func]
    type = KokkosParsedFunction
    expression = '0.5*x'
  []
  [source_func]
    type = KokkosParsedFunction
    expression = '2*x'
  []
  [analytic_solution]
    type = KokkosParsedFunction
    expression = '1-x*x'
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  file_base = diffusion-1d-aux_out
  exodus = true
  execute_on = TIMESTEP_END
[]

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d-internal-neumann.i)

# 2D diffusion MMS test with Neumann normal-gradient BCs on internal block boundaries.
# Exact solution:  u = v = 1.5 - x^2
# Diffusion coeff: D = 1 + 0.5*x*y

[Mesh]
  [cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '0.5 0.5'
    ix = '2 2'
    dy = '0.5'
    iy = '2'
    subdomain_id = '1 2'
  []
  [left_internal]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    new_boundary = left_internal
    primary_block = 1
    paired_block = 2
  []
  [right_internal]
    type = SideSetsBetweenSubdomainsGenerator
    input = left_internal
    new_boundary = right_internal
    primary_block = 2
    paired_block = 1
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    block = 1
  []
  [v]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    block = 2
  []
[]

[LinearFVKernels]
  [diffusion_left]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
    block = 1
  []
  [source_left]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
    block = 1
  []
  [diffusion_right]
    type = KokkosLinearFVDiffusion
    variable = v
    diffusion_coeff = coeff_func_kokkos
    block = 2
  []
  [source_right]
    type = KokkosLinearFVSource
    variable = v
    source_density = source_func_kokkos
    scaling_factor = unit_fn
    block = 2
  []
[]

[LinearFVBCs]
  [dirichlet_left]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = left
    functor = analytic_solution_kokkos
  []
  [neumann_left_internal]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = left_internal
    functor = left_internal_gradient
  []
  [dirichlet_right]
    type = KokkosLinearFVFunctorDirichletBC
    variable = v
    boundary = right
    functor = analytic_solution_kokkos
  []
  [neumann_right_internal]
    type = KokkosLinearFVFunctorNeumannBC
    variable = v
    boundary = right_internal
    functor = right_internal_gradient
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2.0 + 2.0*x*y'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '1.5 - x*x'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '1.5 - x*x'
  []
  [left_internal_gradient]
    type = KokkosParsedFunction
    expression = '-1.0'
  []
  [right_internal_gradient]
    type = KokkosParsedFunction
    expression = '1.0'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [left_error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
    block = 1
  []
  [right_error]
    type = ElementL2FunctorError
    approximate = v
    exact = analytic_solution
    execute_on = FINAL
    block = 2
  []
  [error]
    type = ParsedPostprocessor
    expression = 'sqrt(left*left + right*right)'
    pp_names = 'left_error right_error'
    pp_symbols = 'left right'
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-1d-radial.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
    xmin = 1
    xmax = 2
  []
  coord_type = RZ
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = unit_fn
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dirichlet]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = 'left right'
    functor = analytic_solution_kokkos
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = 4
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '5-x*x'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '5-x*x'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-12'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = FINAL
  []
[]

(test/tests/kokkos/linearfvkernels/advection-diffusion/kokkos_advection_diffusion-1d.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 2
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [advection]
    type = KokkosLinearFVAdvection
    variable = u
    velocity = '0.5 0 0'
  []
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = unit_fn
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [inflow]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = left
    functor = analytic_solution_kokkos
  []
  [outflow]
    type = KokkosLinearFVFunctorNeumannBC
    variable = u
    boundary = right
    functor = zero_fn
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [zero_fn]
    type = KokkosParsedFunction
    expression = 0.0
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = 'x - 3.0'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + (1.0 - x) * (1.0 - x)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '1.0 + (1.0 - x) * (1.0 - x)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -pc_factor_mat_solver_type -mat_mumps_icntl_14'
  petsc_options_value = 'lu       NONZERO               1e-12                     mumps                    50'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/linearfvkernels/diffusion/kokkos_diffusion-2d.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 1
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
  []
[]

[LinearFVKernels]
  [diffusion]
    type = KokkosLinearFVDiffusion
    variable = u
    diffusion_coeff = coeff_func_kokkos
  []
  [source]
    type = KokkosLinearFVSource
    variable = u
    source_density = source_func_kokkos
    scaling_factor = unit_fn
  []
[]

[LinearFVBCs]
  [dir]
    type = KokkosLinearFVFunctorDirichletBC
    variable = u
    boundary = "left right top bottom"
    functor = analytic_solution_kokkos
  []
[]

[Functions]
  [unit_fn]
    type = KokkosParsedFunction
    expression = 1.0
  []
  [coeff_func_kokkos]
    type = KokkosParsedFunction
    expression = '1.0 + 0.5*x*y'
  []
  [source_func_kokkos]
    type = KokkosParsedFunction
    expression = '2*(1.5-y*y) + 2*x*y*(1.5-y*y) + 2*(1.5-x*x) + 2*x*y*(1.5-x*x)'
  []
  [analytic_solution_kokkos]
    type = KokkosParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = '(1.5-x*x)*(1.5-y*y)'
  []
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_tol = 1e-10
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = 'FINAL'
  []
[]

(test/tests/kokkos/fe-fv-interplay/multisystem.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Problem]
  nl_sys_names = 'u_sys'
  linear_sys_names = 'v_sys'
[]

[Variables]
  [u]
    solver_sys = 'u_sys'
  []
  [v]
    type = MooseLinearVariableFVReal
    solver_sys = 'v_sys'
  []
[]

[Kernels]
  [diff]
    type = KokkosDiffusion
    variable = u
  []
  [coupled]
    type = CoupledForce
    variable = u
    v = v
  []
[]

[LinearFVKernels]
  [diff]
    type = KokkosLinearFVDiffusion
    diffusion_coeff = 'unity'
    variable = v
  []
  [coupled]
    type = LinearFVSource
    source_density = u
    variable = v
  []
[]

[BCs]
  [left]
    type = KokkosDirichletBC
    boundary = 'left'
    variable = u
    value = 0
  []
  [right]
    type = KokkosDirichletBC
    boundary = 'right'
    variable = u
    value = 1
  []
[]

[LinearFVBCs]
  [left]
    type = KokkosLinearFVFunctorDirichletBC
    boundary = 'left'
    variable = v
    functor = 'zero'
  []
  [right]
    type = KokkosLinearFVFunctorDirichletBC
    boundary = 'right'
    variable = v
    functor = 'unity'
  []
[]

[Functions]
  [zero]
    type = KokkosParsedFunction
    expression = '0'
  []
  [unity]
    type = KokkosParsedFunction
    expression = '1'
  []
[]

[Postprocessors]
  [fe_avg]
    type = ElementAverageValue
    variable = u
    execute_on = FINAL
  []
  [fv_avg]
    type = ElementAverageFunctorPostprocessor
    functor = v
    execute_on = FINAL
    evaluation_type = CELL_AVERAGE
  []
[]

[Convergence]
  [fixed_point]
    type = IterationCountConvergence
    converge_at_max_iterations = true
    min_iterations = 10
    max_iterations = 10
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  system_names = 'u_sys v_sys'
  multi_system_fixed_point = true
  multi_system_fixed_point_convergence = fixed_point
  nl_abs_tol = 1e-12
  l_tol = 1e-12
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
  [console]
    type = Console
    execute_postprocessors_on = FINAL
  []
[]

Example Syntax
Input Parameters
Input Files