InterceptedElementModifier

InterceptedElementModifier is a MeshModifier that classifies each element of a background mesh as inside or outside a geometry and assigns it one of two subdomain IDs (subdomain_id_inside or subdomain_id_outside). The geometry is described either by a signed-distance Function (via signed_dist_function) or by an in-out test user object (via in_out_test, a PointInPolyhedronCheckUO).

For each element the modifier:

classifies the element as fully inside or fully outside only when all of its nodes fall on the same side of the geometry (using the threshold value for the signed-distance case) and the quadrature estimate of the active-area fraction agrees (fully active or fully inactive). Requiring both guards against a surface that crosses the element or encloses a small region even though every node lies on one side;
otherwise estimates, via quadrature of order qrule_order, the active-area fraction of the element that lies inside the retained domain and compares 1 - fraction against the lambda threshold to decide the assignment. Elements whose active fraction lands exactly on the cut are resolved with a fuzzy comparison so the classification is reproducible across platforms.

is_domain_inside_surface selects which side of the surface is the retained (inside) domain. Set it to true when the retained domain is the region enclosed by the surface (signed distance below threshold, or points reported inside by the in-out test), and to false when the retained domain is the region outside the surface. When mark_intercepted is enabled, every partially intercepted element is instead assigned subdomain_id_intercepted rather than being resolved by the lambda cut.

Usage

Provide exactly one geometry source: either signed_dist_function or in_out_test. Supplying both, or neither, is an error. Because the geometric in-out test requires a replicated surface mesh, run these tests with mesh_mode = REPLICATED.

Marks elements as inside, outside, or intercepted based on a given distance function or geometry.

Input Parameters

is_domain_inside_surfaceFalseWhen true, the retained (inside) domain is the region enclosed by the surface (signed distance below 'threshold', or points reported inside by the in-out test); when false, the retained domain is the region outside the surface.
Default:False
C++ Type:bool
Controllable:No
Description:When true, the retained (inside) domain is the region enclosed by the surface (signed distance below 'threshold', or points reported inside by the in-out test); when false, the retained domain is the region outside the surface.
subdomain_id_insideID for inside elements.
C++ Type:unsigned short
Controllable:No
Description:ID for inside elements.
subdomain_id_outsideID for outside elements.
C++ Type:unsigned short
Controllable:No
Description:ID for outside elements.

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
in_out_testThe name of the in-out test user object. Exactly one of 'in_out_test' and 'signed_dist_function' must be provided; providing neither or both is invalid.
C++ Type:UserObjectName
Controllable:No
Description:The name of the in-out test user object. Exactly one of 'in_out_test' and 'signed_dist_function' must be provided; providing neither or both is invalid.
lambda0.5Threshold applied to the inactive fraction of a partially active element.
Default:0.5
C++ Type:Real
Unit:(no unit assumed)
Range:lambda >= 0 & lambda <= 1
Controllable:No
Description:Threshold applied to the inactive fraction of a partially active element.
mark_interceptedFalseWhether to assign a dedicated subdomain ID when intercepted.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to assign a dedicated subdomain ID when intercepted.
moving_boundariesMoving boundaries between subdomains. These boundaries (both sidesets and nodesets) will be updated for elements that change subdomain. The subdomains that each moving boundary lies between shall be specified using the parameter 'moving_boundary_subdomain_pairs'. If one boundary and multiple subdomain pairs are specified, then it is assumed that the pairs all apply to the boundary. A boundary will be created on the mesh if it does not already exist.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Moving boundaries between subdomains. These boundaries (both sidesets and nodesets) will be updated for elements that change subdomain. The subdomains that each moving boundary lies between shall be specified using the parameter 'moving_boundary_subdomain_pairs'. If one boundary and multiple subdomain pairs are specified, then it is assumed that the pairs all apply to the boundary. A boundary will be created on the mesh if it does not already exist.
moving_boundary_subdomain_pairsThe subdomain pairs associated with each moving boundary. For each pair of subdomains, only the element side from the first subdomain will be added to the moving boundary, i.e., the side normal is pointing from the first subdomain to the second subdomain. The pairs shall be delimited by ';'. If a pair only has one subdomain, the moving boundary is associated with the subdomain's external boundary, i.e., when the elements have no neighboring elements.
C++ Type:std::vector<std::vector<SubdomainName>>
Controllable:No
Description:The subdomain pairs associated with each moving boundary. For each pair of subdomains, only the element side from the first subdomain will be added to the moving boundary, i.e., the side normal is pointing from the first subdomain to the second subdomain. The pairs shall be delimited by ';'. If a pair only has one subdomain, the moving boundary is associated with the subdomain's external boundary, i.e., when the elements have no neighboring elements.
nearby_distance_threshold-1Threshold for considering elements as 'nearby' in the K-D tree search. Only elements within this distance will be considered for polynomial fitting.
Default:-1
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:Threshold for considering elements as 'nearby' in the K-D tree search. Only elements within this distance will be considered for polynomial fitting.
nearby_kd_tree_leaf_max_size10Maximum number of elements in a leaf node of the K-D tree used to search for nearby elements. Only needed if 'reinitialization_strategy' is set to POLYNOMIAL_NEARBY.
Default:10
C++ Type:int
Controllable:No
Description:Maximum number of elements in a leaf node of the K-D tree used to search for nearby elements. Only needed if 'reinitialization_strategy' is set to POLYNOMIAL_NEARBY.
old_subdomain_reinitializedTrueThis parameter must be set with a non-empty list in 'reinitialize_subdomains'. When set to the default true, the element's old subdomain is not considered when determining if an element should be reinitialized. If set to false, only elements whose old subdomain was not in 'reinitialize_subdomains' are reinitialized.
Default:True
C++ Type:bool
Controllable:No
Description:This parameter must be set with a non-empty list in 'reinitialize_subdomains'. When set to the default true, the element's old subdomain is not considered when determining if an element should be reinitialized. If set to false, only elements whose old subdomain was not in 'reinitialize_subdomains' are reinitialized.
polynomial_fittersList of NodalPatchRecovery UserObjects used for polynomial fitting during variable reinitialization. Required only if 'reinitialization_strategy' includes POLYNOMIAL_NEIGHBOR, POLYNOMIAL_WHOLE, or POLYNOMIAL_NEARBY.
C++ Type:std::vector<UserObjectName>
Controllable:No
Description:List of NodalPatchRecovery UserObjects used for polynomial fitting during variable reinitialization. Required only if 'reinitialization_strategy' includes POLYNOMIAL_NEIGHBOR, POLYNOMIAL_WHOLE, or POLYNOMIAL_NEARBY.
qrule_order9Quadrature order used to estimate the active fraction.
Default:9
C++ Type:int
Range:qrule_order >= 0 & qrule_order <= 10
Controllable:No
Description:Quadrature order used to estimate the active fraction.
reinitialization_strategyIC The strategy used to reinitialize the solution when elements change subdomain. If multiple strategies are provided, each strategy will be applied to the corresponding variable. If only one strategy is provided, it will be applied to all variables.
Default:IC
C++ Type:std::vector<MooseEnum>
Options:IC, POLYNOMIAL_NEIGHBOR, POLYNOMIAL_WHOLE, POLYNOMIAL_NEARBY, NONE
Controllable:No
Description:The strategy used to reinitialize the solution when elements change subdomain. If multiple strategies are provided, each strategy will be applied to the corresponding variable. If only one strategy is provided, it will be applied to all variables.
reinitialize_subdomainsANY_BLOCK_ID By default, any element which changes subdomain is reinitialized. If a list of subdomains (IDs or names) is provided, then only elements whose new subdomain is in the list will be reinitialized. If an empty list is set, then no elements will be reinitialized.
Default:ANY_BLOCK_ID
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:By default, any element which changes subdomain is reinitialized. If a list of subdomains (IDs or names) is provided, then only elements whose new subdomain is in the list will be reinitialized. If an empty list is set, then no elements will be reinitialized.
reinitialize_variablesWhich variables to reinitialize when subdomain changes.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Which variables to reinitialize when subdomain changes.
restore_overridden_dofsA list of boolean flags, one for each variable in 'reinitialize_variables', specifying whether overridden DOF values should be restored after reinitialization for each variable. This is useful when the solved values on these DOFs should be preserved. If the list is empty, overridden DOF values will NOT be restored for any variable by default.
C++ Type:std::vector<bool>
Controllable:No
Description:A list of boolean flags, one for each variable in 'reinitialize_variables', specifying whether overridden DOF values should be restored after reinitialization for each variable. This is useful when the solved values on these DOFs should be preserved. If the list is empty, overridden DOF values will NOT be restored for any variable by default.
signed_dist_functionSigned distance function to evaluate. Exactly one of 'signed_dist_function' and 'in_out_test' must be provided; providing neither or both is invalid.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Signed distance function to evaluate. Exactly one of 'signed_dist_function' and 'in_out_test' must be provided; providing neither or both is invalid.
skip_restore_subdomain_changesFalseSkip restoring the subdomain changes if the timestep is not advanced.
Default:False
C++ Type:bool
Controllable:No
Description:Skip restoring the subdomain changes if the timestep is not advanced.
subdomain_id_intercepted65535Whether to assign a dedicated subdomain ID to intercepted elements.
Default:65535
C++ Type:unsigned short
Controllable:No
Description:Whether to assign a dedicated subdomain ID to intercepted elements.
threshold0Threshold for inside/outside classification.
Default:0
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:Threshold for inside/outside classification.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, MULTISYSTEM_FIXED_POINT_ITERATION_END, FINAL, CUSTOM, TRANSFER
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(modules/shifted_boundary_method/test/tests/in_out_test/intercepted_no_test.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_enclosed_surface.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_mark_intercepted.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_enclosed_surface_function.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_signed_function.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_edge_clip.i)
(modules/shifted_boundary_method/test/tests/in_out_test/3D_lambda0p5.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_lambda0p5.i)
(modules/shifted_boundary_method/test/tests/in_out_test/3D_lambda1.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_lambda0.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_lambda1.i)
(modules/shifted_boundary_method/test/tests/in_out_test/3D_lambda0.i)
(modules/shifted_boundary_method/test/tests/in_out_test/2D_triangle_clip.i)

(modules/shifted_boundary_method/test/tests/in_out_test/intercepted_no_test.i)

# InterceptedElementModifier requires either an 'in_out_test' user object or a
# 'signed_dist_function' to classify elements. This input supplies neither, so
# initialSetup() must error out. Used as a RunException coverage test for that
# configuration guard.

[Problem]
  solve = false
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    subdomain_ids = 1
  []
  add_subdomain_ids = '2'
[]

[MeshModifiers]
  [intercepted]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    is_domain_inside_surface = true
    execute_on = 'INITIAL'
  []
[]

[Executioner]
  type = Steady
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_enclosed_surface.i)

# A closed curve lies entirely within one coarse element, so every element node is outside while
# interior quadrature points are inside. The element must still be marked as intercepted.
radius = 0.3
n_seg = 32

[Problem]
  solve = false
[]

[Mesh]
  [surface]
    type = ParsedCurveGenerator
    x_formula = '0.5 + ${radius} * cos(t)'
    y_formula = '0.5 + ${radius} * sin(t)'
    section_bounding_t_values = '0 ${fparse 2*pi}'
    nums_segments = '${n_seg}'
    is_closed_loop = true
    save_with_name = surface
  []
  [domain]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    subdomain_ids = 1
  []
  add_subdomain_ids = '2 3'
  final_generator = domain
[]

[UserObjects]
  [surface_builder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = surface
  []
  [in_out_test]
    type = PointInPolyhedronCheckUO
    builder = surface_builder
  []
[]

[MeshModifiers]
  [intercepted]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    is_domain_inside_surface = true
    in_out_test = in_out_test
    mark_intercepted = true
    subdomain_id_intercepted = 3
    execute_on = INITIAL
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 3
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_mark_intercepted.i)

# Same immersed ellipse as 2D_lambda0p5.i, but with mark_intercepted = true so
# elements the surface cuts through are assigned a dedicated subdomain
# (subdomain_id_intercepted) instead of being resolved by the lambda fraction.
# This exercises the mark_intercepted return path in
# InterceptedElementModifier::computeSubdomainID and the corresponding branch of
# SBMElementSubdomainModifierBase.
nx = 16
lambda = 0.5
a = 1.6
b = 1.0
cx = 2.03
cy = 1.97
n_seg = 48
[Problem]
  solve = false
[]

[Mesh]
  [shift_boundary_mesh]
    type = ParsedCurveGenerator
    x_formula = '${cx} + ${a} * cos(t)'
    y_formula = '${cy} + ${b} * sin(t)'
    section_bounding_t_values = '0 ${fparse 2*pi}'
    nums_segments = '${n_seg}'
    is_closed_loop = true
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '4'
    dy = '4'
    ix = '${nx}'
    iy = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = '2 3' # outside block and intercepted block
  final_generator = 'gen'
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []

  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    mark_intercepted = true
    subdomain_id_intercepted = 3
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_enclosed_surface_function.i)

# A level-set curve lies entirely within one coarse element, so every element node is outside while
# interior quadrature points are inside. The element must still be marked as intercepted.
radius = 0.3

[Problem]
  solve = false
[]

[Mesh]
  [domain]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    subdomain_ids = 1
  []
  add_subdomain_ids = '2 3'
[]

[Functions]
  [level_set]
    type = ParsedFunction
    expression = '(x - 0.5)^2 + (y - 0.5)^2 - ${fparse radius^2}'
  []
[]

[MeshModifiers]
  [intercepted]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    is_domain_inside_surface = true
    signed_dist_function = level_set
    mark_intercepted = true
    subdomain_id_intercepted = 3
    execute_on = INITIAL
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 3
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_signed_function.i)

# Same immersed ellipse as 2D_lambda0p5.i, but the InterceptedElementModifier is
# driven by a signed level-set function (signed_dist_function) instead of a
# geometric in-out UserObject. This exercises the SIGNED_DISTANCE branch of
# InterceptedElementModifier::computeSubdomainID. The level set is negative
# inside the ellipse and positive outside, matching is_domain_inside_surface = true.
nx = 16
lambda = 0.5
a = 1.6
b = 1.0
cx = 2.03
cy = 1.97
[Problem]
  solve = false
[]

[Mesh]
  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '4'
    dy = '4'
    ix = '${nx}'
    iy = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[Functions]
  [level_set]
    type = ParsedFunction
    expression = '((x - ${cx}) / ${a})^2 + ((y - ${cy}) / ${b})^2 - 1'
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    signed_dist_function = level_set
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_edge_clip.i)

# A single coarse element whose four nodes all lie outside a circle, while the circle bulges
# through the bottom edge so a finite interior region is inside. The node-only test would call
# the element fully outside; the occupied-ratio guard in the GEOMETRY branch (active_nodes == 0
# requires ratio_active == 0.0) must instead classify it as intercepted.
radius = 0.4
n_seg = 64

[Problem]
  solve = false
[]

[Mesh]
  [surface]
    type = ParsedCurveGenerator
    # Circle centered below the domain so the top cap crosses the element's bottom edge.
    x_formula = '0.5 + ${radius} * cos(t)'
    y_formula = '-0.3 + ${radius} * sin(t)'
    section_bounding_t_values = '0 ${fparse 2*pi}'
    nums_segments = '${n_seg}'
    is_closed_loop = true
    save_with_name = surface
  []
  [domain]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    subdomain_ids = 1
  []
  add_subdomain_ids = '2 3'
  final_generator = domain
[]

[UserObjects]
  [surface_builder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = surface
  []
  [in_out_test]
    type = PointInPolyhedronCheckUO
    builder = surface_builder
  []
[]

[MeshModifiers]
  [intercepted]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    is_domain_inside_surface = true
    in_out_test = in_out_test
    mark_intercepted = true
    subdomain_id_intercepted = 3
    execute_on = INITIAL
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 3
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/3D_lambda0p5.i)

nx = 16
lambda = 0.5
# Immersed triaxial ellipsoid: three distinct semi-axes make the boundary
# anisotropic so PCA has a well-separated shortest axis, giving a reproducible
# auto ray direction. Off-grid center keeps the surface cutting elements at
# generic fractions with no node/quadrature point landing exactly on it.
ax = 1.5
ay = 1.15
az = 0.85
cx = 2.03
cy = 1.97
cz = 2.05
[Problem]
  solve = false
[]

[Mesh]
  [ball]
    type = SphereMeshGenerator
    radius = 1.0
    nr = 1
    elem_type = TET4
  []
  [shell]
    type = LowerDBlockFromSidesetGenerator
    input = ball
    sidesets = '0'
    new_block_id = 100
  []
  [extract]
    type = BlockToMeshConverterGenerator
    input = shell
    target_blocks = '100'
  []
  [scale]
    type = TransformGenerator
    transform = SCALE
    vector_value = '${ax} ${ay} ${az}'
    input = extract
  []
  [shift_boundary_mesh]
    type = TransformGenerator
    transform = TRANSLATE
    vector_value = '${cx} ${cy} ${cz}'
    input = scale
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 3
    dx = '4'
    dy = '4'
    dz = '4'
    ix = '${nx}'
    iy = '${nx}'
    iz = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []
  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_lambda0p5.i)

nx = 16
lambda = 0.5
# Immersed ellipse geometry: distinct semi-axes make the boundary anisotropic so
# PCA has a well-separated minor axis, giving a reproducible auto ray direction.
# Off-grid center keeps the arc cutting elements at generic fractions with no
# node/quadrature point landing exactly on the surface.
a = 1.6
b = 1.0
cx = 2.03
cy = 1.97
n_seg = 48
[Problem]
  solve = false
[]

[Mesh]
  [shift_boundary_mesh]
    type = ParsedCurveGenerator
    x_formula = '${cx} + ${a} * cos(t)'
    y_formula = '${cy} + ${b} * sin(t)'
    section_bounding_t_values = '0 ${fparse 2*pi}'
    nums_segments = '${n_seg}'
    is_closed_loop = true
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '4'
    dy = '4'
    ix = '${nx}'
    iy = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[Functions]
  [level_set]
    type = ParsedFunction
    expression = '((x - ${cx}) / ${a})^2 + ((y - ${cy}) / ${b})^2 - 1'
  []
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []

  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
  [signed_function_test]
    type = PointInSignedFunctionCheckUO
    function = level_set
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/3D_lambda1.i)

nx = 16
lambda = 1
# Immersed triaxial ellipsoid: three distinct semi-axes make the boundary
# anisotropic so PCA has a well-separated shortest axis, giving a reproducible
# auto ray direction. Off-grid center keeps the surface cutting elements at
# generic fractions with no node/quadrature point landing exactly on it.
ax = 1.5
ay = 1.15
az = 0.85
cx = 2.03
cy = 1.97
cz = 2.05
[Problem]
  solve = false
[]

[Mesh]
  [ball]
    type = SphereMeshGenerator
    radius = 1.0
    nr = 1
    elem_type = TET4
  []
  [shell]
    type = LowerDBlockFromSidesetGenerator
    input = ball
    sidesets = '0'
    new_block_id = 100
  []
  [extract]
    type = BlockToMeshConverterGenerator
    input = shell
    target_blocks = '100'
  []
  [scale]
    type = TransformGenerator
    transform = SCALE
    vector_value = '${ax} ${ay} ${az}'
    input = extract
  []
  [shift_boundary_mesh]
    type = TransformGenerator
    transform = TRANSLATE
    vector_value = '${cx} ${cy} ${cz}'
    input = scale
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 3
    dx = '4'
    dy = '4'
    dz = '4'
    ix = '${nx}'
    iy = '${nx}'
    iz = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []
  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_lambda0.i)

nx = 16
lambda = 0
# Immersed ellipse geometry: distinct semi-axes make the boundary anisotropic so
# PCA has a well-separated minor axis, giving a reproducible auto ray direction.
# Off-grid center keeps the arc cutting elements at generic fractions with no
# node/quadrature point landing exactly on the surface.
a = 1.6
b = 1.0
cx = 2.03
cy = 1.97
n_seg = 48
[Problem]
  solve = false
[]

[Mesh]
  [shift_boundary_mesh]
    type = ParsedCurveGenerator
    x_formula = '${cx} + ${a} * cos(t)'
    y_formula = '${cy} + ${b} * sin(t)'
    section_bounding_t_values = '0 ${fparse 2*pi}'
    nums_segments = '${n_seg}'
    is_closed_loop = true
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '4'
    dy = '4'
    ix = '${nx}'
    iy = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []

  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_lambda1.i)

nx = 16
lambda = 1
# Immersed ellipse geometry: distinct semi-axes make the boundary anisotropic so
# PCA has a well-separated minor axis, giving a reproducible auto ray direction.
# Off-grid center keeps the arc cutting elements at generic fractions with no
# node/quadrature point landing exactly on the surface.
a = 1.6
b = 1.0
cx = 2.03
cy = 1.97
n_seg = 48
[Problem]
  solve = false
[]

[Mesh]
  [shift_boundary_mesh]
    type = ParsedCurveGenerator
    x_formula = '${cx} + ${a} * cos(t)'
    y_formula = '${cy} + ${b} * sin(t)'
    section_bounding_t_values = '0 ${fparse 2*pi}'
    nums_segments = '${n_seg}'
    is_closed_loop = true
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 2
    dx = '4'
    dy = '4'
    ix = '${nx}'
    iy = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []

  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/3D_lambda0.i)

nx = 16
lambda = 0
# Immersed triaxial ellipsoid: three distinct semi-axes make the boundary
# anisotropic so PCA has a well-separated shortest axis, giving a reproducible
# auto ray direction. Off-grid center keeps the surface cutting elements at
# generic fractions with no node/quadrature point landing exactly on it.
ax = 1.5
ay = 1.15
az = 0.85
cx = 2.03
cy = 1.97
cz = 2.05
[Problem]
  solve = false
[]

[Mesh]
  [ball]
    type = SphereMeshGenerator
    radius = 1.0
    nr = 1
    elem_type = TET4
  []
  [shell]
    type = LowerDBlockFromSidesetGenerator
    input = ball
    sidesets = '0'
    new_block_id = 100
  []
  [extract]
    type = BlockToMeshConverterGenerator
    input = shell
    target_blocks = '100'
  []
  [scale]
    type = TransformGenerator
    transform = SCALE
    vector_value = '${ax} ${ay} ${az}'
    input = extract
  []
  [shift_boundary_mesh]
    type = TransformGenerator
    transform = TRANSLATE
    vector_value = '${cx} ${cy} ${cz}'
    input = scale
    save_with_name = 'shift_boundary_mesh'
  []

  [gen]
    type = CartesianMeshGenerator
    dim = 3
    dx = '4'
    dy = '4'
    dz = '4'
    ix = '${nx}'
    iy = '${nx}'
    iz = '${nx}'
    subdomain_id = '1'
  []

  add_subdomain_ids = 2 # outside block
  add_sideset_names = 'SBMinterface'
  final_generator = 'gen'
[]

[UserObjects]
  [TreeBuilder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = shift_boundary_mesh
  []
  [inout_test]
    type = PointInPolyhedronCheckUO
    builder = TreeBuilder
  []
[]

[MeshModifiers]
  [IntercpetedESM]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    lambda = ${lambda}
    is_domain_inside_surface = true
    in_out_test = inout_test
    execute_on = 'INITIAL'
    execution_order_group = 0
  []
  [SBMinterface]
    type = SidesetAroundSubdomainUpdater
    inner_subdomains = 1
    outer_subdomains = 2
    update_sideset_name = 'SBMinterface'
    assign_outer_surface_sides = false
    execute_on = 'INITIAL'
    execution_order_group = 1
    block = '1 2' # need to override default block
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 1
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/shifted_boundary_method/test/tests/in_out_test/2D_triangle_clip.i)

# Test a triangular closed surface with sharp corners and intercepted elements.

[Problem]
  solve = false
[]

[Mesh]
  [surface]
    type = ParsedCurveGenerator
    # Piecewise-linear triangle A->B->C; is_closed_loop adds the closing edge C->A.
    # Apex A sits at a cell center (0.5625, 0.8125) with a narrow wedge, so the apex cell has all
    # four nodes outside the triangle while a finite sliver is inside.
    constant_names = 'Ax Ay Bx By Cx Cy'
    constant_expressions = '0.5625 0.8125 0.30 0.20 0.72 0.20'
    x_formula = 'if(t < 1, Ax + t * (Bx - Ax), Bx + (t - 1) * (Cx - Bx))'
    y_formula = 'if(t < 1, Ay + t * (By - Ay), By + (t - 1) * (Cy - By))'
    section_bounding_t_values = '0 1 2'
    nums_segments = '10 10'
    is_closed_loop = true
    save_with_name = surface
  []
  [domain]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 8
    ny = 8
    subdomain_ids = 1
  []
  add_subdomain_ids = '2 3'
  final_generator = domain
[]

[UserObjects]
  [surface_builder]
    type = SBMSurfaceMeshBuilder
    check_watertightness = true
    surface_mesh = surface
  []
  [in_out_test]
    type = PointInPolyhedronCheckUO
    builder = surface_builder
  []
[]

[MeshModifiers]
  [intercepted]
    type = InterceptedElementModifier
    subdomain_id_inside = 1
    subdomain_id_outside = 2
    is_domain_inside_surface = true
    in_out_test = in_out_test
    mark_intercepted = true
    subdomain_id_intercepted = 3
    execute_on = INITIAL
  []
[]

[Variables]
  [u]
    initial_condition = 1
    block = 3
  []
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

Usage
Input Parameters
Input Files