SELF_Points_t Module

  1. SELF_Points_t.f90
  2. SELF_Points_t

A point-cloud container with type-bound procedures to (1) locate each physical point inside a SEMQuad/SEMHex element-of-elements and recover its reference (computational) coordinates via a Newton inverse-map, and (2) sample MappedScalar2D / MappedScalar3D fields at the located points.

The point-location uses a uniform-grid spatial hash built from per-element axis-aligned bounding boxes of the discrete control-grid (geometry%x). For each candidate element, a Newton iteration on

X(xi) = sum_{i,j[,k]} x_node(i,j[,k]) * l_i(s) * l_j(t) [* l_k(u)]

is driven to convergence using the high-order Jacobian dX/dxi (interpolated covariant-basis tensor dxds). Points that fall outside every element this rank owns are marked with the sentinel elements(p) = 0 and their evaluated field values are returned as zero.


Uses

  • module~~self_points_t~~UsesGraph module~self_points_t SELF_Points_t module~self_constants SELF_Constants module~self_points_t->module~self_constants module~self_mappedscalar_3d~2 SELF_MappedScalar_3D module~self_points_t->module~self_mappedscalar_3d~2 module~self_geometry_2d SELF_Geometry_2D module~self_points_t->module~self_geometry_2d module~self_geometry_3d SELF_Geometry_3D module~self_points_t->module~self_geometry_3d module~self_lagrange~3 SELF_Lagrange module~self_points_t->module~self_lagrange~3 module~self_mappedscalar_2d SELF_MappedScalar_2D module~self_points_t->module~self_mappedscalar_2d iso_c_binding iso_c_binding module~self_constants->iso_c_binding iso_fortran_env iso_fortran_env module~self_constants->iso_fortran_env module~self_mappedscalar_3d_t SELF_MappedScalar_3D_t module~self_mappedscalar_3d~2->module~self_mappedscalar_3d_t module~self_geometry_2d->module~self_constants module~self_geometry_2d->module~self_lagrange~3 module~self_supportroutines SELF_SupportRoutines module~self_geometry_2d->module~self_supportroutines module~self_tensor_2d SELF_Tensor_2D module~self_geometry_2d->module~self_tensor_2d module~self_scalar_2d~2 SELF_Scalar_2D module~self_geometry_2d->module~self_scalar_2d~2 module~self_mesh_2d~2 SELF_Mesh_2D module~self_geometry_2d->module~self_mesh_2d~2 module~self_data SELF_Data module~self_geometry_2d->module~self_data module~self_vector_2d~2 SELF_Vector_2D module~self_geometry_2d->module~self_vector_2d~2 module~self_geometry_3d->module~self_constants module~self_geometry_3d->module~self_lagrange~3 module~self_mesh_3d SELF_Mesh_3D module~self_geometry_3d->module~self_mesh_3d module~self_vector_3d SELF_Vector_3D module~self_geometry_3d->module~self_vector_3d module~self_geometry_3d->module~self_supportroutines module~self_geometry_3d->module~self_data module~self_tensor_3d SELF_Tensor_3D module~self_geometry_3d->module~self_tensor_3d module~self_scalar_3d~2 SELF_Scalar_3D module~self_geometry_3d->module~self_scalar_3d~2 module~self_lagrange~3->module~self_constants module~self_lagrange~3->iso_c_binding module~self_lagrange_t SELF_Lagrange_t module~self_lagrange~3->module~self_lagrange_t module~self_lagrange~3->iso_fortran_env module~self_mappedscalar_2d_t SELF_MappedScalar_2D_t module~self_mappedscalar_2d->module~self_mappedscalar_2d_t module~self_mesh_3d_t SELF_Mesh_3D_t module~self_mesh_3d->module~self_mesh_3d_t module~self_vector_3d_t SELF_Vector_3D_t module~self_vector_3d->module~self_vector_3d_t module~self_lagrange_t->module~self_constants module~self_lagrange_t->iso_c_binding module~self_lagrange_t->iso_fortran_env module~self_lagrange_t->module~self_supportroutines module~self_quadrature SELF_Quadrature module~self_lagrange_t->module~self_quadrature module~self_hdf5 SELF_HDF5 module~self_lagrange_t->module~self_hdf5 HDF5 HDF5 module~self_lagrange_t->HDF5 module~self_mappedscalar_2d_t->module~self_constants module~self_mappedscalar_2d_t->module~self_geometry_2d module~self_mappedscalar_2d_t->module~self_lagrange~3 module~self_mappedscalar_2d_t->iso_c_binding module~self_mappedscalar_2d_t->module~self_tensor_2d module~self_mappedscalar_2d_t->module~self_scalar_2d~2 module~self_mappedscalar_2d_t->module~self_mesh_2d~2 module~self_domaindecomposition SELF_DomainDecomposition module~self_mappedscalar_2d_t->module~self_domaindecomposition FEQParse FEQParse module~self_mappedscalar_2d_t->FEQParse module~self_supportroutines->module~self_constants module~self_supportroutines->iso_fortran_env module~self_mappedscalar_3d_t->module~self_constants module~self_mappedscalar_3d_t->module~self_geometry_3d module~self_mappedscalar_3d_t->module~self_lagrange~3 module~self_mappedscalar_3d_t->iso_c_binding module~self_mappedscalar_3d_t->module~self_mesh_3d module~self_mappedscalar_3d_t->module~self_tensor_3d module~self_mappedscalar_3d_t->module~self_scalar_3d~2 module~self_mappedscalar_3d_t->module~self_domaindecomposition module~self_mappedscalar_3d_t->FEQParse module~self_tensor_2d_t SELF_Tensor_2D_t module~self_tensor_2d->module~self_tensor_2d_t module~self_scalar_2d~2->module~self_constants module~self_scalar_2d~2->iso_c_binding module~self_scalar_2d_t SELF_Scalar_2D_t module~self_scalar_2d~2->module~self_scalar_2d_t module~self_mesh_2d_t SELF_Mesh_2D_t module~self_mesh_2d~2->module~self_mesh_2d_t module~self_data->module~self_constants module~self_data->module~self_lagrange~3 module~self_data->iso_c_binding module~self_data->module~self_hdf5 module~self_data->FEQParse module~self_metadata SELF_Metadata module~self_data->module~self_metadata module~self_data->HDF5 module~self_vector_2d_t SELF_Vector_2D_t module~self_vector_2d~2->module~self_vector_2d_t module~self_tensor_3d_t SELF_Tensor_3D_t module~self_tensor_3d->module~self_tensor_3d_t module~self_scalar_3d~2->module~self_constants module~self_scalar_3d~2->iso_c_binding module~self_scalar_3d_t SELF_Scalar_3D_t module~self_scalar_3d~2->module~self_scalar_3d_t module~self_quadrature->module~self_constants module~self_quadrature->iso_fortran_env module~self_hdf5->module~self_constants module~self_hdf5->iso_fortran_env module~self_hdf5->HDF5 mpi mpi module~self_hdf5->mpi module~self_domaindecomposition_t SELF_DomainDecomposition_t module~self_domaindecomposition->module~self_domaindecomposition_t module~self_tensor_2d_t->module~self_constants module~self_tensor_2d_t->module~self_lagrange~3 module~self_tensor_2d_t->iso_c_binding module~self_tensor_2d_t->module~self_data module~self_tensor_2d_t->module~self_hdf5 module~self_tensor_2d_t->FEQParse module~self_tensor_2d_t->module~self_metadata module~self_tensor_2d_t->HDF5 module~self_scalar_2d_t->module~self_constants module~self_scalar_2d_t->module~self_lagrange~3 module~self_scalar_2d_t->iso_c_binding module~self_scalar_2d_t->module~self_data module~self_scalar_2d_t->module~self_hdf5 module~self_scalar_2d_t->FEQParse module~self_scalar_2d_t->module~self_metadata module~self_scalar_2d_t->HDF5 module~self_mesh_2d_t->module~self_constants module~self_mesh_2d_t->module~self_lagrange~3 module~self_mesh_2d_t->iso_c_binding module~self_mesh_2d_t->module~self_supportroutines module~self_mesh_2d_t->module~self_quadrature module~self_mesh_2d_t->module~self_hdf5 module~self_mesh_2d_t->module~self_domaindecomposition module~self_mesh_2d_t->HDF5 module~self_mesh SELF_Mesh module~self_mesh_2d_t->module~self_mesh module~self_metadata->module~self_hdf5 module~self_metadata->HDF5 module~self_vector_2d_t->module~self_constants module~self_vector_2d_t->module~self_lagrange~3 module~self_vector_2d_t->iso_c_binding module~self_vector_2d_t->module~self_data module~self_vector_2d_t->module~self_hdf5 module~self_vector_2d_t->FEQParse module~self_vector_2d_t->module~self_metadata module~self_vector_2d_t->HDF5 module~self_tensor_3d_t->module~self_constants module~self_tensor_3d_t->module~self_lagrange~3 module~self_tensor_3d_t->iso_c_binding module~self_tensor_3d_t->module~self_data module~self_tensor_3d_t->module~self_hdf5 module~self_tensor_3d_t->FEQParse module~self_tensor_3d_t->module~self_metadata module~self_tensor_3d_t->HDF5 module~self_mesh_3d_t->module~self_constants module~self_mesh_3d_t->module~self_lagrange~3 module~self_mesh_3d_t->iso_c_binding module~self_mesh_3d_t->module~self_supportroutines module~self_mesh_3d_t->module~self_hdf5 module~self_mesh_3d_t->module~self_domaindecomposition module~self_mesh_3d_t->HDF5 module~self_mesh_3d_t->module~self_mesh module~self_vector_3d_t->module~self_constants module~self_vector_3d_t->module~self_lagrange~3 module~self_vector_3d_t->iso_c_binding module~self_vector_3d_t->module~self_data module~self_vector_3d_t->module~self_hdf5 module~self_vector_3d_t->FEQParse module~self_vector_3d_t->module~self_metadata module~self_vector_3d_t->HDF5 module~self_scalar_3d_t->module~self_constants module~self_scalar_3d_t->module~self_lagrange~3 module~self_scalar_3d_t->iso_c_binding module~self_scalar_3d_t->module~self_data module~self_scalar_3d_t->module~self_hdf5 module~self_scalar_3d_t->FEQParse module~self_scalar_3d_t->module~self_metadata module~self_scalar_3d_t->HDF5 module~self_domaindecomposition_t->module~self_constants module~self_domaindecomposition_t->module~self_lagrange~3 module~self_domaindecomposition_t->iso_c_binding module~self_domaindecomposition_t->module~self_supportroutines module~self_domaindecomposition_t->mpi module~self_mesh->module~self_constants module~self_mesh->iso_c_binding module~self_mesh->module~self_domaindecomposition

Used by

  • module~~self_points_t~~UsedByGraph module~self_points_t SELF_Points_t module~self_points~2 SELF_Points module~self_points~2->module~self_points_t module~self_points SELF_Points module~self_points->module~self_points_t

Contents

Derived Types

Functions

Subroutines


Derived Types

type, public :: Points_t

Components

TypeVisibilityAttributesNameInitial
real(kind=prec), public, pointer:: coordinates(:,:)=> null()

Reference coordinates (s,t[,u]) in [-1,1]^nDim, shape (1:nPoints, 1:nDim). Defined only where elements(p) > 0.
integer, public, pointer:: elements(:)=> null()

Element id (rank-local) containing each point; 0 = not found.
real(kind=prec), public, pointer:: lS_cache(:,:)=> null()

Lagrange basis at coordinates(p,1), shape (0:nCached, 1:nPoints). Filled by LocatePoints for points with elements(p) > 0.
real(kind=prec), public, pointer:: lT_cache(:,:)=> null()

Lagrange basis at coordinates(p,2), shape (0:nCached, 1:nPoints).
real(kind=prec), public, pointer:: lU_cache(:,:)=> null()

Lagrange basis at coordinates(p,3), shape (0:nCached, 1:nPoints). Allocated only for nDim = 3.
integer, public :: nCached =0

Polynomial degree at which the per-point Lagrange basis cache is valid. Zero means no cache. The cache is filled by LocatePoints and consumed by EvaluateScalar when the field's interpolant degree matches.
integer, public :: nDim =0
integer, public :: nPoints =0
real(kind=prec), public, allocatable:: x(:,:)

Physical coordinates, shape (1:nPoints, 1:nDim). User input.

Type-Bound Procedures

generic, public :: DiracDelta => DiracDelta_2D_Points_t, DiracDelta_3D_Points_t
procedure, public :: DiracDelta_2D_Points_t
procedure, public :: DiracDelta_3D_Points_t
procedure, public :: EvalScalar_2D_Points_t
procedure, public :: EvalScalar_3D_Points_t
generic, public :: EvaluateScalar => EvalScalar_2D_Points_t, EvalScalar_3D_Points_t
procedure, public :: Free => Free_Points_t
procedure, public :: Init => Init_Points_t
generic, public :: LocatePoints => LocatePoints_2D_Points_t, LocatePoints_3D_Points_t
procedure, public :: LocatePoints_2D_Points_t
procedure, public :: LocatePoints_3D_Points_t
procedure, public :: SetPoints => SetPoints_Points_t

Functions

public pure function ClampCell(rIdx, nCells) result(c)

Convert a (signed, possibly out-of-range) real cell index to an integer cell index clamped to [0, nCells-1].

Arguments

TypeIntentOptionalAttributesName
real(kind=prec), intent(in) :: rIdx
integer, intent(in) :: nCells

Return Value integer


Subroutines

public subroutine BuildElementBBoxes_2D(geometry, N, nElem, bbMin, bbMax)

Axis-aligned bounding box of each element. The box is taken over the element's boundary nodes (geometry%x%boundary), which are evaluated at the element edges (reference coordinate = +/-1) and therefore reach the true element boundary and corners. Using the interior nodes alone is not sufficient: for Gauss quadrature the interior nodes are strictly inside [-1,1], so a box built from them under-covers the element by a fixed fraction of its size and rejects points lying on element edges/corners. The boundary nodes give the correct extent for both Gauss and Gauss-Lobatto node sets.

Arguments

TypeIntentOptionalAttributesName
type(SEMQuad), intent(in) :: geometry
integer, intent(in) :: N
integer, intent(in) :: nElem
real(kind=prec), intent(out) :: bbMin(1:2,1:nElem)
real(kind=prec), intent(out) :: bbMax(1:2,1:nElem)

public subroutine BuildElementBBoxes_3D(geometry, N, nElem, bbMin, bbMax)

Axis-aligned bounding box of each element, taken over the boundary nodes (geometry%x%boundary) which are evaluated on the element faces (reference coordinate = +/-1) and so reach the true element boundary, edges and corners. See BuildElementBBoxes_2D for why the interior nodes alone are insufficient (Gauss interior nodes under-cover the element).

Arguments

TypeIntentOptionalAttributesName
type(SEMHex), intent(in) :: geometry
integer, intent(in) :: N
integer, intent(in) :: nElem
real(kind=prec), intent(out) :: bbMin(1:3,1:nElem)
real(kind=prec), intent(out) :: bbMax(1:3,1:nElem)

public subroutine DiracDelta_2D_Points_t(this, geometry, scalar)

Scatter a discrete Dirac delta of unit strength (S = 1) onto a 2D MappedScalar, one variable per stored point. Variable p of scalar receives the delta associated with point p.

Read more…

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(in) :: this
type(SEMQuad), intent(in) :: geometry
class(MappedScalar2D_t), intent(inout) :: scalar

public subroutine DiracDelta_3D_Points_t(this, geometry, scalar)

Scatter a discrete Dirac delta of unit strength (S = 1) onto a 3D MappedScalar, one variable per stored point. See DiracDelta_2D_Points_t for the full specification; this is the direct 3D analogue.

Read more…

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(in) :: this
type(SEMHex), intent(in) :: geometry
class(MappedScalar3D_t), intent(inout) :: scalar

public subroutine EvalScalar_2D_Points_t(this, scalar, values)

Evaluate a 2D MappedScalar at all located points by tensor-product Lagrange interpolation at the stored reference coordinates. Points with elements(p) == 0 receive a value of zero. When LocatePoints has cached the per-point basis at the matching polynomial degree, this routine reuses it and skips Lagrange-polynomial evaluation altogether.

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(in) :: this
class(MappedScalar2D_t), intent(in) :: scalar
real(kind=prec), intent(out) :: values(1:this%nPoints,1:scalar%nVar)

public subroutine EvalScalar_3D_Points_t(this, scalar, values)

Evaluate a 3D MappedScalar at all located points by tensor-product Lagrange interpolation. Points with elements(p) == 0 receive zero. When LocatePoints has cached the basis at the matching degree, this routine reuses it.

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(in) :: this
class(MappedScalar3D_t), intent(in) :: scalar
real(kind=prec), intent(out) :: values(1:this%nPoints,1:scalar%nVar)

public subroutine Free_Points_t(this)

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(inout) :: this

public subroutine Init_Points_t(this, nPoints, nDim)

Allocate storage for a point cloud of size nPoints in nDim dimensions. nDim must be 2 or 3.

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(out) :: this
integer, intent(in) :: nPoints
integer, intent(in) :: nDim

public subroutine LocatePoints_2D_Points_t(this, geometry)

Locate each stored physical point inside the 2D SEMQuad geometry. On exit, elements(p) holds the (rank-local) element id and coordinates(p,:) holds the (s,t) reference coordinates, both for points that resolve. Points that resolve to no element are marked with elements(p) = 0.

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(inout) :: this
type(SEMQuad), intent(in) :: geometry

public subroutine LocatePoints_3D_Points_t(this, geometry)

Locate each stored physical point inside the 3D SEMHex geometry. On exit, elements(p) and coordinates(p,1:3) hold the located element id and reference (s,t,u) for points that resolve; elements(p) = 0 otherwise.

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(inout) :: this
type(SEMHex), intent(in) :: geometry

public subroutine NewtonInverse_2D(geometry, iEl, N, xTarget, xi, converged)

Newton inverse-map for the 2D SEM element iEl: solve X(xi) = xTarget for the reference coordinate xi in R^2, where X is the high-order interpolant. The Jacobian dX/dxi is taken from geometry%dxds (the covariant basis tensor), interpolated to xi via Lagrange basis.

Read more…

Arguments

TypeIntentOptionalAttributesName
type(SEMQuad), intent(in) :: geometry
integer, intent(in) :: iEl
integer, intent(in) :: N
real(kind=prec), intent(in) :: xTarget(2)
real(kind=prec), intent(out) :: xi(2)
logical, intent(out) :: converged

public subroutine NewtonInverse_3D(geometry, iEl, N, xTarget, xi, converged)

Newton inverse-map for the 3D SEM element iEl. See NewtonInverse_2D.

Arguments

TypeIntentOptionalAttributesName
type(SEMHex), intent(in) :: geometry
integer, intent(in) :: iEl
integer, intent(in) :: N
real(kind=prec), intent(in) :: xTarget(3)
real(kind=prec), intent(out) :: xi(3)
logical, intent(out) :: converged

public subroutine SetPoints_Points_t(this, xIn)

Copy user-supplied physical coordinates into the cloud. xIn must be shape (nPoints, nDim) matching the init dimensions.

Arguments

TypeIntentOptionalAttributesName
class(Points_t), intent(inout) :: this
real(kind=prec), intent(in) :: xIn(:,:)