ply_poly_project_module Module

The polynomial projection describes the change from modal to nodal representation and vice-versa.

The method to be used for this transformation is configured in a table that contains the kind of transformation and then further options to the transformation. There are three kinds of transformation available:

  • 'fpt' Fast polynomial transformation, only available if linked against FFTW.
  • 'l2p' Standard projection, evaluate each polynomial for each point.
  • 'fxt' Fast transformation based on multipole method, enabled by the (included) FXTPACK library.

By default the nodal representation uses as many nodes as there are modes in the modal representation. This can be changed with the factor setting. There will factor times number of modes nodes used in the transformation. This oversampling allows for dealiasing of the nodal representation. A different set of points will be used depending on the kind of transformation to be used:

  • FPT uses Chebyshev integration nodes
  • L2P may make use of either Chebyshev or Gauss-Legendre nodes
  • FXT Gauss-Legendre integration nodes

If the Chebyshev nodes are used for the nodal representation, the interval boundaries can be included by setting lobattoPoints=true. In this case there will also be at least one point more be used in the nodal representation than there are modes in the Legendre series.

If FPT is configured but the executable is not linked against the FFTW, there will be a warning, and the simulation uses the L2P method instead. The L2P method is also the default when no kind is provided at all.

For further options of the individual projection kinds, see their respective descriptions:

A minimalistic configuration for the projection method looks as follows:

  projection = {
    kind = 'l2p',
    factor = 1.5
  }

The name of the table (here projection) is arbitrary and defined by the application. An application may load multiple projection definitions with differing names.


Uses

  • module~~ply_poly_project_module~~UsesGraph module~ply_poly_project_module ply_poly_project_module module~ply_nodes_module ply_nodes_module module~ply_poly_project_module->module~ply_nodes_module module~ply_dynarray_project_module ply_dynarray_project_module module~ply_poly_project_module->module~ply_dynarray_project_module module~ply_nodes_header_module ply_nodes_header_module module~ply_poly_project_module->module~ply_nodes_header_module module~tem_logging_module tem_logging_module module~ply_poly_project_module->module~tem_logging_module module~ply_legfpt_module ply_legFpt_module module~ply_poly_project_module->module~ply_legfpt_module module~ply_legfpt_2d_module ply_legFpt_2D_module module~ply_poly_project_module->module~ply_legfpt_2d_module module~ply_dof_module ply_dof_module module~ply_poly_project_module->module~ply_dof_module module~tem_tools_module tem_tools_module module~ply_poly_project_module->module~tem_tools_module module~ply_prj_header_module ply_prj_header_module module~ply_poly_project_module->module~ply_prj_header_module module~ply_fxt_module ply_fxt_module module~ply_poly_project_module->module~ply_fxt_module module~ply_l2p_module ply_l2p_module module~ply_poly_project_module->module~ply_l2p_module module~ply_legfpt_3d_module ply_legFpt_3D_module module~ply_poly_project_module->module~ply_legfpt_3d_module module~tem_aux_module tem_aux_module module~ply_poly_project_module->module~tem_aux_module module~env_module env_module module~ply_poly_project_module->module~env_module module~ply_nodes_module->module~ply_nodes_header_module module~ply_nodes_module->module~tem_aux_module module~ply_nodes_module->module~env_module fftw_wrap fftw_wrap module~ply_nodes_module->fftw_wrap module~ply_nodeset_module ply_nodeset_module module~ply_nodes_module->module~ply_nodeset_module module~aotus_module aotus_module module~ply_nodes_module->module~aotus_module module~ply_dynarray_project_module->module~tem_logging_module module~ply_dynarray_project_module->module~ply_prj_header_module module~ply_dynarray_project_module->module~env_module module~ply_dynarray_project_module->module~aotus_module module~ply_nodes_header_module->module~env_module module~ply_legfpt_module->module~env_module module~ply_legfpt_module->fftw_wrap module~ply_fpt_header_module ply_fpt_header_module module~ply_legfpt_module->module~ply_fpt_header_module iso_c_binding iso_c_binding module~ply_legfpt_module->iso_c_binding module~tem_compileconf_module tem_compileconf_module module~ply_legfpt_module->module~tem_compileconf_module module~ply_polybaseexc_module ply_polyBaseExc_module module~ply_legfpt_module->module~ply_polybaseexc_module module~ply_legfpt_2d_module->module~ply_legfpt_module module~ply_legfpt_2d_module->module~env_module module~ply_legfpt_2d_module->fftw_wrap module~ply_legfpt_2d_module->iso_c_binding module~ply_dof_module->module~env_module module~ply_prj_header_module->module~tem_logging_module module~ply_prj_header_module->module~tem_tools_module module~ply_prj_header_module->module~tem_aux_module module~ply_prj_header_module->module~env_module module~ply_prj_header_module->fftw_wrap module~aot_out_module aot_out_module module~ply_prj_header_module->module~aot_out_module module~ply_prj_header_module->module~ply_fpt_header_module module~ply_fxt_header_module ply_fxt_header_module module~ply_prj_header_module->module~ply_fxt_header_module module~ply_l2p_header_module ply_l2p_header_module module~ply_prj_header_module->module~ply_l2p_header_module module~ply_prj_header_module->module~aotus_module module~ply_fxt_module->module~env_module module~ply_fxt_module->module~ply_fxt_header_module fxt_fwrap fxt_fwrap module~ply_fxt_module->fxt_fwrap module~ply_l2p_module->module~tem_logging_module module~ply_l2p_module->module~tem_aux_module module~ply_l2p_module->module~env_module module~ply_space_integration_module ply_space_integration_module module~ply_l2p_module->module~ply_space_integration_module module~ply_l2p_module->module~ply_l2p_header_module module~ply_l2p_module->module~ply_nodeset_module module~ply_modg_basis_module ply_modg_basis_module module~ply_l2p_module->module~ply_modg_basis_module module~ply_l2p_module->module~tem_compileconf_module module~ply_lagrange_module ply_lagrange_module module~ply_l2p_module->module~ply_lagrange_module module~ply_legfpt_3d_module->module~ply_legfpt_module module~ply_legfpt_3d_module->module~env_module module~ply_legfpt_3d_module->fftw_wrap module~ply_legfpt_3d_module->iso_c_binding module~ply_fpt_header_module->module~ply_nodes_header_module module~ply_fpt_header_module->module~tem_logging_module module~ply_fpt_header_module->module~tem_tools_module module~ply_fpt_header_module->module~tem_aux_module module~ply_fpt_header_module->module~env_module module~ply_fpt_header_module->module~aot_out_module module~ply_fpt_header_module->module~aotus_module module~ply_fpt_header_module->module~tem_compileconf_module module~tem_float_module tem_float_module module~ply_fpt_header_module->module~tem_float_module module~ply_fxt_header_module->module~ply_nodes_header_module module~ply_fxt_header_module->module~tem_logging_module module~ply_fxt_header_module->module~tem_aux_module module~ply_fxt_header_module->module~env_module module~ply_fxt_header_module->module~aot_out_module module~ply_fxt_header_module->module~aotus_module module~ply_fxt_header_module->module~tem_float_module module~ply_space_integration_module->module~env_module module~tem_param_module tem_param_module module~ply_space_integration_module->module~tem_param_module module~ply_l2p_header_module->module~ply_nodes_header_module module~ply_l2p_header_module->module~tem_logging_module module~ply_l2p_header_module->module~tem_tools_module module~ply_l2p_header_module->module~tem_aux_module module~ply_l2p_header_module->module~env_module module~ply_l2p_header_module->module~aot_out_module module~ply_l2p_header_module->module~aotus_module module~ply_l2p_header_module->module~tem_float_module module~ply_nodeset_module->module~env_module module~ply_nodeset_module->module~tem_param_module module~ply_modg_basis_module->module~ply_dof_module module~ply_modg_basis_module->module~env_module module~ply_modg_basis_module->module~ply_space_integration_module module~ply_polybaseexc_module->module~tem_logging_module module~ply_polybaseexc_module->module~env_module module~ply_polybaseexc_module->fftw_wrap module~ply_polybaseexc_module->module~ply_fpt_header_module module~ply_polybaseexc_module->iso_c_binding module~tem_gamma_module tem_gamma_module module~ply_polybaseexc_module->module~tem_gamma_module module~ply_polybaseexc_module->module~tem_float_module module~ply_polybaseexc_module->module~tem_param_module module~ply_lagrange_module->module~env_module module~ply_lagrange_module->module~ply_nodeset_module

Used by

  • module~~ply_poly_project_module~~UsedByGraph module~ply_poly_project_module ply_poly_project_module module~ply_oversample_module ply_oversample_module module~ply_oversample_module->module~ply_poly_project_module module~sdr_proto2treelm_module sdr_proto2treelm_module module~sdr_proto2treelm_module->module~ply_poly_project_module module~sdr_proto2treelm_module->module~ply_oversample_module program~seeder seeder program~seeder->module~sdr_proto2treelm_module

Contents


Interfaces

public interface assignment(=)

public interface ply_poly_project_m2n

  • private subroutine ply_poly_project_m2n_multiVar(me, dim, nVars, modal_data, nodal_data)

    Convert nDoF modes to nodal values.

    Arguments

    TypeIntentOptionalAttributesName
    type(ply_poly_project_type), intent(inout) :: me
    integer, intent(in) :: dim
    integer, intent(in) :: nVars

    The number of variables to project. If a variable consists of more than one component, the number of components has to be passed. If there are more than one variable, the sum of all components has to be passed (e.g. 6 when there are two three-dimensional vectors).

    real(kind=rk), intent(inout) :: modal_data(:,:)
    real(kind=rk), intent(inout) :: nodal_data(:,:)

public interface ply_poly_project_n2m

  • private subroutine ply_poly_project_n2m_multiVar(me, dim, nVars, nodal_data, modal_data)

    Convert nodal values to nDoFs modes.

    Arguments

    TypeIntentOptionalAttributesName
    type(ply_poly_project_type), intent(inout) :: me
    integer, intent(in) :: dim
    integer, intent(in) :: nVars
    real(kind=rk), intent(inout) :: nodal_data(:,:)
    real(kind=rk), intent(inout) :: modal_data(:,:)

Derived Types

type, public :: ply_prj_body_type

Additional data, required for the projection.

Components

TypeVisibilityAttributesNameInitial
type(ply_legFpt_type), private :: fpt

The fast polynomial transformation which will be used in case of nonlinear equations. It is used if fpt is choses as projection method in the lua file

type(ply_fxt_type), private :: fxt

The Legendre Polynomial type for the Fast Orthogonal Function Transform via fxtpack. It is used if 'fxt' is chosen as projection method in the lua file

type(ply_l2p_type), private :: l2p

Projection method which cam be used for transfoamtion from modal to nodal space and vice versa. It is used if 'l2p' is chosen as projection method in the lua file

real(kind=rk), private, allocatable:: nodes(:,:)

Volume quadrature points in the reference element

type(ply_faceNodes_type), private, allocatable:: faces(:,:)

Facial quadrature nodes (reference element) for all three spatial direction and left and right face. These points are necessary to transfer boundary conditions given in physical space to modal space by projection (l2p or fpt)

integer, private :: nQuadPoints

quadrature points including oversampling factor

integer, private :: ndofs

degree of freedom of the scheme depending on maxPolyDegree

integer, private :: oversamp_dofs
integer, private :: min_dofs

type, public :: ply_poly_project_type

Projection definition.

Components

TypeVisibilityAttributesNameInitial
integer, private :: basisType

Polynomial basis type.

Read more…
character(len=labelLen), private :: kind

Kind of projection. Currently available: - 'l2p', L2-Projection - 'fpt', Fast Polynomial Transformation. Requires the FFTW. - 'fxt', Fast Polynomial Transformation. uses FXTPACK

integer, private :: maxPolyDegree

The maximal polynomial degree per spatial direction.

integer, private :: oversamp_degree

Using oversampling, the modal space need to be extended according

integer, private :: min_degree
integer, private :: nQuadPointsPerDir

quadrature points including oversampling factor

logical, private :: lobattoPoints =.false.

Logical to indicate whether Chebyshev-Lobatto points or simple Chebyshev points are used

type(ply_prj_body_type), private :: body_1d

projection header consits of general information like which kind of projection is used In the body datatype, there is for each dimension the main data for the projection method stored

type(ply_prj_body_type), private :: body_2d
type(ply_prj_body_type), private :: body_3d

Subroutines

public subroutine ply_fill_project_list(proj_list, dyn_projectArray, scheme_dim)

Fill ups the bodys accroding to the DA.

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(out), allocatable:: proj_list(:)
type(dyn_projectionarray_type), intent(in) :: dyn_projectArray
integer, intent(in) :: scheme_dim

public subroutine ply_poly_project_fillbody(me, proj_init, scheme_dim)

Fill the body of the projection with all required data, ply_poly_project_define has to be used beforehand to set necessary header information.

Read more…

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(inout) :: me
type(ply_prj_init_type), intent(in) :: proj_init
integer, intent(in) :: scheme_dim

public subroutine ply_get_quadpoints_faces(poly_proj, idir, ialign, points)

function to provide the coordinates from the quadrature points on the faces

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(in) :: poly_proj
integer, intent(in) :: idir
integer, intent(in) :: ialign
real(kind=rk), intent(inout), allocatable:: points(:,:)

public subroutine ply_get_quadpoints_faces_2d(poly_proj, idir, ialign, points)

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(in) :: poly_proj
integer, intent(in) :: idir
integer, intent(in) :: ialign
real(kind=rk), intent(out), allocatable:: points(:,:)

public subroutine ply_get_quadpoints_faces_1d(poly_proj, idir, ialign, points)

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(in) :: poly_proj
integer, intent(in) :: idir
integer, intent(in) :: ialign
real(kind=rk), intent(out), allocatable:: points(:,:)

private subroutine Copy_poly_project(left, right)

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(out) :: left

fpt to copy to

type(ply_poly_project_type), intent(in) :: right

fpt to copy from

private subroutine Copy_poly_project_body(left, right)

Arguments

TypeIntentOptionalAttributesName
type(ply_prj_body_type), intent(out) :: left
type(ply_prj_body_type), intent(in) :: right

private subroutine ply_poly_project_m2n_multiVar(me, dim, nVars, modal_data, nodal_data)

Convert nDoF modes to nodal values.

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(inout) :: me
integer, intent(in) :: dim
integer, intent(in) :: nVars

The number of variables to project. If a variable consists of more than one component, the number of components has to be passed. If there are more than one variable, the sum of all components has to be passed (e.g. 6 when there are two three-dimensional vectors).

real(kind=rk), intent(inout) :: modal_data(:,:)
real(kind=rk), intent(inout) :: nodal_data(:,:)

private subroutine ply_poly_project_n2m_multiVar(me, dim, nVars, nodal_data, modal_data)

Convert nodal values to nDoFs modes.

Arguments

TypeIntentOptionalAttributesName
type(ply_poly_project_type), intent(inout) :: me
integer, intent(in) :: dim
integer, intent(in) :: nVars
real(kind=rk), intent(inout) :: nodal_data(:,:)
real(kind=rk), intent(inout) :: modal_data(:,:)