ply_LegPolyProjection_module

Module for projection of Q Legendre Polynomials from parent cell to child cells.

Uses

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Variables

Type	Visibility	Attributes		Name		Initial
integer,	private,	parameter	::	ply_QLegendrePoly_prp	=	1	Parameter to specify Legendre polynomials as the degrees of freedoms of the elements. The multidimensional polynomias are build as Q-polynomials. The projection is a L2-Projection onto the ansatz function of the finer elements.

Derived Types

type, public :: ply_subsample_type

Components

Type	Visibility		Name		Initial
logical,	public	::	isActive	=	.false.	Is subsampling active
integer,	public	::	sampling_lvl			The current sampling lvl.
integer,	public	::	projectionType	=	ply_QLegendrePoly_prp	The type of projection we use to subsample the elemental data.
integer,	public	::	caplevel	=	20	Maximal Level down to which subsampling should be done.
integer,	public	::	minsub	=	0	Minimal subsampling depth:
integer,	public	::	maxsub	=	0	Maximal subsampling depth:
real(kind=rk),	public	::	eps_osci			Maximum allowed oscillation of the solution. For adaptive subsampling only.
real(kind=rk),	public	::	dofReducFactor			Factor for the reduction of the degrees of freedom in one subsampling step (per spatial direction).
logical,	public	::	adaptiveDofReduction			Indicator for limitation of total memory consumption
integer,	public	::	AbsUpperBoundLevel			Absolute upper bound level to refine to.

type, public :: ply_array_type

Components

Type	Visibility	Attributes		Name		Initial
real(kind=rk),	public,	allocatable	::	dat(:)

type, private :: ply_ProjCoeff_type

Datatype storing the coefficients arising for the projection of solutions on a parent cell to its children during the subsampling routines.

Components

Type	Visibility	Attributes		Name		Initial
real(kind=rk),	public,	allocatable	::	projCoeff(:,:,:)			Array holding all the projection coefficients for the projection of a degree of freedom on the parent element (first index) to a degree of freedom on the child element (second index) for a given child element (third index). Therefore the dimension of this array is (nDofs, nDofs, 8).

Functions

private function ply_QLegOneDimCoeff(nDofsOneDim, nChildDofsOneDim) result(projCoeffOneDim)

Routine to create one-dimensional projection coefficient for a coarse element to a fine element.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	nDofsOneDim	The number of dofs in one dimension.
integer,	intent(in)			::	nChildDofsOneDim	The number of dofs in one dimension for the children.

Return Value real(kind=rk), allocatable, (:,:,:)

Projected one-dimensional coefficients.

First index is Legendre polynomial on the parent element, second index is the Legendre polynomial on the child element, third index is left or right projection.

private function ply_QLegSqNorm(polyIndex) result(sqNorm)

Function to calculate the squared L2-Norm of a given Legendre polynomial on the reference element [-1,+1].

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	polyIndex	The Legendre polynomial index to calculate the squared norm for. The first polynomial has index 1.

Return Value real(kind=rk)

The squared L2 Norm of the Legendre polynomial.

private function ply_legVal(points, nPoints, maxPolyDegree) result(val)

Evaluate a given set of Legendre polynomials a given set of 1D points.

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	points(:)	A given set of 1D points.
integer,	intent(in)	::	nPoints	The number of points to evaluate the polynomials at.
integer,	intent(in)	::	maxPolyDegree	The maximal polynomial degree to evaluate for.

Return Value real(kind=rk), allocatable, (:,:)

Function values for for all Legendre polynomials up to degree maxPolyDegree at all given points. Therefore the dimension of this array is (maxPolyDegree+1, nPoints)

Subroutines

public subroutine ply_QPolyProjection(subsamp, dofReduction, tree, meshData, varDofs, ndims, varcomps, refine_tree, new_refine_tree, newMeshData, newVarDofs)

Subsampling by L2-Projection of the Q-Tensorproduct Legendre polynomials.

Arguments

Type	Intent	Attributes		Name
type(ply_subsample_type),	intent(in)		::	subsamp	Parameters for the subsampling.
real(kind=rk),	intent(in)		::	dofReduction(:)	Factor for reducion of degrees of freedom.
type(treelmesh_type),	intent(in)		::	tree	The tree the data is written for.
type(ply_array_type),	intent(in)		::	meshData(:)	The data to sub-sample.
integer,	intent(in)		::	varDofs(:)	The number of degrees of freedom for each scalar variable.
integer,	intent(in)		::	ndims	Number of dimensions in the polynomial representation.
integer,	intent(in)		::	varcomps(:)	Number of components
logical,	intent(in)		::	refine_tree(:)	Logical array that marks elements for refinement from the last sampling
logical,	intent(in)		::	new_refine_tree(:)	Logical array that marks elements for refinment.
type(ply_array_type),	intent(out),	allocatable	::	newMeshData(:)	The subsampled data.
integer,	intent(out),	allocatable	::	newVarDofs(:)	The number of dofs for the subsampled dofs.

public subroutine ply_gauleg(x1, x2, x, w, nIntP)

subroutine to create gauss points and weights for one-dimensional integration on the interval [x1,x2].

Arguments

Type	Intent	Attributes		Name
real(kind=rk),	intent(in)		::	x1	lower limit of integration interval
real(kind=rk),	intent(in)		::	x2	upper limit of integration interval
real(kind=rk),	intent(inout),	allocatable	::	x(:)	The coordinates of the gauss points on the interval [-1,1]. The array has the length nIntP.
real(kind=rk),	intent(inout),	allocatable	::	w(:)	The quadrature weights. The array has the length nIntP.
integer,	intent(in)		::	nIntP	The number of integration points.

private subroutine ply_initQLegProjCoeff(dofType, nDofs, ndims, nChilds, nChildDofs, projection)

Routine to initialize the projection coefficients for a usage in the subsampling routine to project degrees of freedoms of a parent cell to the degrees of freedoms of a child cell if the degrees of freedoms are Q-Legendre polynomials.

Arguments

Type	Intent		Name
integer,	intent(in)	::	dofType	The type of degrees of freedom we have in our cells.
integer,	intent(in)	::	nDofs	The number of degrees of freedom for the parent cells.
integer,	intent(in)	::	ndims	The number of dimensions in the polynomial representation.
integer,	intent(in)	::	nChilds	The number of child cells.
integer,	intent(in)	::	nChildDofs	The number of degrees of freedom for the child cells.
type(ply_ProjCoeff_type),	intent(out)	::	projection	The subsampling coefficients that will be initialized by this routine.

private subroutine ply_dofToQPoly(dof, nDofs, ndims, xAnsFunc, yAnsFunc, zAnsFunc)

Subroutine to convert linearized dof index to ansatz function number for Q-Polynomials.

Arguments

Type	Intent		Name
integer,	intent(in)	::	dof	The linearized degree of freedom index.
integer,	intent(in)	::	nDofs	The number of dofs for all directions.
integer,	intent(in)	::	ndims	The number of Dimensions in the polynomial representation.
integer,	intent(out)	::	xAnsFunc	The ansatz function number in x direction.
integer,	intent(out)	::	yAnsFunc	The ansatz function number in y direction.
integer,	intent(out)	::	zAnsFunc	The ansatz function number in z direction.

private subroutine ply_subsampleData(tree, meshData, nDofs, nChildDofs, nComponents, projection, projection_oneDof, refine_tree, new_refine_tree, ndims, subsamp, newMeshData)

Routine to subsample mesh information for one refinement level.

Arguments

Type	Intent	Optional	Attributes		Name
type(treelmesh_type),	intent(in)			::	tree	The tree the data is written for.
real(kind=rk),	intent(in)			::	meshData(:)	The data to sub-sample.
integer,	intent(in)			::	nDofs	The number of degrees of freedom for each scalar variable.
integer,	intent(in)			::	nChildDofs	The number of degrees of freedom per scalar variable on the child elements.
integer,	intent(in)			::	nComponents	Number of components
type(ply_ProjCoeff_type),	intent(in)			::	projection	Projection coefficients for the given data.
type(ply_ProjCoeff_type),	intent(in),	optional		::	projection_oneDof	Projection coeffiecients for the the reduction to polynomial degree of 0.
logical,	intent(in),	optional		::	refine_tree(:)	Logical array that marks all elements for refinement from the last sampling lvl.
logical,	intent(in)			::	new_refine_tree(:)	Logical array that marks all elements for refinement
integer,	intent(in)			::	ndims	The number of dimensions in the polynomial representation.
type(ply_subsample_type),	intent(in)			::	subsamp	Parameters for the subsampling.
real(kind=rk),	intent(out),		allocatable	::	newMeshData(:)	The subsampled data.

private subroutine ply_projDataToChild(parentData, nParentDofs, nChildDofs, nComponents, nChilds, projection, childData)

Subroutine to project elemental data from a parent cell to one of its children.

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	parentData(:)	Linearized data for a single variable (can have multiple components) and a single degree of freedom of the parent cell.
integer,	intent(in)	::	nParentDofs	The number of dofs of the parent element.
integer,	intent(in)	::	nChildDofs	The total number of dofs for the child cells.
integer,	intent(in)	::	nComponents	The number of componentns of the given variable.
integer,	intent(in)	::	nChilds	The number of children.
type(ply_ProjCoeff_type),	intent(in)	::	projection	The information about the projection coefficients for the parent dofs to the child dofs.
real(kind=rk),	intent(out)	::	childData(:)	The created childData.

ply_LegPolyProjection_module Module

Contents

Variables

Derived Types

Functions

Subroutines

Uses

Variables

Derived Types

type, public :: ply_subsample_type

Components

type, public :: ply_array_type

Components

type, private :: ply_ProjCoeff_type

Components

Functions

private function ply_QLegOneDimCoeff(nDofsOneDim, nChildDofsOneDim) result(projCoeffOneDim)

Arguments

Return Value real(kind=rk), allocatable, (:,:,:)

private function ply_QLegSqNorm(polyIndex) result(sqNorm)

Arguments

Return Value real(kind=rk)

private function ply_legVal(points, nPoints, maxPolyDegree) result(val)

Arguments

Return Value real(kind=rk), allocatable, (:,:)

Subroutines

public subroutine ply_QPolyProjection(subsamp, dofReduction, tree, meshData, varDofs, ndims, varcomps, refine_tree, new_refine_tree, newMeshData, newVarDofs)

Arguments

public subroutine ply_gauleg(x1, x2, x, w, nIntP)

Arguments

private subroutine ply_initQLegProjCoeff(dofType, nDofs, ndims, nChilds, nChildDofs, projection)

Arguments

private subroutine ply_dofToQPoly(dof, nDofs, ndims, xAnsFunc, yAnsFunc, zAnsFunc)

Arguments

private subroutine ply_subsampleData(tree, meshData, nDofs, nChildDofs, nComponents, projection, projection_oneDof, refine_tree, new_refine_tree, ndims, subsamp, newMeshData)

Arguments

private subroutine ply_projDataToChild(parentData, nParentDofs, nChildDofs, nComponents, nChilds, projection, childData)

Arguments