Parameters for the plain L2 projection method to transform between Legendre modes and nodal representation.

This method utilizes the L2 projection from Legendre to Lagrange polynomials or the other way around. A numerical Gauss-Legendre Quadrature is used to compute the integral over the product of both functions. The Lagrange polynomials can be defined on any nodeset, see also ply_nodeset_module.

Available options for the nodes to project onto are:

• 'gauss-legendre' these are the Gauss-Legendre integration points that are also used for the numerical integration (this is the default).
• 'chebyshev' these are the nodes from the Chebyshev integration.

The set of nodes to use is configured by the nodes_kind option, and if nodes_kind = 'chebyshev' it is also possible to make use of Lobatto points to include the interval boundaries in the nodal representation. This is achieved by setting lobattoPoints = true, by default this is false.

The configuration table for a projection with L2P may, for example, look as follows:

  projection = {
kind = 'l2p',
factor = 1.5,
nodes_kind = 'chebyshev',
lobattoPoints = true
}


The example illustrates the three possible settings for the L2P transformation method:

• factor - Oversampling factor to avoid aliasing.
• nodes_kind - Selection of set of nodes to use in the nodal representation.
• lobattoPoints - Whether to include interval bounds, only available for Chebyshev nodes.

## Interfaces

• ### private pure subroutine Copy_l2p_header(left, right)

#### Arguments

TypeIntentOptionalAttributesName

fpt to copy to

fpt to copy from

• ### private pure function isEqual(left, right) result(equality)

This function provides the test for equality of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is equal??

• ### private pure function isUnequal(left, right) result(unequality)

This function provides the test for unequality of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is unequal??

• ### private pure function isSmaller(left, right) result(small)

This function provides a < comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is smaller??

• ### private pure function isSmallerOrEqual(left, right) result(small)

This function provides a <= comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is smaller??

• ### private pure function isGreater(left, right) result(great)

This function provides a > comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is greater??

• ### private pure function isGreaterOrEqual(left, right) result(great)

This function provides a >= comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is greater??

## Derived Types

l2p projection header type, consisting of the node header which give information about the type and number of points for the projection

#### Components

TypeVisibilityAttributesNameInitial
real(kind=rk), private :: factor

## Functions

### private pure function isEqual(left, right) result(equality)

This function provides the test for equality of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is equal??

### private pure function isUnequal(left, right) result(unequality)

This function provides the test for unequality of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is unequal??

### private pure function isSmaller(left, right) result(small)

This function provides a < comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is smaller??

### private pure function isSmallerOrEqual(left, right) result(small)

This function provides a <= comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is smaller??

### private pure function isGreater(left, right) result(great)

This function provides a > comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is greater??

### private pure function isGreaterOrEqual(left, right) result(great)

This function provides a >= comparison of two projections.

#### Arguments

TypeIntentOptionalAttributesName

projection to compare

projection to compare against

is greater??

## Subroutines

Load settings to describe a projection method from a Lua table.

#### Arguments

TypeIntentOptionalAttributesName
type(flu_State), intent(inout) :: conf
integer, intent(in) :: thandle

### public subroutine ply_l2p_header_define(me, factor, nodes_kind, lobattoPoints)

#### Arguments

TypeIntentOptionalAttributesName

integer, intent(in), optional :: factor

Oversampling factor to use in the projection, defaults to 1.

character(len=*), optional :: nodes_kind

Set of nodes to use in the nodal representation.

May be 'gauss-legendre' or 'chebyshev', defaults to 'gauss-legendre'

logical, intent(in), optional :: lobattoPoints

Wether to use Lobatto points (include interval bounds) when using the chebyshev nodes, defaults to .false..

Write L2P settings into a Lua table.

#### Arguments

TypeIntentOptionalAttributesName
type(aot_out_type), intent(inout) :: conf

#### Arguments

TypeIntentOptionalAttributesName