Derived type representing a 2D reference element. More...

Inheritance diagram for scale_element_base::elementbase2d:

Public Member Functions
procedure	generate_l2projmat (elem, elem_in, l2projmat)
	Generate a projection matrix for L2 projection. This matrix maps nodal values on elem_in to nodal values on elem. It is intended for p-restriction, i.e. elem order <= elem_in order.
procedure	generate_interpmat (elem, elem_in, interpmat)
	Generate an interpolation matrix by p-prolongation. This matrix maps nodal values on elem_in to nodal values on elem. It is intended for p-prolongation, i.e. elem order >= elem_in order.
procedure	generate_modaltruncationmat (elem, polyorder_tr, truncatemat)
	Generate a nodal-to-nodal transfer matrix to remove several high modes.
Public Member Functions inherited from scale_element_base::elementbase
procedure	islumpedmatrix (elem)
	Get a flag whether the lumped mass matrix is used.

Public Attributes
integer	polyorder
	Polynomial order.
integer	nfp
	Number of nodes on an element face.
integer, dimension(:,:), allocatable	fmask
	Array saving indices to extract nodal values on the faces.
real(rp), dimension(:), allocatable	x1
	Array saving x1-coordinate of nodes within the reference element.
real(rp), dimension(:), allocatable	x2
	Array saving x2-coordinate of nodes within the reference element.
real(rp), dimension(:,:), allocatable	dx1
	Elementwise differential matrix for the x1-coordinate direction (Dx1 = M^-1 Sx1)
real(rp), dimension(:,:), allocatable	dx2
	Elementwise differential matrix for the x2-coordinate direction (Dx2 = M^-1 Sx2)
real(rp), dimension(:,:), allocatable	sx1
	Elementwise stiffness matrix for the x1-coordinate direction.
real(rp), dimension(:,:), allocatable	sx2
	Elementwise stiffness matrix for the x2-coordinate direction.
Public Attributes inherited from scale_element_base::elementbase
integer	np
	Number of nodes within an element.
integer	nfaces
	Number of faces.
integer	nfptot
	Total number of nodes on faces.
integer	nv
	Number of vertices with an element.
real(rp), dimension(:,:), allocatable	v
	The Vandermonde matrix (V) whose size is Np x Np.
real(rp), dimension(:,:), allocatable	invv
	Inversion of the Vandermonde matrix (V^-1) whose size is Np x Np.
real(rp), dimension(:,:), allocatable	m
	Mass matrix (M) whose size is Np x Np.
real(rp), dimension(:,:), allocatable	invm
	Inversion of the mass matrix (M^-1) whose size Np x NP.
real(rp), dimension(:,:), allocatable	lift
	Lifting matrix with element boundary integrals whose size Np x NfpTot.
real(rp), dimension(:), allocatable	intweight_lgl
	Weights of gaussian quadrature with the LGL nodes.

Detailed Description

Derived type representing a 2D reference element.

Definition at line 71 of file scale_element_base.F90.

Member Function/Subroutine Documentation

◆ generate_l2projmat()

procedure scale_element_base::elementbase2d::generate_l2projmat	(	class(elementbase2d), intent(in)	elem,
		class(elementbase2d), intent(in)	elem_in,
		real(rp), dimension(elem%np,elem_in%np), intent(out)	l2projmat )

Generate a projection matrix for L2 projection. This matrix maps nodal values on elem_in to nodal values on elem. It is intended for p-restriction, i.e. elem order <= elem_in order.

With an orthogonal Legendre modal basis, this corresponds to L2 projection onto the polynomial space represented by elem.

Definition at line 85 of file scale_element_base.F90.

◆ generate_interpmat()

procedure scale_element_base::elementbase2d::generate_interpmat	(	class(elementbase2d), intent(in)	elem,
		class(elementbase2d), intent(in)	elem_in,
		real(rp), dimension(elem%np,elem_in%np), intent(out)	interpmat )

Generate an interpolation matrix by p-prolongation. This matrix maps nodal values on elem_in to nodal values on elem. It is intended for p-prolongation, i.e. elem order >= elem_in order.

In Legendre modal space, higher modes not present in elem_in are set to zero.

Definition at line 86 of file scale_element_base.F90.

◆ generate_modaltruncationmat()

procedure scale_element_base::elementbase2d::generate_modaltruncationmat	(	class(elementbase2d), intent(in)	elem,
		integer, intent(in)	polyorder_tr,
		real(rp), dimension(elem%np,elem%np), intent(out)	truncatemat )

Generate a nodal-to-nodal transfer matrix to remove several high modes.

Definition at line 87 of file scale_element_base.F90.

References scale_element_base::elementbase2d_final(), and scale_element_base::elementbase2d_init().

Member Data Documentation

◆ polyorder

integer scale_element_base::elementbase2d::polyorder

Polynomial order.

Definition at line 72 of file scale_element_base.F90.

72 integer :: PolyOrder !< Polynomial order

◆ nfp

integer scale_element_base::elementbase2d::nfp

Number of nodes on an element face.

Definition at line 73 of file scale_element_base.F90.

73 integer :: Nfp !< Number of nodes on an element face

◆ fmask

integer, dimension(:,:), allocatable scale_element_base::elementbase2d::fmask

Array saving indices to extract nodal values on the faces.

Definition at line 74 of file scale_element_base.F90.

74 integer, allocatable :: Fmask(:,:) !< Array saving indices to extract nodal values on the faces

◆ x1

real(rp), dimension(:), allocatable scale_element_base::elementbase2d::x1

Array saving x1-coordinate of nodes within the reference element.

Definition at line 76 of file scale_element_base.F90.

76 real(RP), allocatable :: x1(:) !< Array saving x1-coordinate of nodes within the reference element

◆ x2

real(rp), dimension(:), allocatable scale_element_base::elementbase2d::x2

Array saving x2-coordinate of nodes within the reference element.

Definition at line 77 of file scale_element_base.F90.

77 real(RP), allocatable :: x2(:) !< Array saving x2-coordinate of nodes within the reference element

◆ dx1

real(rp), dimension(:,:), allocatable scale_element_base::elementbase2d::dx1

Elementwise differential matrix for the x1-coordinate direction (Dx1 = M^-1 Sx1)

Definition at line 79 of file scale_element_base.F90.

79 real(RP), allocatable :: Dx1(:,:) !< Elementwise differential matrix for the x1-coordinate direction (Dx1 = M^-1 Sx1)

◆ dx2

real(rp), dimension(:,:), allocatable scale_element_base::elementbase2d::dx2

Elementwise differential matrix for the x2-coordinate direction (Dx2 = M^-1 Sx2)

Definition at line 80 of file scale_element_base.F90.

80 real(RP), allocatable :: Dx2(:,:) !< Elementwise differential matrix for the x2-coordinate direction (Dx2 = M^-1 Sx2)

◆ sx1

real(rp), dimension(:,:), allocatable scale_element_base::elementbase2d::sx1

Elementwise stiffness matrix for the x1-coordinate direction.

Definition at line 82 of file scale_element_base.F90.

82 real(RP), allocatable :: Sx1(:,:) !< Elementwise stiffness matrix for the x1-coordinate direction

◆ sx2

real(rp), dimension(:,:), allocatable scale_element_base::elementbase2d::sx2

Elementwise stiffness matrix for the x2-coordinate direction.

Definition at line 83 of file scale_element_base.F90.

83 real(RP), allocatable :: Sx2(:,:) !< Elementwise stiffness matrix for the x2-coordinate direction

The documentation for this type was generated from the following file:

scale_element_base.F90

Public Member Functions

Public Attributes