scale_element_operation_tensorprod3d_interp Module Reference

module FElib / Element / Interpolation with 3D tensor product elements More...

Data Types
type	elementoptrtensorprod3dinterp
	Derived type for interpolation operation with 3D tensor product element. More...

Functions/Subroutines
subroutine	elementoptrtensorprod3dinterp_init (this, elem, polyorder_h_ip)

Detailed Description

module FElib / Element / Interpolation with 3D tensor product elements

Description

A module for providing interpolation operations assuming a 3D tensor product element with (p+1)^3 DOF

Author

Yuta Kawai, Xuanzhengbo Ren, and Team SCALE

Function/Subroutine Documentation

elementoptrtensorprod3dinterp_init()

subroutine scale_element_operation_tensorprod3d_interp::elementoptrtensorprod3dinterp_init	(	class(elementoptrtensorprod3dinterp), intent(inout)	this,
		type(elementbase3d), intent(in), target	elem,
		integer, intent(in)	polyorder_h_ip )

Definition at line 70 of file scale_element_operation_tensorprod3D_interp.F90.

    use scale_linalgebra, only: linalgebra_inv
    use scale_polynomial, only: &
      polynomial_genlegendrepoly,    &
      polynomial_gengausslegendrept, &
      polynomial_gengausslegendreptintweight
    use scale_element_line, only: lineelement
    use scale_prc
    implicit none
    class(ElementOptrTensorProd3DInterp), intent(inout) :: this
    type(ElementBase3D), intent(in), target :: elem
    integer, intent(in) :: Polyorder_h_ip
 
    real(RP) :: r_int1D_i(Polyorder_h_ip+1)
    real(RP) :: r_int1Dw_i(Polyorder_h_ip+1)
    real(RP) :: P_int1D_ori_h(Polyorder_h_ip+1,elem%PolyOrder_h+1)
    real(RP) :: Vint1D(Polyorder_h_ip+1,elem%PolyOrder_h+1)
 
    real(RP) :: P1D_gl_h(Polyorder_h_ip+1,Polyorder_h_ip+1)
    real(RP) :: P1D_gll_h(elem%Nnode_h1D,Polyorder_h_ip+1)
    real(RP) :: Vint1D_gl(elem%Nnode_h1D,Polyorder_h_ip+1)
 
    integer :: p1, p1_
    integer :: n_, l_
 
    type(LineElement) :: elem1D
    !----------------------------------------
 
    this%elem => elem
    this%PolyOrder_h_intrp = polyorder_h_ip
    this%NnodeH1D_GL = polyorder_h_ip + 1
    this%Np3D_hGLvGLL = this%NnodeH1D_GL**2 * elem%Nnode_v
    this%Np3D = elem%Np
 
    allocate( this%IntrpMat1D_gll2gl(this%NnodeH1D_GL,elem%Nnode_h1D) )
    allocate( this%IntrpMat1D_gll2gl_tr(elem%Nnode_h1D,this%NnodeH1D_GL) )
 
    !-
    call elem1d%Init( elem%PolyOrder_h, .false. )
    r_int1d_i(:) = polynomial_gengausslegendrept( this%NnodeH1D_GL )
    r_int1dw_i(:) = polynomial_gengausslegendreptintweight(this%NnodeH1D_GL )
    p_int1d_ori_h(:,:) = polynomial_genlegendrepoly( elem%PolyOrder_h, r_int1d_i )
 
    do p1_=1,this%NnodeH1D_GL
      n_ = p1_
      do p1=1, elem%Nnode_h1D
        l_ = p1
        vint1d(n_,l_) = p_int1d_ori_h(p1_,p1) * sqrt( real(p1-1,kind=rp) + 0.5_rp )
      end do
    end do
    this%IntrpMat1D_gll2gl(:,:) = matmul( vint1d, elem1d%invV )
    this%IntrpMat1D_gll2gl_tr(:,:) = transpose(this%IntrpMat1D_gll2gl)
 
    !-
    allocate( this%V1D_GL(this%NnodeH1D_GL,polyorder_h_ip+1) )
    allocate( this%inv_V1D_GL(polyorder_h_ip+1,this%NnodeH1D_GL) )
    allocate( this%IntrpMat1D_gl2gll(elem%Nnode_h1D,this%NnodeH1D_GL) )
    allocate( this%IntrpMat1D_gl2gll_tr(this%NnodeH1D_GL,elem%Nnode_h1D) )
 
    p1d_gl_h(:,:) = polynomial_genlegendrepoly( polyorder_h_ip, r_int1d_i )
    p1d_gll_h(:,:) = polynomial_genlegendrepoly( polyorder_h_ip, elem1d%x1 )
 
    do p1_=1, this%NnodeH1D_GL
      n_ = p1_
      do p1=1, polyorder_h_ip+1
        l_ = p1
        this%V1D_GL(n_,l_) = p1d_gl_h(p1_,p1) * sqrt( real(p1-1,kind=rp) + 0.5_rp )
      end do
    end do
    this%inv_V1D_GL(:,:) = linalgebra_inv( this%V1D_GL(:,:) )
 
    vint1d_gl(:,:) = 0.0_rp
    do p1_=1,this%elem%Nnode_h1D
      n_ = p1_
      do p1=1, this%NnodeH1D_GL
        l_ = p1
        vint1d_gl(n_,l_) = p1d_gll_h(p1_,p1) * sqrt( real(p1-1,kind=rp) + 0.5_rp )
      end do
    end do
    this%IntrpMat1D_gl2gll(:,:) = matmul( vint1d_gl, this%inv_V1D_GL )
    this%IntrpMat1D_gl2gll_tr(:,:) = transpose(this%IntrpMat1D_gl2gll(:,:))
 
    !-
    call elem1d%Final()
    return

References scale_linalgebra::linalgebra_inv(), scale_polynomial::polynomial_gengausslegendrept(), scale_polynomial::polynomial_gengausslegendreptintweight(), and scale_polynomial::polynomial_genlegendrepoly().