GetInterpolation

This subroutine performs interpolation of a scalar from its spatial nodal values.

$$u=u_{I}N^{I}$$

  MODULE PURE SUBROUTINE getInterpolation_1(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:)
    !! Interpolation value of of scalar
    REAL(DFP), INTENT(IN) :: val(:)
    !! spatial nodal values of scalar
  END SUBROUTINE getInterpolation_1

The subroutine performs interpolation of a scalar from its space-time nodal values.

$$u=u^{a}_{I}N^{I}T_{a}$$

The resultant represents the interpolation value of val at spatial-quadrature points

  MODULE PURE SUBROUTINE getInterpolation_2(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), INTENT(INOUT), ALLOCATABLE :: interpol(:)
    !! Interpolation of scalar
    REAL(DFP), INTENT(IN) :: val(:, :)
    !! space-time nodal values of scalar
  END SUBROUTINE getInterpolation_2

The following subroutine performs interpolation of a scalar from its space-time nodal values.

$$u=u^{a}_{I}N^{I}T_{a}$$

The resultant represents the interpolation value of val at spatial-temporal quadrature points

  MODULE PURE SUBROUTINE getInterpolation_3(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    REAL(DFP), INTENT(INOUT), ALLOCATABLE :: interpol(:,:)
    !! space-time Interpolation of scalar
    REAL(DFP), INTENT(IN) :: val(:, :)
    !! space-time nodal values of scalar
  END SUBROUTINE getInterpolation_3

The following rotuine returns the interpolation of scalar variable. The scalar variable can be

• constant
• spatial nodal values
• spatial quadrature values
• space-time nodal values

This routine calls [[../configuration/interpolation]] function from the same module.

  MODULE PURE SUBROUTINE scalar_getInterpolation_4(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:)
    !! interpolation of scalar
    TYPE(FEVariable_), INTENT(IN) :: val
    !! Scalar FE variable
  END SUBROUTINE scalar_getInterpolation_4

The following subroutine performs interpolation of a scalar [[FEVariable_]]. The FE Variable can be a

• constant
• spatial nodal values
• spatial quadrature values
• space-time nodal values

$$u=u^{a}_{I}N^{I}T_{a}$$

The resultant represents the interpolation value of val at spatial-quadrature points.

  MODULE PURE SUBROUTINE scalar_getInterpolation_5(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :)
    !! space-time interpolation of scalar
    TYPE(FEVariable_), INTENT(IN) :: val
    !! scalar FE variable
  END SUBROUTINE scalar_getInterpolation_5

The following subroutine performs interpolation of a vector from its spatial nodal values.

$$u_{i}=u_{iI}N^{I}$$

  MODULE PURE SUBROUTINE vector_getInterpolation_1(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :)
    !! interpolation of vector
    REAL(DFP), INTENT(IN) :: val(:, :)
    !! nodal values of vector in `xiJ` format
  END SUBROUTINE vector_getInterpolation_1

This subroutine performs interpolation of a vector from its space-time nodal values

$$u_{i}=u^{a}_{iI}N^{I}T_{a}$$

  MODULE PURE SUBROUTINE vector_getInterpolation_2(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), INTENT(INOUT), ALLOCATABLE :: interpol(:, :)
    !!
    REAL(DFP), INTENT(IN) :: val(:, :, :)
    !! space-time nodal values of vector in `xiJa` format
  END SUBROUTINE vector_getInterpolation_2

This subroutine performs interpolation of a vector from its space-time nodal values

$$u_{i}=u^{a}_{iI}N^{I}T_{a}$$

  MODULE PURE SUBROUTINE vector_getInterpolation_3(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    REAL(DFP), INTENT(INOUT), ALLOCATABLE :: interpol(:, :,:)
    !!
    REAL(DFP), INTENT(IN) :: val(:, :, :)
    !! space-time nodal values of vector in `xiJa` format
  END SUBROUTINE vector_getInterpolation_3

The following routine returns the interpolation of vector variable. The vector variable can be+

• constant
• spatial nodal values
• spatial quadrature values
• space-time nodal values

NOTE This routine calls [[../configuration/interpolation]] function from the same module.

  MODULE PURE SUBROUTINE vector_getInterpolation_4(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :)
    !! interpolation of vector
    TYPE(FEVariable_), INTENT(IN) :: val
    !! vector FEvariable
  END SUBROUTINE vector_getInterpolation_4

The following routine returns the interpolation of vector variable. The vector variable can be+

• constant
• spatial nodal values
• spatial quadrature values
• space-time nodal values

NOTE This routine calls [[#Interpolation]] function from the same module.

  MODULE PURE SUBROUTINE vector_getInterpolation_5(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :, :)
    !! space-time interpolation of vector
    TYPE(FEVariable_), INTENT(IN) :: val
    !! vector FEvariable
  END SUBROUTINE vector_getInterpolation_5

The following subroutine performs interpolation of matrix

  MODULE PURE SUBROUTINE matrix_getInterpolation_1(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :, :)
    !! interpolation of matrix
    REAL(DFP), INTENT(IN) :: val(:, :, :)
    !! nodal value of matrix
  END SUBROUTINE matrix_getInterpolation_1

The following subroutine performs interpolation of matrix from its space-time nodal values

  MODULE PURE SUBROUTINE matrix_getInterpolation_2(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), INTENT(INOUT), ALLOCATABLE :: interpol(:, :, :)
    REAL(DFP), INTENT(IN) :: val(:, :, :, :)
    !! space-time nodal value of matrix
  END SUBROUTINE matrix_getInterpolation_2

The following subroutine performs interpolation of matrix from its space-time nodal values

  MODULE PURE SUBROUTINE matrix_getInterpolation_3(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    REAL(DFP), INTENT(INOUT), ALLOCATABLE :: interpol(:, :, :,:)
    !! space-time interpolation
    REAL(DFP), INTENT(IN) :: val(:, :, :, :)
    !! space-time nodal value of matrix
  END SUBROUTINE matrix_getInterpolation_3

The following subroutine performs interpolation of matrix FEVariable

  MODULE PURE SUBROUTINE matrix_getInterpolation_4(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :, :)
    !! interpolation of matrix
    TYPE(FEVariable_), INTENT(IN) :: val
    !! matrix fe variable
  END SUBROUTINE matrix_getInterpolation_4

  MODULE PURE SUBROUTINE matrix_getInterpolation_5(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: interpol(:, :, :, :)
    !! space-time interpolation of matrix
    TYPE(FEVariable_), INTENT(IN) :: val
    !! matrix fe variable
  END SUBROUTINE matrix_getInterpolation_5

• Returns the interpolation of a [[FEVariable_]]
• The result is returned in interpol
• interpol is a FEVariable
• The rank of interpol is same as the rank of val
• interpol is defined on Quadrature, that is, interpol is QuadratureVariable
• The val can have following ranks; scalar, vector, matrix
• the val can be defined on quadrature (do nothing) or nodal (interpol)
• The vartype of val can be constant, space, time, spacetime

  MODULE PURE SUBROUTINE master_getInterpolation_1(obj, interpol, val)
    CLASS(ElemshapeData_), INTENT(IN) :: obj
    TYPE(FEVariable_), INTENT(INOUT) :: interpol
    TYPE(FEVariable_), INTENT(IN) :: val
  END SUBROUTINE master_getInterpolation_1

The following routine returns the interpolation of a [[fevariable_]]

• The result is returned in interpol
• interpol is a FEVariable
• The rank of interpol is same as the rank of val
• interpol is defined on Quadrature, that is, interpol is QuadratureVariable
• The val can have following ranks; scalar, vector, matrix
• the val can be defined on quadrature (do nothing) or nodal (interpol)
• The vartype of val can be constant, space, time, spacetime

  MODULE PURE SUBROUTINE master_getInterpolation_2(obj, interpol, val)
    CLASS(STElemshapeData_), INTENT(IN) :: obj(:)
    TYPE(FEVariable_), INTENT(INOUT) :: interpol
    TYPE(FEVariable_), INTENT(IN) :: val
  END SUBROUTINE master_getInterpolation_2

To learn more these methods check out the following pages.

• [[ElemshapeData_test_21]] Use of getInterpolation, interpolation of [[FEVariable]] in the form of [[FEVariable_]] for scalars
• [[ElemshapeData_test_22]] Use of getInterpolation, interpolation of [[FEVariable]] in the form of [[FEVariable_]] for vectors
• [[ElemshapeData_test_23]] Use of getInterpolation, interpolation of [[FEVariable]] in the form of [[FEVariable_]] for matrix.