GetProjectionOfdNdXt

There are several interfaces to this generic method. In general, it takes the projection $\frac{dN}{dx}$ on the convective velocity $c$ , that is:

M^{I}=c_{k}\frac{\partial N^{I}}{\partial x_{k}}

Here, $c$ is the convective velocity, (that is a vector variable). It can be

a constant
a function of spatial coordinates given in terms of
- spatial nodal values
- quadrature values

If $c$ changes in space then it should be wrapped inside an instance of [[FEVariable_]].

You can learn about this method from the following pages

[[ElemshapeData_test_11]] for [[ReferenceTriangle]], constant velocity $c$
[[ElemshapeData_test_12]] for [[ReferenceTriangle]], nodal values of velocity $c$
[[ElemshapeData_test_13]] for [[ReferenceTriangle]], velocity $c$ is defined at the quadrature points.

This subroutine computes the projcetion cdNdXt on the vector val. Here the vector val is constant in space and time.

P^{I}=c_{i}\frac{\partial N^{I}}{\partial x_{i}}

MODULE PURE SUBROUTINE GetProjectionOfdNdXt(obj, cdNdXt, val)
  CLASS(ElemshapeData_), INTENT(IN) :: obj
  REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: cdNdXt(:, :)
  !! returned $c_{i}\frac{\partial N^{I}}{\partial x_{i}}$
  REAL(DFP), INTENT(IN) :: val(:)
  !! constant value of vector
END SUBROUTINE GetProjectionOfdNdXt

The following subroutine computes the projcetion cdNdXt on the vector val. Here the vector val is constant in space and time.

P^{I}=c_{i}\frac{\partial N^{I}}{\partial x_{i}}

MODULE PURE SUBROUTINE GetProjectionOfdNdXt(obj, cdNdXt, val)
  CLASS(ElemshapeData_), INTENT(IN) :: obj
  !! ElemshapeData object
  REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: cdNdXt(:, :)
  !! returned $c_{i}\frac{\partial N^{I}}{\partial x_{i}}$
  CLASS(FEVariable_), INTENT(IN) :: val
  !! constant value of vector
END SUBROUTINE GetProjectionOfdNdXt