mod_hessian_operator_cell_to_cell Module Reference

Hessian operator from cells to cells.

Functions/Subroutines
subroutine	hessian_operator_cell_to_cell (field, hessian, order)
	Hessian matrix using n-th order centered differences. More...
subroutine	hessian_operator_cell_to_cell_generic (scheme_first, scheme_second, field, field_res)
	Compute the hessian of field on cells with the given scheme. More...

Function/Subroutine Documentation

hessian_operator_cell_to_cell()

subroutine mod_hessian_operator_cell_to_cell::hessian_operator_cell_to_cell	(	double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:,:,:), intent(inout)	hessian,
		integer	order
	)

Hessian matrix using n-th order centered differences.

The Hessian of \( \phi \) is the matrix

\begin{align} \mathbf{H} \phi &= \begin{pmatrix} \frac{\partial^2 \phi}{\partial x \partial x} & \frac{\partial^2 \phi}{\partial x \partial y} & \frac{\partial^2 \phi}{\partial x \partial z} \\ \frac{\partial^2 \phi}{\partial y \partial x} & \frac{\partial^2 \phi}{\partial y \partial y} & \frac{\partial^2 \phi}{\partial y \partial z} \\ \frac{\partial^2 \phi}{\partial z \partial x} & \frac{\partial^2 \phi}{\partial z \partial y} & \frac{\partial^2 \phi}{\partial z \partial z} \end{pmatrix} \,. \end{align}

The actual scheme is selected using the order and direction arguments. The former selects the order of finites differences, while the latter select the centering

Valid values for order is 2 and 4.

Parameters

[in]	field	cell field to derivate
[in,out]	hessian	rank-5 cell field holding the Hessian
[in]	order	of the finite-difference scheme

hessian_operator_cell_to_cell_generic()

subroutine mod_hessian_operator_cell_to_cell::hessian_operator_cell_to_cell_generic	(	class(t_fd_scheme), intent(inout)	scheme_first,
		class(t_fd_scheme), intent(inout)	scheme_second,
		double precision, dimension(:,:,:), intent(in)	field,
		double precision, dimension(:,:,:,:,:), intent(inout)	field_res
	)

Parameters

[in,out]	scheme_first	the FD scheme
[in,out]	scheme_second	the FD scheme
[in]	field	the input field for which we comptue the gradient
[in,out]	field_res	the resulting gradient field