fv_frechet_operators_diff_implicit_gradient.m File Reference

computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U. More...

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Functions
function [ L_I_diff_jac , bdir_I_diff_jac ] =	fv_frechet_operators_diff_implicit_gradient (model, model_data, U, NU_ind)
	computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U.

Detailed Description

computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U.

Definition in file fv_frechet_operators_diff_implicit_gradient.m.

Function Documentation

function [ L_I_diff_jac , bdir_I_diff_jac ] = fv_frechet_operators_diff_implicit_gradient	(		model,
			model_data,
			U,
			NU_ind
	)

computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U.

function computing the jacobian in U of the implicit diffusion contribution of \(L_I\) and \(b_I\) to the time evolution matrices for a finite volume time step \(L_I U^{k+1} = L_E U^k + b_E + b_I\). With the help of the returned Jacobian L_I_diff_jac the Frechet derivative \(DL_I ({U})\) is approximated.

Note

The *_implicit functions perform a dt increase in model before evaluating the data functions.

Note: This only works when diffusivity is averaged on edge points by arithmetic mean, adapt the function, if you want to use geometric or harmonic mean functions.

Parameters

model	model
model_data	model data
U	U
NU_ind	NU ind

Return values

L_I_diff_jac	a sparse matrix with jacobian of diffusion contributions to \(L_I\).
bdir_I_diff_jac	and offset vector containing the Dirichlet value contributions of the diffusion parts.

Required fields of model:

• diffusivity_derivative_ptr —  diffusivity derivative ptr
• diffusivity_ptr —  diffusivity ptr

Definition at line 17 of file fv_frechet_operators_diff_implicit_gradient.m.