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fv_frechet_operators_diff_implicit_gradient3.m File Reference

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

Go to the source code of this file.

Functions

function spm = fv_frechet_operators_diff_implicit_gradient3 (model, model_data, U, NU_ind)
 computes a jacobian of implicit non-linear diffusion contributions to time evolution matrices at a point U. More...
 

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_gradient3.m.

Function Documentation

function spm = fv_frechet_operators_diff_implicit_gradient3 (   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.
Parameters
modelmodel
model_datamodel data
UU
NU_indNU ind
Return values
spma struct containing all arguments for the creation of a sparse matrix with the sparse command.
Required fields of model_data:
  • grid —  a structure containing geometry information of a mesh used for discretizations
Required fields of model:
  • mean_ptr —  mean ptr
  • mean_deriv1_ptr —  mean deriv1 ptr
  • mean_deriv2_ptr —  mean deriv2 ptr
  • verbose —  flag indicating the verbosity level of informative output
  • diffusivity_ptr —  diffusivity ptr
  • diffusivity_derivative_ptr —  diffusivity derivative ptr
  • dirichlet_values_ptr —  dirichlet values ptr
  • laplacian_ptr —  laplacian ptr
  • laplacian_derivative_ptr —  laplacian derivative ptr
Generated fields of spm:
  • sn —  sn
  • sm —  sm
  • si —  si
  • sj —  sj
  • svals —  svals

Definition at line 17 of file fv_frechet_operators_diff_implicit_gradient3.m.