rbmatlab  1.16.09
 All Classes Namespaces Files Functions Variables Modules Pages
Functions
fv_operators_neumann_explicit.m File Reference

computes a neumann contribution matrix for finite volume time evolution operators, or their Frechet derivative More...

Go to the source code of this file.

Functions

function [
L_E_neu ,
b_E_neu ] = 
fv_operators_neumann_explicit (model, model_data, U, NU_ind)
 computes a neumann contribution matrix for finite volume time evolution operators, or their Frechet derivative More...
 

Detailed Description

computes a neumann contribution matrix for finite volume time evolution operators, or their Frechet derivative

Definition in file fv_operators_neumann_explicit.m.

Function Documentation

function [ L_E_neu , b_E_neu ] = fv_operators_neumann_explicit (   model,
  model_data,
  U,
  NU_ind 
)

computes a neumann contribution matrix for finite volume time evolution operators, or their Frechet derivative

This function computes the neumann boundary contribution operator \(L_{\text{neu}}\) and a corresponding vector \( b_{\text{neu}}\) that can be used by fv_operators_implicit_explicit() to build evolution matrices for a finite volume time step \(L_I U^{k+1} = L_E U^k + b_E + b_I\). This operator contribution must be activated via the flag model.operators_neumann_implicit

The analytical terms inspiring this operator look like \( f(u) \cdot n = b_{\text{neu}}(u) \quad \text{on }\partial \Omega_{\text{neu}},\) where \(f\) can be some flux function, e.g. chosen via the model.conv_flux_ptr and \(b_{\text{neu}}(u)\) is the neumann boundary condition selected via model.neumann_values_ptr.

See also
fv_operators_conv_explicit_engquist_osher(), fv_operators_diff_implicit_gradient(), fv_operators_diff_implicit_gradient_tensor()
Parameters
modelmodel
model_datamodel data
UU
NU_indNU ind
Return values
L_E_neusparse matrix \(L_{\text{neu}}\)
b_E_neuoffset vector \(b_{\text{neu}}\)
Required fields of model:
  • neumann_values_ptr — 
  • decomp_mode —  flag indicating the operation mode of the function:
    • 0 (complete) : no affine parameter dependence or decomposition is performed.
    • 1 (components) : for each output argument a cell array of output matrices is returned representing the \(q\)-th component independent of the parameters given in mu_names.
    • 2 (coefficients) : returns a vector where each coordinate represents the \(q\)-the coefficient \(\sigma_{\cdot}^{q}(\mu)\) dependent on the parameters given in mu_names.
  • verbose —  flag indicating the verbosity level of informative output
  • flux_linear —  flux linear
  • conv_flux_ptr —  conv flux ptr
  • conv_flux_derivative_ptr —  conv flux derivative ptr
Required fields of model_data:
  • grid —  a structure containing geometry information of a mesh used for discretizations

Definition at line 17 of file fv_operators_neumann_explicit.m.

Here is the caller graph for this function: