models/inspiration/praktikum_ellipt_model.m File Reference

small example of a model, i.e. a structure describing the data functions and geometry information of a general elliptic equation consisting of diffusion, convection, reaction equation: More...

Go to the source code of this file.

Functions
function model =	praktikum_ellipt_model ( params)
	small example of a model, i.e. a structure describing the data functions and geometry information of a general elliptic equation consisting of diffusion, convection, reaction equation:
function res =	praktikumelliptmodel>all_dirichlet_boundary_type ( glob, params)
function res =	praktikumelliptmodel>mixed_boundary_type ( glob, params)
function res =	praktikumelliptmodel>my_normals ( glob, params)

---

Detailed Description

small example of a model, i.e. a structure describing the data functions and geometry information of a general elliptic equation consisting of diffusion, convection, reaction equation:

Definition in file praktikum_ellipt_model.m.

---

Function Documentation

function model = praktikum_ellipt_model

(

params

)

small example of a model, i.e. a structure describing the data functions and geometry information of a general elliptic equation consisting of diffusion, convection, reaction equation:

• div ( a(x) grad u(x)) + div (b(x) u(x)) + c(x) u(x) = f(x) on Omega u(x)) = g_D(x) on Gamma_D a(x) grad u(x)) = g_N(x) on Gamma_N

Here, we denote the functions as u: solution (if known, useful for validation purpose) f: source a: diffusivity b: velocity c: reaction g_D: Dirichlet boundary values g_N: Neumann boundary values

Each function allows the evaluation in many points simultaneuously by

model.source(glob) or model.source(glob,params)

where glob is a n times 2 matrix of row-wise points. The result is a n times 1 vector of resulting values of f.

additionally, the model has a function, which determines, whether

a point lies on a Dirichlet or Neumann boundary

model.boundary_type(glob) 0 no boundary (inner edge or point) -1 indicates Dirichlet-boundary -2 indicates Neumann-boundary

The data functions given in this model are given on the exercise sheet Omega = [-1,1]^2 \ [0,1]^2 with Gamma_D = ecke oben rechts, Gamma_N = rand vom ursprünglichen 4eck

-div ( a div(u)) = f u = g_D on Gamma_D (a div(u))*n = g_N on Gamma_N

with exact solution u(x) = ||x||^(alpha),

params is an optional parameter, perhaps useful later

Parameters:

params

params

Return values:

model

model

Required fields of params:

• all_dirichlet_boundary —  all dirichlet boundary

Generated fields of model:

• source —  source
• reaction —  reaction
• velocity —  velocity
• diffusivity —  diffusivity
• boundary_type —  boundary type
• dirichlet_values —  dirichlet values
• normals —  normals
• neumann_values —  neumann values
• solution —  solution

Definition at line 1 of file praktikum_ellipt_model.m.