UDIRICHLET = DIRICHLET_VALUES([X],[Y], MODEL) Examples dirichlet_values([0,1,2],[1,1,1],struct(name_dirichlet_values, homogeneous, ... c_dir, 1)) dirichlet_values([0:0.1:1],[0],struct(name_dirichlet_values, xstripes, ... c_dir, [0 1 2], ... dir_borders, [0.3 0.6])) dirichlet_values([0:0.1:1],[0],struct(name_dirichlet_values, box, ... c_dir, 1, ... dir_box_xrange, [0.3 0.6], ... dir_box_yrange, [-0.1 0.1])) More...

Functions
function Udirichlet =	dirichlet_values ( model, X, Y)
	UDIRICHLET = DIRICHLET_VALUES([X],[Y], MODEL) Examples dirichlet_values([0,1,2],[1,1,1],struct(`name_dirichlet_values`, `homogeneous`, ... `c_dir`, 1)) dirichlet_values([0:0.1:1],[0],struct(`name_dirichlet_values`, `xstripes`, ... `c_dir`, [0 1 2], ... `dir_borders`, [0.3 0.6])) dirichlet_values([0:0.1:1],[0],struct(`name_dirichlet_values`, `box`, ... `c_dir`, 1, ... `dir_box_xrange`, [0.3 0.6], ... `dir_box_yrange`, [-0.1 0.1]))

Detailed Description

UDIRICHLET = DIRICHLET_VALUES([X],[Y], MODEL) Examples dirichlet_values([0,1,2],[1,1,1],struct(name_dirichlet_values, homogeneous, ... c_dir, 1)) dirichlet_values([0:0.1:1],[0],struct(name_dirichlet_values, xstripes, ... c_dir, [0 1 2], ... dir_borders, [0.3 0.6])) dirichlet_values([0:0.1:1],[0],struct(name_dirichlet_values, box, ... c_dir, 1, ... dir_box_xrange, [0.3 0.6], ... dir_box_yrange, [-0.1 0.1]))

Definition in file dirichlet_values.m.

Function Documentation

function Udirichlet = dirichlet_values	(	model,
		X,
		Y
	)

UDIRICHLET = DIRICHLET_VALUES([X],[Y], MODEL) Examples dirichlet_values([0,1,2],[1,1,1],struct(name_dirichlet_values, homogeneous, ... c_dir, 1)) dirichlet_values([0:0.1:1],[0],struct(name_dirichlet_values, xstripes, ... c_dir, [0 1 2], ... dir_borders, [0.3 0.6])) dirichlet_values([0:0.1:1],[0],struct(name_dirichlet_values, box, ... c_dir, 1, ... dir_box_xrange, [0.3 0.6], ... dir_box_yrange, [-0.1 0.1]))

function computing dirichlet-values by pointwise evaluations zero Udirichlet = 0 homogeneous Udirichlet = c_dir leftright Udirichlet = c_dir_left for x <= dir_middle Udirichlet = c_dir_right for x > dir_middle xstripes values constant in stripes divided by x-coordinats n+1 values are given in c_dir the separating coodrinates in dir_borders box: values constant model.c_dir in box given by model.dir_box_xrange and dir_box_yrange weighted_boxes: values constant model.c_dir in box given by (beta=1): model.dir_box_xrange{1} and dir_box_yrange{1} (beta=0): model.dir_box_xrange{2} and dir_box_yrange{2} for intermediate betas, the two boxes are weighted gauss_convcomb: convex combination of gaussian distributions at left border function_ptr : dirichlet function given by function

pointer to complete evaluation: model.dirichlet_values_ptr Function must allow call U = f(X,Y,model), where X, Y are vectors of the same size. Return is a vector of values in the corresponding points. decomp_function_ptr : dirichlet function given by function pointer to components and coefficients: model.dirichlet_values_coefficients_ptr Function must allow call U = f([],[],model) Return is a vector of length Q with (parameter dependent) coefficients in U. model.dirichlet_values_components_ptr Functions must allow call U = f(X,Y,model), where X, Y are vectors of the same size. Return of components is a cell array of vectors of the same size as X and Y with the point values of the components. Linear combination of components by coefficients then yields the complete evaluation.

in case of gld-dirichlet-value: upper wall value c_dir, remaining 0.0

Function supports affine decomposition, i.e. different operation modes guided by optional field affine_decomp_mode in model.

See also:: the contents.txt for general explanation

in coefficients mode, the parameters in brackets are empty

Parameters:

model	model
X	X
Y	Y

Return values:

Udirichlet Udirichlet

Required fields of model:

name_dirichlet_values — zero, homogeneous, leftright, uplow
c_dir(s) — boundary value(s) in case of homogeneous dirichlet value or stripes or box
c_dir_left — left dirichlet value
c_dir_right — left dirichlet value
c_dir_up — upper dirichlet value
c_dir_low — lower dirichlet value
dir_middle — coordinate for separatin between two domains
dir_borders — coordinates for separation between stripes
dir_box_xrange — x-coordinate interval for dirichlet box
dir_box_yrange — y-coordinate interval for dirichlet box
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 -th component independent of the parameters given in mu_names.
- 2 (coefficients) : returns a vector where each coordinate represents the -the coefficient $\sigma_{\cdot}^{q}(\mu)$ dependent on the parameters given in mu_names.
c_dir — c dir
beta — beta
udir_xscale — udir xscale
udir_amplitude — udir amplitude
udir_height — udir height
dirichlet_values_coefficients_ptr — dirichlet values coefficients ptr
dirichlet_values_components_ptr — dirichlet values components ptr
dirichlet_values_ptr — dirichlet values ptr

Optional fields of model:

mu_names — names of fields to be regarded as parameters in vector mu
affine_decomp_mode — operation mode of the function none (default): no parameter dependence or decomposition is performed. output is as described above.
components — For each output argument a cell array of output arguments is returned representing the q-th component independent of the parameters given in mu_names
coefficients — For each output argument a cell array of output arguments is returned representing the q-th coefficient dependent of the parameters given in mu_names

Documentation Update:

Definition at line 1 of file dirichlet_values.m.

Functions

Detailed Description

Function Documentation