dirichlet_values.m File Reference

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...

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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])) More...

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 \(q\)-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.
• 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 17 of file dirichlet_values.m.