scm_minimal_model.m

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function model = scm_minimal_model(size)
%model = scm_minimal_model(size)
%
% a minimal-example of size = size(input) with the following matrices:
% A =(1 0 0 ...   1   b = (0        K = (1 0 ...     0
%     1 1 0  ...  0        0             0 1 0 ...   0
%     0 1 1 0 ... 0       ...            0 0 1 0 ... 0
%       .....              0)               .....
%     0 ...     0 1)                     0 ....    0 1)
%
% with A^1 = K and A^2 holding the rest of A so that A = (1-mu)*A^1 + mu*A^2
% This is coercive for mu = 0 (with alpha = beta = 1) and inf-sup stable
% (but not coercive) for mu = 1.
% This minimal model is used in the scm_demo to proof, that the 'lin_stat'
% inf-sup code is actually working.

% Dominik Garmatter 20.09 2012

if nargin == 0
    model.size = 100;
else
    if ceil(size/2) == size/2
        model.size = size;
    else
        error('size has to be an even positiv number')
    end
end

model.rb_problem_type = 'lin_stat';
model.verbose = 30;
model.set_mu = @set_mu_default;
model.get_mu = @get_mu_default;
model.gen_model_data = @scm_minimal_model_gen_model_data;
model.get_inner_product_matrix = @(model_data) model_data.inner_product_matrix;
model.mu_names = {'mu'};
model.mu = 0;
model.mu_ranges = {[1e-10 1]};
model.decomp_mode = 0;
model.operators = @scm_minimal_model_operators;
model.use_scm = 1;
% some (not neccessary) settings for scm_offline.m:
model.scm_M_alpha = 70;
model.scm_M_plus = 200;
model.scm_eps_tol = eps;
model.scm_size_C = 50;

function model_data = scm_minimal_model_gen_model_data(model)

model_data = [];
model_data.inner_product_matrix = speye(model.size);


function [A,b] = scm_minimal_model_operators(model, model_data)


if ~isfield(model, 'decomp_mode')
    model.decomp_mode = 0;
end

H = model.size;


decomp_mode = model.decomp_mode;
if decomp_mode == 0
    b = zeros(H,1);
    A = (1-model.mu)*speye(H) + model.mu*(sparse(diag(ones(H-1,1),-1)) + sparse(1,H,1,H,H,1));
elseif decomp_mode == 1
    b = {zeros(H,1)};
    A = {speye(H); sparse(diag(ones(H-1,1),-1)) + sparse(1,H,1,H,H,1)};
else % decomp_mode = 2
    b = 1;
    A = [1-model.mu; model.mu];
end