nonlin_symmetry_model.m

function model=nonlin_symmetry_model(params)
% function model=nonlin_symmetry_model(params)
%
% optional fields of params:
%  size: problem size ( 0.1, 0.2, 0.5, 1, 2, 3, ... )

if nargin < 1 || ~isfield(params, 'size')
  params.size = 1;
end

model = nonlin_evol_model_default;
model.name = 'nonlin_symmetry';
model.gridtype = 'rectgrid';
model.xnumintervals = 120 * params.size;
model.ynumintervals = 60 * params.size;
model.xrange = [0,2];
model.yrange = [0,1];

% set all to neuman-boundary by specifying "rectangles", all
% boundary within is set to boundary type
%model.bnd_rect_corner1 = [-1; ...
%                           -1];
%model.bnd_rect_corner2 = [ 2; ...
%                           2];

% -1 means dirichlet, -2 means neumann
%model.bnd_rect_index =   [-2]; % first is dirichlet, second neuman

% time discretization
model.T = 0.3;
model.nt = 100 * params.size; % guess and adjust later
%model.nt = 25 * params.size; % guess and adjust later

%model.T = 0.4;
%model.nt = 80; % guess and adjust later
%model.nt = 100; % guess and adjust later
%model.T = 0.1;
%model.nt = 50; % guess and adjust later
%model.400 => non-bounded u

% output settings
model.verbose = 1;
model.debug = 0;

% data functions
%model.name_init_values = 'blobs'; 
%model.radius = 0.1;
%model.gamma = 100;
%model.beta = 1; % init data weight between 0 and 1

% name of function in rbmatlab/datafunc/init_values
model.init_values_ptr = @init_values_waveproduct; 
% parameters for data functions
model.c_init_min = 0.0;
model.c_init_max = 1.0;
model.c_init_phase_x = 0.0;
model.c_init_phase_y = 0.0;
model.c_init_freq_x = 2*pi;
model.c_init_freq_y = 2*pi;
%model.c_init_lo = 1.0;
%model.c_init_lo = 0.0;
%model.c_init_lo = -1.0;

% name of function in RBmatlab/datafunc/dirichlet_values
%model.name_dirichlet_values = 'homogeneous';
%model.c_dir = 0;

% name of function in RBmatlab/datafunc/neuman_values
%model.name_neuman_values = 'homogeneous';
%model.c_neu = 0;

%model.name_neuman_values = 'homogeneous';
%model.c_neu = 0;

% convective flux
%model.name_flux = 'burgers_parabola';
model.conv_flux_ptr = @conv_flux_burgers;
%| \todo this could also be done explicitly (analytic derivative)
model.conv_flux_derivative_ptr = @conv_flux_forward_difference;
% for simplifying computation in case of linear flux:
model.flux_linear = 0;
% diagonal velocity field
model.flux_vx = 1;
model.flux_vy = 1;
%model.flux_quad_degree = 2;
model.flux_pdeg = 1; % burgers exponent

% rb-formulation
%model.mu_names = {'c_init_lo','vrot_angle'}; 
model.mu_names = {'flux_pdeg'}; 
model.mu_ranges = {[1,2]};
model.rb_problem_type = 'nonlin_evol';
%model.problem_type = 'lin_evol';

% finite volume settings
%model.name_convective_num_flux = 'lax-friedrichs';
%model.lxf_lambda = 1.66
%model.lxf_lambda = 1.25;
%model.lxf_lambda = 0.35355;
%model.lxf_lambda = fv_search_max_lxf_lambda([],model);
%keyboard;
model.num_conv_flux_ptr = @fv_num_conv_flux_engquist_osher;
model.fv_expl_conv_weight = 1.0;
model.fv_impl_conv_weight = 0.0;
model.ei_space_operators = { model.L_E_local_ptr };
model.newton_solver = false;
model.newton_steps  = 60;
model.operators_conv_implicit    = ...
  @fv_operators_conv_explicit_engquist_osher;
model.implicit_gradient_operators_algorithm = ...
  @fv_operators_conv_explicit_engquist_osher;

% projection of analytical initial data to discrete function
model.init_values_algorithm = @fv_init_values;
model.implicit_operators_algorithm = @fv_operators_implicit;
% get mass matrix for inner product computation from DOF-vectors
model.data_const_in_time = 1;

% settings for empirical interpolation
par.range = model.mu_ranges;
model.ei_numintervals = [9]; % 8x8 parameter grid
model.Mmax = 300;
%model.Mmax = 160; % take 150 for sim, 10 for error-est
model.ei_detailed_savepath = ['nonlin_symmetry_detailed_', ...
                              num2str(length(model.ei_numintervals))];
model.ei_operator_savepath = ['nonlin_symmetry_ei_operator_', ...
                              num2str(length(model.ei_numintervals))];
model.ei_time_indices = 1:model.nt;

model.CRB_generation_mode = 'param-time-space-grid';
model.ei_target_error = 'interpol';

model.flux_quad_degree = 1;

% settings for reduced basis generation
%model.operators_algorithm = 'fv_operators_implicit_explicit';
%model.init_values_algorithm = 'fv_init_values';
%model.inner_product_matrix_algorithm = 'fv_inner_product_matrix';
%model.lxf_lambda = 1.0194e+003;
%model.data_const_in_time = 1;
model.error_norm = 'l2';
%                   'RB_extension_max_error_snapshot'}; 
model.RB_stop_timeout = 2*60*60; % 2 hours              
model.RB_stop_epsilon = 1e-5; 
model.RB_error_indicator = 'error'; % true error
%model.RB_error_indicator = 'estimator'; % Delta from rb_simulation
model.RB_stop_Nmax = 135;
model.RB_generation_mode = 'greedy_uniform_fixed';
model.RB_numintervals = model.ei_numintervals;
model.RB_detailed_train_savepath = model.ei_detailed_savepath;

model.t               = 0;
model.tstep           = 1;
model.decomp_mode     = 0;
model.orthonormalize  = @model_orthonormalize_qr;
model.ei_time_indices = 1:model.nt+1;
model.plot            = @fv_plot;
%model.mu              = zeros(size(model.mu_names));

model.enable_error_estimator = 1;
model.Mstrich = 1;

%| \docupdate