1 function rb_sim_data = lin_stat_rb_simulation(model,reduced_data)
2 %
function rb_sim_data = lin_stat_rb_simulation(model,reduced_data)
4 %
function performing a reduced simulation
6 % B. Haasdonk 22.2.2011
10 old_mode = model.decomp_mode;
11 model.decomp_mode = 2; % coefficients
13 [A_coeff,f_coeff] = ...
14 model.operators(model,[]);
16 AN = lincomb_sequence(reduced_data.AN_comp, A_coeff);
17 fN = lincomb_sequence(reduced_data.fN_comp, f_coeff);
27 % plus error estimator
28 % res_norm = ... % residual norm
30 %
for elliptic compliant
case, X-norm (=H10-norm) error estimator:
31 Q_r = size(reduced_data.G,1);
32 neg_auN_coeff = -A_coeff * uN';
33 res_coeff = [f_coeff; neg_auN_coeff(:)];
34 res_norm_sqr = res_coeff
' * reduced_data.G * res_coeff;
36 % direct computation (expensive):
39 neg_auN_coeff = neg_auN_coeff(:);
40 Q_f = length(f_coeff);
41 res_norm_sqr_ff = f_coeff' * reduced_data.G(1:Q_f,1:Q_f) * f_coeff;
42 res_norm_sqr_fAu = f_coeff
' * reduced_data.G(1:Q_f,(Q_f+1):end) * neg_auN_coeff;
43 res_norm_sqr_Auf = neg_auN_coeff' * reduced_data.G((Q_f+1):end,1:Q_f) * f_coeff;
44 res_norm_sqr_AuAu = neg_auN_coeff
' * reduced_data.G((Q_f+1):end,(Q_f+1):end) * neg_auN_coeff;
46 model_data = gen_model_data(model);
47 detailed_data = gen_detailed_data(model,model_data);
48 model.decomp_mode = 0;
49 [A,f] = model.operators(model,model_data);
50 model.decomp_mode = 2;
51 resAu = A * (detailed_data.RB(:,1:model.N) * uN);
54 % residuum functional is res * v
55 % riesz representant: v_r' K v = (v_r,v) = res*v
57 K = model.get_inner_product_matrix(detailed_data);
61 % res_norm_sqr = (v_r,v_r) = v_r
' K v_r = v_r' * res;
62 res_norm_sqr2 = v_r
' * res;
63 res_norm_sqr2_ff = v_rf' * resf;
64 res_norm_sqr2_fAu = v_rf
' * resAu;
65 res_norm_sqr2_Auf = v_rAu' * resf;
66 res_norm_sqr2_AuAu = v_rAu
' * resAu;
70 % prevent possibly negative numerical disturbances:
71 res_norm_sqr = max(res_norm_sqr,0);
72 res_norm = sqrt(res_norm_sqr);
73 % if the SCM is being used perform an online-phase and use the resulting
74 % lower bound. Otherwise use the old code.
76 rb_sim_data.Delta = ...
77 res_norm/model.coercivity_alpha(model);
78 rb_sim_data.Delta_s = ...
79 res_norm_sqr/model.coercivity_alpha(model);
80 elseif model.use_scm == 1
81 if ~isfield(reduced_data, 'scm_offline_data
')
82 error('There are no scm_offline_data to work with. They must be included in the reduced_data!
')
84 constant_LB = scm_lower_bound(model, reduced_data);
85 rb_sim_data.Delta = ...
87 rb_sim_data.Delta_s = ...
88 res_norm_sqr/constant_LB;
91 if model.compute_output_functional
94 model.operators_output(model,reduced_data);
96 lincomb_sequence(reduced_data.lN_comp,l_coeff);
97 rb_sim_data.s = lN(:)' * rb_sim_data.uN;
98 % rb_sim_data.Delta_s = ...;
101 model.decomp_mode = old_mode;