Basics3_Nonlinear.m

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namespace demos{


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function  Basics3_Nonlinear() {


/*  Please see Basics1 and Basics2 for more elementary setups. For the
 * burgers model, most of the setup has been moved into class constructors
 * of classes inheriting from models.BaseFullModel and models.BaseFirstOrderSystem. */

dim = 500;

/* % Model and system setup
 * The original burgers model has a nonzero initial condition and no inputs.
 * we add the same things here as also been used in the a-posteriori error
 * estimation paper. */
m = models.burgers.Burgers(dim,2);
/*  This solver solves the linear part implicitly and the nonlinear party
 * explicitly. */
m.ODESolver= solvers.SemiImplicitEuler(m);
/*  This determines the plot angle for the burgers plots. */
m.PlotAzEl= [-49 34];
m.SaveTag= sprintf(" burgers_d%d_fx1_bs1 ",m.Dimension);

s = m.System;
/*  Zero initial value */
s.x0= dscomponents.ConstInitialValue(zeros(dim,1));
/*  Add Inputs */
x = linspace(m.Omega(1),m.Omega(2),dim+2);
x = x(2:end-1);
pos1 = logical((x >= .1) .* (x <= .3));
pos2 = logical((x >= .6) .* (x <= .7));
s.Inputs[1] = @(t)[sin(2*t*pi); (t>.2)*(t<.4)];
B = zeros(dim,2);
B(pos1,1) = 4*exp(-((x(pos1)-.2)/.03).^2);
B(pos2,2) = 4;
s.B= dscomponents.LinearInputConv(B);

/* % Setup reduction */
m.TrainingInputs= 1;

/*  Sampling - log-grid */
p = m.System.Params(1);
p.Range= [0.01, 0.06];
p.Desired= 20;
p.Spacing= " log ";
m.Sampler= sampling.GridSampler;

/*  Space reduction
 * m.ComputeTrajectoryFxiData = true; */
p = spacereduction.PODReducer;
/*  p.IncludeTrajectoryFxiData = true; */
p.IncludeFiniteDifferences= false;
p.IncludeBSpan= true;
p.Mode= " abs ";
p.Value= 50;
m.SpaceReducer= p;

/*  Approximation of nonlinearity: Choose DEIM method here */
a = approx.DEIM;
a.MaxOrder= 100;
m.Approx= a;

/*  Run offline phase */
m.offlineGenerations;
save basic3_nonlinear;
/* load basic3_nonlinear; */

/* % Build reduced model and do some analysis
 * Details on construction of reduced models see Basics2! */
r = m.buildReducedModel;
/*  Set the reduced DEIM approximation order to 25, and 10 orders for the
 * error estimator. */
r.System.f.Order= [25 10];
mu = m.getRandomParam(1,1);
ma = ModelAnalyzer(r);
ma.compareRedFull(mu,1);
ma.analyzeError(mu,1);

/* % Goodie: start the DEIM error estimator analyzer! */
DEIMEstimatorAnalyzer(r);
}
};