Regarding a change in step-26 initial condition

[Pawan Kumar]

Dear all;

To incorporate adaptive mesh refinement after each time steps in my ongoing work, I am trying to make follwoing small changes in step-26:

i. Initial condition 

ii. A rectangular domain

iii. Homogeneous Neumann BC.

But I am getting some errors(negative values) in the obtained initial condition plot. The changes I have done in the following ways(also the code and initial plot is attached for your reference):

The initial values class is defined and called similar to step 23/31:

Template <int dim>
class InitialValues : public Function<dim>
{
public:
	InitialValues()
: Function<dim>(1)
  {}
	virtual double value(const Point<dim> & p,
			const unsigned int component = 0) const;
};
template <int dim>
double InitialValues<dim>::value(const Point<dim> &p,
		const unsigned int component) const
		{
	Assert (component == 0, ExcInternalError());
	const double radius = 0.2;
	const double sigma = 0.1;

	const double centerx = 0.0;
	const double centery = 0.0;
	const double dx =  pow(p[0]-centerx,2);
	const double dy =  pow(p[1]-centery,2);
	const double distance = sqrt(dx+dy);

	double f_val = exp(-(dx+dy)/(2*pow(sigma,2)));

	if ((distance-radius)<1e-25)
		return f_val;
	else
		return 0;

		}

VectorTools::project(dof_handler,
			constraints,
			QGauss<dim>(fe.degree + 1),
			InitialValues<dim>(),
			old_solution);

The grid is generation:

GridGenerator::hyper_cube(triangulation,-1,1);

Due to homogeneous Neumann BC, I have removed the boundary class and related functions.

I could not understand the reason for this, could someone please guide me in this regard?

Thanks & Regards

Pawan

[Wolfgang Bangerth]

On 3/13/20 6:08 AM, Pawan Kumar wrote:
>
> To incorporate adaptive mesh refinement after each time steps in my ongoing work, I am trying to make follwoing small changes in step-26:
>
>
> i. Initial condition
>
> ii. A rectangular domain
>
> iii. Homogeneous Neumann BC.
>
>
> But I am getting some errors(negative values) in the obtained initial condition plot.

That is to be expected. The *projection* of a non-negative function
will, in general, not be a non-negative function. The reason is
essentially the same as when you do a truncated Fourier series of a
discontinuous function: You get Gibb's phenomenon.

If these negative values bother you, try *interpolating* the initial
conditions instead of projecting them.

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Pawan Kumar]

Dear Prof. Bangerth,

Thank you very much for the explanation. Interpolation of the initial condition works pretty well!

Thanks & Regards

Pawan

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