Re: [deal.II] Re: Why fe.shape_value( const unsigned int i, const Point< dim > & p ) return a negative number?

2018-05-07 Thread Zhao Yidong 
Thanks a lot! I get the same answer by using quadrature.point(q), and I get 
the similar answer after I transfer the real space point into reference 
space( [0, 1]x[0, 1] ), and then use fe.shape_value(reference_point).

Best
Yidong

在 2018年5月7日星期一 UTC+8下午2:37:22，Wolfgang Bangerth写道：
>
> On 05/07/2018 02:20 PM, Zhao Yidong wrote: 
> > 
> > 2.Iterate on every quadrature point in every cell, store them. (These 
> points 
> > are in real space right?) 
> > | 
> > 
> > for(unsignedq=0;q > 
> > Pointpoint =fe_values.quadrature_point(q); 
> > 
> > | 
> > 
> > 3. Use fe.shape_value() to get shape value at every degree of a cell, 
> > store_point is the point I store in the 2nd step. 
> > | 
> > 
> > doubleshapeValue =fe.shape_value(i,store_point);// shape value 
> > 
> > | 
>
> This is your problem. 'store_point' lives in real space, but 
> 'fe.shape_value' 
> wants a point on the reference cell. You need to call 
>fe.shape_value (quadrature.point(q)); 
>
> Best 
>   W. 
>
>
> -- 
>  
> Wolfgang Bangerth  email: bang...@colostate.edu 
>  
> www: http://www.math.colostate.edu/~bangerth/ 
>
>

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Re: [deal.II] Re: Why fe.shape_value( const unsigned int i, const Point< dim > & p ) return a negative number?

2018-05-07 Thread Wolfgang Bangerth 

On 05/07/2018 02:20 PM, Zhao Yidong wrote:


2.Iterate on every quadrature point in every cell, store them. (These points 
are in real space right?)

|

for(unsignedq=0;q

Re: [deal.II] Re: Why fe.shape_value( const unsigned int i, const Point< dim > & p ) return a negative number?

2018-05-07 Thread Zhao Yidong 
Thank you very much!

My fe is FE_Q(1) type:

FE_Q(1)

I make comparison like this:
1.Create fe_values like this:

FEValues fe_values(fe, quadrature,

   update_values |

   update_quadrature_points | 

   update_gradients |
   update_JxW_values);

2.Iterate on every quadrature point in every cell, store them. (These 
points are in real space right?)

for (unsigned q=0; qvertex(numberPoint);
Use these nodes, I transfer the real point into a reference point.

2. I use these points in reference space to calculate shape function:

double shapeValue = fe.shape_value(i, reference_point); // shape value
This also gives me different answer with fe_values

I will check can I get the same answer if I transfer the real point into 
reference point(in [0,1]x[0,1]).

(My understanding of gradient is differential, so can I calculate it by 
finite difference?
I can get forward_point = current_point + Point(epsilon, 0, 0)
and backward_point = current_point - Point(-epsilon, 0, 0)
to calculate gradient[0] = (shape_function(forward_point) - 
shape_function(backward_point)) / 2*epsilon,

and the same way for gradient[1], gradient[2] in 3d space ?)

Thanks again!

Best
Yidong










在 2018年5月7日星期一 UTC+8下午1:20:34，Wolfgang Bangerth写道：
>
> On 05/06/2018 09:05 AM, Zhao Yidong wrote: 
> > 
> > Indeed, my problem is this: 
> > 1. I have fe which is a FiniteElement class, and I have fe_values which 
> is a 
> > FEValues class. I also have QGauss quadrature to create fe_values. 
> > 2. I iterate on every quadrature point in a iteration on every cell, 
> store the 
> > quadrature points. 
> > 3. Use fe_values.value(i, q) to calculate shape functions, and 
> > fe.shape_value(i, point) to calculate another shape function, but find 
> they 
> > are different. 
> > 
> > So I want to know what's the difference between this two methods? 
> Because I 
> > want to separate the fe and quadrature points, so can I use 
> fe.shape_value to 
> > calculate the shape functions? 
>
> FiniteElement defines shape functions on the reference element. FEValues 
> describes these shape functions on the real cell. For many elements, you 
> get 
> the same result whether you 
> * evaluate the shape function on the reference cell at a quadrature point 
>also defined on the reference cell (via FiniteElement::shape_value and 
>Quadrature::point) 
> * evaluate the shape function on the real cell at a quadrature point 
>also defined on the real cell (via FEValues::shape_value, with 
> quadrature 
>point locations also available from FEValues). 
>
> But there are also elements for which this is not true. It's not clear to 
> me 
> what exactly you do in your comparison -- can you show a piece of code? 
>
> (You will have to use FEValues anyway at one point if you also want the 
> *gradients* of the shape functions -- these are never the same on 
> reference 
> and real cell.) 
>
> Best 
>   W. 
>
> -- 
>  
> Wolfgang Bangerth  email: bang...@colostate.edu 
>  
> www: http://www.math.colostate.edu/~bangerth/ 
>
>

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[deal.II] Re: Why fe.shape_value( const unsigned int i, const Point< dim > & p ) return a negative number?

2018-05-05 Thread Zhao Yidong 
Thanks a lot, it's really clear to understand by the help of the website 
you share!

Indeed, my problem is this:
1. I have fe which is a FiniteElement class, and I have fe_values which is 
a FEValues class. I also have QGauss quadrature to create fe_values.
2. I iterate on every quadrature point in a iteration on every cell, store 
the quadrature points.
3. Use fe_values.value(i, q) to calculate shape functions, and 
fe.shape_value(i, point) to calculate another shape function, but find they 
are different.

So I want to know what's the difference between this two methods? Because I 
want to separate the fe and quadrature points, so can I use fe.shape_value 
to calculate the shape functions?

Thanks again!

在 2018年5月6日星期日 UTC+8上午6:08:55，Denis Davydov写道：
>
> Hi,
>
> it's perfectly fine for a general FE shape functions to be negative at 
> some points, that's clearly the case for quadratic
>
> http://hplgit.github.io/INF5620/doc/pub/sphinx-fem/._main_fem003.html#fem-approx-fe-fig-p2
>  
>
> Denis.
>
> On Saturday, May 5, 2018 at 3:11:24 AM UTC+2, Zhao Yidong wrote:
>>
>> Hi everyone!
>> I use fe, which is FESystem class, but I find fe.shape_value( const 
>> unsigned int i, const Point< dim > & p ) (the document is here: 
>> https://www.dealii.org/8.5.0/doxygen/deal.II/classFE__Poly.html#a8c769a449d25d54e756fc67cca5dd30b)
>>  
>> sometimes returns a negative number which seems not right.
>>
>> The Point I send into the function locates in the reference space ( [-1, 
>> 1]x[-1, 1] ), I also try the Point in the real space, but also get negative 
>> numbers sometimes.
>>
>> Thanks any response!
>>
>

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[deal.II] Re: Why fe.shape_value( const unsigned int i, const Point< dim > & p ) return a negative number?

2018-05-05 Thread Denis Davydov 
Hi,

it's perfectly fine for a general FE shape functions to be negative at some 
points, that's clearly the case for quadratic
http://hplgit.github.io/INF5620/doc/pub/sphinx-fem/._main_fem003.html#fem-approx-fe-fig-p2
 

Denis.

On Saturday, May 5, 2018 at 3:11:24 AM UTC+2, Zhao Yidong wrote:
>
> Hi everyone!
> I use fe, which is FESystem class, but I find fe.shape_value( const 
> unsigned int i, const Point< dim > & p ) (the document is here: 
> https://www.dealii.org/8.5.0/doxygen/deal.II/classFE__Poly.html#a8c769a449d25d54e756fc67cca5dd30b)
>  
> sometimes returns a negative number which seems not right.
>
> The Point I send into the function locates in the reference space ( [-1, 
> 1]x[-1, 1] ), I also try the Point in the real space, but also get negative 
> numbers sometimes.
>
> Thanks any response!
>

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