[petsc-users] Compute integral using DMPlexComputeIntegralFEM

[David Andrs]

Hi Matt!

Thanks for getting back to this.  I found a mistake in my hand calculation
- I used wrong shape functions (pretty stupid mistake :face_palm:).

Thanks again for your help,

David

On Wed, Oct 4, 2023 at 10:13 AM Matthew Knepley <knepley at gmail.com> wrote:

> On Fri, Sep 8, 2023 at 6:26 PM David Andrs <andrsd at gmail.com> wrote:
>
>> Hi all!
>>
>> I am trying to use DMPlexComputeIntegralFEM to compute an integral
>> $\int_\Omega u d\Omega$. My domain is a square (-1, 1)^2 (2x2 QUAD4
>> elements), I add first order Lagrange FE field on it, set the solution
>> vector (computed by a previous simulation).
>>
>> The value I am seeing computed by PETSc is -4, but the hand-calculated
>> value of this integral is -4.6. I also checked this in paraview using the
>> ‘Integrate Variables’ filter and it also returns -4.6 (this was to double
>> check that my hand-calculated value is correct).
>>
>
> Sorry it took so long. You caught me at a bad time.
>
> Something must be wrong with your analytic integrals. Here is me doing
> them by hand. You have a 3x3 vertex arrangement with coefficients
>
>    1  0 -3
>   -2 -1 -2
>   -3  0  1
>
> From the symmetry, the integrals of the cells along each diagonal must be
> equal. Now, the shape functions for Q_1 are
>
>      (1 - x) y            x y
>
>   (1 - x)(1 - y)     x (1 - y)
>
> Thus the integral for the lower left cell is
>
>   \int^1_0 dx \int^1_0 dy -3 + 3 x + y - 2 xy = -3 + 3/2 + 1/2 - 2/4 = -1.5
>
> which is also the upper right cell. The integral for the lower right cell
> is
>
>   \int^1_0 dx \int^1_0 dy x - y - 2 xy = 1/2 - 1/2 - 2/4 = -1/2
>
> which is also the upper left cell. Thus we get -1.5 - 1.5 - 0.5 - 0.5 =
> -4, which is what Plex gets.
>
>   THanks,
>
>     Matt
>
> So, I must be missing something obvious in my code. Attached is the
>> minimal PETSc code to show what I am doing. This is against PETSc 3.19.4.
>>
>> Thanks in advance for your help,
>>
>> David
>>
>> --
>>
>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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