Hi,
This type of integral can be computed with the tools presented in the Step-85
tutorial:
https://www.dealii.org/developer/doxygen/deal.II/step_85.html
which you can use if you install the master branch of deal.II (or wait for the
soon-released 9.4 version).
In particular, take a look at the assemble_system() function in Step-85 and the
NonMatching::FEValues class:
https://www.dealii.org/developer/doxygen/deal.II/classNonMatching_1_1FEValues.html
Best,
Simon
On 13/06/2022 15:17, Oleg Kmechak wrote:
Hello there,
Facing such a problem.
Want to evaluate integral over circle (see picture below). Integral has such a
form:
I = Integral[ solution_value(x, y) * my_func(x, y) * dx dy, over circle].
Currently I am using the simplest way to evaluate such integral - rectangular
approximation. And most time cost part - is using
Functions::FEFieldFunction<dim> to get solution_value(x, y). Solving FEM is
faster than evaluation of such integrals.
Also, my_func(x, y) has hidden parameter 'order'. Basically, I am using
integral to expand field around tip (in the center of circle) into series. And
also with higher order, accuracy of series parameter (result of integration) is
poorer.
So maybe once again. How to evaluate fast and accurately integral over such
circle (not whole domain)?
Also, maybe I can introduce a function which is equal to 1 inside of circle and
0 - outside. And then integrate over whole domain.
Also, maybe I can adopt The deal.II Library: Integrators (dealii.org)
<https://www.dealii.org/current/doxygen/deal.II/group__Integrators.html> to fit
my function but not sure how I can do it.
Best regards,
Oleg Kmechak
Inkedinit_river_with_boundary_cond_LI.jpg
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