Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Let's say a quantity :math:`G` with 3 components :math:`X,Y,Z`

The mesh has 3 geometric entities (meshes or nodes): :math:`\mathit{X1},\mathit{X2},\mathit{X3}`

First of all, 2 fields :math:`\mathit{ch1}` and :math:`\mathit{ch2}` are made by assigning the quantity :math:`G` to the geometric entities :math:`\mathit{X1}`, :math:`\mathit{X2}` and :math:`\mathit{X3}`.


+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|Entity              |:math:`\mathit{X1}`                    |:math:`\mathit{X2}`                    |:math:`\mathit{X3}`                    |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|Component           |:math:`X`          |:math:`Y`|:math:`Z`|:math:`X`          |:math:`Y`|:math:`Z`|:math:`X`          |:math:`Y`|:math:`Z`|
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch1}`|                   |         |         |                   |         |         |                   |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch2}`|                   |         |         |                   |         |         |                   |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+

Fields :math:`\mathit{ch3}` and :math:`\mathit{ch4}` are then defined by CREA_CHAMP operation ASSE.

We must then obtain:


+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|Entity              |:math:`\mathit{X1}`                    |:math:`\mathit{X2}`                    |:math:`\mathit{X3}`                    |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|Component           |:math:`X`          |:math:`Y`|:math:`Z`|:math:`X`          |:math:`Y`|:math:`Z`|:math:`X`          |:math:`Y`|:math:`Z`|
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch1}`|                   |         |         |                   |         |         |                   |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch2}`|                   |         |         |                   |         |         |                   |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch3}`|                   |         |         |                   |         |         |                   |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch4}`|                   |         |         |                   |         |         |                   |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+

To test the different scenarios of the operation 'ASSE' of the CREA_CHAMP command, this calculation is done for 5 types of fields:


.. csv-table::

    "A", "cham_no", "trips"
    "B", "cham_elem/ELNO ", "constraints"
    "C", "cham_elem/ELGA ", "constraints"
    "D", "cham_elem/ELNO ", "internal variables"
    "E", "cham_elem/ELGA ", "internal variables"



Benchmark results
----------------------

For the 5 previous scenarios, we test the values greased and underlined in the table below:


+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|Entity              |:math:`\mathit{X1}`                    |:math:`\mathit{X2}`                    |:math:`\mathit{X3}`                    |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|Component           |:math:`X`          |:math:`Y`|:math:`Z`|:math:`X`          |:math:`Y`|:math:`Z`|:math:`X`          |:math:`Y`|:math:`Z`|
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch3}`|                   |         |         |**1.**             |         |         |**1.**             |**12.**  |**9.**   |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+
|:math:`\mathit{ch4}`|                   |         |         |                   |         |         |**18.**            |         |         |
+--------------------+-------------------+---------+---------+-------------------+---------+---------+-------------------+---------+---------+


Uncertainties about the solution
----------------------------

No uncertainty.