[Getfem-commits] r4978 - /trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst

[Yves . Renard]

Author: renard
Date: Tue Apr 28 19:51:03 2015
New Revision: 4978

URL: http://svn.gna.org/viewcvs/getfem?rev=4978&view=rev
Log:
Div doc

Modified:
    trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst

Modified: trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst
URL: 
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst?rev=4978&r1=4977&r2=4978&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst        (original)
+++ trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst        Tue Apr 28 
19:51:03 2015
@@ -32,7 +32,7 @@
 
   - Test functions corresponding to the variables. It is identified by the 
prefix ``Test_`` followed by the variable name. For instance  ``Test_u``, 
``Test_v``, ``Test_p``, ``Test_pressure``, ``Test_electric_field``. For the 
tangent system, second order test functions are denoted ``Test2_`` followed by 
the variable name.
 
-  - The gradient of a variable or of test functions are identified by 
``Grad_`` followed by the variable name or by ``Test_`` or ``Test2_`` followed 
itself by the variable name. This is available for fem variables only. For 
instance ``Grad_u``, ``Grad_pressure``, ``Grad_electric_field`` and 
``Grad_Test_u``, ``Grad_Test2_v``.
+  - The gradient of a variable or of test functions are identified by 
``Grad_`` followed by the variable name or by ``Test_`` or ``Test2_`` followed 
itself by the variable name. This is available for fem variables only. For 
instance ``Grad_u``, ``Grad_pressure``, ``Grad_electric_field`` and 
``Grad_Test_u``, ``Grad_Test2_v``. For vector fields, ``Div_u`` and 
``Div_Test_u`` are some shortcuts for ``Trace(Grad_u)`` and 
``Trace(Grad_Test_u)``, respectively.
 
   - The Hessian of a variable or of test functions are identified by ``Hess_`` 
followed by the variable name or by ``Test_`` or ``Test2_`` followed itself by 
the variable name. This is available for fem variables only. For instance 
``Hess_u``, ``Hess_v``, ``Hess_p``, ``Hess_Test2_v``, ``Hess_Test_p``, 
``Hess_Test_pressure``.
 
@@ -118,11 +118,11 @@
 
 or:: 
 
-  lambda*Trace(Grad_u)*Trace(Grad_Test_u) + mu*(Grad_u + Grad_u'):Grad_Test_u 
- my_f.Test_u
+  lambda*Div_u*Div_Test_u + mu*(Grad_u + Grad_u'):Grad_Test_u - my_f.Test_u
 
 Here again, the coefficients ``lambda`` and ``mu`` can be given constants, or 
scalar field or explicit expression or even expression coming from some other 
variables in order to couples some problems. For instance, if the coefficients 
depends on a temperature field one can write::
 
-  my_f1(theta)*Trace(Grad_u)*Trace(Grad_Test_u)
+  my_f1(theta)*Div_u*Div_Test_u
   + my_f2(theta)*(Grad_u + Grad_u'):Grad_Test_u - my_f.Grad_Test_u
 
 where ``theta`` is the temperature which can be the solution to a Poisson 
equation::
@@ -363,7 +363,7 @@
 The variables
 *************
 
-A list of variables should be given to the ``ga_worspace`` object (directly or 
through a model object). The variables are described on a finite element method 
or can be a simple vector of unknowns. This means that it is possible also to 
couple algebraic equations to pde ones on a model. A variable name should begin 
by a letter (case sensitive) or an underscore followed by a letter, a number or 
an underscore. Some name are reserved, this is the case of operators names 
(``Det``, ``Norm``, ``Trace``, ``Deviator``, ...) and thus cannot be used as 
variable names. The name should not begin by ``Test_``, ``Test2_``, ``Grad_`` 
or ``Hess_``. The variable name should not correspond to a predefined function 
(``sin``, ``cos``, ``acos`` ...) and to constants (``pi``, ``Normal``, ``X``, 
``Id`` ...).
+A list of variables should be given to the ``ga_worspace`` object (directly or 
through a model object). The variables are described on a finite element method 
or can be a simple vector of unknowns. This means that it is possible also to 
couple algebraic equations to pde ones on a model. A variable name should begin 
by a letter (case sensitive) or an underscore followed by a letter, a number or 
an underscore. Some name are reserved, this is the case of operators names 
(``Det``, ``Norm``, ``Trace``, ``Deviator``, ...) and thus cannot be used as 
variable names. The name should not begin by ``Test_``, ``Test2_``, ``Grad_``, 
``Div_`` or ``Hess_``. The variable name should not correspond to a predefined 
function (``sin``, ``cos``, ``acos`` ...) and to constants (``pi``, ``Normal``, 
``X``, ``Id`` ...).
 
 The constants or data
 *********************
@@ -381,7 +381,7 @@
 Gradient
 ********
 
-The gradient of a variable or of test functions are identified by ``Grad_`` 
followed by the variable name or by ``Test_`` followed itself by the variable 
name. This is available for fem variables (or constants) only. For instance 
``Grad_u``, ``Grad_v``, ``Grad_p``, ``Grad_pressure``, ``Grad_electric_field`` 
and ``Grad_Test_u``, ``Grad_Test_v``, ``Grad_Test_p``, ``Grad_Test_pressure``, 
``Grad_Test_electric_field``. The gradient is either a vector for scalar 
variables or a matrix for vector field variables. In the latter case, the first 
index corresponds to the vector field dimension and the second one to the index 
of the partial derivative.
+The gradient of a variable or of test functions are identified by ``Grad_`` 
followed by the variable name or by ``Test_`` followed itself by the variable 
name. This is available for fem variables (or constants) only. For instance 
``Grad_u``, ``Grad_v``, ``Grad_p``, ``Grad_pressure``, ``Grad_electric_field`` 
and ``Grad_Test_u``, ``Grad_Test_v``, ``Grad_Test_p``, ``Grad_Test_pressure``, 
``Grad_Test_electric_field``. The gradient is either a vector for scalar 
variables or a matrix for vector field variables. In the latter case, the first 
index corresponds to the vector field dimension and the second one to the index 
of the partial derivative.  ``Div_u`` and ``Div_Test_u`` are some optimized 
shortcuts for ``Trace(Grad_u)`` and ``Trace(Grad_Test_u)``, respectively.
 
 Hessian
 *******
@@ -638,9 +638,11 @@
   Interpolate(X, transname)
   Interpolate(u, transname)
   Interpolate(Grad_u, transname)
+  Interpolate(Div_u, transname)
   Interpolate(Hess_u, transname)
   Interpolate(Test_u, transname)
   Interpolate(Grad_Test_u, transname)
+  Interpolate(Div_Test_u, transname)
   Interpolate(Hess_Test_u, transname)
 
 where ``u`` is the name of the variable to be interpolated.
@@ -687,9 +689,11 @@
 
   Elementary_transformation(u, transname)
   Elementary_transformation(Grad_u, transname)
+  Elementary_transformation(Div_u, transname)
   Elementary_transformation(Hess_u, transname)
   Elementary_transformation(Test_u, transname)
   Elementary_transformation(Grad_Test_u, transname)
+  Elementary_transformation(Div_Test_u, transname)
   Elementary_transformation(Hess_Test_u, transname)
 
 where ``u`` is one of the fem variables of the model/workspace. For the 
moment, the only available elementary transformation is the the one for the 
projection on rotated RT0 element for two-dimensional elements which can be 
added thanks to the function (defined in :file:`getfem/linearized_plate.h`)::