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[Getfem-commits] r4978 - /trunk/getfem/doc/sphinx/source/userdoc/gasm_hi
From: |
Yves . Renard |
Subject: |
[Getfem-commits] r4978 - /trunk/getfem/doc/sphinx/source/userdoc/gasm_high.rst |
Date: |
Tue, 28 Apr 2015 17:51:05 -0000 |
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`)::
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