* </dd>
*
*
- * <dt class="glossary">@anchor GlossBoundaryForm <b>%Boundary form</b></dt>
+ * <dt class="glossary">@anchor GlossBoundaryForm <b>Boundary form</b></dt>
*
* <dd>For a dim-dimensional triangulation in dim-dimensional space,
* the boundary form is a vector defined on faces. It is the vector
* </dd>
*
*
- * <dt class="glossary">@anchor GlossBoundaryIndicator <b>%Boundary indicator</b></dt>
+ * <dt class="glossary">@anchor GlossBoundaryIndicator <b>Boundary indicator</b></dt>
*
* <dd> In a Triangulation object, every part of the boundary may be
* associated with a unique number (of type types::boundary_id) that
* VectorTools::interpolate_boundary_values,
* VectorTools::compute_no_normal_flux_constraints.
*
- * @note %Boundary indicators are inherited from mother faces and edges to
+ * @note Boundary indicators are inherited from mother faces and edges to
* their children upon mesh refinement. Some more information about boundary
* indicators is also presented in a section of the documentation of the
* Triangulation class.
# replace double dashes in comments by —
$text =~ s!--!—!g;
- # we sometimes escape words with % (as in "%Boundary
- # conditions") because doxygen would otherwise link the word
- # to a class name. This isn't necessary in the index because
- # the text already appears in a hyperref, so get rid of the
- # percent sign
+ # we sometimes escape words with % (as in "boundary %Function")
+ # because doxygen would otherwise link the word to a class name. This
+ # isn't necessary in the index because the text already appears in a
+ # hyperref, so get rid of the percent sign
$text =~ s!\%!!g;
print " <li><a href=\"#$reftext\">$text</a>\n";
* <td>step-3</td>
* <td> Actually solve Laplace's
* problem. Object-orientation. Assembling matrices and
- * vectors. %Boundary values.
+ * vectors. Boundary values.
* </td></tr>
*
* <tr valign="top">
*
* <tr valign="top">
* <td>step-34</td>
- * <td> %Boundary element methods (BEM) of low order: Exterior irrotational
+ * <td> Boundary element methods (BEM) of low order: Exterior irrotational
* flow. The ParsedFunction class.
* </td></tr>
*
* </tr>
*
* <tr valign="top">
- * <td> %Boundary element methods, curved manifolds
+ * <td> Boundary element methods, curved manifolds
* </td>
* <td>
* step-32,
and Cataldo Manigrasso, SISSA, Trieste, Italy). It
explains in detail how to use the
library for the solution of problems defined on codimension
- one manifolds, such as, for example, %Boundary Element Methods.
+ one manifolds, such as, for example, Boundary Element Methods.
<br>
(Luca Heltai, 2009/09/23)
</p>
form, and consequently a symmetric (if indefinite) system matrix.
-<h3>%Boundary conditions</h3>
+<h3>Boundary conditions</h3>
@dealiiVideoLecture{21.5}
(@dealiiVideoLectureSeeAlso{21.55,21.6,21.65})
// that this time the matrix on the left is the mass matrix (which we
// copy again in order to be able to apply boundary conditions, and
// the right hand side is $MV^{n-1} - k\left[ \theta A U^n +
- // (1-\theta) AU^{n-1}\right]$ plus forcing terms. %Boundary values
+ // (1-\theta) AU^{n-1}\right]$ plus forcing terms. Boundary values
// are applied in the same way as before, except that now we have to
// use the BoundaryValuesV class:
laplace_matrix.vmult (system_rhs, solution_u);
into something that can solve whatever you want to solve.
-<h3>%Boundary and initial conditions</h3>
+<h3>Boundary and initial conditions</h3>
Since the Boussinesq equations are derived under the assumption that inertia
of the fluid's motion does not play a role, the flow field is at each time
\quad \mathbf{x}\in \partial\Omega,
\f]
-which is the %Boundary Integral Equation (BIE) we were looking for,
+which is the Boundary Integral Equation (BIE) we were looking for,
where the quantity $\alpha(\mathbf{x})$ is the fraction of angle or
solid angle by which the point $\mathbf{x}$ sees the domain of
integration $\mathbb{R}^n\backslash\Omega$.
<h3>The numerical approximation</h3>
-Numerical approximations of %Boundary Integral Equations (BIE) are commonly
+Numerical approximations of Boundary Integral Equations (BIE) are commonly
referred to as the boundary element method or panel method (the latter
expression being used mostly in the computational fluid dynamics community).
The goal of the following test problem is to solve the integral
{\cal S}_{i}(t) &=& (\psi_i,S(x,t))_\Omega.
@f}
See also step-24 and step-26 to understand how we arrive here.
-%Boundary terms are not necessary due to the chosen boundary conditions for
+Boundary terms are not necessary due to the chosen boundary conditions for
the current problem. To use the Runge-Kutta methods, we recast this
as follows:
@f{eqnarray*}
to something more interesting.
In the default scenario, $\Gamma$ has co-dimension one, and this tutorial
-program implements the Fictitious %Boundary Method. As it turns out, the same
+program implements the Fictitious Boundary Method. As it turns out, the same
techniques are used in the Variational Immersed Finite Element Method, and
the coupling operator $C$ defined above is the same in almost all of these
non-matching methods.
International Journal of Multiphase Flow 25 (5). Pergamon: 755–94.
- Boffi, D., L. Gastaldi, L. Heltai, and C.S. Peskin. 2008. “On the
- Hyper-Elastic Formulation of the Immersed %Boundary Method.” Computer Methods
+ Hyper-Elastic Formulation of the Immersed Boundary Method.” Computer Methods
in Applied Mechanics and Engineering 197 (25–28).
- Heltai, L., and F. Costanzo. 2012. “Variational Implementation of Immersed
So $S$ is some sort of Neumann to Dirichlet map, and we would like to have a
good approximation for the Dirichlet to Neumann map. A possibility would be to
-use a %Boundary Element approximation of the problem on $\Gamma$, and construct a
+use a Boundary Element approximation of the problem on $\Gamma$, and construct a
rough approximation of the hyper-singular operator for the Poisson problem
associated to $\Gamma$, which is precisely a Dirichlet to Neumann map.
const Quadrature<dim-1>& quadrature);
/**
- * %Boundary form of the transformation of the cell at the <tt>i</tt>th
+ * Boundary form of the transformation of the cell at the <tt>i</tt>th
* quadrature point. See
* @ref GlossBoundaryForm.
*
* to pertain to a particular region of the domain, material ids are inherited
* by child cells from their parent upon mesh refinement.
*
- * %Boundary indicators on lower dimensional objects (these have no material
+ * Boundary indicators on lower dimensional objects (these have no material
* id) indicate the number of a boundary component. The weak formulation of the
* partial differential equation may have different boundary conditions on
* different parts of the boundary. The boundary indicator can be used in
* creating the matrix or the right hand side vector to indicate these
* different parts of the model (this use is like the material id of cells).
- * %Boundary indicators may be in the range from zero to
+ * Boundary indicators may be in the range from zero to
* numbers::internal_face_boundary_id-1. The value
* numbers::internal_face_boundary_id is reserved to denote interior lines (in
* 2D) and interior lines and quads (in 3D), which do not have a boundary
* coefficient which will then be used for all components.
*
*
- * <h3>%Boundary values</h3>
+ * <h3>Boundary values</h3>
*
* If the face is at the boundary, i.e. there is no neighboring cell to which
* the jump in the gradiend could be computed, there are two possibilities:
* others.
*
*
- * <h3>%Boundary conditions</h3>
+ * <h3>Boundary conditions</h3>
*
* The apply_boundary_values() function inserts boundary conditions into a
* system of equations. To actually do this you have to specify a list of
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