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amdis
amdis-core
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294df099
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294df099
authored
Sep 29, 2020
by
Müller, Felix
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docs/reference/DOFVector.md
docs/reference/DOFVector.md
+14
-14
docs/reference/GridFunctions.md
docs/reference/GridFunctions.md
+2
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docs/reference/Operators.md
docs/reference/Operators.md
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docs/reference/DOFVector.md
View file @
294df099
...
...
@@ -3,7 +3,7 @@
The class
[
`DOFVector`
](
#class-dofvector
)
acts as a container for storing the coefficients of the solution discrete function.
It is attached to a global basis to give its coefficients a meaning. A
[
`DiscreteFunction`
](
#class-discretefunction
)
goes
one step further and transforms a DOFVector or subspaces of a DOFVector (with respecto to a sub basis)
into a
[
`GridFunction`
](
/reference
/GridFunctions
)
that allows to use it like a function defined on a grid.
into a
[
`GridFunction`
](
..
/GridFunctions
)
that allows to use it like a function defined on a grid.
Let $
`\{\phi_i\}`
$ be the set of basis functions of a finite-element space $
`V`
$. A function $
`u\in V`
$ can be represented
as
...
...
@@ -68,21 +68,21 @@ The `value_type` is often the same as `T`, but might be just something similar,
[
`interpolate_noalias`
](
#function-dofvectorinterpolate
)
| Interpolation of GridFunction to DOFVector assuming no aliasing
[
`operator<<`
](
#function-dofvectorinterpolate
)
| Operator for the interpolation
??? seealso "Functions inherited from
[
`VectorFacade`
](
/reference
/MatVecBase/#class-vectorfacade
)
"
??? seealso "Functions inherited from
[
`VectorFacade`
](
..
/MatVecBase/#class-vectorfacade
)
"
Function | Descriptions
--------------------------------|---------------------------------------------
[
`basis`
](
/reference
/MatVecBase#function-vectorbasebasis
)
| Return the GlobalBasis associated with the vector
[
`backend`
](
/reference
/MatVecBase#function-vectorbasebackend
)
| Return the backend vector wrapper implementing the actual algebra
[
`localSize,globalSize`
](
/reference
/MatVecBase#function-vectorbasesize
)
| The number of entries in the local part of the vector
[
`resize,resizeZero`
](
/reference
/MatVecBase#function-vectorbaseglobalSize
)
| Resize the vector to the size of the basis
[
`init`
](
/reference
/MatVecBase#function-vectorbaseglobalSize
)
| Prepare the vector for insertion of values
[
`finish`
](
/reference
/MatVecBase#function-vectorbaseglobalSize
)
| Finish the insertion of values
[
`at`
](
/reference
/MatVecBase#function-vectorbaseat
)
| Return the value of the vector at the given local index
[
`insert,set,add`
](
/reference
/MatVecBase#function-vectorbaseinsert
)
| Insert a single value into the matrix
[
`gather`
](
/reference
/MatVecBase#function-vectorbasegather
)
| Extract values from the vector referring to the given local indices
[
`scatter`
](
/reference
/MatVecBase#function-vectorbasescatter
)
| Insert a block of values into the vector
[
`copy`
](
/reference
/MatVecBase#function-vectorbasescatter
)
| Copies a block of values into the vector
[
`forEach`
](
/reference
/MatVecBase#function-vectorbasescatter
)
| Apply a functor to each value at given indices
[
`basis`
](
..
/MatVecBase#function-vectorbasebasis
)
| Return the GlobalBasis associated with the vector
[
`backend`
](
..
/MatVecBase#function-vectorbasebackend
)
| Return the backend vector wrapper implementing the actual algebra
[
`localSize,globalSize`
](
..
/MatVecBase#function-vectorbasesize
)
| The number of entries in the local part of the vector
[
`resize,resizeZero`
](
..
/MatVecBase#function-vectorbaseglobalSize
)
| Resize the vector to the size of the basis
[
`init`
](
..
/MatVecBase#function-vectorbaseglobalSize
)
| Prepare the vector for insertion of values
[
`finish`
](
..
/MatVecBase#function-vectorbaseglobalSize
)
| Finish the insertion of values
[
`at`
](
..
/MatVecBase#function-vectorbaseat
)
| Return the value of the vector at the given local index
[
`insert,set,add`
](
..
/MatVecBase#function-vectorbaseinsert
)
| Insert a single value into the matrix
[
`gather`
](
..
/MatVecBase#function-vectorbasegather
)
| Extract values from the vector referring to the given local indices
[
`scatter`
](
..
/MatVecBase#function-vectorbasescatter
)
| Insert a block of values into the vector
[
`copy`
](
..
/MatVecBase#function-vectorbasescatter
)
| Copies a block of values into the vector
[
`forEach`
](
..
/MatVecBase#function-vectorbasescatter
)
| Apply a functor to each value at given indices
## function `DOFVector::DOFVector`
...
...
docs/reference/GridFunctions.md
View file @
294df099
...
...
@@ -35,7 +35,7 @@ elementary terms.
### Examples of expressions
Before we give examples where and how to use GridFunctions, we demonstrate what an
`Expression`
could be, to create a GridFunction from. In the following examples,
we assume that a
[
ProblemStat
](
reference
/Problem#class-problemstat
)
named
`prob`
is already
we assume that a
[
ProblemStat
](
..
/Problem#class-problemstat
)
named
`prob`
is already
created and initialized.
#### 1. Discrete Functions
...
...
@@ -95,7 +95,7 @@ prob.addMatrixOperator(opB, Row, Col);
auto
opL
=
makeOperator
(
LinearForm
,
Expression
);
prob
.
addVectorOperator
(
opL
,
Row
);
```
See also
[
makeOperator()
](
reference
/Operators#function-makeoperator
)
.
See also
[
makeOperator()
](
..
/Operators#function-makeoperator
)
.
#### 2. Usage of GridFunctions in BoundaryConditions:
```
c++
...
...
docs/reference/Operators.md
View file @
294df099
...
...
@@ -19,9 +19,9 @@ auto makeOperator(Tag tag, Expr&& expr, QuadratureArgs&&... args)
```
Constructs a
`GridFunctionOperator`
that can be passed to a
[
`ProblemStat`
](
reference
/Problem#class-problemstat
)
in the member functions
[
`addMatrixOperator()`
](
reference
/Problem#function-problemstataddmatrixoperator
)
or
[
`addVectorOperator()`
](
reference
/Problem#function-problemstataddvectoroperator
)
.
[
`ProblemStat`
](
..
/Problem#class-problemstat
)
in the member functions
[
`addMatrixOperator()`
](
..
/Problem#function-problemstataddmatrixoperator
)
or
[
`addVectorOperator()`
](
..
/Problem#function-problemstataddvectoroperator
)
.
The
`tag`
therby identifies which type of operator to create, the
`expr`
is used
as a coefficient function in the operator and the optional quadrature arguments
are used to determine a quadrature rule for the integration of the operator on an
...
...
@@ -35,14 +35,14 @@ element.
zero-order terms, first-order terms, and second-order terms. See the examples below.
`Expr expr`
: An
`Expression`
is anything, a
[
`GridFunction`
](
reference
/GridFunctions
)
can
: An
`Expression`
is anything, a
[
`GridFunction`
](
..
/GridFunctions
)
can
be created from, sometimes also called PreGridFunction. It includes constants,
functors callable with GlobalCoordinates, and any combination of GridFunctions.
`QuadratureArgs args...`
: Arguments that are passed to a quadrature creator. Anything that needs
a quadrature formula needs to determine the (approximative) polynomial degree
of the GridFunctions. If the
[
`GridFunction`
](
reference
/GridFunctions
)
builds a
of the GridFunctions. If the
[
`GridFunction`
](
..
/GridFunctions
)
builds a
polynomial expression, it can be deduced automatically, i.e. if it includes constants,
DOFVectors, and arithmetic operator
`operator+`
,
`operator-`
, or
`operator*`
. If
the polynomial order can not be deduced, the compiler gives an error. Then, this
...
...
@@ -112,7 +112,7 @@ special basis, like a taylor-hood basis.
### Examples
#### Tags and expressions
The general procedure to describe a PDE is to decompose it into individual terms and add
all of them to a
[
`ProblemStat`
](
reference
/Problem#class-problemstat
)
:
all of them to a
[
`ProblemStat`
](
..
/Problem#class-problemstat
)
:
```
c++
using
Grid
=
/* any dune grid type */
;
using
Traits
=
TaylorHoodBasis
<
Grid
>
;
...
...
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