DUNE-FEM (unstable)
affinegeometry.hh
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3// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
53 static void Ax ( const FieldMatrix< ctype, m, n > &A, const FieldVector< ctype, n > &x, FieldVector< ctype, m > &ret )
64 static void ATx ( const FieldMatrix< ctype, m, n > &A, const FieldVector< ctype, m > &x, FieldVector< ctype, n > &ret )
75 static void AB ( const FieldMatrix< ctype, m, n > &A, const FieldMatrix< ctype, n, p > &B, FieldMatrix< ctype, m, p > &ret )
89 static void ATBT ( const FieldMatrix< ctype, m, n > &A, const FieldMatrix< ctype, p, m > &B, FieldMatrix< ctype, n, p > &ret )
177 static void Lx ( const FieldMatrix< ctype, n, n > &L, const FieldVector< ctype, n > &x, FieldVector< ctype, n > &ret )
188 static void LTx ( const FieldMatrix< ctype, n, n > &L, const FieldVector< ctype, n > &x, FieldVector< ctype, n > &ret )
235 static bool cholesky_L ( const FieldMatrix< ctype, n, n > &A, FieldMatrix< ctype, n, n > &ret, const bool checkSingular = false )
344 static bool spdInvAx ( FieldMatrix< ctype, n, n > &A, FieldVector< ctype, n > &x, const bool checkSingular = false )
440 static bool leftInvAx ( const FieldMatrix< ctype, m, n > &A, const FieldVector< ctype, m > &x, FieldVector< ctype, n > &y )
476 static bool xTRightInvA ( const FieldMatrix< ctype, m, n > &A, const FieldVector< ctype, n > &x, FieldVector< ctype, m > &y )
533 typedef Geo::ReferenceElement< Geo::ReferenceElementImplementation< ctype, mydimension > > ReferenceElement;
554 integrationElement_ = MatrixHelper::template rightInvA< mydimension, coorddimension >( jacobianTransposed_, jacobianInverseTransposed_ );
570 integrationElement_ = MatrixHelper::template rightInvA< mydimension, coorddimension >( jacobianTransposed_, jacobianInverseTransposed_ );
657 const JacobianTransposed &jacobianTransposed ([[maybe_unused]] const LocalCoordinate &local) const
668 const JacobianInverseTransposed &jacobianInverseTransposed ([[maybe_unused]] const LocalCoordinate &local) const
Implementation of the Geometry interface for affine geometries.
Definition: affinegeometry.hh:498
AffineGeometry(const ReferenceElement &refElement, const CoordVector &coordVector)
Create affine geometry from reference element and a vector of vertex coordinates.
Definition: affinegeometry.hh:565
AffineGeometry(Dune::GeometryType gt, const GlobalCoordinate &origin, const JacobianTransposed &jt)
Create affine geometry from GeometryType, one vertex, and the Jacobian matrix.
Definition: affinegeometry.hh:558
FieldVector< ctype, mydimension > LocalCoordinate
Type for local coordinate vector.
Definition: affinegeometry.hh:511
Dune::GeometryType type() const
Obtain the type of the reference element.
Definition: affinegeometry.hh:583
static const int mydimension
Dimension of the geometry.
Definition: affinegeometry.hh:505
AffineGeometry(const ReferenceElement &refElement, const GlobalCoordinate &origin, const JacobianTransposed &jt)
Create affine geometry from reference element, one vertex, and the Jacobian matrix.
Definition: affinegeometry.hh:550
JacobianInverse jacobianInverse(const LocalCoordinate &local) const
Obtain the Jacobian's inverse.
Definition: affinegeometry.hh:690
AffineGeometry(Dune::GeometryType gt, const CoordVector &coordVector)
Create affine geometry from GeometryType and a vector of vertex coordinates.
Definition: affinegeometry.hh:575
ctype integrationElement(const LocalCoordinate &local) const
Obtain the integration element.
Definition: affinegeometry.hh:640
FieldMatrix< ctype, mydimension, coorddimension > JacobianInverse
Type for the inverse Jacobian matrix.
Definition: affinegeometry.hh:529
FieldMatrix< ctype, coorddimension, mydimension > Jacobian
Type for the Jacobian matrix.
Definition: affinegeometry.hh:526
const JacobianInverseTransposed & jacobianInverseTransposed(const LocalCoordinate &local) const
Obtain the transposed of the Jacobian's inverse.
Definition: affinegeometry.hh:668
FieldMatrix< ctype, mydimension, coorddimension > JacobianTransposed
Type for the transposed Jacobian matrix.
Definition: affinegeometry.hh:520
GlobalCoordinate corner(int i) const
Obtain coordinates of the i-th corner.
Definition: affinegeometry.hh:589
int corners() const
Obtain number of corners of the corresponding reference element.
Definition: affinegeometry.hh:586
FieldMatrix< ctype, coorddimension, mydimension > JacobianInverseTransposed
Type for the transposed inverse Jacobian matrix.
Definition: affinegeometry.hh:523
static const int coorddimension
Dimension of the world space.
Definition: affinegeometry.hh:508
GlobalCoordinate global(const LocalCoordinate &local) const
Evaluate the mapping.
Definition: affinegeometry.hh:603
GlobalCoordinate center() const
Obtain the centroid of the mapping's image.
Definition: affinegeometry.hh:595
Jacobian jacobian(const LocalCoordinate &local) const
Obtain the Jacobian.
Definition: affinegeometry.hh:679
FieldVector< ctype, coorddimension > GlobalCoordinate
Type for coordinate vector in world space.
Definition: affinegeometry.hh:514
bool affine() const
Always true: this is an affine geometry.
Definition: affinegeometry.hh:580
const JacobianTransposed & jacobianTransposed(const LocalCoordinate &local) const
Obtain the transposed of the Jacobian.
Definition: affinegeometry.hh:657
Volume volume() const
Obtain the volume of the element.
Definition: affinegeometry.hh:646
FieldMatrix< K, COLS, ROWS > transposed() const
Return transposed of the matrix as FieldMatrix.
Definition: fmatrix.hh:171
This class provides access to geometric and topological properties of a reference element.
Definition: referenceelement.hh:52
CoordinateField volume() const
obtain the volume of the reference element
Definition: referenceelement.hh:228
GeometryType type(int i, int c) const
obtain the type of subentity (i,c)
Definition: referenceelement.hh:167
Coordinate position(int i, int c) const
position of the barycenter of entity (i,c)
Definition: referenceelement.hh:190
int size(int c) const
number of subentities of codimension c
Definition: referenceelement.hh:94
Unique label for each type of entities that can occur in DUNE grids.
Definition: type.hh:114
Implements a matrix constructed from a given type representing a field and compile-time given number ...
Implements a vector constructed from a given type representing a field and a compile-time given size.
bool gt(const T &first, const T &second, typename EpsilonType< T >::Type epsilon)
test if first greater than second
Definition: float_cmp.cc:158
Class providing access to the singletons of the reference elements.
Definition: referenceelements.hh:128
A unique label for each type of element that can occur in a grid.
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