Class representing a finite element. More...
#include <FiniteElement.h>
Public Member Functions | |
| FiniteElement (size_t n=0, size_t i=0) | |
| Default constructor. | |
| virtual size_t | getNoBasis () const |
| Returns the number of bases. | |
| virtual const Vector & | basis (char) const |
| Returns a const reference to the basis function values. | |
| virtual Vector & | basis (char) |
| Returns a reference to the basis function values. | |
| virtual const Matrix & | grad (char) const |
| Returns a const reference to the basis function derivatives. | |
| virtual const Matrix3D & | hess (char) const |
| Returns a const reference to the basis function 2nd-derivatives. | |
| virtual const Matrix4D & | hess2 (char) const |
| Returns a const reference to the basis function 3nd-derivatives. | |
 Public Member Functions inherited from ItgPoint | |
| ItgPoint (size_t i=0) | |
| Default constructor. | |
| ItgPoint (double a, double b=0.0, double c=0.0, size_t i=0) | |
| Constructor initializing the spline domain parameters. | |
| ItgPoint (const double *par, size_t i=0) | |
| Alternative constructor initializing the spline domain parameters. | |
| virtual | ~ItgPoint () |
| Empty destructor. | |
Public Attributes | |
| double | detJxW |
| Weighted determinant of the coordinate mapping. | |
| Vector | N |
| Basis function values. | |
| Matrix | dNdX |
| First derivatives (gradient) of the basis functions. | |
| Matrix3D | d2NdX2 |
| Second derivatives of the basis functions. | |
| Matrix4D | d3NdX3 |
| Third derivatives of the basis functions. | |
| Matrix | G |
| Covariant basis / Matrix used for stabilized methods. | |
| Matrix | H |
| Hessian. | |
| Matrix | P |
| Matrix holding Piola-mapped basis function values. More... | |
| Matrix | dPdX |
| Matrix holding Piola-mapped basis derivatives. More... | |
| short int | p |
| Polynomial order of the basis in u-direction. | |
| short int | q |
| Polynomial order of the basis in v-direction. | |
| short int | r |
| Polynomial order of the basis in r-direction. | |
| double | age |
| Time since birth of this element. | |
| double | h |
| Characteristic element size/diameter. | |
| Vec3Vec | XC |
| Array with element corner coordinate vectors. | |
| Vector | Navg |
| Volume-averaged basis function values. | |
| Matrix | Xn |
| Matrix of element nodal coordinates. | |
| Tensor | Te |
| Local-to-global element transformation matrix. | |
| std::vector< Tensor > | Tn |
| Array of element nodal rotation matrices. | |
| Vec3Vec | En |
| Array of nodal eccentricity vectors. | |
| Public Attributes inherited from ItgPoint | |
| size_t | iGP |
| Global integration point counter. | |
| double | u |
| First spline parameter of the point. | |
| double | v |
| Second spline parameter of the point. | |
| double | w |
| Third spline parameter of the point. | |
| int | iel |
| Identifier of the element containing this point. | |
| size_t | idx |
| Global index (0-based) of the element containing this point. | |
| double | xi |
| First local coordinate within current element. | |
| double | eta |
| Second local coordinate within current element. | |
| double | zeta |
| Third local coordinate within current element. | |
Protected Member Functions | |
| virtual Matrix & | grad (char) |
| Returns a reference to the basis function derivatives. | |
| virtual Matrix3D & | hess (char) |
| Returns a reference to the basis function 2nd-derivatives. | |
| virtual std::ostream & | write (std::ostream &os) const |
| Writes the finite element object to the given output stream. | |
Friends | |
| std::ostream & | operator<< (std::ostream &os, const FiniteElement &fe) |
| Global output stream operator. | |
Detailed Description
Class representing a finite element.
Member Data Documentation
◆ dPdX
| Matrix FiniteElement::dPdX |
Matrix holding Piola-mapped basis derivatives.
The column index i is cumulative, e.g., if N1 is the number of functions in basis 1 and N2 is the number of functions in basis 2, then 1 ≤ i ≤ N1 for the first basis and N1+1 ≤ i ≤ N1+N2 for the second basis. This matrix is therefore of dimension 4×(N1+N2), where the two first rows are the X-derivatives and the two last rows are the Y-derivatives.
Referenced by PiolaOperators::Weak::Gradient(), PiolaOperators::Residual::Gradient(), PiolaOperators::Weak::Laplacian(), PiolaOperators::Residual::Laplacian(), MxFiniteElement::piolaGradient(), and write().
◆ P
| Matrix FiniteElement::P |
Matrix holding Piola-mapped basis function values.
The column index i is cumulative, e.g., if N1 is the number of functions in basis 1 and N2 is the number of functions in basis 2, then 1 ≤ i ≤ N1 for the first basis and N1+1 ≤ i ≤ N1+N2 for the second basis. This matrix is therefore of dimension 2×(N1+N2).
Referenced by PiolaOperators::Weak::Convection(), PiolaOperators::Residual::Convection(), ASMs2Dmx::evalSolutionPiola(), ASMu2Dmx::evalSolutionPiola(), PiolaOperators::Weak::Mass(), MxFiniteElement::piolaBasis(), PiolaOperators::Weak::Source(), and write().
The documentation for this class was generated from the following files:
- src/ASM/FiniteElement.h
- src/ASM/FiniteElement.C
