Manicore
Library to implement schemes on ndimensionnal manifolds.

Classes providing support to compute mass matrices. More...
Classes  
struct  Manicore::dCell_traces< dimension, 1 > 
Specialization for edges. More...  
Functions  
template<size_t dimension, size_t d>  
Manicore::requires (d > 0 &&d<=dimension) struct dCell_mass  
Compute the mass matrices of a dcell. More...  
Classes providing support to compute mass matrices.
Manicore::requires  (  d  , 
0 &&d<=  dimension  
) 
Compute the mass matrices of a dcell.
Interface with quadrature rule.
Compute the traces matrices of a dcell onto its boundary.
dimension  Dimension of the manifold 
d  Dimension of the cell 
dimension  Dimension of the manifold 
d  Dimension of the cell 
Generate the quadrature rule and implement the evaluate of every quantity used.
< Cell index
< Polynomial degree
< Quadrature rule to use
< Integral object generating the quadrature
Do nothing
Mass matrices of all form degree
masses[k] is the mass for the kforms
< Cell index
< Polynomial degree
< Quadrature degree
< Masses of all the cell of dimension d1
< Integral object for the dimension d
< Integral object for the dimension d1
Do nothing
Trace matrices for all form degree and all boundary cell
traces[k][i_b] is the trace for a kform on the i_bboundary cell, using relative index
starTraces[k][i_b] is \( \star \text{tr} \star^{1} \) of a \(dk\)form on the i_bboundary cell, using relative index
The trace of dform is not included. The array uses the global dimension to give an uniform interface, however only the first d elements are used.
< Mesh used for the quadrature
Generic interface to generate quadrature rule on any dimension
< Cell index
< Degree of exactness
Evaluate the polynomial basis on a cell
< Cell index
< Polynomial degree
< Quadrature rule
Evaluate the polynomial basis on a quadrature of the boundary
< Cell index
< Relative index of the boundary (e.g. between 0 and 2 for a triangle)
< Polynomial degree
< Quadrature rule on the boundary
Evaluate the volume form on a quadrature of the boundary
< Cell index
< Quadrature rule
Evaluate the pullback by I of the \(L^2\) product on the exterior algebra of the exterior algebra on the reference element.
Compute the matrix of \( I_T^* (\langle \cdot , \cdot \rangle_{g}) \).
l  Form degree 
< Cell index
< Quadrature rule
Evaluate the pullback by I of the \(L^2\) product on the exterior algebra of the exterior algebra on the reference element composed with the trace on the right.
Compute the matrix of \( I_F^* (\langle \cdot , I_F^* J_T^* \cdot \rangle_{g}) \).
l  Form degree 
< Cell index
< Relative index of the boundary
< Quadrature rule on the boundary
Evaluate the pullback by I of the \(L^2\) product on the exterior algebra of the exterior algebra on the reference element composed with the trace on the right and the Hodge star on both side.
Compute the matrix of \( I_F^* (\langle \cdot , \star I_F^* J_T^* \star^{1} \cdot \rangle_{g}) \). Expect a \(dl\) form on the right and a \(d1l\) form on the left.
l  Hodge dual of the form degree 
< Cell index
< Relative index of the boundary
< Quadrature rule on the boundary
Access the mesh associated with this object
< Cell index
< Polynomial degree
< Quadrature degree
< Masses of all the cell of dimension d1
< Integral object for the dimension d
< Integral object for the dimension d1
Do nothing
Trace matrices for all form degree and all boundary cell
traces[k][i_b] is the trace for a kform on the i_bboundary cell, using relative index
starTraces[k][i_b] is \( \star \text{tr} \star^{1} \) of a \(dk\)form on the i_bboundary cell, using relative index
The trace of dform is not included. The array uses the global dimension to give an uniform interface, however only the first d elements are used.
< Mesh used for the quadrature
Generic interface to generate quadrature rule on any dimension
< Cell index
< Degree of exactness
Evaluate the polynomial basis on a cell
< Cell index
< Polynomial degree
< Quadrature rule
Evaluate the polynomial basis on a quadrature of the boundary
< Cell index
< Relative index of the boundary (e.g. between 0 and 2 for a triangle)
< Polynomial degree
< Quadrature rule on the boundary
Evaluate the volume form on a quadrature of the boundary
< Cell index
< Quadrature rule
Evaluate the pullback by I of the \(L^2\) product on the exterior algebra of the exterior algebra on the reference element.
Compute the matrix of \( I_T^* (\langle \cdot , \cdot \rangle_{g}) \).
l  Form degree 
< Cell index
< Quadrature rule
Evaluate the pullback by I of the \(L^2\) product on the exterior algebra of the exterior algebra on the reference element composed with the trace on the right.
Compute the matrix of \( I_F^* (\langle \cdot , I_F^* J_T^* \cdot \rangle_{g}) \).
l  Form degree 
< Cell index
< Relative index of the boundary
< Quadrature rule on the boundary
Evaluate the pullback by I of the \(L^2\) product on the exterior algebra of the exterior algebra on the reference element composed with the trace on the right and the Hodge star on both side.
Compute the matrix of \( I_F^* (\langle \cdot , \star I_F^* J_T^* \star^{1} \cdot \rangle_{g}) \). Expect a \(dl\) form on the right and a \(d1l\) form on the left.
l  Hodge dual of the form degree 
< Cell index
< Relative index of the boundary
< Quadrature rule on the boundary
Access the mesh associated with this object