Public Member Functions  
HarmonicEquations ()  
Empty Constructor. More...  
virtual double  u (const unsigned &n) const 
Access function: Eigenfunction value at local node n Note that solving the eigenproblem does not assign values to this storage space. It is used for output purposes only. More...  
void  output (ostream &outfile) 
Output the eigenfunction with default number of plot points. More...  
void  output (ostream &outfile, const unsigned &nplot) 
Output FE representation of soln: x,y,u or x,y,z,u at Nplot plot points. More...  
void  fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix) 
Assemble the contributions to the jacobian and mass matrices. More...  
double  interpolated_u (const Vector< double > &s) const 
Return FE representation of function value u(s) at local coordinate s. More...  
Protected Member Functions  
virtual double  dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const =0 
Shape/test functions and derivs w.r.t. to global coords at local coord. s; return Jacobian of mapping. More...  
virtual double  dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const =0 
Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping. More...  
virtual int  u_local_eqn (const unsigned &n) 
Access function that returns the local equation number of the unknown in the problem. Default is to assume that it is the first (only) value stored at the node. More...  
A class for all elements that solve the simple onedimensional eigenvalue problem
These elements are very closely related to the Poisson elements and could inherit from them. They are here developed from scratch for pedagogical purposes. This class contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.
Definition at line 74 of file harmonic.cc.

inline 
Empty Constructor.
Definition at line 79 of file harmonic.cc.

protectedpure virtual 
Shape/test functions and derivs w.r.t. to global coords at local coord. s; return Jacobian of mapping.
Implemented in QHarmonicElement< NNODE_1D >.

protectedpure virtual 
Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping.
Implemented in QHarmonicElement< NNODE_1D >.

inline 
Assemble the contributions to the jacobian and mass matrices.
Definition at line 119 of file harmonic.cc.

inline 
Return FE representation of function value u(s) at local coordinate s.
Definition at line 174 of file harmonic.cc.

inline 
Output the eigenfunction with default number of plot points.
Definition at line 88 of file harmonic.cc.
Referenced by QHarmonicElement< NNODE_1D >::output().

inline 
Output FE representation of soln: x,y,u or x,y,z,u at Nplot plot points.
Definition at line 96 of file harmonic.cc.

inlinevirtual 
Access function: Eigenfunction value at local node n Note that solving the eigenproblem does not assign values to this storage space. It is used for output purposes only.
Definition at line 84 of file harmonic.cc.

inlineprotectedvirtual 
Access function that returns the local equation number of the unknown in the problem. Default is to assume that it is the first (only) value stored at the node.
Definition at line 211 of file harmonic.cc.