LineBasis

FunctionSpace/CMakeLists.txt

@@ -16,13 +16,15 @@ set(SRC
   CurlBasis.cpp
   DivBasis.cpp
 
-  QuadNodeBasis.cpp
-  QuadEdgeBasis.cpp
-
   LagrangeGenerator.cpp
   LagrangeBasis.cpp
   TriLagrangeBasis.cpp
 
+  LineNodeBasis.cpp
+
+  QuadNodeBasis.cpp
+  QuadEdgeBasis.cpp
+
   TriNodeBasis.cpp
   TriEdgeBasis.cpp
   TriNedelecBasis.cpp

FunctionSpace/LineNodeBasis.cpp

+#include "LineNodeBasis.h"
+#include "Legendre.h"
+
+using namespace std;
+
+LineNodeBasis::LineNodeBasis(int order){
+  // Set Basis Type //
+  this->order = order;
+  
+  type = 0;
+  dim  = 1;
+
+  nVertex = 2;
+  nEdge   = (order - 1);
+  nFace   = 0;
+  nCell   = 0;
+
+  nEdgeClosure = 2;
+  nFaceClosure = 0;
+
+  size = nVertex + nEdge + nFace + nCell;
+
+  // Legendre Polynomial //
+  Polynomial* intLegendre = new Polynomial[order];
+  Legendre::integrated(intLegendre, order);
+
+  // Basis //
+  node = new vector<Polynomial*>(nVertex);
+  edge = new vector<vector<Polynomial*>*>(nEdgeClosure);
+  face = new vector<vector<Polynomial*>*>(nFaceClosure);
+  cell = new vector<Polynomial*>(nCell);
+
+  (*edge)[0] = new vector<Polynomial*>(nEdge);
+  (*edge)[1] = new vector<Polynomial*>(nEdge);
+
+
+  // Vertex Based (Lagrange) //
+  (*node)[0] = 
+    new Polynomial(Polynomial(1, 0, 0, 0) - 
+		   Polynomial(1, 1, 0, 0) *
+		   0.5);
+
+  (*node)[1] = 
+    new Polynomial(Polynomial(1, 0, 0, 0) + 
+		   Polynomial(1, 1, 0, 0) *
+		   0.5);
+  
+  
+  // Edge Based //
+  const int permutation[2] = {0, 1};
+  const Polynomial    x[2] = {
+    Polynomial(+1, 1, 0, 0),
+    Polynomial(-1, 1, 0, 0)
+  };
+  
+  for(int c = 0; c < 2; c++){
+    unsigned int i = 0;
+    
+    for(int l = 1; l < order; l++){
+      (*(*edge)[c])[i] = 
+	new Polynomial(intLegendre[l].compose(x[permutation[c]]));
+      
+      i++;
+    }
+  }
+
+
+  // Free Temporary Sapce //
+  delete[] intLegendre;
+}
+
+LineNodeBasis::~LineNodeBasis(void){
+  // Vertex Based //
+  for(int i = 0; i < nVertex; i++)
+    delete (*node)[i];
+  
+  delete node;
+
+
+  // Edge Based //
+  for(int c = 0; c < 2; c++){
+    for(int i = 0; i < nEdge; i++)
+      delete (*(*edge)[c])[i];
+    
+    delete (*edge)[c];
+  }
+  
+  delete edge;
+
+
+  // Face Based //
+  delete face;
+
+
+  // Cell Based //
+  delete cell;
+}

FunctionSpace/LineNodeBasis.h

+#ifndef _LINENODEBASIS_H_
+#define _LINENODEBASIS_H_
+
+#include "BasisScalar.h"
+
+/**
+   @class LineNodeBasis
+   @brief A Node Basis for Lines
+ 
+   This class can instantiate a Node-Based Basis 
+   (high or low order) for Lines.@n
+   
+   It uses an @em adaptation of
+   <a href="http://www.hpfem.jku.at/publications/szthesis.pdf">Zaglmayr's</a>  
+   Basis for @em high @em order Polynomial%s generation.@n
+
+   This Basis is a restriction of a Quad Basis to @f$y = 0@f$.@n
+   
+   It also uses the following mapping: @f$x = \frac{u + 1}{2}@f$.
+ */
+
+class LineNodeBasis: public BasisScalar{
+ public:
+  //! @param order The order of the Basis
+  //!
+  //! Returns a new Node-Basis for Lines of the given order
+  LineNodeBasis(int order);
+  
+  //! Deletes this Basis
+  //!
+  virtual ~LineNodeBasis(void);
+};
+
+#endif