4 #ifndef DUNE_LOCALFUNCTIONS_QKLOCALBASIS_HH 5 #define DUNE_LOCALFUNCTIONS_QKLOCALBASIS_HH 9 #include <dune/common/fvector.hh> 10 #include <dune/common/fmatrix.hh> 11 #include <dune/common/power.hh> 13 #include <dune/geometry/type.hh> 33 template<
class D,
class R,
int k,
int d>
37 static R p (
int i, D x)
40 for (
int j=0; j<=k; j++)
41 if (j!=i) result *= (k*x-j)/(i-j);
46 static R dp (
int i, D x)
50 for (
int j=0; j<=k; j++)
53 R prod( (k*1.0)/(i-j) );
54 for (
int l=0; l<=k; l++)
56 prod *= (k*x-l)/(i-l);
64 static R ddp (
int j, D x)
68 for (
int i=0; i<=k; i++)
75 for (
int m=0; m<=k; m++)
80 R prod( (k*1.0)/(j-m) );
81 for (
int l=0; l<=k; l++)
82 if (l!=i && l!=j && l!=m)
83 prod *= (k*x-l)/(j-l);
87 result += sum * ( (k*1.0)/(j-i) );
94 static Dune::FieldVector<int,d> multiindex (
int i)
96 Dune::FieldVector<int,d> alpha;
97 for (
int j=0; j<d; j++)
106 typedef LocalBasisTraits<D,d,Dune::FieldVector<D,d>,R,1,Dune::FieldVector<R,1>,Dune::FieldMatrix<R,1,d> >
Traits;
111 return StaticPower<k+1,d>::power;
116 std::vector<typename Traits::RangeType>& out)
const 119 for (
size_t i=0; i<
size(); i++)
122 Dune::FieldVector<int,d> alpha(multiindex(i));
128 for (
int j=0; j<d; j++)
129 out[i] *= p(alpha[j],in[j]);
139 std::vector<typename Traits::JacobianType>& out)
const 144 for (
size_t i=0; i<
size(); i++)
147 Dune::FieldVector<int,d> alpha(multiindex(i));
150 for (
int j=0; j<d; j++)
154 out[i][0][j] = dp(alpha[j],in[j]);
157 for (
int l=0; l<d; l++)
159 out[i][0][j] *= p(alpha[l],in[l]);
171 std::vector<typename Traits::RangeType>& out)
const 176 for (
size_t i=0; i<
size(); i++)
179 Dune::FieldVector<int,d> alpha(multiindex(i));
185 for (std::size_t l=0; l<d; l++)
190 out[i][0] *= p(alpha[l],in[l]);
193 out[i][0] *= dp(alpha[l],in[l]);
196 out[i][0] *= ddp(alpha[l],in[l]);
199 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: qklocalbasis.hh:138
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: qklocalbasis.hh:115
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:31
D DomainType
domain type
Definition: localbasis.hh:43
LocalBasisTraits< D, d, Dune::FieldVector< D, d >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, d > > Traits
Definition: qklocalbasis.hh:106
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:15
Lagrange shape functions of order k on the reference cube.
Definition: qklocalbasis.hh:34
unsigned int order() const
Polynomial order of the shape functions.
Definition: qklocalbasis.hh:206
unsigned int size() const
number of shape functions
Definition: qklocalbasis.hh:109
void partial(const std::array< unsigned int, d > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of any order of all shape functions.
Definition: qklocalbasis.hh:169