4 #ifndef DUNE_LOCALFUNCTIONS_WHITNEY_EDGES0_5_BASIS_HH 5 #define DUNE_LOCALFUNCTIONS_WHITNEY_EDGES0_5_BASIS_HH 10 #include <dune/common/fmatrix.hh> 11 #include <dune/common/fvector.hh> 33 template<
class Geometry,
class RF>
35 private EdgeS0_5Common<Geometry::mydimension, typename Geometry::ctype>
48 typedef FieldVector<RangeField, dimRange>
Range;
50 typedef FieldMatrix<RangeField, dimRange, dimDomainGlobal>
Jacobian;
60 static const P1LocalBasis& p1LocalBasis;
68 std::vector<typename P1Basis::Traits::Jacobian> p1j;
70 std::vector<typename Traits::DomainField> edgel;
80 template<
typename VertexOrder>
88 P1Basis(p1LocalBasis, geo).evaluateJacobian(xl, p1j);
91 for(std::size_t i = 0; i <
s; ++i) {
92 edgel[i] = (geo.corner(
refelem.subEntity(i,dim-1,0,dim))-
93 geo.corner(
refelem.subEntity(i,dim-1,1,dim))
95 const typename VertexOrder::iterator& edgeVertexOrder =
96 vertexOrder.begin(dim-1, i);
97 if(edgeVertexOrder[0] > edgeVertexOrder[1])
103 std::size_t
size ()
const {
return s; }
107 std::vector<typename Traits::Range>& out)
const 113 std::vector<typename P1LocalBasis::Traits::RangeType> p1v;
116 for(std::size_t i = 0; i <
s; i++) {
117 const std::size_t i0 =
refelem.subEntity(i,dim-1,0,dim);
118 const std::size_t i1 =
refelem.subEntity(i,dim-1,1,dim);
119 out[i].axpy( p1v[i0], p1j[i1][0]);
120 out[i].axpy(-p1v[i1], p1j[i0][0]);
127 std::vector<typename Traits::Jacobian>& out)
const 131 for(std::size_t i = 0; i <
s; i++) {
132 const std::size_t i0 =
refelem.subEntity(i,dim-1,0,dim);
133 const std::size_t i1 =
refelem.subEntity(i,dim-1,1,dim);
134 for(std::size_t j = 0; j < dim; j++)
135 for(std::size_t k = 0; k < dim; k++)
136 out[i][j][k] = edgel[i] *
137 (p1j[i0][0][k]*p1j[i1][0][j]-p1j[i1][0][k]*p1j[i0][0][j]);
144 std::vector<typename Traits::Range>& out)
const 146 auto totalOrder = std::accumulate(
order.begin(),
order.end(), 0);
147 if (totalOrder == 0) {
149 }
else if (totalOrder==1) {
150 auto const k = std::distance(
order.begin(), std::find(
order.begin(),
order.end(), 1));
153 for (std::size_t i = 0; i <
s; i++)
155 const std::size_t i0 =
refelem.subEntity(i,dim-1,0,dim);
156 const std::size_t i1 =
refelem.subEntity(i,dim-1,1,dim);
157 for(std::size_t j = 0; j < dim; j++)
158 out[i][j] = edgel[i] *
159 (p1j[i0][0][k]*p1j[i1][0][j] - p1j[i1][0][k]*p1j[i0][0][j]);
162 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
167 std::size_t
order ()
const {
return 1; }
170 template<
class Geometry,
class RF>
176 #endif // DUNE_LOCALFUNCTIONS_WHITNEY_EDGES0_5_BASIS_HH Geometry::ctype DomainField
Definition: whitney/edges0.5/basis.hh:40
static const std::size_t dimRange
Definition: whitney/edges0.5/basis.hh:47
RF RangeField
Definition: whitney/edges0.5/basis.hh:46
Common base class for edge elements.
Definition: common.hh:17
FieldVector< DomainField, dimDomainGlobal > DomainGlobal
Definition: whitney/edges0.5/basis.hh:44
Basis for order 0.5 (lowest order) edge elements on simplices.
Definition: whitney/edges0.5/basis.hh:34
Linear Lagrange shape functions on the simplex.
Definition: p1localbasis.hh:27
std::size_t size() const
number of shape functions
Definition: whitney/edges0.5/basis.hh:103
std::size_t s
The number of base functions.
Definition: common.hh:32
void evaluateJacobian(const typename Traits::DomainLocal &, std::vector< typename Traits::Jacobian > &out) const
Evaluate all Jacobians.
Definition: whitney/edges0.5/basis.hh:126
EdgeS0_5Basis(const Geometry &geo, const VertexOrder &vertexOrder)
Construct an EdgeS0_5Basis.
Definition: whitney/edges0.5/basis.hh:81
static const std::size_t dimDomainLocal
Definition: whitney/edges0.5/basis.hh:41
RefElem refelem
The reference element for this edge element.
Definition: common.hh:24
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:15
static const std::size_t dimDomainGlobal
Definition: whitney/edges0.5/basis.hh:42
FieldMatrix< RangeField, dimRange, dimDomainGlobal > Jacobian
Definition: whitney/edges0.5/basis.hh:50
FieldVector< RangeField, dimRange > Range
Definition: whitney/edges0.5/basis.hh:48
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: p1localbasis.hh:41
FieldVector< DomainField, dimDomainLocal > DomainLocal
Definition: whitney/edges0.5/basis.hh:43
Convert a simple scalar local basis into a global basis.
Definition: localtoglobaladaptors.hh:63
export type traits for function signature
Definition: whitney/edges0.5/basis.hh:39
void evaluateFunction(const typename Traits::DomainLocal &xl, std::vector< typename Traits::Range > &out) const
Evaluate all shape functions.
Definition: whitney/edges0.5/basis.hh:106
void partial(const std::array< unsigned int, dim > &order, const typename Traits::DomainLocal &in, std::vector< typename Traits::Range > &out) const
Evaluate partial derivatives of all shape functions.
Definition: whitney/edges0.5/basis.hh:142
std::size_t order() const
Polynomial order of the shape functions.
Definition: whitney/edges0.5/basis.hh:167