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;
61 static const P1LocalBasis& p1LocalBasis;
69 std::vector<typename P1Basis::Traits::Jacobian> p1j;
71 std::vector<typename Traits::DomainField> edgel;
81 template<
typename VertexOrder>
92 for(std::size_t i = 0; i < s; ++i) {
93 edgel[i] = (geo.corner(refelem.subEntity(i,dim-1,0,dim))-
94 geo.corner(refelem.subEntity(i,dim-1,1,dim))
96 const typename VertexOrder::iterator& edgeVertexOrder =
97 vertexOrder.begin(dim-1, i);
98 if(edgeVertexOrder[0] > edgeVertexOrder[1])
104 std::size_t
size ()
const {
return s; }
108 std::vector<typename Traits::Range>& out)
const
114 std::vector<typename P1LocalBasis::Traits::RangeType> p1v;
115 p1LocalBasis.evaluateFunction(xl, p1v);
117 for(std::size_t i = 0; i < s; i++) {
118 const std::size_t i0 = refelem.subEntity(i,dim-1,0,dim);
119 const std::size_t i1 = refelem.subEntity(i,dim-1,1,dim);
120 out[i].axpy( p1v[i0], p1j[i1][0]);
121 out[i].axpy(-p1v[i1], p1j[i0][0]);
128 std::vector<typename Traits::Jacobian>& out)
const
132 for(std::size_t i = 0; i < s; i++) {
133 const std::size_t i0 = refelem.subEntity(i,dim-1,0,dim);
134 const std::size_t i1 = refelem.subEntity(i,dim-1,1,dim);
135 for(std::size_t j = 0; j < dim; j++)
136 for(std::size_t k = 0; k < dim; k++)
137 out[i][j][k] = edgel[i] *
138 (p1j[i0][0][k]*p1j[i1][0][j]-p1j[i1][0][k]*p1j[i0][0][j]);
145 std::vector<typename Traits::Range>& out)
const
147 auto totalOrder = std::accumulate(
order.begin(),
order.end(), 0);
148 if (totalOrder == 0) {
150 }
else if (totalOrder==1) {
151 auto const k = std::distance(
order.begin(), std::find(
order.begin(),
order.end(), 1));
154 for (std::size_t i = 0; i < s; i++)
156 const std::size_t i0 = refelem.subEntity(i,dim-1,0,dim);
157 const std::size_t i1 = refelem.subEntity(i,dim-1,1,dim);
158 for(std::size_t j = 0; j < dim; j++)
159 out[i][j] = edgel[i] *
160 (p1j[i0][0][k]*p1j[i1][0][j] - p1j[i1][0][k]*p1j[i0][0][j]);
163 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
168 std::size_t
order ()
const {
return 1; }
171 template<
class Geometry,
class RF>
172 const typename EdgeS0_5Basis<Geometry, RF>::P1LocalBasis&
173 EdgeS0_5Basis<Geometry, RF>::p1LocalBasis = P1LocalBasis();
Definition: bdfmcube.hh:16
Convert a simple scalar local basis into a global basis.
Definition: localtoglobaladaptors.hh:63
void evaluateJacobian(const typename Traits::DomainLocal &in, std::vector< typename Traits::Jacobian > &out) const
Definition: localtoglobaladaptors.hh:123
Basis for order 0.5 (lowest order) edge elements on simplices.
Definition: whitney/edges0.5/basis.hh:36
EdgeS0_5Basis(const Geometry &geo, const VertexOrder &vertexOrder)
Construct an EdgeS0_5Basis.
Definition: whitney/edges0.5/basis.hh:82
void evaluateJacobian(const typename Traits::DomainLocal &, std::vector< typename Traits::Jacobian > &out) const
Evaluate all Jacobians.
Definition: whitney/edges0.5/basis.hh:127
void evaluateFunction(const typename Traits::DomainLocal &xl, std::vector< typename Traits::Range > &out) const
Evaluate all shape functions.
Definition: whitney/edges0.5/basis.hh:107
std::size_t size() const
number of shape functions
Definition: whitney/edges0.5/basis.hh:104
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:143
std::size_t order() const
Polynomial order of the shape functions.
Definition: whitney/edges0.5/basis.hh:168
export type traits for function signature
Definition: whitney/edges0.5/basis.hh:39
FieldVector< DomainField, dimDomainGlobal > DomainGlobal
Definition: whitney/edges0.5/basis.hh:44
static const std::size_t dimRange
Definition: whitney/edges0.5/basis.hh:47
static const std::size_t dimDomainLocal
Definition: whitney/edges0.5/basis.hh:41
FieldMatrix< RangeField, dimRange, dimDomainGlobal > Jacobian
Definition: whitney/edges0.5/basis.hh:50
static const std::size_t dimDomainGlobal
Definition: whitney/edges0.5/basis.hh:42
RF RangeField
Definition: whitney/edges0.5/basis.hh:46
FieldVector< DomainField, dimDomainLocal > DomainLocal
Definition: whitney/edges0.5/basis.hh:43
FieldVector< RangeField, dimRange > Range
Definition: whitney/edges0.5/basis.hh:48
Geometry::ctype DomainField
Definition: whitney/edges0.5/basis.hh:40
Common base class for edge elements.
Definition: common.hh:17
RefElem refelem
The reference element for this edge element.
Definition: common.hh:24
std::size_t s
The number of base functions.
Definition: common.hh:32