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| OrthonormalPolynomialBasis () |
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template<class LFE > |
| OrthonormalPolynomialBasis (const LFE &lfe) |
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int | size (int l) |
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template<typename Point , typename Result > |
void | evaluateFunction (const Point &x, Result &r) const |
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template<typename Point , typename Result > |
void | evaluateJacobian (const Point &x, Result &r) const |
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template<typename Point , typename Result > |
void | evaluateFunction (int l, const Point &x, Result &r) const |
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template<typename Point , typename Result > |
void | evaluateJacobian (int l, const Point &x, Result &r) const |
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template<typename FieldType, int k, int d, Dune::GeometryType::BasicType bt, typename ComputationFieldType = FieldType, BasisType basisType = BasisType::Pk>
class Dune::PB::OrthonormalPolynomialBasis< FieldType, k, d, bt, ComputationFieldType, basisType >
Integrate monomials over the reference element.
Computes an L_2 orthonormal basis of P_k on the given reference element. The basis polynomials are stored in a monomial representation. With the matrix coeffs private to this class we have
with n_k : the dimension of P_k alpha_j : the exponents of the j-th monomial
The class can be used to evaluate polynomials with any degree l smaller or equal to the compile-time parameter k.
Calculating derivatives. From (1) we have
where beta_jr = alpha_jr-1 if r=s and alpha_jr else.
- Template Parameters
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FieldType | Type to represent coefficients after computation. |
k | The polynomial degreee. |
d | The space dimension. |
GeometryType::BasicType | The reference element |
ComputationFieldType | Type to do computations with. Might be high precission. |
basisType | Type of the polynomial basis. eiter Pk or Qk |
template<typename FieldType, int k, int d, Dune::GeometryType::BasicType bt, typename ComputationFieldType = FieldType, BasisType basisType = BasisType::Pk>
template<typename Point , typename Result >
template<typename FieldType, int k, int d, Dune::GeometryType::BasicType bt, typename ComputationFieldType = FieldType, BasisType basisType = BasisType::Pk>
template<typename Point , typename Result >