Reference documentation for deal.II version 9.2.0
|
Namespaces | |
internal | |
Classes | |
class | HermiteInterpolation |
class | HermiteLikeInterpolation |
class | Hierarchical |
class | LagrangeEquidistant |
class | Legendre |
class | Lobatto |
class | Monomial |
class | PiecewisePolynomial |
class | Polynomial |
Functions | |
std::vector< Polynomial< double > > | generate_complete_Lagrange_basis (const std::vector< Point< 1 >> &points) |
template<typename Number > | |
Number | jacobi_polynomial_value (const unsigned int degree, const int alpha, const int beta, const Number x) |
template<typename Number > | |
std::vector< Number > | jacobi_polynomial_roots (const unsigned int degree, const int alpha, const int beta) |
std::vector< PiecewisePolynomial< double > > | generate_complete_Lagrange_basis_on_subdivisions (const unsigned int n_subdivisions, const unsigned int base_degree) |
A namespace in which classes relating to the description of 1d polynomial spaces are declared.
std::vector< Polynomial< double > > Polynomials::generate_complete_Lagrange_basis | ( | const std::vector< Point< 1 >> & | points | ) |
Given a set of points along the real axis, this function returns all Lagrange polynomials for interpolation of these points. The number of polynomials is equal to the number of points and the maximum degree is one less.
Definition at line 834 of file polynomial.cc.
Number Polynomials::jacobi_polynomial_value | ( | const unsigned int | degree, |
const int | alpha, | ||
const int | beta, | ||
const Number | x | ||
) |
Definition at line 845 of file polynomial.h.
std::vector< Number > Polynomials::jacobi_polynomial_roots | ( | const unsigned int | degree, |
const int | alpha, | ||
const int | beta | ||
) |
Compute the roots of the Jacobi polynomials on the unit interval \([0, 1]\) of the given degree. These roots are used in several places inside the deal.II library, such as the Gauss-Lobatto quadrature formula or for the Hermite-like interpolation.
The algorithm uses a Newton algorithm, using the zeros of the Chebyshev polynomials as an initial guess. This code has been tested for alpha and beta equal to zero (Legendre case), one (Gauss-Lobatto case) as well as two, so be careful when using it for other values as the Newton iteration might or might not converge.
Definition at line 886 of file polynomial.h.
std::vector< PiecewisePolynomial< double > > Polynomials::generate_complete_Lagrange_basis_on_subdivisions | ( | const unsigned int | n_subdivisions, |
const unsigned int | base_degree | ||
) |
Generates a complete Lagrange basis on a subdivision of the unit interval in smaller intervals for a given degree on the subintervals and number of intervals.
Definition at line 134 of file polynomials_piecewise.cc.