Basis.h File Reference

Basis polynomials in \( d=1,2,3 \) dimensions and orders \( p=1,2,3,4 \). More...

#include "pbat/Aliases.h"
#include <cmath>
#include <numbers>

Go to the source code of this file.

Classes
struct	pbat::math::polynomial::MonomialBasis< Dims, Order >
	Polynomial basis \( \left\{ \Pi_{i=1}^{d} \mathbf{X}_i^{p_i} \; \text{s.t.} \; 0 \leq \sum_{i=1}^d p_i \leq p \right\} \) in dimensions \( d \) and order \( p \). More...
struct	pbat::math::polynomial::OrthonormalBasis< Dims, Order >
	Orthonormal polynomial basis \( \left\{ P_i(X) \right\} \) in dimensions \( d \) and order \( p \). More...
struct	pbat::math::polynomial::DivergenceFreeBasis< Dims, Order >
	Divergence-free polynomial basis \( \left\{ \mathbf{P}_i(X) \; \text{s.t.} \; \nabla_X \mathbf{P}_i = 0 \right\} \) in dimensions \( d \) and order \( p \). More...

Namespaces
namespace	pbat
	The main namespace of the library.
namespace	pbat::math
	Math related functionality.
namespace	pbat::math::polynomial
	The namespace for the Polynomial module.

Detailed Description

Basis polynomials in \( d=1,2,3 \) dimensions and orders \( p=1,2,3,4 \).

Author

Quoc-Minh Ton-That (tonth.nosp@m.at.q.nosp@m.uocmi.nosp@m.nh@g.nosp@m.mail..nosp@m.com)

All the polynomials defined are based on expressions computed symbolically in the script polynomial_basis.py (or equivalently polynomial_basis.ipynb).

Date

2025-02-27

Copyright

Copyright (c) 2025