Defines Lagrange polynomials in the 2D on the reference square \([-1,1]^2\) or reference triangle \( Conv\{(-1,-1),(1,-1),(-1,1)\} \), where \(Conv\) is the convex hull.
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#include <ptems/spaces/lagrangepolynomials.hpp>
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| template<typename T > |
| static T * | Polynomials (const ReferenceElement< 2 > &refElement, const Vector< 2 > &pt, T *result, std::size_t polydeg) |
| | Computes the value of the Lagrange polynomials, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) equidistributed points on the reference square or triangle, respectively, and zero at the rest, where \(p\) is the polynomial degree. More...
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| template<typename T > |
| static FuncAndGradData< 2, T > * | Gradient (const ReferenceElement< 2 > &refElement, const Vector< 2 > &pt, FuncAndGradData< 2, T > *result, std::size_t polydeg) |
| | Computes the value of the Lagrange polynomials, and their first order (partial) derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) equidistributed points on the reference square or triangle, respectively, and zero at the rest, where \(p\) is the polynomial degree. More...
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| template<typename T > |
| static FuncGradAndHessianData< 2, T > * | Hessian (const ReferenceElement< 2 > &refElement, const Vector< 2 > &pt, FuncGradAndHessianData< 2, T > *result, std::size_t polydeg) |
| | Computes the value of the Lagrange polynomials, and their first and second order (partial) derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) equidistributed points on the reference square or triangle, respectively, and zero at the rest, where \(p\) is the polynomial degree. More...
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| static constexpr std::size_t | NumberDoFs (const ReferenceElement< 2 > &element, std::size_t polydeg) |
| | Gets the number of degrees of freedom required for a polynomial of the specified degree on the specified reference element. More...
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Defines Lagrange polynomials in the 2D on the reference square \([-1,1]^2\) or reference triangle \( Conv\{(-1,-1),(1,-1),(-1,1)\} \), where \(Conv\) is the convex hull.
◆ Gradient()
Computes the value of the Lagrange polynomials, and their first order (partial) derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) equidistributed points on the reference square or triangle, respectively, and zero at the rest, where \(p\) is the polynomial degree.
- Template Parameters
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- Parameters
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| refElement | Reference element - either the reference square or triangle |
| pt | The point to compute the values of the Lagrange polynomial at |
| result | Array of at least \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) entries, depending on refElement, to store the result into |
| polydeg | The polynomial degree of the Lagrange basis functions |
- Returns
- Pointer to the entry AFTER the last basis filled (
=result+N where N is the number of basis functions depending on the reference element)
◆ Hessian()
Computes the value of the Lagrange polynomials, and their first and second order (partial) derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) equidistributed points on the reference square or triangle, respectively, and zero at the rest, where \(p\) is the polynomial degree.
- Template Parameters
-
- Parameters
-
| refElement | Reference element - either the reference square or triangle |
| pt | The point to compute the values of the Lagrange polynomial at |
| result | Array of at least \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) entries, depending on refElement, to store the result into |
| polydeg | The polynomial degree of the Lagrange basis functions |
- Returns
- Pointer to the entry AFTER the last basis filled (
=result+N where N is the number of basis functions depending on the reference element)
◆ NumberDoFs()
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inlinestaticconstexprinherited |
Gets the number of degrees of freedom required for a polynomial of the specified degree on the specified reference element.
- Parameters
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| element | The reference element (triangle or square) |
| polydeg | The degree of the polynomial |
- Returns
- The number of degrees of freedom
◆ Polynomials()
Computes the value of the Lagrange polynomials, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) equidistributed points on the reference square or triangle, respectively, and zero at the rest, where \(p\) is the polynomial degree.
- Template Parameters
-
- Parameters
-
| refElement | Reference element - either the reference square or triangle |
| pt | The point to compute the values of the Lagrange polynomial at |
| result | Array of at least \((p+1)^2\) or \(\frac{(p+1)(p+2}2\) entries, depending on refElement, to store the result into |
| polydeg | The polynomial degree of the Lagrange basis functions |
- Returns
- Pointer to the entry AFTER the last basis filled (
=result+N where N is the number of basis functions depending on the reference element)
The documentation for this struct was generated from the following file:
- ptems/spaces/lagrangepolynomials.hpp
1.9.1