Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi/Gauss-Radau-Jacobi/Gauss-Lobatto points zgj at the arbitrary location z. More...

#include <Intrepid2_Polylib.hpp>

Public Member Functions
template<>
KOKKOS_INLINE_FUNCTION zViewType::value_type	getValue (const ordinal_type i, const typename zViewType::value_type z, const zViewType zgj, const ordinal_type np, const double alpha, const double beta)

template<>
KOKKOS_INLINE_FUNCTION zViewType::value_type	getValue (const ordinal_type i, const typename zViewType::value_type z, const zViewType zgrj, const ordinal_type np, const double alpha, const double beta)

template<>
KOKKOS_INLINE_FUNCTION zViewType::value_type	getValue (const ordinal_type i, const typename zViewType::value_type z, const zViewType zgrj, const ordinal_type np, const double alpha, const double beta)

template<>
KOKKOS_INLINE_FUNCTION zViewType::value_type	getValue (const ordinal_type i, const typename zViewType::value_type z, const zViewType zglj, const ordinal_type np, const double alpha, const double beta)

Static Public Member Functions
template<typename zViewType >
static KOKKOS_INLINE_FUNCTION zViewType::value_type	getValue (const ordinal_type i, const typename zViewType::value_type z, const zViewType zgj, const ordinal_type np, const double alpha, const double beta)

Detailed Description

template<EPolyType polyType>
struct Intrepid2::Polylib::Serial::LagrangianInterpolant< polyType >

Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi/Gauss-Radau-Jacobi/Gauss-Lobatto points zgj at the arbitrary location z.

$-1 \leq z \leq 1$

POLYTYPE_GAUSS Uses the defintion of the Lagrangian interpolant:
$\begin{array}{rcl} h_j(z) = \left\{ \begin{array}{ll} \displaystyle \frac{P_{np}^{\alpha,\beta}(z)} {[P_{np}^{\alpha,\beta}(z_j)]^\prime (z-z_j)} & \mbox{if $z \ne z_j$}\\ & \\ 1 & \mbox{if $z=z_j$} \end{array} \right. \end{array}$

Gauss-Radau-Jacobi (Left) Uses the defintion of the Lagrangian interpolant:
% $\begin{array}{rcl} h_j(z) = \left\{ \begin{array}{ll} \displaystyle \frac{(1+z) P_{np-1}^{\alpha,\beta+1}(z)} {((1+z_j) [P_{np-1}^{\alpha,\beta+1}(z_j)]^\prime + P_{np-1}^{\alpha,\beta+1}(z_j) ) (z-z_j)} & \mbox{if $z \ne z_j$}\\ & \\ 1 & \mbox{if $z=z_j$} \end{array} \right. \end{array}$

Gauss-Radau-Jacobi (Right) Uses the defintion of the Lagrangian interpolant:
% $\begin{array}{rcl} h_j(z) = \left\{ \begin{array}{ll} \displaystyle \frac{(1-z) P_{np-1}^{\alpha+1,\beta}(z)} {((1-z_j) [P_{np-1}^{\alpha+1,\beta}(z_j)]^\prime - P_{np-1}^{\alpha+1,\beta}(z_j) ) (z-z_j)} & \mbox{if $z \ne z_j$}\\ & \\ 1 & \mbox{if $z=z_j$} \end{array} \right. \end{array}$

Gauss-Lobatto Uses the defintion of the Lagrangian interpolant:
% $\begin{array}{rcl} h_j(z) = \left\{ \begin{array}{ll} \displaystyle \frac{(1-z^2) P_{np-2}^{\alpha+1,\beta+1}(z)} {((1-z^2_j) [P_{np-2}^{\alpha+1,\beta+1}(z_j)]^\prime - 2 z_j P_{np-2}^{\alpha+1,\beta+1}(z_j) ) (z-z_j)}&\mbox{if $z \ne z_j$}\\ & \\ 1 & \mbox{if $z=z_j$} \end{array} \right. \end{array}$

Definition at line 382 of file Intrepid2_Polylib.hpp.

The documentation for this struct was generated from the following file:

http://docs.trilinos.org/r13.0/packages/intrepid2/src/Shared/Intrepid2_Polylib.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

template<EPolyType polyType> struct Intrepid2::Polylib::Serial::LagrangianInterpolant< polyType >

template<EPolyType polyType>
struct Intrepid2::Polylib::Serial::LagrangianInterpolant< polyType >