PetscDTGaussLobattoLegendreQuadrature

creates a set of the locations and weights of the Gauss-Lobatto-Legendre nodes of a given size on the domain \([-1,1]\)

Synopsis

#include "petscdt.h" 
PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt npoints, PetscGaussLobattoLegendreCreateType type, PetscReal x[], PetscReal w[])

Not Collective

Input Parameters

• npoints - number of grid nodes

• type - PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA or PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON

Output Parameters

• x - quadrature points, pass in an array of length npoints

• w - quadrature weights, pass in an array of length npoints

Notes

For n > 30 the Newton approach computes duplicate (incorrect) values for some nodes because the initial guess is apparently not close enough to the desired solution

These are useful for implementing spectral methods based on Gauss-Lobatto-Legendre (GLL) nodes

See https://epubs.siam.org/doi/abs/10.1137/110855442 https://epubs.siam.org/doi/abs/10.1137/120889873 for better ways to compute GLL nodes

See Also

PetscDTGaussQuadrature(), PetscGaussLobattoLegendreCreateType

Level

intermediate

Location

src/dm/dt/interface/dt.c

Examples

src/tao/unconstrained/tutorials/burgers_spectral.c
src/ksp/ksp/tutorials/ex68.c
src/tao/unconstrained/tutorials/spectraladjointassimilation.c
src/ts/tutorials/ex50.c
src/ksp/ksp/tutorials/ex69.c

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