petsc-3.12.4 2020-02-04
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# 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 Parameter

| n | - number of grid nodes
| type | - PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA or PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON

### Output Arguments

| x | - quadrature points
| w | - quadrature weights

### 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()

### Level

intermediate

### Location

src/dm/dt/interface/dt.c

### Examples

src/ksp/ksp/examples/tutorials/ex68.c.html
src/ksp/ksp/examples/tutorials/ex69.c.html
src/ts/examples/tutorials/ex50.c.html
src/tao/unconstrained/examples/tutorials/spectraladjointassimilation.c.html
Index of all DT routines
Table of Contents for all manual pages
Index of all manual pages