PetscDTPTrimmedEvalJet#

Evaluate the jet (function and derivatives) of a basis of the trimmed polynomial k-forms up to a given degree.

Synopsis#

#include "petscdt.h" 
PetscErrorCode PetscDTPTrimmedEvalJet(PetscInt dim, PetscInt npoints, const PetscReal points[], PetscInt degree, PetscInt formDegree, PetscInt jetDegree, PetscReal p[])

Input Parameters#

dim - the number of variables in the multivariate polynomials
npoints - the number of points to evaluate the polynomials at
points - [npoints x dim] array of point coordinates
degree - the degree (sum of degrees on the variables in a monomial) of the trimmed polynomial space to evaluate. There are ((dim + degree) choose (dim + formDegree)) x ((degree + formDegree - 1) choose (formDegree)) polynomials in this space. (You can use PetscDTPTrimmedSize() to compute this size.)
formDegree - the degree of the form
jetDegree - the maximum order partial derivative to evaluate in the jet. There are ((dim + jetDegree) choose dim) partial derivatives in the jet. Choosing jetDegree = 0 means to evaluate just the function and no derivatives

Output Parameter#

p - an array containing the evaluations of the PKD polynomials’ jets on the points.

Notes#

The size of p is PetscDTPTrimmedSize() x ((dim + formDegree) choose dim) x ((dim + k) choose dim) x npoints,which also describes the order of the dimensions of this four-dimensional array:

the first (slowest varying) dimension is basis function index; the second dimension is component of the form; the third dimension is jet index; the fourth (fastest varying) dimension is the index of the evaluation point.

The ordering of the basis functions is not graded, so the basis functions are not nested by degree like PetscDTPKDEvalJet(). The basis functions are not an L2-orthonormal basis on any particular domain.

The implementation is based on the description of the trimmed polynomials up to degree r as the direct sum of polynomials up to degree (r-1) and the Koszul differential applied to homogeneous polynomials of degree (r-1).

Level#

advanced

Location#

src/dm/dt/interface/dt.c

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