petsc-3.13.6 2020-09-29

PetscDTAltVStar

Apply a power of the Hodge star operator, which maps k-forms to (N-k) forms, to a k-form

Synopsis

#include "petscdt.h" 
PetscErrorCode PetscDTAltVStar(PetscInt N, PetscInt k, PetscInt pow, const PetscReal *w, PetscReal *starw)

Input Arguments

	N	- the dimension of the vector space, N >= 0
	k	- the degree k of the k-form w, 0 <= k <= N
	pow	- the number of times to apply the Hodge star operator: pow < 0 indicates that the inverse of the Hodge star operator should be applied \|pow\| times.
	w	- a k-form, size [N choose k]

Output Arguments

starw = (star)^pow w. Each degree of freedom of a k -form is associated with a subset S of k coordinates of the N dimensional vector space: the Hodge start operator (star) maps that degree of freedom to the degree of freedom associated with S', the complement of S, with a sign change if the permutation of coordinates {S[0], ... S[k-1], S'[0], ... S'[N-k- 1]} is an odd permutation. This implies (star)^2 w = (-1)^{k(N-k)} w, and (star)^4 w = w.

Level

intermediate

Location