petsc-3.14.6 2021-03-30
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Push forward a quadrature functional under an affine transformation.


#include "petscdt.h" 
PetscErrorCode PetscQuadraturePushForward(PetscQuadrature q, PetscInt imageDim, const PetscReal origin[], const PetscReal originImage[], const PetscReal J[], PetscInt formDegree, PetscQuadrature *Jinvstarq)
Collecive on PetscQuadrature

Input Arguments

q - the quadrature functional
imageDim - the dimension of the image of the transformation
origin - a point in the original space
originImage - the image of the origin under the transformation
J - the Jacobian of the image: an [imageDim x dim] matrix in row major order
formDegree - transform the quadrature weights as k-forms of this form degree (if the number of components is a multiple of (dim choose formDegree), it is assumed that they represent multiple k-forms) [see PetscDTAltVPullback() for interpretation of formDegree]

Output Arguments

Jinvstarq - a quadrature rule where each point is the image of a point in the original quadrature rule, and where the k-form weights have been pulled-back by the pseudoinverse of J to the k-form weights in the image space.

Note: the new quadrature rule will have a different number of components if spaces have different dimensions. For example, pushing a 2-form forward from a two dimensional space to a three dimensional space changes the number of components from 1 to 3.

See Also

PetscDTAltVPullback(), PetscDTAltVPullbackMatrix()




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