PetscDualSpaceTransformType#

The type of function transform

Notes#

These transforms, and their inverses, are used to move functions and functionals between the reference element and real space. Suppose that we have a mapping $$\phi$$ which maps the reference cell to real space, and its Jacobian $$J$$. If we want to transform function $$F$$ on the reference element, so that it acts on real space, we use the pushforward transform $$\sigma^*$$. The pullback $$\sigma_*$$ is the inverse transform.

Covariant Piola: $\sigma^*(F) = J^{-T} F \circ \phi^{-1)$

Contravariant Piola: $\sigma^*(F) = 1/|J| J F \circ \phi^{-1)$


References#

• Rognes, Kirby, and Logg, Efficient Assembly of Hdiv and Hrot Conforming Finite Elements, SISC, 31(6), 4130- 4151, arXiv 1205.3085, 2010

PetscDualSpaceGetDeRahm()