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

See Also#

PetscDualSpaceGetDeRahm()

Level#

beginner

Location#

include/petscfetypes.h


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Index of all FE routines
Table of Contents for all manual pages
Index of all manual pages