PetscDualSpaceTransformType#

Values#

• IDENTITY_TRANSFORM - make no changes in the function

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

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

Note#

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. [RKL09]

References#

See Also#

PetscDualSpaceGetDeRahm()

Level#

intermediate

Location#

include/petscdualspace.h

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