PetscDualSpaceTransformType#
The type of function transform
Values#
IDENTITY_TRANSFORM
- make no changes in the functionCOVARIANT_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 which maps the reference cell to real space, and its Jacobian . If we want to transform function on the reference element, so that it acts on real space, we use the pushforward transform . The pullback is the inverse transform. [RKL09]
References#
Marie E Rognes, Robert C Kirby, and Anders Logg. Efficient assembly of H(div) and H(curl) conforming finite elements. SIAM Journal on Scientific Computing, 31(6):4130–4151, 2009.
See Also#
Level#
intermediate
Location#
Index of all DUALSPACE routines
Table of Contents for all manual pages
Index of all manual pages