1: #if !defined(PETSCFETYPES_H)
  2: #define PETSCFETYPES_H

  4: /*S
  5:   PetscSpace - PETSc object that manages a linear space, e.g. the space of d-dimensional polynomials of given degree

  7:   Level: beginner

  9: .seealso: PetscSpaceCreate(), PetscDualSpaceCreate(), PetscSpaceSetType(), PetscSpaceType
 10: S*/
 11: typedef struct _p_PetscSpace *PetscSpace;

 13: /*S
 14:   PetscDualSpace - PETSc object that manages the dual space to a linear space, e.g. the space of evaluation functionals at the vertices of a triangle

 16:   Level: beginner

 18: .seealso: PetscDualSpaceCreate(), PetscSpaceCreate(), PetscDualSpaceSetType(), PetscDualSpaceType
 19: S*/
 20: typedef struct _p_PetscDualSpace *PetscDualSpace;

 22: /*MC
 23:   PetscDualSpaceReferenceCell - The type of reference cell

 25:   Notes: This is used only for automatic creation of reference cells. A PetscDualSpace can accept an arbitary DM for a reference cell.

 27:   Level: beginner

 29: .seealso: PetscSpace
 30: M*/
 31: typedef enum { PETSCDUALSPACE_REFCELL_SIMPLEX, PETSCDUALSPACE_REFCELL_TENSOR } PetscDualSpaceReferenceCell;
 32: PETSC_EXTERN const char * const PetscDualSpaceReferenceCells[];

 34: /*MC
 35:   PetscDualSpaceTransformType - The type of function transform

 37:   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.

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

 42:   Note: For details, please see Rognes, Kirby, and Logg, Efficient Assembly of Hdiv and Hrot Conforming Finite Elements, SISC, 31(6), 4130-4151, arXiv 1205.3085, 2010

 44:   Level: beginner

 46: .seealso: PetscDualSpaceGetDeRahm()
 47: M*/
 48: typedef enum {IDENTITY_TRANSFORM, COVARIANT_PIOLA_TRANSFORM, CONTRAVARIANT_PIOLA_TRANSFORM} PetscDualSpaceTransformType;

 50: /*S
 51:   PetscFE - PETSc object that manages a finite element space, e.g. the P_1 Lagrange element

 53:   Level: beginner

 55: .seealso: PetscFECreate(), PetscSpaceCreate(), PetscDualSpaceCreate(), PetscFESetType(), PetscFEType
 56: S*/
 57: typedef struct _p_PetscFE *PetscFE;

 59: /*MC
 60:   PetscFEJacobianType - indicates which pointwise functions should be used to fill the Jacobian matrix

 62:   Level: beginner

 64: .seealso: PetscFEIntegrateJacobian()
 65: M*/
 66: typedef enum { PETSCFE_JACOBIAN, PETSCFE_JACOBIAN_PRE, PETSCFE_JACOBIAN_DYN } PetscFEJacobianType;

 68: #endif