#if !defined(PETSCFETYPES_H)
#define PETSCFETYPES_H

/* SUBMANSEC = FE */

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

  Level: beginner

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

/*S
  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

  Level: beginner

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

/*MC
  PetscDualSpaceReferenceCell - The type of reference cell

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

  Level: beginner

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

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

  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

  Level: beginner

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

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

  Level: beginner

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

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

  Level: beginner

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

#endif