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: /*MC
 14:   PetscSpacePolynomialType - The type of polynomial space

 16:   Notes:
 17: $ PETSCSPACE_POLYNOMIALTYPE_P - This is the normal polynomial space of degree q, P_q or Q_q.
 18: $ PETSCSPACE_POLYNOMIALTYPE_PMINUS_HDIV - This is the smallest polynomial space contained in P_q/Q_q such that the divergence is in P_{q-1}/Q_{q-1}. Making this space is straightforward:
 19: $   P^-_q = P_{q-1} + P_{(q-1)} x
 20: $ where P_{(q-1)} is the space of homogeneous polynomials of degree q-1.
 21: $ PETSCSPACE_POLYNOMIALTYPE_PMINUS_HCURL - This is the smallest polynomial space contained in P_q/Q_q such that the curl is in P_{q-1}/Q_{q-1}. Making this space is straightforward:
 22: $   P^-_q = P_{q-1} + P_{(q-1)} rot x
 23: $ where P_{(q-1)} is the space of homogeneous polynomials of degree q-1, and rot x is (-y, x) in 2D, and (z - y, x - z, y - x) in 3D, being the generators of the rotation algebra.

 25:   Level: beginner

 27: .seealso: PetscSpace
 28: M*/
 29: typedef enum { PETSCSPACE_POLYNOMIALTYPE_P, PETSCSPACE_POLYNOMIALTYPE_PMINUS_HDIV, PETSCSPACE_POLYNOMIALTYPE_PMINUS_HCURL } PetscSpacePolynomialType;
 30: PETSC_EXTERN const char * const PetscSpacePolynomialTypes[];

 32: /*S
 33:   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

 35:   Level: beginner

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

 41: /*MC
 42:   PetscDualSpaceReferenceCell - The type of reference cell

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

 46:   Level: beginner

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

 53: /*MC
 54:   PetscDualSpaceTransformType - The type of function transform

 56:   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.

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

 61:   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

 63:   Level: beginner

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

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

 72:   Level: beginner

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

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

 81:   Level: beginner

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

 87: #endif