#if !defined(PETSCFETYPES_H) #define PETSCFETYPES_H /*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; /*MC PetscSpacePolynomialType - The type of polynomial space Notes: $PETSCSPACE_POLYNOMIALTYPE_P - This is the normal polynomial space of degree q, P_q or Q_q.$ 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: $P^-_q = P_{q-1} + P_{(q-1)} x$ where P_{(q-1)} is the space of homogeneous polynomials of degree q-1. $PETSCSPACE_POLYNOMIALTYPE_PMINUS_HCURL - This is the smallest polynomial space contained in P_q/Q_q such that the curl is in P_{q-1}/Q_{q-1}. Making this space is straightforward:$ P^-_q = P_{q-1} + P_{(q-1)} rot x $where P_{(q-1)} is the space of homogeneous polynomials of degree q-1, and rot x is (-y, x) in 2D, and (z - y, x - z, y - x) in 3D, being the generators of the rotation algebra. Level: beginner .seealso: PetscSpace M*/ typedef enum { PETSCSPACE_POLYNOMIALTYPE_P, PETSCSPACE_POLYNOMIALTYPE_PMINUS_HDIV, PETSCSPACE_POLYNOMIALTYPE_PMINUS_HCURL } PetscSpacePolynomialType; PETSC_EXTERN const char * const PetscSpacePolynomialTypes[]; /*S PetscDualSpace - PETSc object that manages the dual space to a linear space, e.g. the space of evaluation functionals at the vertices of a triangle Level: beginner .seealso: PetscDualSpaceCreate(), PetscSpaceCreate(), PetscDualSpaceSetType(), PetscDualSpaceType S*/ typedef struct _p_PetscDualSpace *PetscDualSpace; /*MC PetscDualSpaceReferenceCell - The type of reference cell Notes: This is used only for automatic creation of reference cells. A PetscDualSpace can accept an arbitary DM for a reference cell. Level: beginner .seealso: PetscSpace M*/ typedef enum { PETSCDUALSPACE_REFCELL_SIMPLEX, PETSCDUALSPACE_REFCELL_TENSOR } PetscDualSpaceReferenceCell; PETSC_EXTERN const char * const PetscDualSpaceReferenceCells[]; /*MC PetscDualSpaceTransformType - The type of function transform Notes: These transforms, and their inverses, are used to move functions and functionals between the reference element and real space. Suppose that we have a mapping$\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