1: const char help[] = "Construct and set a Lagrange dual space from options, then view it to\n"
  2:                     "understand the effects of different parameters.";

  4: #include <petscfe.h>
  5: #include <petscdmplex.h>

  7: int main(int argc, char **argv)
  8: {
  9:   PetscInt       dim;
 10:   PetscBool      tensorCell;
 11:   DM             K;
 12:   PetscDualSpace dsp;

 14:   PetscFunctionBeginUser;
 15:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
 16:   dim        = 2;
 17:   tensorCell = PETSC_FALSE;
 18:   PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for PETSCDUALSPACELAGRANGE test", "none");
 19:   PetscCall(PetscOptionsRangeInt("-dim", "The spatial dimension", "ex1.c", dim, &dim, NULL, 0, 3));
 20:   PetscCall(PetscOptionsBool("-tensor", "Whether the cell is a tensor product cell or a simplex", "ex1.c", tensorCell, &tensorCell, NULL));
 21:   PetscOptionsEnd();

 23:   PetscCall(PetscDualSpaceCreate(PETSC_COMM_WORLD, &dsp));
 24:   PetscCall(PetscObjectSetName((PetscObject)dsp, "Lagrange dual space"));
 25:   PetscCall(PetscDualSpaceSetType(dsp, PETSCDUALSPACELAGRANGE));
 26:   /* While Lagrange nodes don't require the existence of a reference cell to
 27:    * be refined, when we construct finite element dual spaces we have to be
 28:    * careful about what kind of continuity is maintained when cells are glued
 29:    * together to make a mesh.  The PetscDualSpace object is responsible for
 30:    * conveying continuity requirements to a finite element assembly routines,
 31:    * so a PetscDualSpace needs a reference element: a single element mesh,
 32:    * whose boundary points are the interstitial points in a mesh */
 33:   PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_WORLD, DMPolytopeTypeSimpleShape(dim, (PetscBool)!tensorCell), &K));
 34:   PetscCall(PetscDualSpaceSetDM(dsp, K));
 35:   /* This gives us the opportunity to change the parameters of the dual space
 36:    * from the command line, as we do in the tests below.  When
 37:    * PetscDualSpaceSetFromOptions() is called, it also enables other optional
 38:    * behavior (see the next step) */
 39:   PetscCall(PetscDualSpaceSetFromOptions(dsp));
 40:   /* This step parses the parameters of the dual space into
 41:    * sets of functionals that are assigned to each of the mesh points in K.
 42:    *
 43:    * The functionals can be accessed individually by
 44:    * PetscDualSpaceGetFunctional(), or more efficiently all at once by
 45:    * PetscDualSpaceGetAllData(), which returns a set of quadrature points
 46:    * at which to evaluate a function, and a matrix that takes those
 47:    * evaluations and turns them into the evaluation of the dual space's
 48:    * functionals on the function.
 49:    *
 50:    * (TODO: tutorial for PetscDualSpaceGetAllData() and
 51:    * PetscDualSpaceGetInteriorData().)
 52:    *
 53:    * Because we called PetscDualSpaceSetFromOptions(), we have the opportunity
 54:    * to inspect the results of PetscDualSpaceSetUp() from the command line
 55:    * with "-petscdualspace_view", followed by an optional description of how
 56:    * we would like to see the dual space (see examples in the tests below).
 57:    * */
 58:   PetscCall(PetscDualSpaceSetUp(dsp));
 59:   PetscCall(DMDestroy(&K));
 60:   PetscCall(PetscDualSpaceDestroy(&dsp));
 61:   PetscCall(PetscFinalize());
 62:   return 0;
 63: }

 65: /*TEST

 67:   # quadratic nodes on the triangle
 68:   test:
 69:     suffix: 0
 70:     filter: sed -E "s/\(\+0, \+0\)/(+0., +0.)/g"
 71:     args: -dim 2 -tensor 0 -petscdualspace_order 2 -petscdualspace_view ascii::ascii_info_detail

 73:   # linear nodes on the quadrilateral
 74:   test:
 75:     suffix: 1
 76:     args: -dim 2 -tensor 1 -petscdualspace_order 1 -petscdualspace_lagrange_tensor 1 -petscdualspace_view ascii::ascii_info_detail

 78:   # lowest order Raviart-Thomas / Nedelec edge nodes on the hexahedron
 79:   test:
 80:     suffix: 2
 81:     args: -dim 3 -tensor 1 -petscdualspace_order 1 -petscdualspace_components 3 -petscdualspace_form_degree 1 -petscdualspace_lagrange_trimmed 1 -petscdualspace_lagrange_tensor 1 -petscdualspace_view ascii::ascii_info_detail

 83:   # first order Nedelec second type face nodes on the tetrahedron
 84:   test:
 85:     suffix: 3
 86:     args: -dim 3 -tensor 0 -petscdualspace_order 1 -petscdualspace_components 3 -petscdualspace_form_degree -2 -petscdualspace_view ascii::ascii_info_detail

 88:   ## Comparing different node types

 90:   test:
 91:     suffix: 4
 92:     args: -dim 2 -tensor 0 -petscdualspace_order 3 -petscdualspace_lagrange_continuity 0 -petscdualspace_lagrange_node_type equispaced -petscdualspace_lagrange_node_endpoints 0 -petscdualspace_view ascii::ascii_info_detail

 94:   test:
 95:     suffix: 5
 96:     args: -dim 2 -tensor 0 -petscdualspace_order 3 -petscdualspace_lagrange_continuity 0 -petscdualspace_lagrange_node_type equispaced -petscdualspace_lagrange_node_endpoints 1 -petscdualspace_view ascii::ascii_info_detail

 98:   test:
 99:     suffix: 6
100:     args: -dim 2 -tensor 0 -petscdualspace_order 3 -petscdualspace_lagrange_continuity 0 -petscdualspace_lagrange_node_type gaussjacobi -petscdualspace_lagrange_node_endpoints 0 -petscdualspace_view ascii::ascii_info_detail

102:   test:
103:     suffix: 7
104:     args: -dim 2 -tensor 0 -petscdualspace_order 3 -petscdualspace_lagrange_continuity 0 -petscdualspace_lagrange_node_type gaussjacobi -petscdualspace_lagrange_node_endpoints 1 -petscdualspace_view ascii::ascii_info_detail

106: TEST*/