impls/ptrimmed/spaceptrimmed.c

#include <petsc/private/petscfeimpl.h> /*I "petscfe.h" I*/

static PetscErrorCode PetscSpaceSetFromOptions_Ptrimmed(PetscSpace sp, PetscOptionItems *PetscOptionsObject)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "PetscSpace polynomial options");
  PetscCall(PetscOptionsInt("-petscspace_ptrimmed_form_degree", "form degree of trimmed space", "PetscSpacePTrimmedSetFormDegree", pt->formDegree, &pt->formDegree, NULL));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpacePTrimmedView_Ascii(PetscSpace sp, PetscViewer v)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;
  PetscInt             f, tdegree;

  PetscFunctionBegin;
  f       = pt->formDegree;
  tdegree = f == 0 ? sp->degree : sp->degree + 1;
  PetscCall(PetscViewerASCIIPrintf(v, "Trimmed polynomials %" PetscInt_FMT "%s-forms of degree %" PetscInt_FMT " (P-%" PetscInt_FMT "/\\%" PetscInt_FMT ")\n", PetscAbsInt(f), f < 0 ? "*" : "", sp->degree, tdegree, PetscAbsInt(f)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpaceView_Ptrimmed(PetscSpace sp, PetscViewer viewer)
{
  PetscBool iascii;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  if (iascii) PetscCall(PetscSpacePTrimmedView_Ascii(sp, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpaceDestroy_Ptrimmed(PetscSpace sp)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;

  PetscFunctionBegin;
  PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePTrimmedGetFormDegree_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePTrimmedSetFormDegree_C", NULL));
  if (pt->subspaces) {
    PetscInt d;

    for (d = 0; d < sp->Nv; ++d) PetscCall(PetscSpaceDestroy(&pt->subspaces[d]));
  }
  PetscCall(PetscFree(pt->subspaces));
  PetscCall(PetscFree(pt));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpaceSetUp_Ptrimmed(PetscSpace sp)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;
  PetscInt             Nf;

  PetscFunctionBegin;
  if (pt->setupCalled) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCheck(pt->formDegree >= -sp->Nv && pt->formDegree <= sp->Nv, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Form degree %" PetscInt_FMT " not in valid range [%" PetscInt_FMT ",%" PetscInt_FMT "]", pt->formDegree, sp->Nv, sp->Nv);
  PetscCall(PetscDTBinomialInt(sp->Nv, PetscAbsInt(pt->formDegree), &Nf));
  if (sp->Nc == PETSC_DETERMINE) sp->Nc = Nf;
  PetscCheck(sp->Nc % Nf == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_INCOMP, "Number of components %" PetscInt_FMT " is not a multiple of form dimension %" PetscInt_FMT, sp->Nc, Nf);
  if (sp->Nc != Nf) {
    PetscSpace  subsp;
    PetscInt    nCopies = sp->Nc / Nf;
    PetscInt    Nv, deg, maxDeg;
    PetscInt    formDegree = pt->formDegree;
    const char *prefix;
    const char *name;
    char        subname[PETSC_MAX_PATH_LEN];

    PetscCall(PetscSpaceSetType(sp, PETSCSPACESUM));
    PetscCall(PetscSpaceSumSetConcatenate(sp, PETSC_TRUE));
    PetscCall(PetscSpaceSumSetNumSubspaces(sp, nCopies));
    PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)sp), &subsp));
    PetscCall(PetscObjectGetOptionsPrefix((PetscObject)sp, &prefix));
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)subsp, prefix));
    PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)subsp, "sumcomp_"));
    if (((PetscObject)sp)->name) {
      PetscCall(PetscObjectGetName((PetscObject)sp, &name));
      PetscCall(PetscSNPrintf(subname, PETSC_MAX_PATH_LEN - 1, "%s sum component", name));
      PetscCall(PetscObjectSetName((PetscObject)subsp, subname));
    } else PetscCall(PetscObjectSetName((PetscObject)subsp, "sum component"));
    PetscCall(PetscSpaceSetType(subsp, PETSCSPACEPTRIMMED));
    PetscCall(PetscSpaceGetNumVariables(sp, &Nv));
    PetscCall(PetscSpaceSetNumVariables(subsp, Nv));
    PetscCall(PetscSpaceSetNumComponents(subsp, Nf));
    PetscCall(PetscSpaceGetDegree(sp, &deg, &maxDeg));
    PetscCall(PetscSpaceSetDegree(subsp, deg, maxDeg));
    PetscCall(PetscSpacePTrimmedSetFormDegree(subsp, formDegree));
    PetscCall(PetscSpaceSetUp(subsp));
    for (PetscInt i = 0; i < nCopies; i++) PetscCall(PetscSpaceSumSetSubspace(sp, i, subsp));
    PetscCall(PetscSpaceDestroy(&subsp));
    PetscCall(PetscSpaceSetUp(sp));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  if (sp->degree == PETSC_DEFAULT) {
    sp->degree = 0;
  } else if (sp->degree < 0) {
    SETERRQ(PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Invalid negative degree %" PetscInt_FMT, sp->degree);
  }
  sp->maxDegree = (pt->formDegree == 0 || PetscAbsInt(pt->formDegree) == sp->Nv) ? sp->degree : sp->degree + 1;
  if (pt->formDegree == 0 || PetscAbsInt(pt->formDegree) == sp->Nv) {
    // Convert to regular polynomial space
    PetscCall(PetscSpaceSetType(sp, PETSCSPACEPOLYNOMIAL));
    PetscCall(PetscSpaceSetUp(sp));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  pt->setupCalled = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpaceGetDimension_Ptrimmed(PetscSpace sp, PetscInt *dim)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;
  PetscInt             f;
  PetscInt             Nf;

  PetscFunctionBegin;
  f = pt->formDegree;
  // For PetscSpace, degree refers to the largest complete polynomial degree contained in the space which
  // is equal to the index of a P trimmed space only for 0-forms: otherwise, the index is degree + 1
  PetscCall(PetscDTPTrimmedSize(sp->Nv, f == 0 ? sp->degree : sp->degree + 1, pt->formDegree, dim));
  PetscCall(PetscDTBinomialInt(sp->Nv, PetscAbsInt(pt->formDegree), &Nf));
  *dim *= (sp->Nc / Nf);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  p in [0, npoints), i in [0, pdim), c in [0, Nc)

  B[p][i][c] = B[p][i_scalar][c][c]
*/
static PetscErrorCode PetscSpaceEvaluate_Ptrimmed(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;
  DM                   dm = sp->dm;
  PetscInt             jet, degree, Nf, Ncopies, Njet;
  PetscInt             Nc = sp->Nc;
  PetscInt             f;
  PetscInt             dim = sp->Nv;
  PetscReal           *eval;
  PetscInt             Nb;

  PetscFunctionBegin;
  if (!pt->setupCalled) {
    PetscCall(PetscSpaceSetUp(sp));
    PetscCall(PetscSpaceEvaluate(sp, npoints, points, B, D, H));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  if (H) {
    jet = 2;
  } else if (D) {
    jet = 1;
  } else {
    jet = 0;
  }
  f      = pt->formDegree;
  degree = f == 0 ? sp->degree : sp->degree + 1;
  PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(f), &Nf));
  Ncopies = Nc / Nf;
  PetscCheck(Ncopies == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_PLIB, "Multicopy spaces should have been converted to PETSCSPACESUM");
  PetscCall(PetscDTBinomialInt(dim + jet, dim, &Njet));
  PetscCall(PetscDTPTrimmedSize(dim, degree, f, &Nb));
  PetscCall(DMGetWorkArray(dm, Nb * Nf * Njet * npoints, MPIU_REAL, &eval));
  PetscCall(PetscDTPTrimmedEvalJet(dim, npoints, points, degree, f, jet, eval));
  if (B) {
    PetscInt p_strl = Nf * Nb;
    PetscInt b_strl = Nf;
    PetscInt v_strl = 1;

    PetscInt b_strr = Nf * Njet * npoints;
    PetscInt v_strr = Njet * npoints;
    PetscInt p_strr = 1;

    for (PetscInt v = 0; v < Nf; v++) {
      for (PetscInt b = 0; b < Nb; b++) {
        for (PetscInt p = 0; p < npoints; p++) B[p * p_strl + b * b_strl + v * v_strl] = eval[b * b_strr + v * v_strr + p * p_strr];
      }
    }
  }
  if (D) {
    PetscInt p_strl = dim * Nf * Nb;
    PetscInt b_strl = dim * Nf;
    PetscInt v_strl = dim;
    PetscInt d_strl = 1;

    PetscInt b_strr = Nf * Njet * npoints;
    PetscInt v_strr = Njet * npoints;
    PetscInt d_strr = npoints;
    PetscInt p_strr = 1;

    for (PetscInt v = 0; v < Nf; v++) {
      for (PetscInt d = 0; d < dim; d++) {
        for (PetscInt b = 0; b < Nb; b++) {
          for (PetscInt p = 0; p < npoints; p++) D[p * p_strl + b * b_strl + v * v_strl + d * d_strl] = eval[b * b_strr + v * v_strr + (1 + d) * d_strr + p * p_strr];
        }
      }
    }
  }
  if (H) {
    PetscInt p_strl  = dim * dim * Nf * Nb;
    PetscInt b_strl  = dim * dim * Nf;
    PetscInt v_strl  = dim * dim;
    PetscInt d1_strl = dim;
    PetscInt d2_strl = 1;

    PetscInt b_strr = Nf * Njet * npoints;
    PetscInt v_strr = Njet * npoints;
    PetscInt j_strr = npoints;
    PetscInt p_strr = 1;

    PetscInt *derivs;
    PetscCall(PetscCalloc1(dim, &derivs));
    for (PetscInt d1 = 0; d1 < dim; d1++) {
      for (PetscInt d2 = 0; d2 < dim; d2++) {
        PetscInt j;
        derivs[d1]++;
        derivs[d2]++;
        PetscCall(PetscDTGradedOrderToIndex(dim, derivs, &j));
        derivs[d1]--;
        derivs[d2]--;
        for (PetscInt v = 0; v < Nf; v++) {
          for (PetscInt b = 0; b < Nb; b++) {
            for (PetscInt p = 0; p < npoints; p++) H[p * p_strl + b * b_strl + v * v_strl + d1 * d1_strl + d2 * d2_strl] = eval[b * b_strr + v * v_strr + j * j_strr + p * p_strr];
          }
        }
      }
    }
    PetscCall(PetscFree(derivs));
  }
  PetscCall(DMRestoreWorkArray(dm, Nb * Nf * Njet * npoints, MPIU_REAL, &eval));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscSpacePTrimmedSetFormDegree - Set the form degree of the trimmed polynomials.

  Input Parameters:
+ sp         - the function space object
- formDegree - the form degree

  Options Database Key:
. -petscspace_ptrimmed_form_degree <int> - The trimmed polynomial form degree

  Level: intermediate

.seealso: `PetscSpace`, `PetscDTAltV`, `PetscDTPTrimmedEvalJet()`, `PetscSpacePTrimmedGetFormDegree()`
@*/
PetscErrorCode PetscSpacePTrimmedSetFormDegree(PetscSpace sp, PetscInt formDegree)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  PetscTryMethod(sp, "PetscSpacePTrimmedSetFormDegree_C", (PetscSpace, PetscInt), (sp, formDegree));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  PetscSpacePTrimmedGetFormDegree - Get the form degree of the trimmed polynomials.

  Input Parameter:
. sp - the function space object

  Output Parameter:
. formDegree - the form degree

  Level: intermediate

.seealso: `PetscSpace`, `PetscDTAltV`, `PetscDTPTrimmedEvalJet()`, `PetscSpacePTrimmedSetFormDegree()`
@*/
PetscErrorCode PetscSpacePTrimmedGetFormDegree(PetscSpace sp, PetscInt *formDegree)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  PetscAssertPointer(formDegree, 2);
  PetscTryMethod(sp, "PetscSpacePTrimmedGetFormDegree_C", (PetscSpace, PetscInt *), (sp, formDegree));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpacePTrimmedSetFormDegree_Ptrimmed(PetscSpace sp, PetscInt formDegree)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;

  PetscFunctionBegin;
  pt->formDegree = formDegree;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpacePTrimmedGetFormDegree_Ptrimmed(PetscSpace sp, PetscInt *formDegree)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  PetscAssertPointer(formDegree, 2);
  *formDegree = pt->formDegree;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpaceGetHeightSubspace_Ptrimmed(PetscSpace sp, PetscInt height, PetscSpace *subsp)
{
  PetscSpace_Ptrimmed *pt = (PetscSpace_Ptrimmed *)sp->data;
  PetscInt             dim;

  PetscFunctionBegin;
  PetscCall(PetscSpaceGetNumVariables(sp, &dim));
  PetscCheck(height <= dim && height >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Asked for space at height %" PetscInt_FMT " for dimension %" PetscInt_FMT " space", height, dim);
  if (!pt->subspaces) PetscCall(PetscCalloc1(dim, &pt->subspaces));
  if ((dim - height) <= PetscAbsInt(pt->formDegree)) {
    if (!pt->subspaces[height - 1]) {
      PetscInt    Nc, degree, Nf, Ncopies, Nfsub;
      PetscSpace  sub;
      const char *name;

      PetscCall(PetscSpaceGetNumComponents(sp, &Nc));
      PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(pt->formDegree), &Nf));
      PetscCall(PetscDTBinomialInt((dim - height), PetscAbsInt(pt->formDegree), &Nfsub));
      Ncopies = Nf / Nc;
      PetscCall(PetscSpaceGetDegree(sp, &degree, NULL));

      PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)sp), &sub));
      PetscCall(PetscObjectGetName((PetscObject)sp, &name));
      PetscCall(PetscObjectSetName((PetscObject)sub, name));
      PetscCall(PetscSpaceSetType(sub, PETSCSPACEPTRIMMED));
      PetscCall(PetscSpaceSetNumComponents(sub, Nfsub * Ncopies));
      PetscCall(PetscSpaceSetDegree(sub, degree, PETSC_DETERMINE));
      PetscCall(PetscSpaceSetNumVariables(sub, dim - height));
      PetscCall(PetscSpacePTrimmedSetFormDegree(sub, pt->formDegree));
      PetscCall(PetscSpaceSetUp(sub));
      pt->subspaces[height - 1] = sub;
    }
    *subsp = pt->subspaces[height - 1];
  } else {
    *subsp = NULL;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PetscSpaceInitialize_Ptrimmed(PetscSpace sp)
{
  PetscFunctionBegin;
  PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePTrimmedGetFormDegree_C", PetscSpacePTrimmedGetFormDegree_Ptrimmed));
  PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePTrimmedSetFormDegree_C", PetscSpacePTrimmedSetFormDegree_Ptrimmed));
  sp->ops->setfromoptions    = PetscSpaceSetFromOptions_Ptrimmed;
  sp->ops->setup             = PetscSpaceSetUp_Ptrimmed;
  sp->ops->view              = PetscSpaceView_Ptrimmed;
  sp->ops->destroy           = PetscSpaceDestroy_Ptrimmed;
  sp->ops->getdimension      = PetscSpaceGetDimension_Ptrimmed;
  sp->ops->evaluate          = PetscSpaceEvaluate_Ptrimmed;
  sp->ops->getheightsubspace = PetscSpaceGetHeightSubspace_Ptrimmed;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  PETSCSPACEPTRIMMED = "ptrimmed" - A `PetscSpace` object that encapsulates a trimmed polynomial space.

  Trimmed polynomial spaces are defined for $k$-forms, and are defined by
  $
  \mathcal{P}^-_r \Lambda^k(\mathbb{R}^n) = mathcal{P}_{r-1} \Lambda^k(\mathbb{R}^n) \oplus \kappa [\mathcal{H}_{r-1} \Lambda^{k+1}(\mathbb{R}^n)],
  $
  where $\mathcal{H}_{r-1}$ are homogeneous polynomials and $\kappa$ is the Koszul differential.  This decomposition is detailed in ``Finite element exterior calculus'', Arnold, 2018.

  Level: intermediate

  Notes:
  Trimmed polynomial spaces correspond to several common conformal approximation spaces in the de Rham complex:

  In $H^1$ ($\sim k=0$), trimmed polynomial spaces are identical to the standard polynomial spaces, $\mathcal{P}_r^- \sim P_r$.

  In $H(\text{curl})$, ($\sim k=1$), trimmed polynomial spaces are equivalent to $H(\text{curl})$-Nedelec spaces of the first kind and can be written as
  $
    \begin{cases}
      [P_{r-1}(\mathbb{R}^2)]^2 \oplus \mathrm{rot}(\bf{x}) H_{r-1}(\mathbb{R}^2), & n = 2, \\
      [P_{r-1}(\mathbb{R}^3)]^3 \oplus \bf{x} \times [H_{r-1}(\mathbb{R}^3)]^3, & n = 3.
    \end{cases}
  $

  In $H(\text{div})$ ($\sim k=n-1$), trimmed polynomial spaces are equivalent to Raviart-Thomas spaces ($n=2$) and $H(\text{div})$-Nedelec spaces of the first kind ($n=3$), and can be written as
  $
    [P_{r-1}(\mathbb{R}^n)]^n \oplus \bf{x} H_{r-1}(\mathbb{R}^n).
  $

  In $L_2$, ($\sim k=n$), trimmed polynomial spaces are identical to the standard polynomial spaces of one degree less, $\mathcal{P}_r^- \sim P_{r-1}$.

.seealso: `PetscSpace`, `PetscSpaceType`, `PetscSpaceCreate()`, `PetscSpaceSetType()`, `PetscDTPTrimmedEvalJet()`
M*/

PETSC_EXTERN PetscErrorCode PetscSpaceCreate_Ptrimmed(PetscSpace sp)
{
  PetscSpace_Ptrimmed *pt;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  PetscCall(PetscNew(&pt));
  sp->data = pt;

  pt->subspaces = NULL;
  sp->Nc        = PETSC_DETERMINE;

  PetscCall(PetscSpaceInitialize_Ptrimmed(sp));
  PetscFunctionReturn(PETSC_SUCCESS);
}