Date: 2021-03-03T22:27:07+00:00

Actual source code: fv.c
petsc-3.14.5 2021-03-03
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      1: #include <petsc/private/petscfvimpl.h>
      2: #include <petscdmplex.h>
      3: #include <petscds.h>

      5: PetscClassId PETSCLIMITER_CLASSID = 0;

      7: PetscFunctionList PetscLimiterList              = NULL;
      8: PetscBool         PetscLimiterRegisterAllCalled = PETSC_FALSE;

     10: PetscBool Limitercite = PETSC_FALSE;
     11: const char LimiterCitation[] = "@article{BergerAftosmisMurman2005,\n"
     12:                                "  title   = {Analysis of slope limiters on irregular grids},\n"
     13:                                "  journal = {AIAA paper},\n"
     14:                                "  author  = {Marsha Berger and Michael J. Aftosmis and Scott M. Murman},\n"
     15:                                "  volume  = {490},\n"
     16:                                "  year    = {2005}\n}\n";

     18: /*@C
     19:   PetscLimiterRegister - Adds a new PetscLimiter implementation

     21:   Not Collective

     23:   Input Parameters:
     24: + name        - The name of a new user-defined creation routine
     25: - create_func - The creation routine itself

     27:   Notes:
     28:   PetscLimiterRegister() may be called multiple times to add several user-defined PetscLimiters

     30:   Sample usage:
     31: .vb
     32:     PetscLimiterRegister("my_lim", MyPetscLimiterCreate);
     33: .ve

     35:   Then, your PetscLimiter type can be chosen with the procedural interface via
     36: .vb
     37:     PetscLimiterCreate(MPI_Comm, PetscLimiter *);
     38:     PetscLimiterSetType(PetscLimiter, "my_lim");
     39: .ve
     40:    or at runtime via the option
     41: .vb
     42:     -petsclimiter_type my_lim
     43: .ve

     45:   Level: advanced

     47: .seealso: PetscLimiterRegisterAll(), PetscLimiterRegisterDestroy()

     49: @*/
     50: PetscErrorCode PetscLimiterRegister(const char sname[], PetscErrorCode (*function)(PetscLimiter))
     51: {

     55:   PetscFunctionListAdd(&PetscLimiterList, sname, function);
     56:   return(0);
     57: }

     59: /*@C
     60:   PetscLimiterSetType - Builds a particular PetscLimiter

     62:   Collective on lim

     64:   Input Parameters:
     65: + lim  - The PetscLimiter object
     66: - name - The kind of limiter

     68:   Options Database Key:
     69: . -petsclimiter_type <type> - Sets the PetscLimiter type; use -help for a list of available types

     71:   Level: intermediate

     73: .seealso: PetscLimiterGetType(), PetscLimiterCreate()
     74: @*/
     75: PetscErrorCode PetscLimiterSetType(PetscLimiter lim, PetscLimiterType name)
     76: {
     77:   PetscErrorCode (*r)(PetscLimiter);
     78:   PetscBool      match;

     83:   PetscObjectTypeCompare((PetscObject) lim, name, &match);
     84:   if (match) return(0);

     86:   PetscLimiterRegisterAll();
     87:   PetscFunctionListFind(PetscLimiterList, name, &r);
     88:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) lim), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscLimiter type: %s", name);

     90:   if (lim->ops->destroy) {
     91:     (*lim->ops->destroy)(lim);
     92:     lim->ops->destroy = NULL;
     93:   }
     94:   (*r)(lim);
     95:   PetscObjectChangeTypeName((PetscObject) lim, name);
     96:   return(0);
     97: }

     99: /*@C
    100:   PetscLimiterGetType - Gets the PetscLimiter type name (as a string) from the object.

    102:   Not Collective

    104:   Input Parameter:
    105: . lim  - The PetscLimiter

    107:   Output Parameter:
    108: . name - The PetscLimiter type name

    110:   Level: intermediate

    112: .seealso: PetscLimiterSetType(), PetscLimiterCreate()
    113: @*/
    114: PetscErrorCode PetscLimiterGetType(PetscLimiter lim, PetscLimiterType *name)
    115: {

    121:   PetscLimiterRegisterAll();
    122:   *name = ((PetscObject) lim)->type_name;
    123:   return(0);
    124: }

    126: /*@C
    127:    PetscLimiterViewFromOptions - View from Options

    129:    Collective on PetscLimiter

    131:    Input Parameters:
    132: +  A - the PetscLimiter object to view
    133: .  obj - Optional object
    134: -  name - command line option

    136:    Level: intermediate
    137: .seealso:  PetscLimiter, PetscLimiterView, PetscObjectViewFromOptions(), PetscLimiterCreate()
    138: @*/
    139: PetscErrorCode  PetscLimiterViewFromOptions(PetscLimiter A,PetscObject obj,const char name[])
    140: {

    145:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    146:   return(0);
    147: }

    149: /*@C
    150:   PetscLimiterView - Views a PetscLimiter

    152:   Collective on lim

    154:   Input Parameter:
    155: + lim - the PetscLimiter object to view
    156: - v   - the viewer

    158:   Level: beginner

    160: .seealso: PetscLimiterDestroy()
    161: @*/
    162: PetscErrorCode PetscLimiterView(PetscLimiter lim, PetscViewer v)
    163: {

    168:   if (!v) {PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) lim), &v);}
    169:   if (lim->ops->view) {(*lim->ops->view)(lim, v);}
    170:   return(0);
    171: }

    173: /*@
    174:   PetscLimiterSetFromOptions - sets parameters in a PetscLimiter from the options database

    176:   Collective on lim

    178:   Input Parameter:
    179: . lim - the PetscLimiter object to set options for

    181:   Level: intermediate

    183: .seealso: PetscLimiterView()
    184: @*/
    185: PetscErrorCode PetscLimiterSetFromOptions(PetscLimiter lim)
    186: {
    187:   const char    *defaultType;
    188:   char           name[256];
    189:   PetscBool      flg;

    194:   if (!((PetscObject) lim)->type_name) defaultType = PETSCLIMITERSIN;
    195:   else                                 defaultType = ((PetscObject) lim)->type_name;
    196:   PetscLimiterRegisterAll();

    198:   PetscObjectOptionsBegin((PetscObject) lim);
    199:   PetscOptionsFList("-petsclimiter_type", "Finite volume slope limiter", "PetscLimiterSetType", PetscLimiterList, defaultType, name, 256, &flg);
    200:   if (flg) {
    201:     PetscLimiterSetType(lim, name);
    202:   } else if (!((PetscObject) lim)->type_name) {
    203:     PetscLimiterSetType(lim, defaultType);
    204:   }
    205:   if (lim->ops->setfromoptions) {(*lim->ops->setfromoptions)(lim);}
    206:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
    207:   PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject) lim);
    208:   PetscOptionsEnd();
    209:   PetscLimiterViewFromOptions(lim, NULL, "-petsclimiter_view");
    210:   return(0);
    211: }

    213: /*@C
    214:   PetscLimiterSetUp - Construct data structures for the PetscLimiter

    216:   Collective on lim

    218:   Input Parameter:
    219: . lim - the PetscLimiter object to setup

    221:   Level: intermediate

    223: .seealso: PetscLimiterView(), PetscLimiterDestroy()
    224: @*/
    225: PetscErrorCode PetscLimiterSetUp(PetscLimiter lim)
    226: {

    231:   if (lim->ops->setup) {(*lim->ops->setup)(lim);}
    232:   return(0);
    233: }

    235: /*@
    236:   PetscLimiterDestroy - Destroys a PetscLimiter object

    238:   Collective on lim

    240:   Input Parameter:
    241: . lim - the PetscLimiter object to destroy

    243:   Level: beginner

    245: .seealso: PetscLimiterView()
    246: @*/
    247: PetscErrorCode PetscLimiterDestroy(PetscLimiter *lim)
    248: {

    252:   if (!*lim) return(0);

    255:   if (--((PetscObject)(*lim))->refct > 0) {*lim = NULL; return(0);}
    256:   ((PetscObject) (*lim))->refct = 0;

    258:   if ((*lim)->ops->destroy) {(*(*lim)->ops->destroy)(*lim);}
    259:   PetscHeaderDestroy(lim);
    260:   return(0);
    261: }

    263: /*@
    264:   PetscLimiterCreate - Creates an empty PetscLimiter object. The type can then be set with PetscLimiterSetType().

    266:   Collective

    268:   Input Parameter:
    269: . comm - The communicator for the PetscLimiter object

    271:   Output Parameter:
    272: . lim - The PetscLimiter object

    274:   Level: beginner

    276: .seealso: PetscLimiterSetType(), PETSCLIMITERSIN
    277: @*/
    278: PetscErrorCode PetscLimiterCreate(MPI_Comm comm, PetscLimiter *lim)
    279: {
    280:   PetscLimiter   l;

    285:   PetscCitationsRegister(LimiterCitation,&Limitercite);
    286:   *lim = NULL;
    287:   PetscFVInitializePackage();

    289:   PetscHeaderCreate(l, PETSCLIMITER_CLASSID, "PetscLimiter", "Finite Volume Slope Limiter", "PetscLimiter", comm, PetscLimiterDestroy, PetscLimiterView);

    291:   *lim = l;
    292:   return(0);
    293: }

    295: /*@
    296:   PetscLimiterLimit - Limit the flux

    298:   Input Parameters:
    299: + lim  - The PetscLimiter
    300: - flim - The input field

    302:   Output Parameter:
    303: . phi  - The limited field

    305: Note: Limiters given in symmetric form following Berger, Aftosmis, and Murman 2005
    306: $ The classical flux-limited formulation is psi(r) where
    307: $
    308: $ r = (u[0] - u[-1]) / (u[1] - u[0])
    309: $
    310: $ The second order TVD region is bounded by
    311: $
    312: $ psi_minmod(r) = min(r,1)      and        psi_superbee(r) = min(2, 2r, max(1,r))
    313: $
    314: $ where all limiters are implicitly clipped to be non-negative. A more convenient slope-limited form is psi(r) =
    315: $ phi(r)(r+1)/2 in which the reconstructed interface values are
    316: $
    317: $ u(v) = u[0] + phi(r) (grad u)[0] v
    318: $
    319: $ where v is the vector from centroid to quadrature point. In these variables, the usual limiters become
    320: $
    321: $ phi_minmod(r) = 2 min(1/(1+r),r/(1+r))   phi_superbee(r) = 2 min(2/(1+r), 2r/(1+r), max(1,r)/(1+r))
    322: $
    323: $ For a nicer symmetric formulation, rewrite in terms of
    324: $
    325: $ f = (u[0] - u[-1]) / (u[1] - u[-1])
    326: $
    327: $ where r(f) = f/(1-f). Not that r(1-f) = (1-f)/f = 1/r(f) so the symmetry condition
    328: $
    329: $ phi(r) = phi(1/r)
    330: $
    331: $ becomes
    332: $
    333: $ w(f) = w(1-f).
    334: $
    335: $ The limiters below implement this final form w(f). The reference methods are
    336: $
    337: $ w_minmod(f) = 2 min(f,(1-f))             w_superbee(r) = 4 min((1-f), f)

    339:   Level: beginner

    341: .seealso: PetscLimiterSetType(), PetscLimiterCreate()
    342: @*/
    343: PetscErrorCode PetscLimiterLimit(PetscLimiter lim, PetscReal flim, PetscReal *phi)
    344: {

    350:   (*lim->ops->limit)(lim, flim, phi);
    351:   return(0);
    352: }

    354: static PetscErrorCode PetscLimiterDestroy_Sin(PetscLimiter lim)
    355: {
    356:   PetscLimiter_Sin *l = (PetscLimiter_Sin *) lim->data;
    357:   PetscErrorCode    ierr;

    360:   PetscFree(l);
    361:   return(0);
    362: }

    364: static PetscErrorCode PetscLimiterView_Sin_Ascii(PetscLimiter lim, PetscViewer viewer)
    365: {
    366:   PetscViewerFormat format;
    367:   PetscErrorCode    ierr;

    370:   PetscViewerGetFormat(viewer, &format);
    371:   PetscViewerASCIIPrintf(viewer, "Sin Slope Limiter:\n");
    372:   return(0);
    373: }

    375: static PetscErrorCode PetscLimiterView_Sin(PetscLimiter lim, PetscViewer viewer)
    376: {
    377:   PetscBool      iascii;

    383:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    384:   if (iascii) {PetscLimiterView_Sin_Ascii(lim, viewer);}
    385:   return(0);
    386: }

    388: static PetscErrorCode PetscLimiterLimit_Sin(PetscLimiter lim, PetscReal f, PetscReal *phi)
    389: {
    391:   *phi = PetscSinReal(PETSC_PI*PetscMax(0, PetscMin(f, 1)));
    392:   return(0);
    393: }

    395: static PetscErrorCode PetscLimiterInitialize_Sin(PetscLimiter lim)
    396: {
    398:   lim->ops->view    = PetscLimiterView_Sin;
    399:   lim->ops->destroy = PetscLimiterDestroy_Sin;
    400:   lim->ops->limit   = PetscLimiterLimit_Sin;
    401:   return(0);
    402: }

    404: /*MC
    405:   PETSCLIMITERSIN = "sin" - A PetscLimiter object

    407:   Level: intermediate

    409: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    410: M*/

    412: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_Sin(PetscLimiter lim)
    413: {
    414:   PetscLimiter_Sin *l;
    415:   PetscErrorCode    ierr;

    419:   PetscNewLog(lim, &l);
    420:   lim->data = l;

    422:   PetscLimiterInitialize_Sin(lim);
    423:   return(0);
    424: }

    426: static PetscErrorCode PetscLimiterDestroy_Zero(PetscLimiter lim)
    427: {
    428:   PetscLimiter_Zero *l = (PetscLimiter_Zero *) lim->data;
    429:   PetscErrorCode    ierr;

    432:   PetscFree(l);
    433:   return(0);
    434: }

    436: static PetscErrorCode PetscLimiterView_Zero_Ascii(PetscLimiter lim, PetscViewer viewer)
    437: {
    438:   PetscViewerFormat format;
    439:   PetscErrorCode    ierr;

    442:   PetscViewerGetFormat(viewer, &format);
    443:   PetscViewerASCIIPrintf(viewer, "Zero Slope Limiter:\n");
    444:   return(0);
    445: }

    447: static PetscErrorCode PetscLimiterView_Zero(PetscLimiter lim, PetscViewer viewer)
    448: {
    449:   PetscBool      iascii;

    455:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    456:   if (iascii) {PetscLimiterView_Zero_Ascii(lim, viewer);}
    457:   return(0);
    458: }

    460: static PetscErrorCode PetscLimiterLimit_Zero(PetscLimiter lim, PetscReal f, PetscReal *phi)
    461: {
    463:   *phi = 0.0;
    464:   return(0);
    465: }

    467: static PetscErrorCode PetscLimiterInitialize_Zero(PetscLimiter lim)
    468: {
    470:   lim->ops->view    = PetscLimiterView_Zero;
    471:   lim->ops->destroy = PetscLimiterDestroy_Zero;
    472:   lim->ops->limit   = PetscLimiterLimit_Zero;
    473:   return(0);
    474: }

    476: /*MC
    477:   PETSCLIMITERZERO = "zero" - A PetscLimiter object

    479:   Level: intermediate

    481: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    482: M*/

    484: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_Zero(PetscLimiter lim)
    485: {
    486:   PetscLimiter_Zero *l;
    487:   PetscErrorCode     ierr;

    491:   PetscNewLog(lim, &l);
    492:   lim->data = l;

    494:   PetscLimiterInitialize_Zero(lim);
    495:   return(0);
    496: }

    498: static PetscErrorCode PetscLimiterDestroy_None(PetscLimiter lim)
    499: {
    500:   PetscLimiter_None *l = (PetscLimiter_None *) lim->data;
    501:   PetscErrorCode    ierr;

    504:   PetscFree(l);
    505:   return(0);
    506: }

    508: static PetscErrorCode PetscLimiterView_None_Ascii(PetscLimiter lim, PetscViewer viewer)
    509: {
    510:   PetscViewerFormat format;
    511:   PetscErrorCode    ierr;

    514:   PetscViewerGetFormat(viewer, &format);
    515:   PetscViewerASCIIPrintf(viewer, "None Slope Limiter:\n");
    516:   return(0);
    517: }

    519: static PetscErrorCode PetscLimiterView_None(PetscLimiter lim, PetscViewer viewer)
    520: {
    521:   PetscBool      iascii;

    527:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    528:   if (iascii) {PetscLimiterView_None_Ascii(lim, viewer);}
    529:   return(0);
    530: }

    532: static PetscErrorCode PetscLimiterLimit_None(PetscLimiter lim, PetscReal f, PetscReal *phi)
    533: {
    535:   *phi = 1.0;
    536:   return(0);
    537: }

    539: static PetscErrorCode PetscLimiterInitialize_None(PetscLimiter lim)
    540: {
    542:   lim->ops->view    = PetscLimiterView_None;
    543:   lim->ops->destroy = PetscLimiterDestroy_None;
    544:   lim->ops->limit   = PetscLimiterLimit_None;
    545:   return(0);
    546: }

    548: /*MC
    549:   PETSCLIMITERNONE = "none" - A PetscLimiter object

    551:   Level: intermediate

    553: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    554: M*/

    556: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_None(PetscLimiter lim)
    557: {
    558:   PetscLimiter_None *l;
    559:   PetscErrorCode    ierr;

    563:   PetscNewLog(lim, &l);
    564:   lim->data = l;

    566:   PetscLimiterInitialize_None(lim);
    567:   return(0);
    568: }

    570: static PetscErrorCode PetscLimiterDestroy_Minmod(PetscLimiter lim)
    571: {
    572:   PetscLimiter_Minmod *l = (PetscLimiter_Minmod *) lim->data;
    573:   PetscErrorCode    ierr;

    576:   PetscFree(l);
    577:   return(0);
    578: }

    580: static PetscErrorCode PetscLimiterView_Minmod_Ascii(PetscLimiter lim, PetscViewer viewer)
    581: {
    582:   PetscViewerFormat format;
    583:   PetscErrorCode    ierr;

    586:   PetscViewerGetFormat(viewer, &format);
    587:   PetscViewerASCIIPrintf(viewer, "Minmod Slope Limiter:\n");
    588:   return(0);
    589: }

    591: static PetscErrorCode PetscLimiterView_Minmod(PetscLimiter lim, PetscViewer viewer)
    592: {
    593:   PetscBool      iascii;

    599:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    600:   if (iascii) {PetscLimiterView_Minmod_Ascii(lim, viewer);}
    601:   return(0);
    602: }

    604: static PetscErrorCode PetscLimiterLimit_Minmod(PetscLimiter lim, PetscReal f, PetscReal *phi)
    605: {
    607:   *phi = 2*PetscMax(0, PetscMin(f, 1-f));
    608:   return(0);
    609: }

    611: static PetscErrorCode PetscLimiterInitialize_Minmod(PetscLimiter lim)
    612: {
    614:   lim->ops->view    = PetscLimiterView_Minmod;
    615:   lim->ops->destroy = PetscLimiterDestroy_Minmod;
    616:   lim->ops->limit   = PetscLimiterLimit_Minmod;
    617:   return(0);
    618: }

    620: /*MC
    621:   PETSCLIMITERMINMOD = "minmod" - A PetscLimiter object

    623:   Level: intermediate

    625: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    626: M*/

    628: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_Minmod(PetscLimiter lim)
    629: {
    630:   PetscLimiter_Minmod *l;
    631:   PetscErrorCode    ierr;

    635:   PetscNewLog(lim, &l);
    636:   lim->data = l;

    638:   PetscLimiterInitialize_Minmod(lim);
    639:   return(0);
    640: }

    642: static PetscErrorCode PetscLimiterDestroy_VanLeer(PetscLimiter lim)
    643: {
    644:   PetscLimiter_VanLeer *l = (PetscLimiter_VanLeer *) lim->data;
    645:   PetscErrorCode    ierr;

    648:   PetscFree(l);
    649:   return(0);
    650: }

    652: static PetscErrorCode PetscLimiterView_VanLeer_Ascii(PetscLimiter lim, PetscViewer viewer)
    653: {
    654:   PetscViewerFormat format;
    655:   PetscErrorCode    ierr;

    658:   PetscViewerGetFormat(viewer, &format);
    659:   PetscViewerASCIIPrintf(viewer, "Van Leer Slope Limiter:\n");
    660:   return(0);
    661: }

    663: static PetscErrorCode PetscLimiterView_VanLeer(PetscLimiter lim, PetscViewer viewer)
    664: {
    665:   PetscBool      iascii;

    671:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    672:   if (iascii) {PetscLimiterView_VanLeer_Ascii(lim, viewer);}
    673:   return(0);
    674: }

    676: static PetscErrorCode PetscLimiterLimit_VanLeer(PetscLimiter lim, PetscReal f, PetscReal *phi)
    677: {
    679:   *phi = PetscMax(0, 4*f*(1-f));
    680:   return(0);
    681: }

    683: static PetscErrorCode PetscLimiterInitialize_VanLeer(PetscLimiter lim)
    684: {
    686:   lim->ops->view    = PetscLimiterView_VanLeer;
    687:   lim->ops->destroy = PetscLimiterDestroy_VanLeer;
    688:   lim->ops->limit   = PetscLimiterLimit_VanLeer;
    689:   return(0);
    690: }

    692: /*MC
    693:   PETSCLIMITERVANLEER = "vanleer" - A PetscLimiter object

    695:   Level: intermediate

    697: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    698: M*/

    700: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_VanLeer(PetscLimiter lim)
    701: {
    702:   PetscLimiter_VanLeer *l;
    703:   PetscErrorCode    ierr;

    707:   PetscNewLog(lim, &l);
    708:   lim->data = l;

    710:   PetscLimiterInitialize_VanLeer(lim);
    711:   return(0);
    712: }

    714: static PetscErrorCode PetscLimiterDestroy_VanAlbada(PetscLimiter lim)
    715: {
    716:   PetscLimiter_VanAlbada *l = (PetscLimiter_VanAlbada *) lim->data;
    717:   PetscErrorCode    ierr;

    720:   PetscFree(l);
    721:   return(0);
    722: }

    724: static PetscErrorCode PetscLimiterView_VanAlbada_Ascii(PetscLimiter lim, PetscViewer viewer)
    725: {
    726:   PetscViewerFormat format;
    727:   PetscErrorCode    ierr;

    730:   PetscViewerGetFormat(viewer, &format);
    731:   PetscViewerASCIIPrintf(viewer, "Van Albada Slope Limiter:\n");
    732:   return(0);
    733: }

    735: static PetscErrorCode PetscLimiterView_VanAlbada(PetscLimiter lim, PetscViewer viewer)
    736: {
    737:   PetscBool      iascii;

    743:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    744:   if (iascii) {PetscLimiterView_VanAlbada_Ascii(lim, viewer);}
    745:   return(0);
    746: }

    748: static PetscErrorCode PetscLimiterLimit_VanAlbada(PetscLimiter lim, PetscReal f, PetscReal *phi)
    749: {
    751:   *phi = PetscMax(0, 2*f*(1-f) / (PetscSqr(f) + PetscSqr(1-f)));
    752:   return(0);
    753: }

    755: static PetscErrorCode PetscLimiterInitialize_VanAlbada(PetscLimiter lim)
    756: {
    758:   lim->ops->view    = PetscLimiterView_VanAlbada;
    759:   lim->ops->destroy = PetscLimiterDestroy_VanAlbada;
    760:   lim->ops->limit   = PetscLimiterLimit_VanAlbada;
    761:   return(0);
    762: }

    764: /*MC
    765:   PETSCLIMITERVANALBADA = "vanalbada" - A PetscLimiter object

    767:   Level: intermediate

    769: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    770: M*/

    772: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_VanAlbada(PetscLimiter lim)
    773: {
    774:   PetscLimiter_VanAlbada *l;
    775:   PetscErrorCode    ierr;

    779:   PetscNewLog(lim, &l);
    780:   lim->data = l;

    782:   PetscLimiterInitialize_VanAlbada(lim);
    783:   return(0);
    784: }

    786: static PetscErrorCode PetscLimiterDestroy_Superbee(PetscLimiter lim)
    787: {
    788:   PetscLimiter_Superbee *l = (PetscLimiter_Superbee *) lim->data;
    789:   PetscErrorCode    ierr;

    792:   PetscFree(l);
    793:   return(0);
    794: }

    796: static PetscErrorCode PetscLimiterView_Superbee_Ascii(PetscLimiter lim, PetscViewer viewer)
    797: {
    798:   PetscViewerFormat format;
    799:   PetscErrorCode    ierr;

    802:   PetscViewerGetFormat(viewer, &format);
    803:   PetscViewerASCIIPrintf(viewer, "Superbee Slope Limiter:\n");
    804:   return(0);
    805: }

    807: static PetscErrorCode PetscLimiterView_Superbee(PetscLimiter lim, PetscViewer viewer)
    808: {
    809:   PetscBool      iascii;

    815:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    816:   if (iascii) {PetscLimiterView_Superbee_Ascii(lim, viewer);}
    817:   return(0);
    818: }

    820: static PetscErrorCode PetscLimiterLimit_Superbee(PetscLimiter lim, PetscReal f, PetscReal *phi)
    821: {
    823:   *phi = 4*PetscMax(0, PetscMin(f, 1-f));
    824:   return(0);
    825: }

    827: static PetscErrorCode PetscLimiterInitialize_Superbee(PetscLimiter lim)
    828: {
    830:   lim->ops->view    = PetscLimiterView_Superbee;
    831:   lim->ops->destroy = PetscLimiterDestroy_Superbee;
    832:   lim->ops->limit   = PetscLimiterLimit_Superbee;
    833:   return(0);
    834: }

    836: /*MC
    837:   PETSCLIMITERSUPERBEE = "superbee" - A PetscLimiter object

    839:   Level: intermediate

    841: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    842: M*/

    844: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_Superbee(PetscLimiter lim)
    845: {
    846:   PetscLimiter_Superbee *l;
    847:   PetscErrorCode    ierr;

    851:   PetscNewLog(lim, &l);
    852:   lim->data = l;

    854:   PetscLimiterInitialize_Superbee(lim);
    855:   return(0);
    856: }

    858: static PetscErrorCode PetscLimiterDestroy_MC(PetscLimiter lim)
    859: {
    860:   PetscLimiter_MC *l = (PetscLimiter_MC *) lim->data;
    861:   PetscErrorCode    ierr;

    864:   PetscFree(l);
    865:   return(0);
    866: }

    868: static PetscErrorCode PetscLimiterView_MC_Ascii(PetscLimiter lim, PetscViewer viewer)
    869: {
    870:   PetscViewerFormat format;
    871:   PetscErrorCode    ierr;

    874:   PetscViewerGetFormat(viewer, &format);
    875:   PetscViewerASCIIPrintf(viewer, "MC Slope Limiter:\n");
    876:   return(0);
    877: }

    879: static PetscErrorCode PetscLimiterView_MC(PetscLimiter lim, PetscViewer viewer)
    880: {
    881:   PetscBool      iascii;

    887:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    888:   if (iascii) {PetscLimiterView_MC_Ascii(lim, viewer);}
    889:   return(0);
    890: }

    892: /* aka Barth-Jespersen */
    893: static PetscErrorCode PetscLimiterLimit_MC(PetscLimiter lim, PetscReal f, PetscReal *phi)
    894: {
    896:   *phi = PetscMin(1, 4*PetscMax(0, PetscMin(f, 1-f)));
    897:   return(0);
    898: }

    900: static PetscErrorCode PetscLimiterInitialize_MC(PetscLimiter lim)
    901: {
    903:   lim->ops->view    = PetscLimiterView_MC;
    904:   lim->ops->destroy = PetscLimiterDestroy_MC;
    905:   lim->ops->limit   = PetscLimiterLimit_MC;
    906:   return(0);
    907: }

    909: /*MC
    910:   PETSCLIMITERMC = "mc" - A PetscLimiter object

    912:   Level: intermediate

    914: .seealso: PetscLimiterType, PetscLimiterCreate(), PetscLimiterSetType()
    915: M*/

    917: PETSC_EXTERN PetscErrorCode PetscLimiterCreate_MC(PetscLimiter lim)
    918: {
    919:   PetscLimiter_MC *l;
    920:   PetscErrorCode    ierr;

    924:   PetscNewLog(lim, &l);
    925:   lim->data = l;

    927:   PetscLimiterInitialize_MC(lim);
    928:   return(0);
    929: }

    931: PetscClassId PETSCFV_CLASSID = 0;

    933: PetscFunctionList PetscFVList              = NULL;
    934: PetscBool         PetscFVRegisterAllCalled = PETSC_FALSE;

    936: /*@C
    937:   PetscFVRegister - Adds a new PetscFV implementation

    939:   Not Collective

    941:   Input Parameters:
    942: + name        - The name of a new user-defined creation routine
    943: - create_func - The creation routine itself

    945:   Notes:
    946:   PetscFVRegister() may be called multiple times to add several user-defined PetscFVs

    948:   Sample usage:
    949: .vb
    950:     PetscFVRegister("my_fv", MyPetscFVCreate);
    951: .ve

    953:   Then, your PetscFV type can be chosen with the procedural interface via
    954: .vb
    955:     PetscFVCreate(MPI_Comm, PetscFV *);
    956:     PetscFVSetType(PetscFV, "my_fv");
    957: .ve
    958:    or at runtime via the option
    959: .vb
    960:     -petscfv_type my_fv
    961: .ve

    963:   Level: advanced

    965: .seealso: PetscFVRegisterAll(), PetscFVRegisterDestroy()

    967: @*/
    968: PetscErrorCode PetscFVRegister(const char sname[], PetscErrorCode (*function)(PetscFV))
    969: {

    973:   PetscFunctionListAdd(&PetscFVList, sname, function);
    974:   return(0);
    975: }

    977: /*@C
    978:   PetscFVSetType - Builds a particular PetscFV

    980:   Collective on fvm

    982:   Input Parameters:
    983: + fvm  - The PetscFV object
    984: - name - The kind of FVM space

    986:   Options Database Key:
    987: . -petscfv_type <type> - Sets the PetscFV type; use -help for a list of available types

    989:   Level: intermediate

    991: .seealso: PetscFVGetType(), PetscFVCreate()
    992: @*/
    993: PetscErrorCode PetscFVSetType(PetscFV fvm, PetscFVType name)
    994: {
    995:   PetscErrorCode (*r)(PetscFV);
    996:   PetscBool      match;

    1001:   PetscObjectTypeCompare((PetscObject) fvm, name, &match);
    1002:   if (match) return(0);

    1004:   PetscFVRegisterAll();
    1005:   PetscFunctionListFind(PetscFVList, name, &r);
    1006:   if (!r) SETERRQ1(PetscObjectComm((PetscObject) fvm), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscFV type: %s", name);

    1008:   if (fvm->ops->destroy) {
    1009:     (*fvm->ops->destroy)(fvm);
    1010:     fvm->ops->destroy = NULL;
    1011:   }
    1012:   (*r)(fvm);
    1013:   PetscObjectChangeTypeName((PetscObject) fvm, name);
    1014:   return(0);
    1015: }

    1017: /*@C
    1018:   PetscFVGetType - Gets the PetscFV type name (as a string) from the object.

    1020:   Not Collective

    1022:   Input Parameter:
    1023: . fvm  - The PetscFV

    1025:   Output Parameter:
    1026: . name - The PetscFV type name

    1028:   Level: intermediate

    1030: .seealso: PetscFVSetType(), PetscFVCreate()
    1031: @*/
    1032: PetscErrorCode PetscFVGetType(PetscFV fvm, PetscFVType *name)
    1033: {

    1039:   PetscFVRegisterAll();
    1040:   *name = ((PetscObject) fvm)->type_name;
    1041:   return(0);
    1042: }

    1044: /*@C
    1045:    PetscFVViewFromOptions - View from Options

    1047:    Collective on PetscFV

    1049:    Input Parameters:
    1050: +  A - the PetscFV object
    1051: .  obj - Optional object
    1052: -  name - command line option

    1054:    Level: intermediate
    1055: .seealso:  PetscFV, PetscFVView, PetscObjectViewFromOptions(), PetscFVCreate()
    1056: @*/
    1057: PetscErrorCode  PetscFVViewFromOptions(PetscFV A,PetscObject obj,const char name[])
    1058: {

    1063:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    1064:   return(0);
    1065: }

    1067: /*@C
    1068:   PetscFVView - Views a PetscFV

    1070:   Collective on fvm

    1072:   Input Parameter:
    1073: + fvm - the PetscFV object to view
    1074: - v   - the viewer

    1076:   Level: beginner

    1078: .seealso: PetscFVDestroy()
    1079: @*/
    1080: PetscErrorCode PetscFVView(PetscFV fvm, PetscViewer v)
    1081: {

    1086:   if (!v) {PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) fvm), &v);}
    1087:   if (fvm->ops->view) {(*fvm->ops->view)(fvm, v);}
    1088:   return(0);
    1089: }

    1091: /*@
    1092:   PetscFVSetFromOptions - sets parameters in a PetscFV from the options database

    1094:   Collective on fvm

    1096:   Input Parameter:
    1097: . fvm - the PetscFV object to set options for

    1099:   Options Database Key:
    1100: . -petscfv_compute_gradients <bool> - Determines whether cell gradients are calculated

    1102:   Level: intermediate

    1104: .seealso: PetscFVView()
    1105: @*/
    1106: PetscErrorCode PetscFVSetFromOptions(PetscFV fvm)
    1107: {
    1108:   const char    *defaultType;
    1109:   char           name[256];
    1110:   PetscBool      flg;

    1115:   if (!((PetscObject) fvm)->type_name) defaultType = PETSCFVUPWIND;
    1116:   else                                 defaultType = ((PetscObject) fvm)->type_name;
    1117:   PetscFVRegisterAll();

    1119:   PetscObjectOptionsBegin((PetscObject) fvm);
    1120:   PetscOptionsFList("-petscfv_type", "Finite volume discretization", "PetscFVSetType", PetscFVList, defaultType, name, 256, &flg);
    1121:   if (flg) {
    1122:     PetscFVSetType(fvm, name);
    1123:   } else if (!((PetscObject) fvm)->type_name) {
    1124:     PetscFVSetType(fvm, defaultType);

    1126:   }
    1127:   PetscOptionsBool("-petscfv_compute_gradients", "Compute cell gradients", "PetscFVSetComputeGradients", fvm->computeGradients, &fvm->computeGradients, NULL);
    1128:   if (fvm->ops->setfromoptions) {(*fvm->ops->setfromoptions)(fvm);}
    1129:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
    1130:   PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject) fvm);
    1131:   PetscLimiterSetFromOptions(fvm->limiter);
    1132:   PetscOptionsEnd();
    1133:   PetscFVViewFromOptions(fvm, NULL, "-petscfv_view");
    1134:   return(0);
    1135: }

    1137: /*@
    1138:   PetscFVSetUp - Construct data structures for the PetscFV

    1140:   Collective on fvm

    1142:   Input Parameter:
    1143: . fvm - the PetscFV object to setup

    1145:   Level: intermediate

    1147: .seealso: PetscFVView(), PetscFVDestroy()
    1148: @*/
    1149: PetscErrorCode PetscFVSetUp(PetscFV fvm)
    1150: {

    1155:   PetscLimiterSetUp(fvm->limiter);
    1156:   if (fvm->ops->setup) {(*fvm->ops->setup)(fvm);}
    1157:   return(0);
    1158: }

    1160: /*@
    1161:   PetscFVDestroy - Destroys a PetscFV object

    1163:   Collective on fvm

    1165:   Input Parameter:
    1166: . fvm - the PetscFV object to destroy

    1168:   Level: beginner

    1170: .seealso: PetscFVView()
    1171: @*/
    1172: PetscErrorCode PetscFVDestroy(PetscFV *fvm)
    1173: {
    1174:   PetscInt       i;

    1178:   if (!*fvm) return(0);

    1181:   if (--((PetscObject)(*fvm))->refct > 0) {*fvm = NULL; return(0);}
    1182:   ((PetscObject) (*fvm))->refct = 0;

    1184:   for (i = 0; i < (*fvm)->numComponents; i++) {
    1185:     PetscFree((*fvm)->componentNames[i]);
    1186:   }
    1187:   PetscFree((*fvm)->componentNames);
    1188:   PetscLimiterDestroy(&(*fvm)->limiter);
    1189:   PetscDualSpaceDestroy(&(*fvm)->dualSpace);
    1190:   PetscFree((*fvm)->fluxWork);
    1191:   PetscQuadratureDestroy(&(*fvm)->quadrature);
    1192:   PetscTabulationDestroy(&(*fvm)->T);

    1194:   if ((*fvm)->ops->destroy) {(*(*fvm)->ops->destroy)(*fvm);}
    1195:   PetscHeaderDestroy(fvm);
    1196:   return(0);
    1197: }

    1199: /*@
    1200:   PetscFVCreate - Creates an empty PetscFV object. The type can then be set with PetscFVSetType().

    1202:   Collective

    1204:   Input Parameter:
    1205: . comm - The communicator for the PetscFV object

    1207:   Output Parameter:
    1208: . fvm - The PetscFV object

    1210:   Level: beginner

    1212: .seealso: PetscFVSetType(), PETSCFVUPWIND
    1213: @*/
    1214: PetscErrorCode PetscFVCreate(MPI_Comm comm, PetscFV *fvm)
    1215: {
    1216:   PetscFV        f;

    1221:   *fvm = NULL;
    1222:   PetscFVInitializePackage();

    1224:   PetscHeaderCreate(f, PETSCFV_CLASSID, "PetscFV", "Finite Volume", "PetscFV", comm, PetscFVDestroy, PetscFVView);
    1225:   PetscMemzero(f->ops, sizeof(struct _PetscFVOps));

    1227:   PetscLimiterCreate(comm, &f->limiter);
    1228:   f->numComponents    = 1;
    1229:   f->dim              = 0;
    1230:   f->computeGradients = PETSC_FALSE;
    1231:   f->fluxWork         = NULL;
    1232:   PetscCalloc1(f->numComponents,&f->componentNames);

    1234:   *fvm = f;
    1235:   return(0);
    1236: }

    1238: /*@
    1239:   PetscFVSetLimiter - Set the limiter object

    1241:   Logically collective on fvm

    1243:   Input Parameters:
    1244: + fvm - the PetscFV object
    1245: - lim - The PetscLimiter

    1247:   Level: intermediate

    1249: .seealso: PetscFVGetLimiter()
    1250: @*/
    1251: PetscErrorCode PetscFVSetLimiter(PetscFV fvm, PetscLimiter lim)
    1252: {

    1258:   PetscLimiterDestroy(&fvm->limiter);
    1259:   PetscObjectReference((PetscObject) lim);
    1260:   fvm->limiter = lim;
    1261:   return(0);
    1262: }

    1264: /*@
    1265:   PetscFVGetLimiter - Get the limiter object

    1267:   Not collective

    1269:   Input Parameter:
    1270: . fvm - the PetscFV object

    1272:   Output Parameter:
    1273: . lim - The PetscLimiter

    1275:   Level: intermediate

    1277: .seealso: PetscFVSetLimiter()
    1278: @*/
    1279: PetscErrorCode PetscFVGetLimiter(PetscFV fvm, PetscLimiter *lim)
    1280: {
    1284:   *lim = fvm->limiter;
    1285:   return(0);
    1286: }

    1288: /*@
    1289:   PetscFVSetNumComponents - Set the number of field components

    1291:   Logically collective on fvm

    1293:   Input Parameters:
    1294: + fvm - the PetscFV object
    1295: - comp - The number of components

    1297:   Level: intermediate

    1299: .seealso: PetscFVGetNumComponents()
    1300: @*/
    1301: PetscErrorCode PetscFVSetNumComponents(PetscFV fvm, PetscInt comp)
    1302: {

    1307:   if (fvm->numComponents != comp) {
    1308:     PetscInt i;

    1310:     for (i = 0; i < fvm->numComponents; i++) {
    1311:       PetscFree(fvm->componentNames[i]);
    1312:     }
    1313:     PetscFree(fvm->componentNames);
    1314:     PetscCalloc1(comp,&fvm->componentNames);
    1315:   }
    1316:   fvm->numComponents = comp;
    1317:   PetscFree(fvm->fluxWork);
    1318:   PetscMalloc1(comp, &fvm->fluxWork);
    1319:   return(0);
    1320: }

    1322: /*@
    1323:   PetscFVGetNumComponents - Get the number of field components

    1325:   Not collective

    1327:   Input Parameter:
    1328: . fvm - the PetscFV object

    1330:   Output Parameter:
    1331: , comp - The number of components

    1333:   Level: intermediate

    1335: .seealso: PetscFVSetNumComponents()
    1336: @*/
    1337: PetscErrorCode PetscFVGetNumComponents(PetscFV fvm, PetscInt *comp)
    1338: {
    1342:   *comp = fvm->numComponents;
    1343:   return(0);
    1344: }

    1346: /*@C
    1347:   PetscFVSetComponentName - Set the name of a component (used in output and viewing)

    1349:   Logically collective on fvm
    1350:   Input Parameters:
    1351: + fvm - the PetscFV object
    1352: . comp - the component number
    1353: - name - the component name

    1355:   Level: intermediate

    1357: .seealso: PetscFVGetComponentName()
    1358: @*/
    1359: PetscErrorCode PetscFVSetComponentName(PetscFV fvm, PetscInt comp, const char *name)
    1360: {

    1364:   PetscFree(fvm->componentNames[comp]);
    1365:   PetscStrallocpy(name,&fvm->componentNames[comp]);
    1366:   return(0);
    1367: }

    1369: /*@C
    1370:   PetscFVGetComponentName - Get the name of a component (used in output and viewing)

    1372:   Logically collective on fvm
    1373:   Input Parameters:
    1374: + fvm - the PetscFV object
    1375: - comp - the component number

    1377:   Output Parameter:
    1378: . name - the component name

    1380:   Level: intermediate

    1382: .seealso: PetscFVSetComponentName()
    1383: @*/
    1384: PetscErrorCode PetscFVGetComponentName(PetscFV fvm, PetscInt comp, const char **name)
    1385: {
    1387:   *name = fvm->componentNames[comp];
    1388:   return(0);
    1389: }

    1391: /*@
    1392:   PetscFVSetSpatialDimension - Set the spatial dimension

    1394:   Logically collective on fvm

    1396:   Input Parameters:
    1397: + fvm - the PetscFV object
    1398: - dim - The spatial dimension

    1400:   Level: intermediate

    1402: .seealso: PetscFVGetSpatialDimension()
    1403: @*/
    1404: PetscErrorCode PetscFVSetSpatialDimension(PetscFV fvm, PetscInt dim)
    1405: {
    1408:   fvm->dim = dim;
    1409:   return(0);
    1410: }

    1412: /*@
    1413:   PetscFVGetSpatialDimension - Get the spatial dimension

    1415:   Logically collective on fvm

    1417:   Input Parameter:
    1418: . fvm - the PetscFV object

    1420:   Output Parameter:
    1421: . dim - The spatial dimension

    1423:   Level: intermediate

    1425: .seealso: PetscFVSetSpatialDimension()
    1426: @*/
    1427: PetscErrorCode PetscFVGetSpatialDimension(PetscFV fvm, PetscInt *dim)
    1428: {
    1432:   *dim = fvm->dim;
    1433:   return(0);
    1434: }

    1436: /*@
    1437:   PetscFVSetComputeGradients - Toggle computation of cell gradients

    1439:   Logically collective on fvm

    1441:   Input Parameters:
    1442: + fvm - the PetscFV object
    1443: - computeGradients - Flag to compute cell gradients

    1445:   Level: intermediate

    1447: .seealso: PetscFVGetComputeGradients()
    1448: @*/
    1449: PetscErrorCode PetscFVSetComputeGradients(PetscFV fvm, PetscBool computeGradients)
    1450: {
    1453:   fvm->computeGradients = computeGradients;
    1454:   return(0);
    1455: }

    1457: /*@
    1458:   PetscFVGetComputeGradients - Return flag for computation of cell gradients

    1460:   Not collective

    1462:   Input Parameter:
    1463: . fvm - the PetscFV object

    1465:   Output Parameter:
    1466: . computeGradients - Flag to compute cell gradients

    1468:   Level: intermediate

    1470: .seealso: PetscFVSetComputeGradients()
    1471: @*/
    1472: PetscErrorCode PetscFVGetComputeGradients(PetscFV fvm, PetscBool *computeGradients)
    1473: {
    1477:   *computeGradients = fvm->computeGradients;
    1478:   return(0);
    1479: }

    1481: /*@
    1482:   PetscFVSetQuadrature - Set the quadrature object

    1484:   Logically collective on fvm

    1486:   Input Parameters:
    1487: + fvm - the PetscFV object
    1488: - q - The PetscQuadrature

    1490:   Level: intermediate

    1492: .seealso: PetscFVGetQuadrature()
    1493: @*/
    1494: PetscErrorCode PetscFVSetQuadrature(PetscFV fvm, PetscQuadrature q)
    1495: {

    1500:   PetscQuadratureDestroy(&fvm->quadrature);
    1501:   PetscObjectReference((PetscObject) q);
    1502:   fvm->quadrature = q;
    1503:   return(0);
    1504: }

    1506: /*@
    1507:   PetscFVGetQuadrature - Get the quadrature object

    1509:   Not collective

    1511:   Input Parameter:
    1512: . fvm - the PetscFV object

    1514:   Output Parameter:
    1515: . lim - The PetscQuadrature

    1517:   Level: intermediate

    1519: .seealso: PetscFVSetQuadrature()
    1520: @*/
    1521: PetscErrorCode PetscFVGetQuadrature(PetscFV fvm, PetscQuadrature *q)
    1522: {
    1526:   if (!fvm->quadrature) {
    1527:     /* Create default 1-point quadrature */
    1528:     PetscReal     *points, *weights;

    1531:     PetscQuadratureCreate(PETSC_COMM_SELF, &fvm->quadrature);
    1532:     PetscCalloc1(fvm->dim, &points);
    1533:     PetscMalloc1(1, &weights);
    1534:     weights[0] = 1.0;
    1535:     PetscQuadratureSetData(fvm->quadrature, fvm->dim, 1, 1, points, weights);
    1536:   }
    1537:   *q = fvm->quadrature;
    1538:   return(0);
    1539: }

    1541: /*@
    1542:   PetscFVGetDualSpace - Returns the PetscDualSpace used to define the inner product

    1544:   Not collective

    1546:   Input Parameter:
    1547: . fvm - The PetscFV object

    1549:   Output Parameter:
    1550: . sp - The PetscDualSpace object

    1552:   Note: A simple dual space is provided automatically, and the user typically will not need to override it.

    1554:   Level: intermediate

    1556: .seealso: PetscFVCreate()
    1557: @*/
    1558: PetscErrorCode PetscFVGetDualSpace(PetscFV fvm, PetscDualSpace *sp)
    1559: {
    1563:   if (!fvm->dualSpace) {
    1564:     DM              K;
    1565:     PetscInt        dim, Nc, c;
    1566:     PetscErrorCode  ierr;

    1568:     PetscFVGetSpatialDimension(fvm, &dim);
    1569:     PetscFVGetNumComponents(fvm, &Nc);
    1570:     PetscDualSpaceCreate(PetscObjectComm((PetscObject) fvm), &fvm->dualSpace);
    1571:     PetscDualSpaceSetType(fvm->dualSpace, PETSCDUALSPACESIMPLE);
    1572:     PetscDualSpaceCreateReferenceCell(fvm->dualSpace, dim, PETSC_FALSE, &K); /* TODO: The reference cell type should be held by the discretization object */
    1573:     PetscDualSpaceSetNumComponents(fvm->dualSpace, Nc);
    1574:     PetscDualSpaceSetDM(fvm->dualSpace, K);
    1575:     DMDestroy(&K);
    1576:     PetscDualSpaceSimpleSetDimension(fvm->dualSpace, Nc);
    1577:     /* Should we be using PetscFVGetQuadrature() here? */
    1578:     for (c = 0; c < Nc; ++c) {
    1579:       PetscQuadrature qc;
    1580:       PetscReal      *points, *weights;
    1581:       PetscErrorCode  ierr;

    1583:       PetscQuadratureCreate(PETSC_COMM_SELF, &qc);
    1584:       PetscCalloc1(dim, &points);
    1585:       PetscCalloc1(Nc, &weights);
    1586:       weights[c] = 1.0;
    1587:       PetscQuadratureSetData(qc, dim, Nc, 1, points, weights);
    1588:       PetscDualSpaceSimpleSetFunctional(fvm->dualSpace, c, qc);
    1589:       PetscQuadratureDestroy(&qc);
    1590:     }
    1591:     PetscDualSpaceSetUp(fvm->dualSpace);
    1592:   }
    1593:   *sp = fvm->dualSpace;
    1594:   return(0);
    1595: }

    1597: /*@
    1598:   PetscFVSetDualSpace - Sets the PetscDualSpace used to define the inner product

    1600:   Not collective

    1602:   Input Parameters:
    1603: + fvm - The PetscFV object
    1604: - sp  - The PetscDualSpace object

    1606:   Level: intermediate

    1608:   Note: A simple dual space is provided automatically, and the user typically will not need to override it.

    1610: .seealso: PetscFVCreate()
    1611: @*/
    1612: PetscErrorCode PetscFVSetDualSpace(PetscFV fvm, PetscDualSpace sp)
    1613: {

    1619:   PetscDualSpaceDestroy(&fvm->dualSpace);
    1620:   fvm->dualSpace = sp;
    1621:   PetscObjectReference((PetscObject) fvm->dualSpace);
    1622:   return(0);
    1623: }

    1625: /*@C
    1626:   PetscFVGetCellTabulation - Returns the tabulation of the basis functions at the quadrature points

    1628:   Not collective

    1630:   Input Parameter:
    1631: . fvm - The PetscFV object

    1633:   Output Parameter:
    1634: . T - The basis function values and derviatives at quadrature points

    1636:   Note:
    1637: $ T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    1638: $ T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
    1639: $ T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e

    1641:   Level: intermediate

    1643: .seealso: PetscFEGetCellTabulation(), PetscFVCreateTabulation(), PetscFVGetQuadrature(), PetscQuadratureGetData()
    1644: @*/
    1645: PetscErrorCode PetscFVGetCellTabulation(PetscFV fvm, PetscTabulation *T)
    1646: {
    1647:   PetscInt         npoints;
    1648:   const PetscReal *points;
    1649:   PetscErrorCode   ierr;

    1654:   PetscQuadratureGetData(fvm->quadrature, NULL, NULL, &npoints, &points, NULL);
    1655:   if (!fvm->T) {PetscFVCreateTabulation(fvm, 1, npoints, points, 1, &fvm->T);}
    1656:   *T = fvm->T;
    1657:   return(0);
    1658: }

    1660: /*@C
    1661:   PetscFVCreateTabulation - Tabulates the basis functions, and perhaps derivatives, at the points provided.

    1663:   Not collective

    1665:   Input Parameters:
    1666: + fvm     - The PetscFV object
    1667: . nrepl   - The number of replicas
    1668: . npoints - The number of tabulation points in a replica
    1669: . points  - The tabulation point coordinates
    1670: - K       - The order of derivative to tabulate

    1672:   Output Parameter:
    1673: . T - The basis function values and derviative at tabulation points

    1675:   Note:
    1676: $ T->T[0] = B[(p*pdim + i)*Nc + c] is the value at point p for basis function i and component c
    1677: $ T->T[1] = D[((p*pdim + i)*Nc + c)*dim + d] is the derivative value at point p for basis function i, component c, in direction d
    1678: $ T->T[2] = H[(((p*pdim + i)*Nc + c)*dim + d)*dim + e] is the value at point p for basis function i, component c, in directions d and e

    1680:   Level: intermediate

    1682: .seealso: PetscFECreateTabulation(), PetscTabulationDestroy(), PetscFEGetCellTabulation()
    1683: @*/
    1684: PetscErrorCode PetscFVCreateTabulation(PetscFV fvm, PetscInt nrepl, PetscInt npoints, const PetscReal points[], PetscInt K, PetscTabulation *T)
    1685: {
    1686:   PetscInt         pdim = 1; /* Dimension of approximation space P */
    1687:   PetscInt         cdim;     /* Spatial dimension */
    1688:   PetscInt         Nc;       /* Field components */
    1689:   PetscInt         k, p, d, c, e;
    1690:   PetscErrorCode   ierr;

    1693:   if (!npoints || K < 0) {
    1694:     *T = NULL;
    1695:     return(0);
    1696:   }
    1700:   PetscFVGetSpatialDimension(fvm, &cdim);
    1701:   PetscFVGetNumComponents(fvm, &Nc);
    1702:   PetscMalloc1(1, T);
    1703:   (*T)->K    = !cdim ? 0 : K;
    1704:   (*T)->Nr   = nrepl;
    1705:   (*T)->Np   = npoints;
    1706:   (*T)->Nb   = pdim;
    1707:   (*T)->Nc   = Nc;
    1708:   (*T)->cdim = cdim;
    1709:   PetscMalloc1((*T)->K+1, &(*T)->T);
    1710:   for (k = 0; k <= (*T)->K; ++k) {
    1711:     PetscMalloc1(nrepl*npoints*pdim*Nc*PetscPowInt(cdim, k), &(*T)->T[k]);
    1712:   }
    1713:   if (K >= 0) {for (p = 0; p < nrepl*npoints; ++p) for (d = 0; d < pdim; ++d) for (c = 0; c < Nc; ++c) (*T)->T[0][(p*pdim + d)*Nc + c] = 1.0;}
    1714:   if (K >= 1) {for (p = 0; p < nrepl*npoints; ++p) for (d = 0; d < pdim; ++d) for (c = 0; c < Nc; ++c) for (e = 0; e < cdim; ++e) (*T)->T[1][((p*pdim + d)*Nc + c)*cdim + e] = 0.0;}
    1715:   if (K >= 2) {for (p = 0; p < nrepl*npoints; ++p) for (d = 0; d < pdim; ++d) for (c = 0; c < Nc; ++c) for (e = 0; e < cdim*cdim; ++e) (*T)->T[2][((p*pdim + d)*Nc + c)*cdim*cdim + e] = 0.0;}
    1716:   return(0);
    1717: }

    1719: /*@C
    1720:   PetscFVComputeGradient - Compute the gradient reconstruction matrix for a given cell

    1722:   Input Parameters:
    1723: + fvm      - The PetscFV object
    1724: . numFaces - The number of cell faces which are not constrained
    1725: - dx       - The vector from the cell centroid to the neighboring cell centroid for each face

    1727:   Level: advanced

    1729: .seealso: PetscFVCreate()
    1730: @*/
    1731: PetscErrorCode PetscFVComputeGradient(PetscFV fvm, PetscInt numFaces, PetscScalar dx[], PetscScalar grad[])
    1732: {

    1737:   if (fvm->ops->computegradient) {(*fvm->ops->computegradient)(fvm, numFaces, dx, grad);}
    1738:   return(0);
    1739: }

    1741: /*@C
    1742:   PetscFVIntegrateRHSFunction - Produce the cell residual vector for a chunk of elements by quadrature integration

    1744:   Not collective

    1746:   Input Parameters:
    1747: + fvm          - The PetscFV object for the field being integrated
    1748: . prob         - The PetscDS specifing the discretizations and continuum functions
    1749: . field        - The field being integrated
    1750: . Nf           - The number of faces in the chunk
    1751: . fgeom        - The face geometry for each face in the chunk
    1752: . neighborVol  - The volume for each pair of cells in the chunk
    1753: . uL           - The state from the cell on the left
    1754: - uR           - The state from the cell on the right

    1756:   Output Parameter:
    1757: + fluxL        - the left fluxes for each face
    1758: - fluxR        - the right fluxes for each face

    1760:   Level: developer

    1762: .seealso: PetscFVCreate()
    1763: @*/
    1764: PetscErrorCode PetscFVIntegrateRHSFunction(PetscFV fvm, PetscDS prob, PetscInt field, PetscInt Nf, PetscFVFaceGeom *fgeom, PetscReal *neighborVol,
    1765:                                            PetscScalar uL[], PetscScalar uR[], PetscScalar fluxL[], PetscScalar fluxR[])
    1766: {

    1771:   if (fvm->ops->integraterhsfunction) {(*fvm->ops->integraterhsfunction)(fvm, prob, field, Nf, fgeom, neighborVol, uL, uR, fluxL, fluxR);}
    1772:   return(0);
    1773: }

    1775: /*@
    1776:   PetscFVRefine - Create a "refined" PetscFV object that refines the reference cell into smaller copies. This is typically used
    1777:   to precondition a higher order method with a lower order method on a refined mesh having the same number of dofs (but more
    1778:   sparsity). It is also used to create an interpolation between regularly refined meshes.

    1780:   Input Parameter:
    1781: . fv - The initial PetscFV

    1783:   Output Parameter:
    1784: . fvRef - The refined PetscFV

    1786:   Level: advanced

    1788: .seealso: PetscFVType, PetscFVCreate(), PetscFVSetType()
    1789: @*/
    1790: PetscErrorCode PetscFVRefine(PetscFV fv, PetscFV *fvRef)
    1791: {
    1792:   PetscDualSpace    Q, Qref;
    1793:   DM                K, Kref;
    1794:   PetscQuadrature   q, qref;
    1795:   DMPolytopeType    ct;
    1796:   DMPlexCellRefiner cr;
    1797:   PetscReal        *v0;
    1798:   PetscReal        *jac, *invjac;
    1799:   PetscInt          numComp, numSubelements, s;
    1800:   PetscErrorCode    ierr;

    1803:   PetscFVGetDualSpace(fv, &Q);
    1804:   PetscFVGetQuadrature(fv, &q);
    1805:   PetscDualSpaceGetDM(Q, &K);
    1806:   /* Create dual space */
    1807:   PetscDualSpaceDuplicate(Q, &Qref);
    1808:   DMRefine(K, PetscObjectComm((PetscObject) fv), &Kref);
    1809:   PetscDualSpaceSetDM(Qref, Kref);
    1810:   DMDestroy(&Kref);
    1811:   PetscDualSpaceSetUp(Qref);
    1812:   /* Create volume */
    1813:   PetscFVCreate(PetscObjectComm((PetscObject) fv), fvRef);
    1814:   PetscFVSetDualSpace(*fvRef, Qref);
    1815:   PetscFVGetNumComponents(fv,    &numComp);
    1816:   PetscFVSetNumComponents(*fvRef, numComp);
    1817:   PetscFVSetUp(*fvRef);
    1818:   /* Create quadrature */
    1819:   DMPlexGetCellType(K, 0, &ct);
    1820:   DMPlexCellRefinerCreate(K, &cr);
    1821:   DMPlexCellRefinerGetAffineTransforms(cr, ct, &numSubelements, &v0, &jac, &invjac);
    1822:   PetscQuadratureExpandComposite(q, numSubelements, v0, jac, &qref);
    1823:   PetscDualSpaceSimpleSetDimension(Qref, numSubelements);
    1824:   for (s = 0; s < numSubelements; ++s) {
    1825:     PetscQuadrature  qs;
    1826:     const PetscReal *points, *weights;
    1827:     PetscReal       *p, *w;
    1828:     PetscInt         dim, Nc, npoints, np;

    1830:     PetscQuadratureCreate(PETSC_COMM_SELF, &qs);
    1831:     PetscQuadratureGetData(q, &dim, &Nc, &npoints, &points, &weights);
    1832:     np   = npoints/numSubelements;
    1833:     PetscMalloc1(np*dim,&p);
    1834:     PetscMalloc1(np*Nc,&w);
    1835:     PetscArraycpy(p, &points[s*np*dim], np*dim);
    1836:     PetscArraycpy(w, &weights[s*np*Nc], np*Nc);
    1837:     PetscQuadratureSetData(qs, dim, Nc, np, p, w);
    1838:     PetscDualSpaceSimpleSetFunctional(Qref, s, qs);
    1839:     PetscQuadratureDestroy(&qs);
    1840:   }
    1841:   PetscFVSetQuadrature(*fvRef, qref);
    1842:   DMPlexCellRefinerDestroy(&cr);
    1843:   PetscQuadratureDestroy(&qref);
    1844:   PetscDualSpaceDestroy(&Qref);
    1845:   return(0);
    1846: }

    1848: static PetscErrorCode PetscFVDestroy_Upwind(PetscFV fvm)
    1849: {
    1850:   PetscFV_Upwind *b = (PetscFV_Upwind *) fvm->data;

    1854:   PetscFree(b);
    1855:   return(0);
    1856: }

    1858: static PetscErrorCode PetscFVView_Upwind_Ascii(PetscFV fv, PetscViewer viewer)
    1859: {
    1860:   PetscInt          Nc, c;
    1861:   PetscViewerFormat format;
    1862:   PetscErrorCode    ierr;

    1865:   PetscFVGetNumComponents(fv, &Nc);
    1866:   PetscViewerGetFormat(viewer, &format);
    1867:   PetscViewerASCIIPrintf(viewer, "Upwind Finite Volume:\n");
    1868:   PetscViewerASCIIPrintf(viewer, "  num components: %d\n", Nc);
    1869:   for (c = 0; c < Nc; c++) {
    1870:     if (fv->componentNames[c]) {
    1871:       PetscViewerASCIIPrintf(viewer, "    component %d: %s\n", c, fv->componentNames[c]);
    1872:     }
    1873:   }
    1874:   return(0);
    1875: }

    1877: static PetscErrorCode PetscFVView_Upwind(PetscFV fv, PetscViewer viewer)
    1878: {
    1879:   PetscBool      iascii;

    1885:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    1886:   if (iascii) {PetscFVView_Upwind_Ascii(fv, viewer);}
    1887:   return(0);
    1888: }

    1890: static PetscErrorCode PetscFVSetUp_Upwind(PetscFV fvm)
    1891: {
    1893:   return(0);
    1894: }

    1896: /*
    1897:   neighborVol[f*2+0] contains the left  geom
    1898:   neighborVol[f*2+1] contains the right geom
    1899: */
    1900: static PetscErrorCode PetscFVIntegrateRHSFunction_Upwind(PetscFV fvm, PetscDS prob, PetscInt field, PetscInt Nf, PetscFVFaceGeom *fgeom, PetscReal *neighborVol,
    1901:                                                          PetscScalar uL[], PetscScalar uR[], PetscScalar fluxL[], PetscScalar fluxR[])
    1902: {
    1903:   void             (*riemann)(PetscInt, PetscInt, const PetscReal[], const PetscReal[], const PetscScalar[], const PetscScalar[], PetscInt, const PetscScalar[], PetscScalar[], void *);
    1904:   void              *rctx;
    1905:   PetscScalar       *flux = fvm->fluxWork;
    1906:   const PetscScalar *constants;
    1907:   PetscInt           dim, numConstants, pdim, totDim, Nc, off, f, d;
    1908:   PetscErrorCode     ierr;

    1911:   PetscDSGetTotalComponents(prob, &Nc);
    1912:   PetscDSGetTotalDimension(prob, &totDim);
    1913:   PetscDSGetFieldOffset(prob, field, &off);
    1914:   PetscDSGetRiemannSolver(prob, field, &riemann);
    1915:   PetscDSGetContext(prob, field, &rctx);
    1916:   PetscDSGetConstants(prob, &numConstants, &constants);
    1917:   PetscFVGetSpatialDimension(fvm, &dim);
    1918:   PetscFVGetNumComponents(fvm, &pdim);
    1919:   for (f = 0; f < Nf; ++f) {
    1920:     (*riemann)(dim, pdim, fgeom[f].centroid, fgeom[f].normal, &uL[f*Nc], &uR[f*Nc], numConstants, constants, flux, rctx);
    1921:     for (d = 0; d < pdim; ++d) {
    1922:       fluxL[f*totDim+off+d] = flux[d] / neighborVol[f*2+0];
    1923:       fluxR[f*totDim+off+d] = flux[d] / neighborVol[f*2+1];
    1924:     }
    1925:   }
    1926:   return(0);
    1927: }

    1929: static PetscErrorCode PetscFVInitialize_Upwind(PetscFV fvm)
    1930: {
    1932:   fvm->ops->setfromoptions          = NULL;
    1933:   fvm->ops->setup                   = PetscFVSetUp_Upwind;
    1934:   fvm->ops->view                    = PetscFVView_Upwind;
    1935:   fvm->ops->destroy                 = PetscFVDestroy_Upwind;
    1936:   fvm->ops->integraterhsfunction    = PetscFVIntegrateRHSFunction_Upwind;
    1937:   return(0);
    1938: }

    1940: /*MC
    1941:   PETSCFVUPWIND = "upwind" - A PetscFV object

    1943:   Level: intermediate

    1945: .seealso: PetscFVType, PetscFVCreate(), PetscFVSetType()
    1946: M*/

    1948: PETSC_EXTERN PetscErrorCode PetscFVCreate_Upwind(PetscFV fvm)
    1949: {
    1950:   PetscFV_Upwind *b;
    1951:   PetscErrorCode  ierr;

    1955:   PetscNewLog(fvm,&b);
    1956:   fvm->data = b;

    1958:   PetscFVInitialize_Upwind(fvm);
    1959:   return(0);
    1960: }

    1962: #include <petscblaslapack.h>

    1964: static PetscErrorCode PetscFVDestroy_LeastSquares(PetscFV fvm)
    1965: {
    1966:   PetscFV_LeastSquares *ls = (PetscFV_LeastSquares *) fvm->data;
    1967:   PetscErrorCode        ierr;

    1970:   PetscObjectComposeFunction((PetscObject) fvm, "PetscFVLeastSquaresSetMaxFaces_C", NULL);
    1971:   PetscFree4(ls->B, ls->Binv, ls->tau, ls->work);
    1972:   PetscFree(ls);
    1973:   return(0);
    1974: }

    1976: static PetscErrorCode PetscFVView_LeastSquares_Ascii(PetscFV fv, PetscViewer viewer)
    1977: {
    1978:   PetscInt          Nc, c;
    1979:   PetscViewerFormat format;
    1980:   PetscErrorCode    ierr;

    1983:   PetscFVGetNumComponents(fv, &Nc);
    1984:   PetscViewerGetFormat(viewer, &format);
    1985:   PetscViewerASCIIPrintf(viewer, "Finite Volume with Least Squares Reconstruction:\n");
    1986:   PetscViewerASCIIPrintf(viewer, "  num components: %d\n", Nc);
    1987:   for (c = 0; c < Nc; c++) {
    1988:     if (fv->componentNames[c]) {
    1989:       PetscViewerASCIIPrintf(viewer, "    component %d: %s\n", c, fv->componentNames[c]);
    1990:     }
    1991:   }
    1992:   return(0);
    1993: }

    1995: static PetscErrorCode PetscFVView_LeastSquares(PetscFV fv, PetscViewer viewer)
    1996: {
    1997:   PetscBool      iascii;

    2003:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    2004:   if (iascii) {PetscFVView_LeastSquares_Ascii(fv, viewer);}
    2005:   return(0);
    2006: }

    2008: static PetscErrorCode PetscFVSetUp_LeastSquares(PetscFV fvm)
    2009: {
    2011:   return(0);
    2012: }

    2014: /* Overwrites A. Can only handle full-rank problems with m>=n */
    2015: static PetscErrorCode PetscFVLeastSquaresPseudoInverse_Static(PetscInt m,PetscInt mstride,PetscInt n,PetscScalar *A,PetscScalar *Ainv,PetscScalar *tau,PetscInt worksize,PetscScalar *work)
    2016: {
    2017:   PetscBool      debug = PETSC_FALSE;
    2019:   PetscBLASInt   M,N,K,lda,ldb,ldwork,info;
    2020:   PetscScalar    *R,*Q,*Aback,Alpha;

    2023:   if (debug) {
    2024:     PetscMalloc1(m*n,&Aback);
    2025:     PetscArraycpy(Aback,A,m*n);
    2026:   }

    2028:   PetscBLASIntCast(m,&M);
    2029:   PetscBLASIntCast(n,&N);
    2030:   PetscBLASIntCast(mstride,&lda);
    2031:   PetscBLASIntCast(worksize,&ldwork);
    2032:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2033:   LAPACKgeqrf_(&M,&N,A,&lda,tau,work,&ldwork,&info);
    2034:   PetscFPTrapPop();
    2035:   if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"xGEQRF error");
    2036:   R = A; /* Upper triangular part of A now contains R, the rest contains the elementary reflectors */

    2038:   /* Extract an explicit representation of Q */
    2039:   Q    = Ainv;
    2040:   PetscArraycpy(Q,A,mstride*n);
    2041:   K    = N;                     /* full rank */
    2042:   PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&M,&N,&K,Q,&lda,tau,work,&ldwork,&info));
    2043:   if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"xORGQR/xUNGQR error");

    2045:   /* Compute A^{-T} = (R^{-1} Q^T)^T = Q R^{-T} */
    2046:   Alpha = 1.0;
    2047:   ldb   = lda;
    2048:   BLAStrsm_("Right","Upper","ConjugateTranspose","NotUnitTriangular",&M,&N,&Alpha,R,&lda,Q,&ldb);
    2049:   /* Ainv is Q, overwritten with inverse */

    2051:   if (debug) {                      /* Check that pseudo-inverse worked */
    2052:     PetscScalar  Beta = 0.0;
    2053:     PetscBLASInt ldc;
    2054:     K   = N;
    2055:     ldc = N;
    2056:     BLASgemm_("ConjugateTranspose","Normal",&N,&K,&M,&Alpha,Ainv,&lda,Aback,&ldb,&Beta,work,&ldc);
    2057:     PetscScalarView(n*n,work,PETSC_VIEWER_STDOUT_SELF);
    2058:     PetscFree(Aback);
    2059:   }
    2060:   return(0);
    2061: }

    2063: /* Overwrites A. Can handle degenerate problems and m<n. */
    2064: static PetscErrorCode PetscFVLeastSquaresPseudoInverseSVD_Static(PetscInt m,PetscInt mstride,PetscInt n,PetscScalar *A,PetscScalar *Ainv,PetscScalar *tau,PetscInt worksize,PetscScalar *work)
    2065: {
    2066:   PetscBool      debug = PETSC_FALSE;
    2067:   PetscScalar   *Brhs, *Aback;
    2068:   PetscScalar   *tmpwork;
    2069:   PetscReal      rcond;
    2070: #if defined (PETSC_USE_COMPLEX)
    2071:   PetscInt       rworkSize;
    2072:   PetscReal     *rwork;
    2073: #endif
    2074:   PetscInt       i, j, maxmn;
    2075:   PetscBLASInt   M, N, lda, ldb, ldwork;
    2076:   PetscBLASInt   nrhs, irank, info;

    2080:   if (debug) {
    2081:     PetscMalloc1(m*n,&Aback);
    2082:     PetscArraycpy(Aback,A,m*n);
    2083:   }

    2085:   /* initialize to identity */
    2086:   tmpwork = work;
    2087:   Brhs = Ainv;
    2088:   maxmn = PetscMax(m,n);
    2089:   for (j=0; j<maxmn; j++) {
    2090:     for (i=0; i<maxmn; i++) Brhs[i + j*maxmn] = 1.0*(i == j);
    2091:   }

    2093:   PetscBLASIntCast(m,&M);
    2094:   PetscBLASIntCast(n,&N);
    2095:   PetscBLASIntCast(mstride,&lda);
    2096:   PetscBLASIntCast(maxmn,&ldb);
    2097:   PetscBLASIntCast(worksize,&ldwork);
    2098:   rcond = -1;
    2099:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2100:   nrhs  = M;
    2101: #if defined(PETSC_USE_COMPLEX)
    2102:   rworkSize = 5 * PetscMin(M,N);
    2103:   PetscMalloc1(rworkSize,&rwork);
    2104:   LAPACKgelss_(&M,&N,&nrhs,A,&lda,Brhs,&ldb, (PetscReal *) tau,&rcond,&irank,tmpwork,&ldwork,rwork,&info);
    2105:   PetscFPTrapPop();
    2106:   PetscFree(rwork);
    2107: #else
    2108:   nrhs  = M;
    2109:   LAPACKgelss_(&M,&N,&nrhs,A,&lda,Brhs,&ldb, (PetscReal *) tau,&rcond,&irank,tmpwork,&ldwork,&info);
    2110:   PetscFPTrapPop();
    2111: #endif
    2112:   if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"xGELSS error");
    2113:   /* The following check should be turned into a diagnostic as soon as someone wants to do this intentionally */
    2114:   if (irank < PetscMin(M,N)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Rank deficient least squares fit, indicates an isolated cell with two colinear points");
    2115:   return(0);
    2116: }

    2118: #if 0
    2119: static PetscErrorCode PetscFVLeastSquaresDebugCell_Static(PetscFV fvm, PetscInt cell, DM dm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
    2120: {
    2121:   PetscReal       grad[2] = {0, 0};
    2122:   const PetscInt *faces;
    2123:   PetscInt        numFaces, f;
    2124:   PetscErrorCode  ierr;

    2127:   DMPlexGetConeSize(dm, cell, &numFaces);
    2128:   DMPlexGetCone(dm, cell, &faces);
    2129:   for (f = 0; f < numFaces; ++f) {
    2130:     const PetscInt *fcells;
    2131:     const CellGeom *cg1;
    2132:     const FaceGeom *fg;

    2134:     DMPlexGetSupport(dm, faces[f], &fcells);
    2135:     DMPlexPointLocalRead(dmFace, faces[f], fgeom, &fg);
    2136:     for (i = 0; i < 2; ++i) {
    2137:       PetscScalar du;

    2139:       if (fcells[i] == c) continue;
    2140:       DMPlexPointLocalRead(dmCell, fcells[i], cgeom, &cg1);
    2141:       du   = cg1->centroid[0] + 3*cg1->centroid[1] - (cg->centroid[0] + 3*cg->centroid[1]);
    2142:       grad[0] += fg->grad[!i][0] * du;
    2143:       grad[1] += fg->grad[!i][1] * du;
    2144:     }
    2145:   }
    2146:   PetscPrintf(PETSC_COMM_SELF, "cell[%d] grad (%g, %g)\n", cell, grad[0], grad[1]);
    2147:   return(0);
    2148: }
    2149: #endif

    2151: /*
    2152:   PetscFVComputeGradient - Compute the gradient reconstruction matrix for a given cell

    2154:   Input Parameters:
    2155: + fvm      - The PetscFV object
    2156: . numFaces - The number of cell faces which are not constrained
    2157: . dx       - The vector from the cell centroid to the neighboring cell centroid for each face

    2159:   Level: developer

    2161: .seealso: PetscFVCreate()
    2162: */
    2163: static PetscErrorCode PetscFVComputeGradient_LeastSquares(PetscFV fvm, PetscInt numFaces, const PetscScalar dx[], PetscScalar grad[])
    2164: {
    2165:   PetscFV_LeastSquares *ls       = (PetscFV_LeastSquares *) fvm->data;
    2166:   const PetscBool       useSVD   = PETSC_TRUE;
    2167:   const PetscInt        maxFaces = ls->maxFaces;
    2168:   PetscInt              dim, f, d;
    2169:   PetscErrorCode        ierr;

    2172:   if (numFaces > maxFaces) {
    2173:     if (maxFaces < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Reconstruction has not been initialized, call PetscFVLeastSquaresSetMaxFaces()");
    2174:     SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of input faces %D > %D maxfaces", numFaces, maxFaces);
    2175:   }
    2176:   PetscFVGetSpatialDimension(fvm, &dim);
    2177:   for (f = 0; f < numFaces; ++f) {
    2178:     for (d = 0; d < dim; ++d) ls->B[d*maxFaces+f] = dx[f*dim+d];
    2179:   }
    2180:   /* Overwrites B with garbage, returns Binv in row-major format */
    2181:   if (useSVD) {
    2182:     PetscInt maxmn = PetscMax(numFaces, dim);
    2183:     PetscFVLeastSquaresPseudoInverseSVD_Static(numFaces, maxFaces, dim, ls->B, ls->Binv, ls->tau, ls->workSize, ls->work);
    2184:     /* Binv shaped in column-major, coldim=maxmn.*/
    2185:     for (f = 0; f < numFaces; ++f) {
    2186:       for (d = 0; d < dim; ++d) grad[f*dim+d] = ls->Binv[d + maxmn*f];
    2187:     }
    2188:   } else {
    2189:     PetscFVLeastSquaresPseudoInverse_Static(numFaces, maxFaces, dim, ls->B, ls->Binv, ls->tau, ls->workSize, ls->work);
    2190:     /* Binv shaped in row-major, rowdim=maxFaces.*/
    2191:     for (f = 0; f < numFaces; ++f) {
    2192:       for (d = 0; d < dim; ++d) grad[f*dim+d] = ls->Binv[d*maxFaces + f];
    2193:     }
    2194:   }
    2195:   return(0);
    2196: }

    2198: /*
    2199:   neighborVol[f*2+0] contains the left  geom
    2200:   neighborVol[f*2+1] contains the right geom
    2201: */
    2202: static PetscErrorCode PetscFVIntegrateRHSFunction_LeastSquares(PetscFV fvm, PetscDS prob, PetscInt field, PetscInt Nf, PetscFVFaceGeom *fgeom, PetscReal *neighborVol,
    2203:                                                                PetscScalar uL[], PetscScalar uR[], PetscScalar fluxL[], PetscScalar fluxR[])
    2204: {
    2205:   void             (*riemann)(PetscInt, PetscInt, const PetscReal[], const PetscReal[], const PetscScalar[], const PetscScalar[], PetscInt, const PetscScalar[], PetscScalar[], void *);
    2206:   void              *rctx;
    2207:   PetscScalar       *flux = fvm->fluxWork;
    2208:   const PetscScalar *constants;
    2209:   PetscInt           dim, numConstants, pdim, Nc, totDim, off, f, d;
    2210:   PetscErrorCode     ierr;

    2213:   PetscDSGetTotalComponents(prob, &Nc);
    2214:   PetscDSGetTotalDimension(prob, &totDim);
    2215:   PetscDSGetFieldOffset(prob, field, &off);
    2216:   PetscDSGetRiemannSolver(prob, field, &riemann);
    2217:   PetscDSGetContext(prob, field, &rctx);
    2218:   PetscDSGetConstants(prob, &numConstants, &constants);
    2219:   PetscFVGetSpatialDimension(fvm, &dim);
    2220:   PetscFVGetNumComponents(fvm, &pdim);
    2221:   for (f = 0; f < Nf; ++f) {
    2222:     (*riemann)(dim, pdim, fgeom[f].centroid, fgeom[f].normal, &uL[f*Nc], &uR[f*Nc], numConstants, constants, flux, rctx);
    2223:     for (d = 0; d < pdim; ++d) {
    2224:       fluxL[f*totDim+off+d] = flux[d] / neighborVol[f*2+0];
    2225:       fluxR[f*totDim+off+d] = flux[d] / neighborVol[f*2+1];
    2226:     }
    2227:   }
    2228:   return(0);
    2229: }

    2231: static PetscErrorCode PetscFVLeastSquaresSetMaxFaces_LS(PetscFV fvm, PetscInt maxFaces)
    2232: {
    2233:   PetscFV_LeastSquares *ls = (PetscFV_LeastSquares *) fvm->data;
    2234:   PetscInt              dim,m,n,nrhs,minmn,maxmn;
    2235:   PetscErrorCode        ierr;

    2239:   PetscFVGetSpatialDimension(fvm, &dim);
    2240:   PetscFree4(ls->B, ls->Binv, ls->tau, ls->work);
    2241:   ls->maxFaces = maxFaces;
    2242:   m       = ls->maxFaces;
    2243:   n       = dim;
    2244:   nrhs    = ls->maxFaces;
    2245:   minmn   = PetscMin(m,n);
    2246:   maxmn   = PetscMax(m,n);
    2247:   ls->workSize = 3*minmn + PetscMax(2*minmn, PetscMax(maxmn, nrhs)); /* required by LAPACK */
    2248:   PetscMalloc4(m*n,&ls->B,maxmn*maxmn,&ls->Binv,minmn,&ls->tau,ls->workSize,&ls->work);
    2249:   return(0);
    2250: }

    2252: PetscErrorCode PetscFVInitialize_LeastSquares(PetscFV fvm)
    2253: {
    2255:   fvm->ops->setfromoptions          = NULL;
    2256:   fvm->ops->setup                   = PetscFVSetUp_LeastSquares;
    2257:   fvm->ops->view                    = PetscFVView_LeastSquares;
    2258:   fvm->ops->destroy                 = PetscFVDestroy_LeastSquares;
    2259:   fvm->ops->computegradient         = PetscFVComputeGradient_LeastSquares;
    2260:   fvm->ops->integraterhsfunction    = PetscFVIntegrateRHSFunction_LeastSquares;
    2261:   return(0);
    2262: }

    2264: /*MC
    2265:   PETSCFVLEASTSQUARES = "leastsquares" - A PetscFV object

    2267:   Level: intermediate

    2269: .seealso: PetscFVType, PetscFVCreate(), PetscFVSetType()
    2270: M*/

    2272: PETSC_EXTERN PetscErrorCode PetscFVCreate_LeastSquares(PetscFV fvm)
    2273: {
    2274:   PetscFV_LeastSquares *ls;
    2275:   PetscErrorCode        ierr;

    2279:   PetscNewLog(fvm, &ls);
    2280:   fvm->data = ls;

    2282:   ls->maxFaces = -1;
    2283:   ls->workSize = -1;
    2284:   ls->B        = NULL;
    2285:   ls->Binv     = NULL;
    2286:   ls->tau      = NULL;
    2287:   ls->work     = NULL;

    2289:   PetscFVSetComputeGradients(fvm, PETSC_TRUE);
    2290:   PetscFVInitialize_LeastSquares(fvm);
    2291:   PetscObjectComposeFunction((PetscObject) fvm, "PetscFVLeastSquaresSetMaxFaces_C", PetscFVLeastSquaresSetMaxFaces_LS);
    2292:   return(0);
    2293: }

    2295: /*@
    2296:   PetscFVLeastSquaresSetMaxFaces - Set the maximum number of cell faces for gradient reconstruction

    2298:   Not collective

    2300:   Input parameters:
    2301: + fvm      - The PetscFV object
    2302: - maxFaces - The maximum number of cell faces

    2304:   Level: intermediate

    2306: .seealso: PetscFVCreate(), PETSCFVLEASTSQUARES
    2307: @*/
    2308: PetscErrorCode PetscFVLeastSquaresSetMaxFaces(PetscFV fvm, PetscInt maxFaces)
    2309: {

    2314:   PetscTryMethod(fvm, "PetscFVLeastSquaresSetMaxFaces_C", (PetscFV,PetscInt), (fvm,maxFaces));
    2315:   return(0);
    2316: }