Actual source code: characteristic.c

      1: #include <petsc/private/characteristicimpl.h>
      2: #include <petscdmda.h>
      3: #include <petscviewer.h>

      5: PetscClassId  CHARACTERISTIC_CLASSID;
      6: PetscLogEvent CHARACTERISTIC_SetUp, CHARACTERISTIC_Solve, CHARACTERISTIC_QueueSetup, CHARACTERISTIC_DAUpdate;
      7: PetscLogEvent CHARACTERISTIC_HalfTimeLocal, CHARACTERISTIC_HalfTimeRemote, CHARACTERISTIC_HalfTimeExchange;
      8: PetscLogEvent CHARACTERISTIC_FullTimeLocal, CHARACTERISTIC_FullTimeRemote, CHARACTERISTIC_FullTimeExchange;
      9: /*
     10:    Contains the list of registered characteristic routines
     11: */
     12: PetscFunctionList CharacteristicList              = NULL;
     13: PetscBool         CharacteristicRegisterAllCalled = PETSC_FALSE;

     15: static PetscErrorCode DMDAGetNeighborsRank(DM, PetscMPIInt[]);
     16: static PetscMPIInt    DMDAGetNeighborRelative(DM, PetscReal, PetscReal);

     18: static PetscErrorCode CharacteristicHeapSort(Characteristic, Queue, PetscInt);
     19: static PetscErrorCode CharacteristicSiftDown(Characteristic, Queue, PetscInt, PetscInt);

     21: static PetscErrorCode CharacteristicView(Characteristic c, PetscViewer viewer)
     22: {
     23:   PetscBool iascii;

     25:   PetscFunctionBegin;
     27:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)c), &viewer));
     29:   PetscCheckSameComm(c, 1, viewer, 2);

     31:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
     32:   if (!iascii) PetscTryTypeMethod(c, view, viewer);
     33:   PetscFunctionReturn(PETSC_SUCCESS);
     34: }

     36: PetscErrorCode CharacteristicDestroy(Characteristic *c)
     37: {
     38:   PetscFunctionBegin;
     39:   if (!*c) PetscFunctionReturn(PETSC_SUCCESS);
     41:   if (--((PetscObject)*c)->refct > 0) PetscFunctionReturn(PETSC_SUCCESS);

     43:   PetscTryTypeMethod(*c, destroy);
     44:   PetscCallMPI(MPI_Type_free(&(*c)->itemType));
     45:   PetscCall(PetscFree((*c)->queue));
     46:   PetscCall(PetscFree((*c)->queueLocal));
     47:   PetscCall(PetscFree((*c)->queueRemote));
     48:   PetscCall(PetscFree((*c)->neighbors));
     49:   PetscCall(PetscFree((*c)->needCount));
     50:   PetscCall(PetscFree((*c)->localOffsets));
     51:   PetscCall(PetscFree((*c)->fillCount));
     52:   PetscCall(PetscFree((*c)->remoteOffsets));
     53:   PetscCall(PetscFree((*c)->request));
     54:   PetscCall(PetscFree((*c)->status));
     55:   PetscCall(PetscHeaderDestroy(c));
     56:   PetscFunctionReturn(PETSC_SUCCESS);
     57: }

     59: PetscErrorCode CharacteristicCreate(MPI_Comm comm, Characteristic *c)
     60: {
     61:   Characteristic newC;

     63:   PetscFunctionBegin;
     64:   PetscAssertPointer(c, 2);
     65:   *c = NULL;
     66:   PetscCall(CharacteristicInitializePackage());

     68:   PetscCall(PetscHeaderCreate(newC, CHARACTERISTIC_CLASSID, "Characteristic", "Characteristic", "Characteristic", comm, CharacteristicDestroy, CharacteristicView));
     69:   *c = newC;

     71:   newC->structured          = PETSC_TRUE;
     72:   newC->numIds              = 0;
     73:   newC->velocityDA          = NULL;
     74:   newC->velocity            = NULL;
     75:   newC->velocityOld         = NULL;
     76:   newC->numVelocityComp     = 0;
     77:   newC->velocityComp        = NULL;
     78:   newC->velocityInterp      = NULL;
     79:   newC->velocityInterpLocal = NULL;
     80:   newC->velocityCtx         = NULL;
     81:   newC->fieldDA             = NULL;
     82:   newC->field               = NULL;
     83:   newC->numFieldComp        = 0;
     84:   newC->fieldComp           = NULL;
     85:   newC->fieldInterp         = NULL;
     86:   newC->fieldInterpLocal    = NULL;
     87:   newC->fieldCtx            = NULL;
     88:   newC->itemType            = 0;
     89:   newC->queue               = NULL;
     90:   newC->queueSize           = 0;
     91:   newC->queueMax            = 0;
     92:   newC->queueLocal          = NULL;
     93:   newC->queueLocalSize      = 0;
     94:   newC->queueLocalMax       = 0;
     95:   newC->queueRemote         = NULL;
     96:   newC->queueRemoteSize     = 0;
     97:   newC->queueRemoteMax      = 0;
     98:   newC->numNeighbors        = 0;
     99:   newC->neighbors           = NULL;
    100:   newC->needCount           = NULL;
    101:   newC->localOffsets        = NULL;
    102:   newC->fillCount           = NULL;
    103:   newC->remoteOffsets       = NULL;
    104:   newC->request             = NULL;
    105:   newC->status              = NULL;
    106:   PetscFunctionReturn(PETSC_SUCCESS);
    107: }

    109: /*@
    110:   CharacteristicSetType - Builds Characteristic for a particular solver.

    112:   Logically Collective

    114:   Input Parameters:
    115: + c    - the method of characteristics context
    116: - type - a known method

    118:   Options Database Key:
    119: . -characteristic_type <method> - Sets the method; use -help for a list
    120:     of available methods

    122:   Level: intermediate

    124:   Notes:
    125:   See "include/petsccharacteristic.h" for available methods

    127:   Normally, it is best to use the CharacteristicSetFromOptions() command and
    128:   then set the Characteristic type from the options database rather than by using
    129:   this routine.  Using the options database provides the user with
    130:   maximum flexibility in evaluating the many different Krylov methods.
    131:   The CharacteristicSetType() routine is provided for those situations where it
    132:   is necessary to set the iterative solver independently of the command
    133:   line or options database.  This might be the case, for example, when
    134:   the choice of iterative solver changes during the execution of the
    135:   program, and the user's application is taking responsibility for
    136:   choosing the appropriate method.  In other words, this routine is
    137:   not for beginners.

    139: .seealso: [](ch_ts), `CharacteristicType`
    140: @*/
    141: PetscErrorCode CharacteristicSetType(Characteristic c, CharacteristicType type)
    142: {
    143:   PetscBool match;
    144:   PetscErrorCode (*r)(Characteristic);

    146:   PetscFunctionBegin;
    148:   PetscAssertPointer(type, 2);

    150:   PetscCall(PetscObjectTypeCompare((PetscObject)c, type, &match));
    151:   if (match) PetscFunctionReturn(PETSC_SUCCESS);

    153:   if (c->data) {
    154:     /* destroy the old private Characteristic context */
    155:     PetscUseTypeMethod(c, destroy);
    156:     c->ops->destroy = NULL;
    157:     c->data         = NULL;
    158:   }

    160:   PetscCall(PetscFunctionListFind(CharacteristicList, type, &r));
    161:   PetscCheck(r, PetscObjectComm((PetscObject)c), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown Characteristic type given: %s", type);
    162:   c->setupcalled = 0;
    163:   PetscCall((*r)(c));
    164:   PetscCall(PetscObjectChangeTypeName((PetscObject)c, type));
    165:   PetscFunctionReturn(PETSC_SUCCESS);
    166: }

    168: /*@
    169:   CharacteristicSetUp - Sets up the internal data structures for the
    170:   later use of an iterative solver.

    172:   Collective

    174:   Input Parameter:
    175: . c - iterative context obtained from CharacteristicCreate()

    177:   Level: developer

    179: .seealso: [](ch_ts), `CharacteristicCreate()`, `CharacteristicSolve()`, `CharacteristicDestroy()`
    180: @*/
    181: PetscErrorCode CharacteristicSetUp(Characteristic c)
    182: {
    183:   PetscFunctionBegin;

    186:   if (!((PetscObject)c)->type_name) PetscCall(CharacteristicSetType(c, CHARACTERISTICDA));

    188:   if (c->setupcalled == 2) PetscFunctionReturn(PETSC_SUCCESS);

    190:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_SetUp, c, NULL, NULL, NULL));
    191:   if (!c->setupcalled) PetscUseTypeMethod(c, setup);
    192:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_SetUp, c, NULL, NULL, NULL));
    193:   c->setupcalled = 2;
    194:   PetscFunctionReturn(PETSC_SUCCESS);
    195: }

    197: /*@C
    198:   CharacteristicRegister -  Adds a solver to the method of characteristics package.

    200:   Not Collective, No Fortran Support

    202:   Input Parameters:
    203: + sname    - name of a new user-defined solver
    204: - function - routine to create method context

    206:   Level: advanced

    208:   Example Usage:
    209: .vb
    210:     CharacteristicRegister("my_char", MyCharCreate);
    211: .ve

    213:   Then, your Characteristic type can be chosen with the procedural interface via
    214: .vb
    215:     CharacteristicCreate(MPI_Comm, Characteristic* &char);
    216:     CharacteristicSetType(char,"my_char");
    217: .ve
    218:   or at runtime via the option
    219: .vb
    220:     -characteristic_type my_char
    221: .ve

    223:   Notes:
    224:   CharacteristicRegister() may be called multiple times to add several user-defined solvers.

    226: .seealso: [](ch_ts), `CharacteristicRegisterAll()`, `CharacteristicRegisterDestroy()`
    227: @*/
    228: PetscErrorCode CharacteristicRegister(const char sname[], PetscErrorCode (*function)(Characteristic))
    229: {
    230:   PetscFunctionBegin;
    231:   PetscCall(CharacteristicInitializePackage());
    232:   PetscCall(PetscFunctionListAdd(&CharacteristicList, sname, function));
    233:   PetscFunctionReturn(PETSC_SUCCESS);
    234: }

    236: PetscErrorCode CharacteristicSetVelocityInterpolation(Characteristic c, DM da, Vec v, Vec vOld, PetscInt numComponents, PetscInt components[], PetscErrorCode (*interp)(Vec, PetscReal[], PetscInt, PetscInt[], PetscScalar[], void *), void *ctx)
    237: {
    238:   PetscFunctionBegin;
    239:   c->velocityDA      = da;
    240:   c->velocity        = v;
    241:   c->velocityOld     = vOld;
    242:   c->numVelocityComp = numComponents;
    243:   c->velocityComp    = components;
    244:   c->velocityInterp  = interp;
    245:   c->velocityCtx     = ctx;
    246:   PetscFunctionReturn(PETSC_SUCCESS);
    247: }

    249: PetscErrorCode CharacteristicSetVelocityInterpolationLocal(Characteristic c, DM da, Vec v, Vec vOld, PetscInt numComponents, PetscInt components[], PetscErrorCode (*interp)(void *, PetscReal[], PetscInt, PetscInt[], PetscScalar[], void *), void *ctx)
    250: {
    251:   PetscFunctionBegin;
    252:   c->velocityDA          = da;
    253:   c->velocity            = v;
    254:   c->velocityOld         = vOld;
    255:   c->numVelocityComp     = numComponents;
    256:   c->velocityComp        = components;
    257:   c->velocityInterpLocal = interp;
    258:   c->velocityCtx         = ctx;
    259:   PetscFunctionReturn(PETSC_SUCCESS);
    260: }

    262: PetscErrorCode CharacteristicSetFieldInterpolation(Characteristic c, DM da, Vec v, PetscInt numComponents, PetscInt components[], PetscErrorCode (*interp)(Vec, PetscReal[], PetscInt, PetscInt[], PetscScalar[], void *), void *ctx)
    263: {
    264:   PetscFunctionBegin;
    265: #if 0
    266:   PetscCheck(numComponents <= 2,PETSC_COMM_SELF,PETSC_ERR_SUP, "Fields with more than 2 components are not supported. Send mail to petsc-maint@mcs.anl.gov.");
    267: #endif
    268:   c->fieldDA      = da;
    269:   c->field        = v;
    270:   c->numFieldComp = numComponents;
    271:   c->fieldComp    = components;
    272:   c->fieldInterp  = interp;
    273:   c->fieldCtx     = ctx;
    274:   PetscFunctionReturn(PETSC_SUCCESS);
    275: }

    277: PetscErrorCode CharacteristicSetFieldInterpolationLocal(Characteristic c, DM da, Vec v, PetscInt numComponents, PetscInt components[], PetscErrorCode (*interp)(void *, PetscReal[], PetscInt, PetscInt[], PetscScalar[], void *), void *ctx)
    278: {
    279:   PetscFunctionBegin;
    280: #if 0
    281:   PetscCheck(numComponents <= 2,PETSC_COMM_SELF,PETSC_ERR_SUP, "Fields with more than 2 components are not supported. Send mail to petsc-maint@mcs.anl.gov.");
    282: #endif
    283:   c->fieldDA          = da;
    284:   c->field            = v;
    285:   c->numFieldComp     = numComponents;
    286:   c->fieldComp        = components;
    287:   c->fieldInterpLocal = interp;
    288:   c->fieldCtx         = ctx;
    289:   PetscFunctionReturn(PETSC_SUCCESS);
    290: }

    292: PetscErrorCode CharacteristicSolve(Characteristic c, PetscReal dt, Vec solution)
    293: {
    294:   CharacteristicPointDA2D Qi;
    295:   DM                      da = c->velocityDA;
    296:   Vec                     velocityLocal, velocityLocalOld;
    297:   Vec                     fieldLocal;
    298:   DMDALocalInfo           info;
    299:   PetscScalar           **solArray;
    300:   void                   *velocityArray;
    301:   void                   *velocityArrayOld;
    302:   void                   *fieldArray;
    303:   PetscScalar            *interpIndices;
    304:   PetscScalar            *velocityValues, *velocityValuesOld;
    305:   PetscScalar            *fieldValues;
    306:   PetscMPIInt             rank;
    307:   PetscInt                dim;
    308:   PetscMPIInt             neighbors[9];
    309:   PetscInt                dof;
    310:   PetscInt                gx, gy;
    311:   PetscInt                n, is, ie, js, je, comp;

    313:   PetscFunctionBegin;
    314:   c->queueSize = 0;
    315:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)c), &rank));
    316:   PetscCall(DMDAGetNeighborsRank(da, neighbors));
    317:   PetscCall(CharacteristicSetNeighbors(c, 9, neighbors));
    318:   PetscCall(CharacteristicSetUp(c));
    319:   /* global and local grid info */
    320:   PetscCall(DMDAGetInfo(da, &dim, &gx, &gy, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
    321:   PetscCall(DMDAGetLocalInfo(da, &info));
    322:   is = info.xs;
    323:   ie = info.xs + info.xm;
    324:   js = info.ys;
    325:   je = info.ys + info.ym;
    326:   /* Allocation */
    327:   PetscCall(PetscMalloc1(dim, &interpIndices));
    328:   PetscCall(PetscMalloc1(c->numVelocityComp, &velocityValues));
    329:   PetscCall(PetscMalloc1(c->numVelocityComp, &velocityValuesOld));
    330:   PetscCall(PetscMalloc1(c->numFieldComp, &fieldValues));
    331:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_Solve, NULL, NULL, NULL, NULL));

    333:   /*
    334:      PART 1, AT t-dt/2
    335:     */
    336:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_QueueSetup, NULL, NULL, NULL, NULL));
    337:   /* GET POSITION AT HALF TIME IN THE PAST */
    338:   if (c->velocityInterpLocal) {
    339:     PetscCall(DMGetLocalVector(c->velocityDA, &velocityLocal));
    340:     PetscCall(DMGetLocalVector(c->velocityDA, &velocityLocalOld));
    341:     PetscCall(DMGlobalToLocalBegin(c->velocityDA, c->velocity, INSERT_VALUES, velocityLocal));
    342:     PetscCall(DMGlobalToLocalEnd(c->velocityDA, c->velocity, INSERT_VALUES, velocityLocal));
    343:     PetscCall(DMGlobalToLocalBegin(c->velocityDA, c->velocityOld, INSERT_VALUES, velocityLocalOld));
    344:     PetscCall(DMGlobalToLocalEnd(c->velocityDA, c->velocityOld, INSERT_VALUES, velocityLocalOld));
    345:     PetscCall(DMDAVecGetArray(c->velocityDA, velocityLocal, &velocityArray));
    346:     PetscCall(DMDAVecGetArray(c->velocityDA, velocityLocalOld, &velocityArrayOld));
    347:   }
    348:   PetscCall(PetscInfo(NULL, "Calculating position at t_{n - 1/2}\n"));
    349:   for (Qi.j = js; Qi.j < je; Qi.j++) {
    350:     for (Qi.i = is; Qi.i < ie; Qi.i++) {
    351:       interpIndices[0] = Qi.i;
    352:       interpIndices[1] = Qi.j;
    353:       if (c->velocityInterpLocal) PetscCall(c->velocityInterpLocal(velocityArray, interpIndices, c->numVelocityComp, c->velocityComp, velocityValues, c->velocityCtx));
    354:       else PetscCall(c->velocityInterp(c->velocity, interpIndices, c->numVelocityComp, c->velocityComp, velocityValues, c->velocityCtx));
    355:       Qi.x = Qi.i - velocityValues[0] * dt / 2.0;
    356:       Qi.y = Qi.j - velocityValues[1] * dt / 2.0;

    358:       /* Determine whether the position at t - dt/2 is local */
    359:       Qi.proc = DMDAGetNeighborRelative(da, Qi.x, Qi.y);

    361:       /* Check for Periodic boundaries and move all periodic points back onto the domain */
    362:       PetscCall(DMDAMapCoordsToPeriodicDomain(da, &Qi.x, &Qi.y));
    363:       PetscCall(CharacteristicAddPoint(c, &Qi));
    364:     }
    365:   }
    366:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_QueueSetup, NULL, NULL, NULL, NULL));

    368:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_HalfTimeExchange, NULL, NULL, NULL, NULL));
    369:   PetscCall(CharacteristicSendCoordinatesBegin(c));
    370:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_HalfTimeExchange, NULL, NULL, NULL, NULL));

    372:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_HalfTimeLocal, NULL, NULL, NULL, NULL));
    373:   /* Calculate velocity at t_n+1/2 (local values) */
    374:   PetscCall(PetscInfo(NULL, "Calculating local velocities at t_{n - 1/2}\n"));
    375:   for (n = 0; n < c->queueSize; n++) {
    376:     Qi = c->queue[n];
    377:     if (c->neighbors[Qi.proc] == rank) {
    378:       interpIndices[0] = Qi.x;
    379:       interpIndices[1] = Qi.y;
    380:       if (c->velocityInterpLocal) {
    381:         PetscCall(c->velocityInterpLocal(velocityArray, interpIndices, c->numVelocityComp, c->velocityComp, velocityValues, c->velocityCtx));
    382:         PetscCall(c->velocityInterpLocal(velocityArrayOld, interpIndices, c->numVelocityComp, c->velocityComp, velocityValuesOld, c->velocityCtx));
    383:       } else {
    384:         PetscCall(c->velocityInterp(c->velocity, interpIndices, c->numVelocityComp, c->velocityComp, velocityValues, c->velocityCtx));
    385:         PetscCall(c->velocityInterp(c->velocityOld, interpIndices, c->numVelocityComp, c->velocityComp, velocityValuesOld, c->velocityCtx));
    386:       }
    387:       Qi.x = 0.5 * (velocityValues[0] + velocityValuesOld[0]);
    388:       Qi.y = 0.5 * (velocityValues[1] + velocityValuesOld[1]);
    389:     }
    390:     c->queue[n] = Qi;
    391:   }
    392:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_HalfTimeLocal, NULL, NULL, NULL, NULL));

    394:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_HalfTimeExchange, NULL, NULL, NULL, NULL));
    395:   PetscCall(CharacteristicSendCoordinatesEnd(c));
    396:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_HalfTimeExchange, NULL, NULL, NULL, NULL));

    398:   /* Calculate velocity at t_n+1/2 (fill remote requests) */
    399:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_HalfTimeRemote, NULL, NULL, NULL, NULL));
    400:   PetscCall(PetscInfo(NULL, "Calculating %" PetscInt_FMT " remote velocities at t_{n - 1/2}\n", c->queueRemoteSize));
    401:   for (n = 0; n < c->queueRemoteSize; n++) {
    402:     Qi               = c->queueRemote[n];
    403:     interpIndices[0] = Qi.x;
    404:     interpIndices[1] = Qi.y;
    405:     if (c->velocityInterpLocal) {
    406:       PetscCall(c->velocityInterpLocal(velocityArray, interpIndices, c->numVelocityComp, c->velocityComp, velocityValues, c->velocityCtx));
    407:       PetscCall(c->velocityInterpLocal(velocityArrayOld, interpIndices, c->numVelocityComp, c->velocityComp, velocityValuesOld, c->velocityCtx));
    408:     } else {
    409:       PetscCall(c->velocityInterp(c->velocity, interpIndices, c->numVelocityComp, c->velocityComp, velocityValues, c->velocityCtx));
    410:       PetscCall(c->velocityInterp(c->velocityOld, interpIndices, c->numVelocityComp, c->velocityComp, velocityValuesOld, c->velocityCtx));
    411:     }
    412:     Qi.x              = 0.5 * (velocityValues[0] + velocityValuesOld[0]);
    413:     Qi.y              = 0.5 * (velocityValues[1] + velocityValuesOld[1]);
    414:     c->queueRemote[n] = Qi;
    415:   }
    416:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_HalfTimeRemote, NULL, NULL, NULL, NULL));
    417:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_HalfTimeExchange, NULL, NULL, NULL, NULL));
    418:   PetscCall(CharacteristicGetValuesBegin(c));
    419:   PetscCall(CharacteristicGetValuesEnd(c));
    420:   if (c->velocityInterpLocal) {
    421:     PetscCall(DMDAVecRestoreArray(c->velocityDA, velocityLocal, &velocityArray));
    422:     PetscCall(DMDAVecRestoreArray(c->velocityDA, velocityLocalOld, &velocityArrayOld));
    423:     PetscCall(DMRestoreLocalVector(c->velocityDA, &velocityLocal));
    424:     PetscCall(DMRestoreLocalVector(c->velocityDA, &velocityLocalOld));
    425:   }
    426:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_HalfTimeExchange, NULL, NULL, NULL, NULL));

    428:   /*
    429:      PART 2, AT t-dt
    430:   */

    432:   /* GET POSITION AT t_n (local values) */
    433:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_FullTimeLocal, NULL, NULL, NULL, NULL));
    434:   PetscCall(PetscInfo(NULL, "Calculating position at t_{n}\n"));
    435:   for (n = 0; n < c->queueSize; n++) {
    436:     Qi   = c->queue[n];
    437:     Qi.x = Qi.i - Qi.x * dt;
    438:     Qi.y = Qi.j - Qi.y * dt;

    440:     /* Determine whether the position at t-dt is local */
    441:     Qi.proc = DMDAGetNeighborRelative(da, Qi.x, Qi.y);

    443:     /* Check for Periodic boundaries and move all periodic points back onto the domain */
    444:     PetscCall(DMDAMapCoordsToPeriodicDomain(da, &Qi.x, &Qi.y));

    446:     c->queue[n] = Qi;
    447:   }
    448:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_FullTimeLocal, NULL, NULL, NULL, NULL));

    450:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_FullTimeExchange, NULL, NULL, NULL, NULL));
    451:   PetscCall(CharacteristicSendCoordinatesBegin(c));
    452:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_FullTimeExchange, NULL, NULL, NULL, NULL));

    454:   /* GET VALUE AT FULL TIME IN THE PAST (LOCAL REQUESTS) */
    455:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_FullTimeLocal, NULL, NULL, NULL, NULL));
    456:   if (c->fieldInterpLocal) {
    457:     PetscCall(DMGetLocalVector(c->fieldDA, &fieldLocal));
    458:     PetscCall(DMGlobalToLocalBegin(c->fieldDA, c->field, INSERT_VALUES, fieldLocal));
    459:     PetscCall(DMGlobalToLocalEnd(c->fieldDA, c->field, INSERT_VALUES, fieldLocal));
    460:     PetscCall(DMDAVecGetArray(c->fieldDA, fieldLocal, &fieldArray));
    461:   }
    462:   PetscCall(PetscInfo(NULL, "Calculating local field at t_{n}\n"));
    463:   for (n = 0; n < c->queueSize; n++) {
    464:     if (c->neighbors[c->queue[n].proc] == rank) {
    465:       interpIndices[0] = c->queue[n].x;
    466:       interpIndices[1] = c->queue[n].y;
    467:       if (c->fieldInterpLocal) PetscCall(c->fieldInterpLocal(fieldArray, interpIndices, c->numFieldComp, c->fieldComp, fieldValues, c->fieldCtx));
    468:       else PetscCall(c->fieldInterp(c->field, interpIndices, c->numFieldComp, c->fieldComp, fieldValues, c->fieldCtx));
    469:       for (comp = 0; comp < c->numFieldComp; comp++) c->queue[n].field[comp] = fieldValues[comp];
    470:     }
    471:   }
    472:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_FullTimeLocal, NULL, NULL, NULL, NULL));

    474:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_FullTimeExchange, NULL, NULL, NULL, NULL));
    475:   PetscCall(CharacteristicSendCoordinatesEnd(c));
    476:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_FullTimeExchange, NULL, NULL, NULL, NULL));

    478:   /* GET VALUE AT FULL TIME IN THE PAST (REMOTE REQUESTS) */
    479:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_FullTimeRemote, NULL, NULL, NULL, NULL));
    480:   PetscCall(PetscInfo(NULL, "Calculating %" PetscInt_FMT " remote field points at t_{n}\n", c->queueRemoteSize));
    481:   for (n = 0; n < c->queueRemoteSize; n++) {
    482:     interpIndices[0] = c->queueRemote[n].x;
    483:     interpIndices[1] = c->queueRemote[n].y;

    485:     /* for debugging purposes */
    486:     if (1) { /* hacked bounds test...let's do better */
    487:       PetscScalar im = interpIndices[0];
    488:       PetscScalar jm = interpIndices[1];

    490:       PetscCheck((im >= (PetscScalar)is - 1.) && (im <= (PetscScalar)ie) && (jm >= (PetscScalar)js - 1.) && (jm <= (PetscScalar)je), PETSC_COMM_SELF, PETSC_ERR_LIB, "Nonlocal point: (%g,%g)", (double)PetscAbsScalar(im), (double)PetscAbsScalar(jm));
    491:     }

    493:     if (c->fieldInterpLocal) PetscCall(c->fieldInterpLocal(fieldArray, interpIndices, c->numFieldComp, c->fieldComp, fieldValues, c->fieldCtx));
    494:     else PetscCall(c->fieldInterp(c->field, interpIndices, c->numFieldComp, c->fieldComp, fieldValues, c->fieldCtx));
    495:     for (comp = 0; comp < c->numFieldComp; comp++) c->queueRemote[n].field[comp] = fieldValues[comp];
    496:   }
    497:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_FullTimeRemote, NULL, NULL, NULL, NULL));

    499:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_FullTimeExchange, NULL, NULL, NULL, NULL));
    500:   PetscCall(CharacteristicGetValuesBegin(c));
    501:   PetscCall(CharacteristicGetValuesEnd(c));
    502:   if (c->fieldInterpLocal) {
    503:     PetscCall(DMDAVecRestoreArray(c->fieldDA, fieldLocal, &fieldArray));
    504:     PetscCall(DMRestoreLocalVector(c->fieldDA, &fieldLocal));
    505:   }
    506:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_FullTimeExchange, NULL, NULL, NULL, NULL));

    508:   /* Return field of characteristics at t_n-1 */
    509:   PetscCall(PetscLogEventBegin(CHARACTERISTIC_DAUpdate, NULL, NULL, NULL, NULL));
    510:   PetscCall(DMDAGetInfo(c->fieldDA, NULL, NULL, NULL, NULL, NULL, NULL, NULL, &dof, NULL, NULL, NULL, NULL, NULL));
    511:   PetscCall(DMDAVecGetArray(c->fieldDA, solution, &solArray));
    512:   for (n = 0; n < c->queueSize; n++) {
    513:     Qi = c->queue[n];
    514:     for (comp = 0; comp < c->numFieldComp; comp++) solArray[Qi.j][Qi.i * dof + c->fieldComp[comp]] = Qi.field[comp];
    515:   }
    516:   PetscCall(DMDAVecRestoreArray(c->fieldDA, solution, &solArray));
    517:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_DAUpdate, NULL, NULL, NULL, NULL));
    518:   PetscCall(PetscLogEventEnd(CHARACTERISTIC_Solve, NULL, NULL, NULL, NULL));

    520:   /* Cleanup */
    521:   PetscCall(PetscFree(interpIndices));
    522:   PetscCall(PetscFree(velocityValues));
    523:   PetscCall(PetscFree(velocityValuesOld));
    524:   PetscCall(PetscFree(fieldValues));
    525:   PetscFunctionReturn(PETSC_SUCCESS);
    526: }

    528: PetscErrorCode CharacteristicSetNeighbors(Characteristic c, PetscInt numNeighbors, PetscMPIInt neighbors[])
    529: {
    530:   PetscFunctionBegin;
    531:   c->numNeighbors = (PetscMPIInt)numNeighbors;
    532:   PetscCall(PetscFree(c->neighbors));
    533:   PetscCall(PetscMalloc1(numNeighbors, &c->neighbors));
    534:   PetscCall(PetscArraycpy(c->neighbors, neighbors, numNeighbors));
    535:   PetscFunctionReturn(PETSC_SUCCESS);
    536: }

    538: PetscErrorCode CharacteristicAddPoint(Characteristic c, CharacteristicPointDA2D *point)
    539: {
    540:   PetscFunctionBegin;
    541:   PetscCheck(c->queueSize < c->queueMax, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Exceeded maximum queue size %" PetscInt_FMT, c->queueMax);
    542:   c->queue[c->queueSize++] = *point;
    543:   PetscFunctionReturn(PETSC_SUCCESS);
    544: }

    546: PetscErrorCode CharacteristicSendCoordinatesBegin(Characteristic c)
    547: {
    548:   PetscMPIInt rank, tag = 121;
    549:   PetscInt    i, n;

    551:   PetscFunctionBegin;
    552:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)c), &rank));
    553:   PetscCall(CharacteristicHeapSort(c, c->queue, c->queueSize));
    554:   PetscCall(PetscArrayzero(c->needCount, c->numNeighbors));
    555:   for (i = 0; i < c->queueSize; i++) c->needCount[c->queue[i].proc]++;
    556:   c->fillCount[0] = 0;
    557:   for (n = 1; n < c->numNeighbors; n++) PetscCallMPI(MPIU_Irecv(&c->fillCount[n], 1, MPIU_INT, c->neighbors[n], tag, PetscObjectComm((PetscObject)c), &c->request[n - 1]));
    558:   for (n = 1; n < c->numNeighbors; n++) PetscCallMPI(MPIU_Send(&c->needCount[n], 1, MPIU_INT, c->neighbors[n], tag, PetscObjectComm((PetscObject)c)));
    559:   PetscCallMPI(MPI_Waitall(c->numNeighbors - 1, c->request, c->status));
    560:   /* Initialize the remote queue */
    561:   c->queueLocalMax = c->localOffsets[0] = 0;
    562:   c->queueRemoteMax = c->remoteOffsets[0] = 0;
    563:   for (n = 1; n < c->numNeighbors; n++) {
    564:     c->remoteOffsets[n] = c->queueRemoteMax;
    565:     c->queueRemoteMax += c->fillCount[n];
    566:     c->localOffsets[n] = c->queueLocalMax;
    567:     c->queueLocalMax += c->needCount[n];
    568:   }
    569:   /* HACK BEGIN */
    570:   for (n = 1; n < c->numNeighbors; n++) c->localOffsets[n] += c->needCount[0];
    571:   c->needCount[0] = 0;
    572:   /* HACK END */
    573:   if (c->queueRemoteMax) {
    574:     PetscCall(PetscMalloc1(c->queueRemoteMax, &c->queueRemote));
    575:   } else c->queueRemote = NULL;
    576:   c->queueRemoteSize = c->queueRemoteMax;

    578:   /* Send and Receive requests for values at t_n+1/2, giving the coordinates for interpolation */
    579:   for (n = 1; n < c->numNeighbors; n++) {
    580:     PetscCall(PetscInfo(NULL, "Receiving %" PetscInt_FMT " requests for values from proc %d\n", c->fillCount[n], c->neighbors[n]));
    581:     PetscCallMPI(MPIU_Irecv(&(c->queueRemote[c->remoteOffsets[n]]), c->fillCount[n], c->itemType, c->neighbors[n], tag, PetscObjectComm((PetscObject)c), &c->request[n - 1]));
    582:   }
    583:   for (n = 1; n < c->numNeighbors; n++) {
    584:     PetscCall(PetscInfo(NULL, "Sending %" PetscInt_FMT " requests for values from proc %d\n", c->needCount[n], c->neighbors[n]));
    585:     PetscCallMPI(MPIU_Send(&(c->queue[c->localOffsets[n]]), c->needCount[n], c->itemType, c->neighbors[n], tag, PetscObjectComm((PetscObject)c)));
    586:   }
    587:   PetscFunctionReturn(PETSC_SUCCESS);
    588: }

    590: PetscErrorCode CharacteristicSendCoordinatesEnd(Characteristic c)
    591: {
    592: #if 0
    593:   PetscMPIInt rank;
    594:   PetscInt    n;
    595: #endif

    597:   PetscFunctionBegin;
    598:   PetscCallMPI(MPI_Waitall(c->numNeighbors - 1, c->request, c->status));
    599: #if 0
    600:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)c), &rank));
    601:   for (n = 0; n < c->queueRemoteSize; n++) {
    602:     PetscCheck(c->neighbors[c->queueRemote[n].proc] != rank,PETSC_COMM_SELF,PETSC_ERR_PLIB, "This is messed up, n = %d proc = %d", n, c->queueRemote[n].proc);
    603:   }
    604: #endif
    605:   PetscFunctionReturn(PETSC_SUCCESS);
    606: }

    608: PetscErrorCode CharacteristicGetValuesBegin(Characteristic c)
    609: {
    610:   PetscMPIInt tag = 121;
    611:   PetscInt    n;

    613:   PetscFunctionBegin;
    614:   /* SEND AND RECEIVE FILLED REQUESTS for velocities at t_n+1/2 */
    615:   for (n = 1; n < c->numNeighbors; n++) PetscCallMPI(MPIU_Irecv(&(c->queue[c->localOffsets[n]]), c->needCount[n], c->itemType, c->neighbors[n], tag, PetscObjectComm((PetscObject)c), &c->request[n - 1]));
    616:   for (n = 1; n < c->numNeighbors; n++) PetscCallMPI(MPIU_Send(&(c->queueRemote[c->remoteOffsets[n]]), c->fillCount[n], c->itemType, c->neighbors[n], tag, PetscObjectComm((PetscObject)c)));
    617:   PetscFunctionReturn(PETSC_SUCCESS);
    618: }

    620: PetscErrorCode CharacteristicGetValuesEnd(Characteristic c)
    621: {
    622:   PetscFunctionBegin;
    623:   PetscCallMPI(MPI_Waitall(c->numNeighbors - 1, c->request, c->status));
    624:   /* Free queue of requests from other procs */
    625:   PetscCall(PetscFree(c->queueRemote));
    626:   PetscFunctionReturn(PETSC_SUCCESS);
    627: }

    629: /*
    630:   Based on code from http://linux.wku.edu/~lamonml/algor/sort/heap.html
    631: */
    632: static PetscErrorCode CharacteristicHeapSort(Characteristic c, Queue queue, PetscInt size)
    633: {
    634:   CharacteristicPointDA2D temp;
    635:   PetscInt                n;

    637:   PetscFunctionBegin;
    638:   if (0) { /* Check the order of the queue before sorting */
    639:     PetscCall(PetscInfo(NULL, "Before Heap sort\n"));
    640:     for (n = 0; n < size; n++) PetscCall(PetscInfo(NULL, "%" PetscInt_FMT " %d\n", n, queue[n].proc));
    641:   }

    643:   /* SORTING PHASE */
    644:   for (n = (size / 2) - 1; n >= 0; n--) { PetscCall(CharacteristicSiftDown(c, queue, n, size - 1)); /* Rich had size-1 here, Matt had size*/ }
    645:   for (n = size - 1; n >= 1; n--) {
    646:     temp     = queue[0];
    647:     queue[0] = queue[n];
    648:     queue[n] = temp;
    649:     PetscCall(CharacteristicSiftDown(c, queue, 0, n - 1));
    650:   }
    651:   if (0) { /* Check the order of the queue after sorting */
    652:     PetscCall(PetscInfo(NULL, "Avter  Heap sort\n"));
    653:     for (n = 0; n < size; n++) PetscCall(PetscInfo(NULL, "%" PetscInt_FMT " %d\n", n, queue[n].proc));
    654:   }
    655:   PetscFunctionReturn(PETSC_SUCCESS);
    656: }

    658: /*
    659:   Based on code from http://linux.wku.edu/~lamonml/algor/sort/heap.html
    660: */
    661: static PetscErrorCode CharacteristicSiftDown(Characteristic c, Queue queue, PetscInt root, PetscInt bottom)
    662: {
    663:   PetscBool               done = PETSC_FALSE;
    664:   PetscInt                maxChild;
    665:   CharacteristicPointDA2D temp;

    667:   PetscFunctionBegin;
    668:   while ((root * 2 <= bottom) && (!done)) {
    669:     if (root * 2 == bottom) maxChild = root * 2;
    670:     else if (queue[root * 2].proc > queue[root * 2 + 1].proc) maxChild = root * 2;
    671:     else maxChild = root * 2 + 1;

    673:     if (queue[root].proc < queue[maxChild].proc) {
    674:       temp            = queue[root];
    675:       queue[root]     = queue[maxChild];
    676:       queue[maxChild] = temp;
    677:       root            = maxChild;
    678:     } else done = PETSC_TRUE;
    679:   }
    680:   PetscFunctionReturn(PETSC_SUCCESS);
    681: }

    683: /* [center, left, top-left, top, top-right, right, bottom-right, bottom, bottom-left] */
    684: static PetscErrorCode DMDAGetNeighborsRank(DM da, PetscMPIInt neighbors[])
    685: {
    686:   DMBoundaryType bx, by;
    687:   PetscBool      IPeriodic = PETSC_FALSE, JPeriodic = PETSC_FALSE;
    688:   MPI_Comm       comm;
    689:   PetscMPIInt    rank;
    690:   PetscMPIInt  **procs, pi, pj, pim, pip, pjm, pjp;
    691:   PetscInt       PI, PJ;

    693:   PetscFunctionBegin;
    694:   PetscCall(PetscObjectGetComm((PetscObject)da, &comm));
    695:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    696:   PetscCall(DMDAGetInfo(da, NULL, NULL, NULL, NULL, &PI, &PJ, NULL, NULL, NULL, &bx, &by, NULL, NULL));

    698:   if (bx == DM_BOUNDARY_PERIODIC) IPeriodic = PETSC_TRUE;
    699:   if (by == DM_BOUNDARY_PERIODIC) JPeriodic = PETSC_TRUE;

    701:   neighbors[0] = rank;
    702:   rank         = 0;
    703:   PetscCall(PetscMalloc1(PJ, &procs));
    704:   for (pj = 0; pj < PJ; pj++) {
    705:     PetscCall(PetscMalloc1(PI, &procs[pj]));
    706:     for (pi = 0; pi < PI; pi++) {
    707:       procs[pj][pi] = rank;
    708:       rank++;
    709:     }
    710:   }

    712:   pi  = neighbors[0] % PI;
    713:   pj  = neighbors[0] / PI;
    714:   pim = pi - 1;
    715:   if (pim < 0) pim = (PetscMPIInt)PI - 1;
    716:   pip = (pi + 1) % (PetscMPIInt)PI;
    717:   pjm = pj - 1;
    718:   if (pjm < 0) pjm = (PetscMPIInt)PJ - 1;
    719:   pjp = (pj + 1) % (PetscMPIInt)PJ;

    721:   neighbors[1] = procs[pj][pim];
    722:   neighbors[2] = procs[pjp][pim];
    723:   neighbors[3] = procs[pjp][pi];
    724:   neighbors[4] = procs[pjp][pip];
    725:   neighbors[5] = procs[pj][pip];
    726:   neighbors[6] = procs[pjm][pip];
    727:   neighbors[7] = procs[pjm][pi];
    728:   neighbors[8] = procs[pjm][pim];

    730:   if (!IPeriodic) {
    731:     if (pi == 0) neighbors[1] = neighbors[2] = neighbors[8] = neighbors[0];
    732:     if (pi == PI - 1) neighbors[4] = neighbors[5] = neighbors[6] = neighbors[0];
    733:   }

    735:   if (!JPeriodic) {
    736:     if (pj == 0) neighbors[6] = neighbors[7] = neighbors[8] = neighbors[0];
    737:     if (pj == PJ - 1) neighbors[2] = neighbors[3] = neighbors[4] = neighbors[0];
    738:   }

    740:   for (pj = 0; pj < PJ; pj++) PetscCall(PetscFree(procs[pj]));
    741:   PetscCall(PetscFree(procs));
    742:   PetscFunctionReturn(PETSC_SUCCESS);
    743: }

    745: /*
    746:   SUBDOMAIN NEIGHBORHOOD PROCESS MAP:
    747:     2 | 3 | 4
    748:     __|___|__
    749:     1 | 0 | 5
    750:     __|___|__
    751:     8 | 7 | 6
    752:       |   |
    753: */
    754: static PetscMPIInt DMDAGetNeighborRelative(DM da, PetscReal ir, PetscReal jr)
    755: {
    756:   DMDALocalInfo info;
    757:   PetscReal     is, ie, js, je;

    759:   PetscCallAbort(PETSC_COMM_SELF, DMDAGetLocalInfo(da, &info));
    760:   is = (PetscReal)info.xs - 0.5;
    761:   ie = (PetscReal)info.xs + info.xm - 0.5;
    762:   js = (PetscReal)info.ys - 0.5;
    763:   je = (PetscReal)info.ys + info.ym - 0.5;

    765:   if (ir >= is && ir <= ie) { /* center column */
    766:     if (jr >= js && jr <= je) return 0;
    767:     else if (jr < js) return 7;
    768:     else return 3;
    769:   } else if (ir < is) { /* left column */
    770:     if (jr >= js && jr <= je) return 1;
    771:     else if (jr < js) return 8;
    772:     else return 2;
    773:   } else { /* right column */
    774:     if (jr >= js && jr <= je) return 5;
    775:     else if (jr < js) return 6;
    776:     else return 4;
    777:   }
    778: }