Date: 2022-08-02T03:14:50+00:00

Actual source code: ex1.c

      1: static char help[] = "This example demonstrates the use of DMNetwork interface for solving a simple electric circuit. \n\
      2:                       The example can be found in p.150 of 'Strang, Gilbert. Computational Science and Engineering. Wellesley, MA'.\n\n";

      4: #include <petscdmnetwork.h>
      5: #include <petscksp.h>

      7: /* The topology looks like:

      9:             (0)
     10:             /|\
     11:            / | \
     12:           /  |  \
     13:          R   R   V
     14:         /    |b3  \
     15:     b0 /    (3)    \ b1
     16:       /    /   \    R
     17:      /   R       R   \
     18:     /  /           \  \
     19:    / / b4        b5  \ \
     20:   //                   \\
     21: (1)--------- R -------- (2)
     22:              b2

     24:   Nodes:          (0), ... (3)
     25:   Branches:       b0, ... b5
     26:   Resistances:    R
     27:   Voltage source: V

     29:   Additionally, there is a current source from (1) to (0).
     30: */

     32: /*
     33:   Structures containing physical data of circuit.
     34:   Note that no topology is defined
     35: */

     37: typedef struct {
     38:   PetscInt    id;  /* node id */
     39:   PetscScalar inj; /* current injection (A) */
     40:   PetscBool   gr;  /* boundary node */
     41: } Node;

     43: typedef struct {
     44:   PetscInt    id;  /* branch id */
     45:   PetscScalar r;   /* resistance (ohms) */
     46:   PetscScalar bat; /* battery (V) */
     47: } Branch;

     49: /*
     50:   read_data: this routine fills data structures with problem data.
     51:   This can be substituted by an external parser.
     52: */

     54: PetscErrorCode read_data(PetscInt *pnnode,PetscInt *pnbranch,Node **pnode,Branch **pbranch,PetscInt **pedgelist)
     55: {
     56:   PetscInt          nnode, nbranch, i;
     57:   Branch            *branch;
     58:   Node              *node;
     59:   PetscInt          *edgelist;

     62:   nnode   = 4;
     63:   nbranch = 6;

     65:   PetscCalloc2(nnode,&node,nbranch,&branch);

     67:   for (i = 0; i < nnode; i++) {
     68:     node[i].id  = i;
     69:     node[i].inj = 0;
     70:     node[i].gr = PETSC_FALSE;
     71:   }

     73:   for (i = 0; i < nbranch; i++) {
     74:     branch[i].id  = i;
     75:     branch[i].r   = 1.0;
     76:     branch[i].bat = 0;
     77:   }

     79:   /*
     80:     Branch 1 contains a voltage source of 12.0 V
     81:     From node 0 to 1 there exists a current source of 4.0 A
     82:     Node 3 is grounded, hence the voltage is 0.
     83:   */
     84:   branch[1].bat = 12.0;
     85:   node[0].inj   = -4.0;
     86:   node[1].inj   =  4.0;
     87:   node[3].gr    =  PETSC_TRUE;

     89:   /*
     90:     edgelist is an array of len = 2*nbranch that defines the
     91:     topology of the network. For branch i we have:
     92:       edgelist[2*i]     = from node
     93:       edgelist[2*i + 1] = to node.
     94:   */
     95:   PetscCalloc1(2*nbranch, &edgelist);

     97:   for (i = 0; i < nbranch; i++) {
     98:     switch (i) {
     99:       case 0:
    100:         edgelist[2*i]     = 0;
    101:         edgelist[2*i + 1] = 1;
    102:         break;
    103:       case 1:
    104:         edgelist[2*i]     = 0;
    105:         edgelist[2*i + 1] = 2;
    106:         break;
    107:       case 2:
    108:         edgelist[2*i]     = 1;
    109:         edgelist[2*i + 1] = 2;
    110:         break;
    111:       case 3:
    112:         edgelist[2*i]     = 0;
    113:         edgelist[2*i + 1] = 3;
    114:         break;
    115:       case 4:
    116:         edgelist[2*i]     = 1;
    117:         edgelist[2*i + 1] = 3;
    118:         break;
    119:       case 5:
    120:         edgelist[2*i]     = 2;
    121:         edgelist[2*i + 1] = 3;
    122:         break;
    123:       default:
    124:         break;
    125:     }
    126:   }

    128:   /* assign pointers */
    129:   *pnnode    = nnode;
    130:   *pnbranch  = nbranch;
    131:   *pedgelist = edgelist;
    132:   *pbranch   = branch;
    133:   *pnode     = node;
    134:   return 0;
    135: }

    137: PetscErrorCode FormOperator(DM dmnetwork,Mat A,Vec b)
    138: {
    139:   Branch            *branch;
    140:   Node              *node;
    141:   PetscInt          e,v,vStart,vEnd,eStart, eEnd;
    142:   PetscInt          lofst,lofst_to,lofst_fr,row[2],col[6];
    143:   PetscBool         ghost;
    144:   const PetscInt    *cone;
    145:   PetscScalar       *barr,val[6];

    147:   MatZeroEntries(A);

    149:   VecSet(b,0.0);
    150:   VecGetArray(b,&barr);

    152:   /*
    153:     We define the current i as an "edge characteristic" and the voltage v as a "vertex characteristic".
    154:     We iterate the list of edges and vertices, query the associated voltages and currents
    155:     and use them to write the Kirchoff equations:

    157:     Branch equations: i/r + v_to - v_from     = v_source (battery)
    158:     Node equations:   sum(i_to) - sum(i_from) = i_source
    159:    */
    160:   DMNetworkGetEdgeRange(dmnetwork,&eStart,&eEnd);
    161:   for (e = 0; e < eEnd; e++) {
    162:     DMNetworkGetComponent(dmnetwork,e,0,NULL,(void**)&branch,NULL);
    163:     DMNetworkGetLocalVecOffset(dmnetwork,e,ALL_COMPONENTS,&lofst);

    165:     DMNetworkGetConnectedVertices(dmnetwork,e,&cone);
    166:     DMNetworkGetLocalVecOffset(dmnetwork,cone[0],ALL_COMPONENTS,&lofst_fr);
    167:     DMNetworkGetLocalVecOffset(dmnetwork,cone[1],ALL_COMPONENTS,&lofst_to);

    169:     /* set rhs b for Branch equation */
    170:     barr[lofst] = branch->bat;

    172:     /* set Branch equation */
    173:     row[0] = lofst;
    174:     col[0] = lofst;     val[0] =  1./branch->r;
    175:     col[1] = lofst_to;  val[1] =  1;
    176:     col[2] = lofst_fr;  val[2] = -1;
    177:     MatSetValuesLocal(A,1,row,3,col,val,ADD_VALUES);

    179:     /* set Node equation */
    180:     DMNetworkGetComponent(dmnetwork,cone[0],0,NULL,(void**)&node,NULL);

    182:     /* from node */
    183:     if (!node->gr) { /* not a boundary node */
    184:       row[0] = lofst_fr;
    185:       col[0] = lofst;   val[0] = -1;
    186:       MatSetValuesLocal(A,1,row,1,col,val,ADD_VALUES);
    187:     }

    189:     /* to node */
    190:     DMNetworkGetComponent(dmnetwork,cone[1],0,NULL,(void**)&node,NULL);

    192:     if (!node->gr) { /* not a boundary node */
    193:       row[0] = lofst_to;
    194:       col[0] = lofst;   val[0] = 1;
    195:       MatSetValuesLocal(A,1,row,1,col,val,ADD_VALUES);
    196:     }
    197:   }

    199:   /* set rhs b for Node equation */
    200:   DMNetworkGetVertexRange(dmnetwork,&vStart,&vEnd);
    201:   for (v = vStart; v < vEnd; v++) {
    202:     DMNetworkIsGhostVertex(dmnetwork,v,&ghost);
    203:     if (!ghost) {
    204:       DMNetworkGetComponent(dmnetwork,v,0,NULL,(void**)&node,NULL);
    205:       DMNetworkGetLocalVecOffset(dmnetwork,v,ALL_COMPONENTS,&lofst);

    207:       if (node->gr) { /* a boundary node */
    208:         row[0] = lofst;
    209:         col[0] = lofst;   val[0] = 1;
    210:         MatSetValuesLocal(A,1,row,1,col,val,ADD_VALUES);
    211:       } else {       /* not a boundary node */
    212:         barr[lofst] += node->inj;
    213:       }
    214:     }
    215:   }

    217:   VecRestoreArray(b,&barr);

    219:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    220:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    221:   return 0;
    222: }

    224: int main(int argc,char ** argv)
    225: {
    226:   PetscInt          i, nnode = 0, nbranch = 0, eStart, eEnd, vStart, vEnd;
    227:   PetscMPIInt       size, rank;
    228:   DM                dmnetwork;
    229:   Vec               x, b;
    230:   Mat               A;
    231:   KSP               ksp;
    232:   PetscInt          *edgelist = NULL;
    233:   PetscInt          componentkey[2];
    234:   Node              *node;
    235:   Branch            *branch;
    236:   PetscInt          nE[1];

    238:   PetscInitialize(&argc,&argv,(char*)0,help);
    239:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    240:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    242:   /* "Read" data only for processor 0 */
    243:   if (rank == 0) {
    244:     read_data(&nnode, &nbranch, &node, &branch, &edgelist);
    245:   }

    247:   DMNetworkCreate(PETSC_COMM_WORLD,&dmnetwork);
    248:   DMNetworkRegisterComponent(dmnetwork,"nstr",sizeof(Node),&componentkey[0]);
    249:   DMNetworkRegisterComponent(dmnetwork,"bsrt",sizeof(Branch),&componentkey[1]);

    251:   /* Set local number of nodes/edges, add edge connectivity */
    252:   nE[0] = nbranch;
    253:   DMNetworkSetNumSubNetworks(dmnetwork,PETSC_DECIDE,1);
    254:   DMNetworkAddSubnetwork(dmnetwork,"",nE[0],edgelist,NULL);

    256:   /* Set up the network layout */
    257:   DMNetworkLayoutSetUp(dmnetwork);

    259:   /* Add network components (physical parameters of nodes and branches) and num of variables */
    260:   if (rank == 0) {
    261:     DMNetworkGetEdgeRange(dmnetwork,&eStart,&eEnd);
    262:     for (i = eStart; i < eEnd; i++) {
    263:       DMNetworkAddComponent(dmnetwork,i,componentkey[1],&branch[i-eStart],1);
    264:     }

    266:     DMNetworkGetVertexRange(dmnetwork,&vStart,&vEnd);
    267:     for (i = vStart; i < vEnd; i++) {
    268:       DMNetworkAddComponent(dmnetwork,i,componentkey[0],&node[i-vStart],1);
    269:     }
    270:   }

    272:   /* Network partitioning and distribution of data */
    273:   DMSetUp(dmnetwork);
    274:   DMNetworkDistribute(&dmnetwork,0);

    276:   /* We do not use these data structures anymore since they have been copied to dmnetwork */
    277:   if (rank == 0) {
    278:     PetscFree(edgelist);
    279:     PetscFree2(node,branch);
    280:   }

    282:   /* Create vectors and matrix */
    283:   DMCreateGlobalVector(dmnetwork,&x);
    284:   VecDuplicate(x,&b);
    285:   DMCreateMatrix(dmnetwork,&A);

    287:   /* Assembly system of equations */
    288:   FormOperator(dmnetwork,A,b);

    290:   /* Solve linear system: A x = b */
    291:   KSPCreate(PETSC_COMM_WORLD, &ksp);
    292:   KSPSetOperators(ksp, A, A);
    293:   KSPSetFromOptions(ksp);
    294:   KSPSolve(ksp, b, x);
    295:   VecView(x, PETSC_VIEWER_STDOUT_WORLD);

    297:   /* Free work space */
    298:   VecDestroy(&x);
    299:   VecDestroy(&b);
    300:   MatDestroy(&A);
    301:   KSPDestroy(&ksp);
    302:   DMDestroy(&dmnetwork);
    303:   PetscFinalize();
    304:   return 0;
    305: }

    307: /*TEST

    309:    build:
    310:       requires: !complex double defined(PETSC_HAVE_ATTRIBUTEALIGNED)

    312:    test:
    313:       args: -ksp_monitor_short

    315:    test:
    316:       suffix: 2
    317:       nsize: 2
    318:       args: -petscpartitioner_type simple -ksp_converged_reason

    320: TEST*/