Actual source code: ex3.c

  1: /*$Id: ex3.c,v 1.33 2001/08/07 21:30:54 bsmith Exp $*/

  3: static char help[] = "Solves a linear system in parallel with SLES.  The matrixn
  4: uses simple bilinear elements on the unit square.  To test the paralleln
  5: matrix assembly, the matrix is intentionally laid out across processorsn
  6: differently from the way it is assembled.  Input arguments are:n
  7:   -m <size> : problem sizenn";

  9: /*T
 10:    Concepts: SLES^basic parallel example
 11:    Concepts: Matrices^inserting elements by blocks
 12:    Processors: n
 13: T*/

 15: /* 
 16:   Include "petscsles.h" so that we can use SLES solvers.  Note that this file
 17:   automatically includes:
 18:      petsc.h       - base PETSc routines   petscvec.h - vectors
 19:      petscsys.h    - system routines       petscmat.h - matrices
 20:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 21:      petscviewer.h - viewers               petscpc.h  - preconditioners
 22: */
 23:  #include petscsles.h

 25: /* Declare user-defined routines */
 26: extern int FormElementStiffness(PetscReal,PetscScalar*);
 27: extern int FormElementRhs(PetscReal,PetscReal,PetscReal,PetscScalar*);

 29: int main(int argc,char **args)
 30: {
 31:   Vec         u,b,ustar; /* approx solution, RHS, exact solution */
 32:   Mat         A;           /* linear system matrix */
 33:   SLES        sles;        /* linear solver context */
 34:   KSP         ksp;         /* Krylov subspace method context */
 35:   IS          is;          /* index set - used for boundary conditions */
 36:   int         N;           /* dimension of system (global) */
 37:   int         M;           /* number of elements (global) */
 38:   int         rank;        /* processor rank */
 39:   int         size;        /* size of communicator */
 40:   PetscScalar Ke[16];      /* element matrix */
 41:   PetscScalar r[4];        /* element vector */
 42:   PetscReal   h;           /* mesh width */
 43:   PetscReal   norm;        /* norm of solution error */
 44:   PetscReal   x,y;
 45:   PetscScalar val,zero = 0.0,one = 1.0,none = -1.0;
 46:   int         ierr,idx[4],count,*rows,i,m = 5,start,end,its;

 48:   PetscInitialize(&argc,&args,(char *)0,help);
 49:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 50:   N = (m+1)*(m+1);
 51:   M = m*m;
 52:   h = 1.0/m;
 53:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 54:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 57:          Compute the matrix and right-hand-side vector that define
 58:          the linear system, Au = b.
 59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 61:   /* 
 62:      Create stiffness matrix
 63:   */
 64:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&A);
 65:   MatSetFromOptions(A);
 66:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 67:   end   = start + M/size + ((M%size) > rank);

 69:   /*
 70:      Assemble matrix
 71:   */
 72:   FormElementStiffness(h*h,Ke);
 73:   for (i=start; i<end; i++) {
 74:      /* location of lower left corner of element */
 75:      x = h*(i % m); y = h*(i/m);
 76:      /* node numbers for the four corners of element */
 77:      idx[0] = (m+1)*(i/m) + (i % m);
 78:      idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 79:      MatSetValues(A,4,idx,4,idx,Ke,ADD_VALUES);
 80:   }
 81:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 82:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 84:   /*
 85:      Create right-hand-side and solution vectors
 86:   */
 87:   VecCreate(PETSC_COMM_WORLD,&u);
 88:   VecSetSizes(u,PETSC_DECIDE,N);
 89:   VecSetFromOptions(u);
 90:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 91:   VecDuplicate(u,&b);
 92:   PetscObjectSetName((PetscObject)b,"Right hand side");
 93:   VecDuplicate(b,&ustar);
 94:   VecSet(&zero,u);
 95:   VecSet(&zero,b);

 97:   /* 
 98:      Assemble right-hand-side vector
 99:   */
100:   for (i=start; i<end; i++) {
101:      /* location of lower left corner of element */
102:      x = h*(i % m); y = h*(i/m);
103:      /* node numbers for the four corners of element */
104:      idx[0] = (m+1)*(i/m) + (i % m);
105:      idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
106:      FormElementRhs(x,y,h*h,r);
107:      VecSetValues(b,4,idx,r,ADD_VALUES);
108:   }
109:   VecAssemblyBegin(b);
110:   VecAssemblyEnd(b);

112:   /* 
113:      Modify matrix and right-hand-side for Dirichlet boundary conditions
114:   */
115:   PetscMalloc(4*m*sizeof(int),&rows);
116:   for (i=0; i<m+1; i++) {
117:     rows[i] = i; /* bottom */
118:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
119:   }
120:   count = m+1; /* left side */
121:   for (i=m+1; i<m*(m+1); i+= m+1) {
122:     rows[count++] = i;
123:   }
124:   count = 2*m; /* left side */
125:   for (i=2*m+1; i<m*(m+1); i+= m+1) {
126:     rows[count++] = i;
127:   }
128:   ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
129:   for (i=0; i<4*m; i++) {
130:      x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
131:      val = y;
132:      VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
133:      VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
134:   }
135:   PetscFree(rows);
136:   VecAssemblyBegin(u);
137:   VecAssemblyEnd(u);
138:   VecAssemblyBegin(b);
139:   VecAssemblyEnd(b);

141:   MatZeroRows(A,is,&one);
142:   ISDestroy(is);

144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
145:                 Create the linear solver and set various options
146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

148:   SLESCreate(PETSC_COMM_WORLD,&sles);
149:   SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
150:   SLESGetKSP(sles,&ksp);
151:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
152:   SLESSetFromOptions(sles);

154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
155:                       Solve the linear system
156:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

158:   SLESSolve(sles,b,u,&its);

160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
161:                       Check solution and clean up
162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

164:   /* Check error */
165:   VecGetOwnershipRange(ustar,&start,&end);
166:   for (i=start; i<end; i++) {
167:      x = h*(i % (m+1)); y = h*(i/(m+1));
168:      val = y;
169:      VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
170:   }
171:   VecAssemblyBegin(ustar);
172:   VecAssemblyEnd(ustar);
173:   VecAXPY(&none,ustar,u);
174:   VecNorm(u,NORM_2,&norm);
175:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %dn",norm*h,its);

177:   /* 
178:      Free work space.  All PETSc objects should be destroyed when they
179:      are no longer needed.
180:   */
181:   SLESDestroy(sles); VecDestroy(u);
182:   VecDestroy(ustar); VecDestroy(b);
183:   MatDestroy(A);

185:   /*
186:      Always call PetscFinalize() before exiting a program.  This routine
187:        - finalizes the PETSc libraries as well as MPI
188:        - provides summary and diagnostic information if certain runtime
189:          options are chosen (e.g., -log_summary).
190:   */
191:   PetscFinalize();
192:   return 0;
193: }

195: /* --------------------------------------------------------------------- */
196:    /* element stiffness for Laplacian */
197: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
198: {
200:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
201:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
202:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
203:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
204:   return(0);
205: }
206: /* --------------------------------------------------------------------- */
207: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
208: {
210:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
211:   return(0);
212: }