Actual source code: ex17.c

petsc-3.12.2 2019-11-22
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  2: static char help[] = "Solves a linear system with KSP.  This problem is\n\
  3: intended to test the complex numbers version of various solvers.\n\n";

  5:  #include <petscksp.h>

  7: typedef enum {TEST_1,TEST_2,TEST_3,HELMHOLTZ_1,HELMHOLTZ_2} TestType;
  8: extern PetscErrorCode FormTestMatrix(Mat,PetscInt,TestType);

 10: int main(int argc,char **args)
 11: {
 12:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
 13:   Mat            A;            /* linear system matrix */
 14:   KSP            ksp;         /* KSP context */
 16:   PetscInt       n    = 10,its, dim,p = 1,use_random;
 17:   PetscScalar    none = -1.0,pfive = 0.5;
 18:   PetscReal      norm;
 19:   PetscRandom    rctx;
 20:   TestType       type;
 21:   PetscBool      flg;

 23:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 24:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 25:   PetscOptionsGetInt(NULL,NULL,"-p",&p,NULL);
 26:   switch (p) {
 27:   case 1:  type = TEST_1;      dim = n;   break;
 28:   case 2:  type = TEST_2;      dim = n;   break;
 29:   case 3:  type = TEST_3;      dim = n;   break;
 30:   case 4:  type = HELMHOLTZ_1; dim = n*n; break;
 31:   case 5:  type = HELMHOLTZ_2; dim = n*n; break;
 32:   default: type = TEST_1;      dim = n;
 33:   }

 35:   /* Create vectors */
 36:   VecCreate(PETSC_COMM_WORLD,&x);
 37:   VecSetSizes(x,PETSC_DECIDE,dim);
 38:   VecSetFromOptions(x);
 39:   VecDuplicate(x,&b);
 40:   VecDuplicate(x,&u);

 42:   use_random = 1;
 43:   flg        = PETSC_FALSE;
 44:   PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
 45:   if (flg) {
 46:     use_random = 0;
 47:     VecSet(u,pfive);
 48:   } else {
 49:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
 50:     PetscRandomSetFromOptions(rctx);
 51:     VecSetRandom(u,rctx);
 52:   }

 54:   /* Create and assemble matrix */
 55:   MatCreate(PETSC_COMM_WORLD,&A);
 56:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
 57:   MatSetFromOptions(A);
 58:   MatSetUp(A);
 59:   FormTestMatrix(A,n,type);
 60:   MatMult(A,u,b);
 61:   flg  = PETSC_FALSE;
 62:   PetscOptionsGetBool(NULL,NULL,"-printout",&flg,NULL);
 63:   if (flg) {
 64:     MatView(A,PETSC_VIEWER_STDOUT_WORLD);
 65:     VecView(u,PETSC_VIEWER_STDOUT_WORLD);
 66:     VecView(b,PETSC_VIEWER_STDOUT_WORLD);
 67:   }

 69:   /* Create KSP context; set operators and options; solve linear system */
 70:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 71:   KSPSetOperators(ksp,A,A);
 72:   KSPSetFromOptions(ksp);
 73:   KSPSolve(ksp,b,x);
 74:   /* KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD); */

 76:   /* Check error */
 77:   VecAXPY(x,none,u);
 78:   VecNorm(x,NORM_2,&norm);
 79:   KSPGetIterationNumber(ksp,&its);
 80:   if (norm >= 1.e-12) {
 81:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
 82:   } else {
 83:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12, Iterations %D\n",its);
 84:   }

 86:   /* Free work space */
 87:   VecDestroy(&x); VecDestroy(&u);
 88:   VecDestroy(&b); MatDestroy(&A);
 89:   if (use_random) {PetscRandomDestroy(&rctx);}
 90:   KSPDestroy(&ksp);
 91:   PetscFinalize();
 92:   return ierr;
 93: }

 95: PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
 96: {
 97:   PetscScalar    val[5];
 99:   PetscInt       i,j,Ii,J,col[5],Istart,Iend;

101:   MatGetOwnershipRange(A,&Istart,&Iend);
102:   if (type == TEST_1) {
103:     val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
104:     for (i=1; i<n-1; i++) {
105:       col[0] = i-1; col[1] = i; col[2] = i+1;
106:       MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
107:     }
108:     i    = n-1; col[0] = n-2; col[1] = n-1;
109:     MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
110:     i    = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
111:     MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
112:   } else if (type == TEST_2) {
113:     val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
114:     for (i=2; i<n-1; i++) {
115:       col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
116:       MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
117:     }
118:     i    = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
119:     MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
120:     i    = 1; col[0] = 0; col[1] = 1; col[2] = 2;
121:     MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);
122:     i    = 0;
123:     MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);
124:   } else if (type == TEST_3) {
125:     val[0] = PETSC_i * 2.0;
126:     val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
127:     for (i=1; i<n-3; i++) {
128:       col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
129:       MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);
130:     }
131:     i    = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
132:     MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
133:     i    = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
134:     MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
135:     i    = n-1; col[0] = n-2; col[1] = n-1;
136:     MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
137:     i    = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
138:     MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);
139:   } else if (type == HELMHOLTZ_1) {
140:     /* Problem domain: unit square: (0,1) x (0,1)
141:        Solve Helmholtz equation:
142:           -delta u - sigma1*u + i*sigma2*u = f,
143:            where delta = Laplace operator
144:        Dirichlet b.c.'s on all sides
145:      */
146:     PetscRandom rctx;
147:     PetscReal   h2,sigma1 = 5.0;
148:     PetscScalar sigma2;
149:     PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
150:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
151:     PetscRandomSetFromOptions(rctx);
152:     PetscRandomSetInterval(rctx,0.0,PETSC_i);
153:     h2   = 1.0/((n+1)*(n+1));
154:     for (Ii=Istart; Ii<Iend; Ii++) {
155:       *val = -1.0; i = Ii/n; j = Ii - i*n;
156:       if (i>0) {
157:         J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
158:       }
159:       if (i<n-1) {
160:         J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
161:       }
162:       if (j>0) {
163:         J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
164:       }
165:       if (j<n-1) {
166:         J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
167:       }
168:       PetscRandomGetValue(rctx,&sigma2);
169:       *val = 4.0 - sigma1*h2 + sigma2*h2;
170:       MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
171:     }
172:     PetscRandomDestroy(&rctx);
173:   } else if (type == HELMHOLTZ_2) {
174:     /* Problem domain: unit square: (0,1) x (0,1)
175:        Solve Helmholtz equation:
176:           -delta u - sigma1*u = f,
177:            where delta = Laplace operator
178:        Dirichlet b.c.'s on 3 sides
179:        du/dn = i*alpha*u on (1,y), 0<y<1
180:      */
181:     PetscReal   h2,sigma1 = 200.0;
182:     PetscScalar alpha_h;
183:     PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
184:     h2      = 1.0/((n+1)*(n+1));
185:     alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1);  /* alpha_h = alpha * h */
186:     for (Ii=Istart; Ii<Iend; Ii++) {
187:       *val = -1.0; i = Ii/n; j = Ii - i*n;
188:       if (i>0) {
189:         J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
190:       }
191:       if (i<n-1) {
192:         J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
193:       }
194:       if (j>0) {
195:         J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
196:       }
197:       if (j<n-1) {
198:         J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);
199:       }
200:       *val = 4.0 - sigma1*h2;
201:       if (!((Ii+1)%n)) *val += alpha_h;
202:       MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
203:     }
204:   } else SETERRQ(PetscObjectComm((PetscObject)A),1,"FormTestMatrix: unknown test matrix type");

206:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
207:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

209:   return 0;
210: }

212: /*TEST

214:     build:
215:       requires: complex

217:     test:
218:       args: -ksp_gmres_cgs_refinement_type refine_always -n 6 -ksp_monitor_short -p 5 -norandom -ksp_type gmres -pc_type jacobi -ksp_max_it 15
219:       requires: complex

221:     test:
222:       suffix: 2
223:       nsize: 3
224:       requires: complex
225:       args: -ksp_gmres_cgs_refinement_type refine_always -n 6 -ksp_monitor_short -p 5 -norandom -ksp_type gmres -pc_type jacobi -ksp_max_it 15
226:       output_file: output/ex17_1.out

228:     test:
229:       suffix: superlu_dist
230:       requires: superlu_dist complex
231:       args: -n 6 -p 5 -norandom -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_colperm MMD_ATA 

233:     test:
234:       suffix: superlu_dist_2
235:       requires: superlu_dist complex
236:       nsize: 3
237:       output_file: output/ex17_superlu_dist.out
238:       args: -n 6 -p 5 -norandom -pc_type lu -pc_factor_mat_solver_type superlu_dist -mat_superlu_dist_colperm MMD_ATA

240: TEST*/