Actual source code: ex37.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Computes exp(t*A)*v for an advection diffusion operator with Peclet number.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <idim>, where <idim> = number of subdivisions of the mesh in each spatial direction.\n"
 14:   "  -t <sval>, where <sval> = scalar value that multiplies the argument.\n"
 15:   "  -peclet <sval>, where <sval> = Peclet value.\n"
 16:   "  -steps <ival>, where <ival> = number of time steps.\n\n";

 18: #include <slepcmfn.h>

 20: int main(int argc,char **argv)
 21: {
 22:   Mat                A;           /* problem matrix */
 23:   MFN                mfn;
 24:   FN                 f;
 25:   PetscInt           i,j,Istart,Iend,II,m,n=10,N,steps=5,its,totits=0,ncv,maxit;
 26:   PetscReal          tol,norm,h,h2,peclet=0.5,epsilon=1.0,c,i1h,j1h;
 27:   PetscScalar        t=1e-4,sone=1.0,value,upper,diag,lower;
 28:   Vec                v;
 29:   PetscErrorCode     ierr;
 30:   MFNConvergedReason reason;

 32:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 34:   PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL);
 35:   PetscOptionsGetReal(NULL,NULL,"-peclet",&peclet,NULL);
 36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 37:   PetscOptionsGetInt(NULL,NULL,"-steps",&steps,NULL);
 38:   m = n;
 39:   N = m*n;
 40:   /* interval [0,1], homogeneous Dirichlet boundary conditions */
 41:   h = 1.0/(n+1.0);
 42:   h2 = h*h;
 43:   c = 2.0*epsilon*peclet/h;
 44:   upper = epsilon/h2+c/(2.0*h);
 45:   diag = 2.0*(-2.0*epsilon/h2);
 46:   lower = epsilon/h2-c/(2.0*h);

 48:   PetscPrintf(PETSC_COMM_WORLD,"\nAdvection diffusion via y=exp(%g*A), n=%D, steps=%D, Peclet=%g\n\n",(double)PetscRealPart(t),n,steps,(double)peclet);

 50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51:                 Generate matrix A
 52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 53:   MatCreate(PETSC_COMM_WORLD,&A);
 54:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 55:   MatSetFromOptions(A);
 56:   MatSetUp(A);
 57:   MatGetOwnershipRange(A,&Istart,&Iend);
 58:   for (II=Istart;II<Iend;II++) {
 59:     i = II/n; j = II-i*n;
 60:     if (i>0) { MatSetValue(A,II,II-n,lower,INSERT_VALUES); }
 61:     if (i<m-1) { MatSetValue(A,II,II+n,upper,INSERT_VALUES); }
 62:     if (j>0) { MatSetValue(A,II,II-1,lower,INSERT_VALUES); }
 63:     if (j<n-1) { MatSetValue(A,II,II+1,upper,INSERT_VALUES); }
 64:     MatSetValue(A,II,II,diag,INSERT_VALUES);
 65:   }
 66:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 67:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 68:   MatCreateVecs(A,NULL,&v);

 70:   /*
 71:      Set initial condition v = 256*i^2*(1-i)^2*j^2*(1-j)^2
 72:   */
 73:   for (II=Istart;II<Iend;II++) {
 74:     i = II/n; j = II-i*n;
 75:     i1h = (i+1)*h; j1h = (j+1)*h;
 76:     value = 256.0*i1h*i1h*(1.0-i1h)*(1.0-i1h)*(j1h*j1h)*(1.0-j1h)*(1.0-j1h);
 77:     VecSetValue(v,i+j*n,value,INSERT_VALUES);
 78:   }
 79:   VecAssemblyBegin(v);
 80:   VecAssemblyEnd(v);

 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:                 Create the solver and set various options
 84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 85:   MFNCreate(PETSC_COMM_WORLD,&mfn);
 86:   MFNSetOperator(mfn,A);
 87:   MFNGetFN(mfn,&f);
 88:   FNSetType(f,FNEXP);
 89:   FNSetScale(f,t,sone);
 90:   MFNSetFromOptions(mfn);

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:                       Solve the problem, y=exp(t*A)*v
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 95:   for (i=0;i<steps;i++) {
 96:     MFNSolve(mfn,v,v);
 97:     MFNGetConvergedReason(mfn,&reason);
 98:     if (reason<0) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
 99:     MFNGetIterationNumber(mfn,&its);
100:     totits += its;
101:   }

103:   /*
104:      Optional: Get some information from the solver and display it
105:   */
106:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",totits);
107:   MFNGetDimensions(mfn,&ncv);
108:   PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %D\n",ncv);
109:   MFNGetTolerances(mfn,&tol,&maxit);
110:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);
111:   VecNorm(v,NORM_2,&norm);
112:   PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n",(double)PetscRealPart(t)*steps,(double)norm);

114:   /*
115:      Free work space
116:   */
117:   MFNDestroy(&mfn);
118:   MatDestroy(&A);
119:   VecDestroy(&v);
120:   SlepcFinalize();
121:   return ierr;
122: }

124: /*TEST

126:    test:
127:       suffix: 1
128:       args: -mfn_tol 1e-6

130: TEST*/