Actual source code: ex37.c
slepc-main 2024-11-15
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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: MFNConvergedReason reason;
31: PetscFunctionBeginUser;
32: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
34: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL));
35: PetscCall(PetscOptionsGetReal(NULL,NULL,"-peclet",&peclet,NULL));
36: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
37: PetscCall(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: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nAdvection diffusion via y=exp(%g*A), n=%" PetscInt_FMT ", steps=%" PetscInt_FMT ", Peclet=%g\n\n",(double)PetscRealPart(t),n,steps,(double)peclet));
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Generate matrix A
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
53: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
54: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
55: PetscCall(MatSetFromOptions(A));
56: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
57: for (II=Istart;II<Iend;II++) {
58: i = II/n; j = II-i*n;
59: if (i>0) PetscCall(MatSetValue(A,II,II-n,lower,INSERT_VALUES));
60: if (i<m-1) PetscCall(MatSetValue(A,II,II+n,upper,INSERT_VALUES));
61: if (j>0) PetscCall(MatSetValue(A,II,II-1,lower,INSERT_VALUES));
62: if (j<n-1) PetscCall(MatSetValue(A,II,II+1,upper,INSERT_VALUES));
63: PetscCall(MatSetValue(A,II,II,diag,INSERT_VALUES));
64: }
65: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
66: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
67: PetscCall(MatCreateVecs(A,NULL,&v));
69: /*
70: Set initial condition v = 256*i^2*(1-i)^2*j^2*(1-j)^2
71: */
72: for (II=Istart;II<Iend;II++) {
73: i = II/n; j = II-i*n;
74: i1h = (i+1)*h; j1h = (j+1)*h;
75: value = 256.0*i1h*i1h*(1.0-i1h)*(1.0-i1h)*(j1h*j1h)*(1.0-j1h)*(1.0-j1h);
76: PetscCall(VecSetValue(v,i+j*n,value,INSERT_VALUES));
77: }
78: PetscCall(VecAssemblyBegin(v));
79: PetscCall(VecAssemblyEnd(v));
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Create the solver and set various options
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
85: PetscCall(MFNSetOperator(mfn,A));
86: PetscCall(MFNGetFN(mfn,&f));
87: PetscCall(FNSetType(f,FNEXP));
88: PetscCall(FNSetScale(f,t,sone));
89: PetscCall(MFNSetFromOptions(mfn));
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Solve the problem, y=exp(t*A)*v
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: for (i=0;i<steps;i++) {
95: PetscCall(MFNSolve(mfn,v,v));
96: PetscCall(MFNGetConvergedReason(mfn,&reason));
97: PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
98: PetscCall(MFNGetIterationNumber(mfn,&its));
99: totits += its;
100: }
102: /*
103: Optional: Get some information from the solver and display it
104: */
105: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",totits));
106: PetscCall(MFNGetDimensions(mfn,&ncv));
107: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
108: PetscCall(MFNGetTolerances(mfn,&tol,&maxit));
109: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));
110: PetscCall(VecNorm(v,NORM_2,&norm));
111: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n",(double)PetscRealPart(t)*steps,(double)norm));
113: /*
114: Free work space
115: */
116: PetscCall(MFNDestroy(&mfn));
117: PetscCall(MatDestroy(&A));
118: PetscCall(VecDestroy(&v));
119: PetscCall(SlepcFinalize());
120: return 0;
121: }
123: /*TEST
125: test:
126: suffix: 1
127: args: -mfn_tol 1e-6
129: TEST*/