Actual source code: ex37.c
slepc-3.17.0 2022-03-31
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: SlepcInitialize(&argc,&argv,(char*)0,help);
33: PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL);
34: PetscOptionsGetReal(NULL,NULL,"-peclet",&peclet,NULL);
35: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
36: PetscOptionsGetInt(NULL,NULL,"-steps",&steps,NULL);
37: m = n;
38: N = m*n;
39: /* interval [0,1], homogeneous Dirichlet boundary conditions */
40: h = 1.0/(n+1.0);
41: h2 = h*h;
42: c = 2.0*epsilon*peclet/h;
43: upper = epsilon/h2+c/(2.0*h);
44: diag = 2.0*(-2.0*epsilon/h2);
45: lower = epsilon/h2-c/(2.0*h);
47: 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);
49: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
50: Generate matrix A
51: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
52: MatCreate(PETSC_COMM_WORLD,&A);
53: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
54: MatSetFromOptions(A);
55: MatSetUp(A);
56: MatGetOwnershipRange(A,&Istart,&Iend);
57: for (II=Istart;II<Iend;II++) {
58: i = II/n; j = II-i*n;
59: if (i>0) MatSetValue(A,II,II-n,lower,INSERT_VALUES);
60: if (i<m-1) MatSetValue(A,II,II+n,upper,INSERT_VALUES);
61: if (j>0) MatSetValue(A,II,II-1,lower,INSERT_VALUES);
62: if (j<n-1) MatSetValue(A,II,II+1,upper,INSERT_VALUES);
63: MatSetValue(A,II,II,diag,INSERT_VALUES);
64: }
65: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
66: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
67: 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: VecSetValue(v,i+j*n,value,INSERT_VALUES);
77: }
78: VecAssemblyBegin(v);
79: VecAssemblyEnd(v);
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Create the solver and set various options
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: MFNCreate(PETSC_COMM_WORLD,&mfn);
85: MFNSetOperator(mfn,A);
86: MFNGetFN(mfn,&f);
87: FNSetType(f,FNEXP);
88: FNSetScale(f,t,sone);
89: MFNSetFromOptions(mfn);
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Solve the problem, y=exp(t*A)*v
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: for (i=0;i<steps;i++) {
95: MFNSolve(mfn,v,v);
96: MFNGetConvergedReason(mfn,&reason);
98: MFNGetIterationNumber(mfn,&its);
99: totits += its;
100: }
102: /*
103: Optional: Get some information from the solver and display it
104: */
105: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",totits);
106: MFNGetDimensions(mfn,&ncv);
107: PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv);
108: MFNGetTolerances(mfn,&tol,&maxit);
109: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);
110: VecNorm(v,NORM_2,&norm);
111: 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: MFNDestroy(&mfn);
117: MatDestroy(&A);
118: VecDestroy(&v);
119: SlepcFinalize();
120: return 0;
121: }
123: /*TEST
125: test:
126: suffix: 1
127: args: -mfn_tol 1e-6
129: TEST*/