Actual source code: pdde_stability.c

slepc-3.21.1 2024-04-26
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```  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.
8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11:    This example implements one of the problems found at
12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
13:        The University of Manchester.
14:    The details of the collection can be found at:
15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

18:    The pdde_stability problem is a complex-symmetric QEP from the stability
19:    analysis of a discretized partial delay-differential equation. It requires
20:    complex scalars.
21: */

23: static char help[] = "Stability analysis of a discretized partial delay-differential equation.\n\n"
24:   "The command line options are:\n"
25:   "  -m <m>, grid size, the matrices have dimension n=m*m.\n"
26:   "  -c <a0,b0,a1,b1,a2,b2,phi1>, comma-separated list of 7 real parameters.\n\n";

28: #include <slepcpep.h>

30: #define NMAT 3

32: /*
33:     Function for user-defined eigenvalue ordering criterion.

35:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
36:     one of them as the preferred one according to the criterion.
37:     In this example, the preferred value is the one with absolute value closest to 1.
38: */
39: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
40: {
41:   PetscReal aa,ab;

43:   PetscFunctionBeginUser;
44:   aa = PetscAbsReal(SlepcAbsEigenvalue(ar,ai)-PetscRealConstant(1.0));
45:   ab = PetscAbsReal(SlepcAbsEigenvalue(br,bi)-PetscRealConstant(1.0));
46:   *r = aa > ab ? 1 : (aa < ab ? -1 : 0);
47:   PetscFunctionReturn(PETSC_SUCCESS);
48: }

50: int main(int argc,char **argv)
51: {
52:   Mat            A[NMAT];         /* problem matrices */
53:   PEP            pep;             /* polynomial eigenproblem solver context */
54:   PetscInt       m=15,n,II,Istart,Iend,i,j,k;
55:   PetscReal      h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
56:   PetscScalar    alpha,beta,gamma;
57:   PetscBool      flg,terse;

59:   PetscFunctionBeginUser;
60:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
61: #if !defined(PETSC_USE_COMPLEX)
62:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example requires complex scalars");
63: #endif

65:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
66:   n = m*m;
67:   h = PETSC_PI/(m+1);
68:   gamma = PetscExpScalar(PETSC_i*c[6]);
69:   gamma = gamma/PetscAbsScalar(gamma);
70:   k = 7;
71:   PetscCall(PetscOptionsGetRealArray(NULL,NULL,"-c",c,&k,&flg));
72:   PetscCheck(!flg || k==7,PETSC_COMM_WORLD,PETSC_ERR_USER,"The number of parameters -c should be 7, you provided %" PetscInt_FMT,k);
73:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",n,m));

75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76:                      Compute the polynomial matrices
77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

79:   /* initialize matrices */
80:   for (i=0;i<NMAT;i++) {
81:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
82:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
83:     PetscCall(MatSetFromOptions(A[i]));
84:   }
85:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

87:   /* A[1] has a pattern similar to the 2D Laplacian */
88:   for (II=Istart;II<Iend;II++) {
89:     i = II/m; j = II-i*m;
90:     xi = (i+1)*h; xj = (j+1)*h;
91:     alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
92:     beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
93:     PetscCall(MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES));
94:     if (j>0) PetscCall(MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES));
95:     if (j<m-1) PetscCall(MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES));
96:     if (i>0) PetscCall(MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES));
97:     if (i<m-1) PetscCall(MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES));
98:   }

100:   /* A[0] and A[2] are diagonal */
101:   for (II=Istart;II<Iend;II++) {
102:     i = II/m; j = II-i*m;
103:     xi = (i+1)*h; xj = (j+1)*h;
104:     alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
105:     beta = c[4]+c[5]*xj*(PETSC_PI-xj);
106:     PetscCall(MatSetValue(A[0],II,II,alpha,INSERT_VALUES));
107:     PetscCall(MatSetValue(A[2],II,II,beta,INSERT_VALUES));
108:   }

110:   /* assemble matrices */
111:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
112:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115:                 Create the eigensolver and solve the problem
116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

118:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
119:   PetscCall(PEPSetOperators(pep,NMAT,A));
120:   PetscCall(PEPSetEigenvalueComparison(pep,MyEigenSort,NULL));
121:   PetscCall(PEPSetDimensions(pep,4,PETSC_DEFAULT,PETSC_DEFAULT));
122:   PetscCall(PEPSetFromOptions(pep));
123:   PetscCall(PEPSolve(pep));

125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126:                     Display solution and clean up
127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

129:   /* show detailed info unless -terse option is given by user */
130:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
131:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
132:   else {
133:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
134:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
135:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
136:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
137:   }
138:   PetscCall(PEPDestroy(&pep));
139:   for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
140:   PetscCall(SlepcFinalize());
141:   return 0;
142: }

144: /*TEST

146:    build:
147:       requires: complex

149:    test:
150:       suffix: 1
151:       args: -pep_type {{toar qarnoldi linear}} -pep_ncv 25 -terse
152:       requires: complex double

154: TEST*/
```