Actual source code: test16.c

slepc-3.17.0 2022-03-31
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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.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Illustrates use of NEPSetEigenvalueComparison().\n\n"
 12:   "This is a simplified version of ex20.\n"
 13:   "The command line options are:\n"
 14:   "  -n <n>, where <n> = number of grid subdivisions.\n";

 16: /*
 17:    Solve 1-D PDE
 18:             -u'' = lambda*u
 19:    on [0,1] subject to
 20:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
 21: */

 23: #include <slepcnep.h>

 25: /*
 26:    User-defined routines
 27: */
 28: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
 29: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
 30: PetscErrorCode MyEigenSort(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*);

 32: /*
 33:    User-defined application context
 34: */
 35: typedef struct {
 36:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
 37:   PetscReal   h;       /* mesh spacing */
 38: } ApplicationCtx;

 40: int main(int argc,char **argv)
 41: {
 42:   NEP            nep;             /* nonlinear eigensolver context */
 43:   Mat            F,J;             /* Function and Jacobian matrices */
 44:   ApplicationCtx ctx;             /* user-defined context */
 45:   PetscScalar    target;
 46:   RG             rg;
 47:   PetscInt       n=128;
 48:   PetscBool      terse;

 50:   SlepcInitialize(&argc,&argv,(char*)0,help);
 51:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 52:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n);
 53:   ctx.h = 1.0/(PetscReal)n;
 54:   ctx.kappa = 1.0;

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57:                Prepare nonlinear eigensolver context
 58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 60:   NEPCreate(PETSC_COMM_WORLD,&nep);

 62:   MatCreate(PETSC_COMM_WORLD,&F);
 63:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
 64:   MatSetFromOptions(F);
 65:   MatSeqAIJSetPreallocation(F,3,NULL);
 66:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 67:   MatSetUp(F);
 68:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

 70:   MatCreate(PETSC_COMM_WORLD,&J);
 71:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
 72:   MatSetFromOptions(J);
 73:   MatSeqAIJSetPreallocation(J,3,NULL);
 74:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 75:   MatSetUp(J);
 76:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

 78:   NEPSetType(nep,NEPNLEIGS);
 79:   NEPGetRG(nep,&rg);
 80:   RGSetType(rg,RGINTERVAL);
 81: #if defined(PETSC_USE_COMPLEX)
 82:   RGIntervalSetEndpoints(rg,2.0,400.0,-0.001,0.001);
 83: #else
 84:   RGIntervalSetEndpoints(rg,2.0,400.0,0,0);
 85: #endif
 86:   NEPSetTarget(nep,25.0);
 87:   NEPSetEigenvalueComparison(nep,MyEigenSort,&target);
 88:   NEPSetTolerances(nep,PETSC_SMALL,PETSC_DEFAULT);
 89:   NEPSetFromOptions(nep);
 90:   NEPGetTarget(nep,&target);

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:               Solve the eigensystem and display the solution
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 96:   NEPSolve(nep);

 98:   /* show detailed info unless -terse option is given by user */
 99:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
100:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
101:   else {
102:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
103:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
104:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
105:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
106:   }

108:   NEPDestroy(&nep);
109:   MatDestroy(&F);
110:   MatDestroy(&J);
111:   SlepcFinalize();
112:   return 0;
113: }

115: /* ------------------------------------------------------------------- */
116: /*
117:    FormFunction - Computes Function matrix  T(lambda)

119:    Input Parameters:
120: .  nep    - the NEP context
121: .  lambda - the scalar argument
122: .  ctx    - optional user-defined context, as set by NEPSetFunction()

124:    Output Parameters:
125: .  fun - Function matrix
126: .  B   - optionally different preconditioning matrix
127: */
128: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
129: {
130:   ApplicationCtx *user = (ApplicationCtx*)ctx;
131:   PetscScalar    A[3],c,d;
132:   PetscReal      h;
133:   PetscInt       i,n,j[3],Istart,Iend;
134:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

137:   /*
138:      Compute Function entries and insert into matrix
139:   */
140:   MatGetSize(fun,&n,NULL);
141:   MatGetOwnershipRange(fun,&Istart,&Iend);
142:   if (Istart==0) FirstBlock=PETSC_TRUE;
143:   if (Iend==n) LastBlock=PETSC_TRUE;
144:   h = user->h;
145:   c = user->kappa/(lambda-user->kappa);
146:   d = n;

148:   /*
149:      Interior grid points
150:   */
151:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
152:     j[0] = i-1; j[1] = i; j[2] = i+1;
153:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
154:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
155:   }

157:   /*
158:      Boundary points
159:   */
160:   if (FirstBlock) {
161:     i = 0;
162:     j[0] = 0; j[1] = 1;
163:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
164:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
165:   }

167:   if (LastBlock) {
168:     i = n-1;
169:     j[0] = n-2; j[1] = n-1;
170:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
171:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
172:   }

174:   /*
175:      Assemble matrix
176:   */
177:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
178:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
179:   if (fun != B) {
180:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
181:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
182:   }
183:   PetscFunctionReturn(0);
184: }

186: /* ------------------------------------------------------------------- */
187: /*
188:    FormJacobian - Computes Jacobian matrix  T'(lambda)

190:    Input Parameters:
191: .  nep    - the NEP context
192: .  lambda - the scalar argument
193: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

195:    Output Parameters:
196: .  jac - Jacobian matrix
197: .  B   - optionally different preconditioning matrix
198: */
199: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
200: {
201:   ApplicationCtx *user = (ApplicationCtx*)ctx;
202:   PetscScalar    A[3],c;
203:   PetscReal      h;
204:   PetscInt       i,n,j[3],Istart,Iend;
205:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

208:   /*
209:      Compute Jacobian entries and insert into matrix
210:   */
211:   MatGetSize(jac,&n,NULL);
212:   MatGetOwnershipRange(jac,&Istart,&Iend);
213:   if (Istart==0) FirstBlock=PETSC_TRUE;
214:   if (Iend==n) LastBlock=PETSC_TRUE;
215:   h = user->h;
216:   c = user->kappa/(lambda-user->kappa);

218:   /*
219:      Interior grid points
220:   */
221:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
222:     j[0] = i-1; j[1] = i; j[2] = i+1;
223:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
224:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
225:   }

227:   /*
228:      Boundary points
229:   */
230:   if (FirstBlock) {
231:     i = 0;
232:     j[0] = 0; j[1] = 1;
233:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
234:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
235:   }

237:   if (LastBlock) {
238:     i = n-1;
239:     j[0] = n-2; j[1] = n-1;
240:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
241:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
242:   }

244:   /*
245:      Assemble matrix
246:   */
247:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
248:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
249:   PetscFunctionReturn(0);
250: }

252: /*
253:     Function for user-defined eigenvalue ordering criterion.

255:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
256:     one of them as the preferred one according to the criterion.
257:     In this example, eigenvalues are sorted with respect to the target,
258:     but those on the right of the target are preferred.
259: */
260: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
261: {
262:   PetscReal   a,b;
263:   PetscScalar target = *(PetscScalar*)ctx;

266:   if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
267:   else {
268:     a = SlepcAbsEigenvalue(ar-target,ai);
269:     b = SlepcAbsEigenvalue(br-target,bi);
270:     if (a>b) *r = 1;
271:     else if (a<b) *r = -1;
272:     else *r = 0;
273:   }
274:   PetscFunctionReturn(0);
275: }

277: /*TEST

279:    test:
280:       suffix: 1
281:       args: -nep_nev 4 -nep_ncv 8 -terse
282:       requires: double !complex

284: TEST*/