Actual source code: test16.c

slepc-3.18.3 2023-03-24
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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;

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

 57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 58:                Prepare nonlinear eigensolver context
 59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 61:   NEPCreate(PETSC_COMM_WORLD,&nep);

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

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

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

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:               Solve the eigensystem and display the solution
 95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 97:   NEPSolve(nep);

 99:   /* show detailed info unless -terse option is given by user */
100:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
101:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
102:   else {
103:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
104:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
105:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
106:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
107:   }

109:   NEPDestroy(&nep);
110:   MatDestroy(&F);
111:   MatDestroy(&J);
112:   SlepcFinalize();
113:   return 0;
114: }

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

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

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

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

149:   /*
150:      Interior grid points
151:   */
152:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
153:     j[0] = i-1; j[1] = i; j[2] = i+1;
154:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
155:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
156:   }

158:   /*
159:      Boundary points
160:   */
161:   if (FirstBlock) {
162:     i = 0;
163:     j[0] = 0; j[1] = 1;
164:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
165:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
166:   }

168:   if (LastBlock) {
169:     i = n-1;
170:     j[0] = n-2; j[1] = n-1;
171:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
172:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
173:   }

175:   /*
176:      Assemble matrix
177:   */
178:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
179:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
180:   if (fun != B) {
181:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
182:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
183:   }
184:   return 0;
185: }

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

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

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

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

219:   /*
220:      Interior grid points
221:   */
222:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
223:     j[0] = i-1; j[1] = i; j[2] = i+1;
224:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
225:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
226:   }

228:   /*
229:      Boundary points
230:   */
231:   if (FirstBlock) {
232:     i = 0;
233:     j[0] = 0; j[1] = 1;
234:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
235:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
236:   }

238:   if (LastBlock) {
239:     i = n-1;
240:     j[0] = n-2; j[1] = n-1;
241:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
242:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
243:   }

245:   /*
246:      Assemble matrix
247:   */
248:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
249:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
250:   return 0;
251: }

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

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

267:   if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
268:   else {
269:     a = SlepcAbsEigenvalue(ar-target,ai);
270:     b = SlepcAbsEigenvalue(br-target,bi);
271:     if (a>b) *r = 1;
272:     else if (a<b) *r = -1;
273:     else *r = 0;
274:   }
275:   return 0;
276: }

278: /*TEST

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

285: TEST*/