Actual source code: test3.c

slepc-3.8.3 2018-04-03
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2017, 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[] = "Test the SLP solver with a user-provided EPS.\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*);

 31: /*
 32:    User-defined application context
 33: */
 34: typedef struct {
 35:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
 36:   PetscReal   h;       /* mesh spacing */
 37: } ApplicationCtx;

 39: int main(int argc,char **argv)
 40: {
 41:   NEP            nep;
 42:   EPS            eps;
 43:   ST             st;
 44:   KSP            ksp;
 45:   PC             pc;
 46:   Mat            F,J;
 47:   ApplicationCtx ctx;
 48:   PetscInt       n=128;
 49:   PetscBool      terse;

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

 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:         Create a standalone EPS with appropriate settings
 60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 62:   EPSCreate(PETSC_COMM_WORLD,&eps);
 63:   EPSSetTarget(eps,0.0);
 64:   EPSGetST(eps,&st);
 65:   STSetType(st,STSINVERT);
 66:   STGetKSP(st,&ksp);
 67:   KSPSetType(ksp,KSPBCGS);
 68:   KSPGetPC(ksp,&pc);
 69:   PCSetType(pc,PCBJACOBI);
 70:   EPSSetFromOptions(eps);

 72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 73:                Prepare nonlinear eigensolver context
 74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 76:   NEPCreate(PETSC_COMM_WORLD,&nep);

 78:   /* Create Function and Jacobian matrices; set evaluation routines */
 79:   MatCreate(PETSC_COMM_WORLD,&F);
 80:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
 81:   MatSetFromOptions(F);
 82:   MatSeqAIJSetPreallocation(F,3,NULL);
 83:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 84:   MatSetUp(F);
 85:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

 87:   MatCreate(PETSC_COMM_WORLD,&J);
 88:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
 89:   MatSetFromOptions(J);
 90:   MatSeqAIJSetPreallocation(J,3,NULL);
 91:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 92:   MatSetUp(J);
 93:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

 95:   NEPSetType(nep,NEPSLP);
 96:   NEPSLPSetEPS(nep,eps);
 97:   NEPSetFromOptions(nep);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:                       Solve the eigensystem
101:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

103:   NEPSolve(nep);

105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106:                     Display solution and clean up
107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

109:   /* show detailed info unless -terse option is given by user */
110:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
111:   if (terse) {
112:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
113:   } else {
114:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
115:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
116:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
117:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
118:   }

120:   NEPDestroy(&nep);
121:   EPSDestroy(&eps);
122:   MatDestroy(&F);
123:   MatDestroy(&J);
124:   SlepcFinalize();
125:   return ierr;
126: }

128: /* ------------------------------------------------------------------- */
129: /*
130:    FormFunction - Computes Function matrix  T(lambda)

132:    Input Parameters:
133: .  nep    - the NEP context
134: .  lambda - the scalar argument
135: .  ctx    - optional user-defined context, as set by NEPSetFunction()

137:    Output Parameters:
138: .  fun - Function matrix
139: .  B   - optionally different preconditioning matrix
140: */
141: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
142: {
144:   ApplicationCtx *user = (ApplicationCtx*)ctx;
145:   PetscScalar    A[3],c,d;
146:   PetscReal      h;
147:   PetscInt       i,n,j[3],Istart,Iend;
148:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

151:   /*
152:      Compute Function entries and insert into matrix
153:   */
154:   MatGetSize(fun,&n,NULL);
155:   MatGetOwnershipRange(fun,&Istart,&Iend);
156:   if (Istart==0) FirstBlock=PETSC_TRUE;
157:   if (Iend==n) LastBlock=PETSC_TRUE;
158:   h = user->h;
159:   c = user->kappa/(lambda-user->kappa);
160:   d = n;

162:   /*
163:      Interior grid points
164:   */
165:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
166:     j[0] = i-1; j[1] = i; j[2] = i+1;
167:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
168:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
169:   }

171:   /*
172:      Boundary points
173:   */
174:   if (FirstBlock) {
175:     i = 0;
176:     j[0] = 0; j[1] = 1;
177:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
178:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
179:   }

181:   if (LastBlock) {
182:     i = n-1;
183:     j[0] = n-2; j[1] = n-1;
184:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
185:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
186:   }

188:   /*
189:      Assemble matrix
190:   */
191:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
192:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
193:   if (fun != B) {
194:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
195:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
196:   }
197:   return(0);
198: }

200: /* ------------------------------------------------------------------- */
201: /*
202:    FormJacobian - Computes Jacobian matrix  T'(lambda)

204:    Input Parameters:
205: .  nep    - the NEP context
206: .  lambda - the scalar argument
207: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

209:    Output Parameters:
210: .  jac - Jacobian matrix
211: .  B   - optionally different preconditioning matrix
212: */
213: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
214: {
216:   ApplicationCtx *user = (ApplicationCtx*)ctx;
217:   PetscScalar    A[3],c;
218:   PetscReal      h;
219:   PetscInt       i,n,j[3],Istart,Iend;
220:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

223:   /*
224:      Compute Jacobian entries and insert into matrix
225:   */
226:   MatGetSize(jac,&n,NULL);
227:   MatGetOwnershipRange(jac,&Istart,&Iend);
228:   if (Istart==0) FirstBlock=PETSC_TRUE;
229:   if (Iend==n) LastBlock=PETSC_TRUE;
230:   h = user->h;
231:   c = user->kappa/(lambda-user->kappa);

233:   /*
234:      Interior grid points
235:   */
236:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
237:     j[0] = i-1; j[1] = i; j[2] = i+1;
238:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
239:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
240:   }

242:   /*
243:      Boundary points
244:   */
245:   if (FirstBlock) {
246:     i = 0;
247:     j[0] = 0; j[1] = 1;
248:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
249:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
250:   }

252:   if (LastBlock) {
253:     i = n-1;
254:     j[0] = n-2; j[1] = n-1;
255:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
256:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
257:   }

259:   /*
260:      Assemble matrix
261:   */
262:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
263:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
264:   return(0);
265: }