Actual source code: test3.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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:   Mat            F,J;
 44:   ApplicationCtx ctx;
 45:   PetscInt       n=128;
 46:   PetscBool      terse;

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

 55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 56:         Create a standalone EPS with appropriate settings
 57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 59:   EPSCreate(PETSC_COMM_WORLD,&eps);
 60:   EPSSetType(eps,EPSGD);
 61:   EPSSetFromOptions(eps);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:                Prepare nonlinear eigensolver context
 65:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 67:   NEPCreate(PETSC_COMM_WORLD,&nep);

 69:   /* Create Function and Jacobian matrices; set evaluation routines */
 70:   MatCreate(PETSC_COMM_WORLD,&F);
 71:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
 72:   MatSetFromOptions(F);
 73:   MatSeqAIJSetPreallocation(F,3,NULL);
 74:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 75:   MatSetUp(F);
 76:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

 78:   MatCreate(PETSC_COMM_WORLD,&J);
 79:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
 80:   MatSetFromOptions(J);
 81:   MatSeqAIJSetPreallocation(J,3,NULL);
 82:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
 83:   MatSetUp(J);
 84:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

 86:   NEPSetType(nep,NEPSLP);
 87:   NEPSLPSetEPS(nep,eps);
 88:   NEPSetFromOptions(nep);

 90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 91:                       Solve the eigensystem
 92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 94:   NEPSolve(nep);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97:                     Display solution and clean up
 98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

100:   /* show detailed info unless -terse option is given by user */
101:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
102:   if (terse) {
103:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
104:   } else {
105:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
106:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
107:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
108:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
109:   }

111:   NEPDestroy(&nep);
112:   EPSDestroy(&eps);
113:   MatDestroy(&F);
114:   MatDestroy(&J);
115:   SlepcFinalize();
116:   return ierr;
117: }

119: /* ------------------------------------------------------------------- */
120: /*
121:    FormFunction - Computes Function matrix  T(lambda)

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

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

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

153:   /*
154:      Interior grid points
155:   */
156:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
157:     j[0] = i-1; j[1] = i; j[2] = i+1;
158:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
159:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
160:   }

162:   /*
163:      Boundary points
164:   */
165:   if (FirstBlock) {
166:     i = 0;
167:     j[0] = 0; j[1] = 1;
168:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
169:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
170:   }

172:   if (LastBlock) {
173:     i = n-1;
174:     j[0] = n-2; j[1] = n-1;
175:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
176:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
177:   }

179:   /*
180:      Assemble matrix
181:   */
182:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
183:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
184:   if (fun != B) {
185:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
186:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
187:   }
188:   return(0);
189: }

191: /* ------------------------------------------------------------------- */
192: /*
193:    FormJacobian - Computes Jacobian matrix  T'(lambda)

195:    Input Parameters:
196: .  nep    - the NEP context
197: .  lambda - the scalar argument
198: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

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

214:   /*
215:      Compute Jacobian entries and insert into matrix
216:   */
217:   MatGetSize(jac,&n,NULL);
218:   MatGetOwnershipRange(jac,&Istart,&Iend);
219:   if (Istart==0) FirstBlock=PETSC_TRUE;
220:   if (Iend==n) LastBlock=PETSC_TRUE;
221:   h = user->h;
222:   c = user->kappa/(lambda-user->kappa);

224:   /*
225:      Interior grid points
226:   */
227:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
228:     j[0] = i-1; j[1] = i; j[2] = i+1;
229:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
230:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
231:   }

233:   /*
234:      Boundary points
235:   */
236:   if (FirstBlock) {
237:     i = 0;
238:     j[0] = 0; j[1] = 1;
239:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
240:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
241:   }

243:   if (LastBlock) {
244:     i = n-1;
245:     j[0] = n-2; j[1] = n-1;
246:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
247:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
248:   }

250:   /*
251:      Assemble matrix
252:   */
253:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
254:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
255:   return(0);
256: }

258: /*TEST

260:    test:
261:       suffix: 1
262:       args: -nep_target 21 -terse
263:       requires: !single
264:       output_file: output/test1_1.out

266: TEST*/