Actual source code: ex34.c

petsc-master 2019-05-21
Report Typos and Errors
  1: static const char help[] = "An elastic wave equation driven by Dieterich-Ruina friction\n";
  2: /*
  3: This whole derivation comes from Erickson, Birnir, and Lavallee [2010]. The model comes from the continuum limit in Carlson and Langer [1989],

  5:   u_{tt}   = c^2 u_{xx} - \tilde\gamma^2 u - (\gamma^2 / \xi) (\theta + \ln(u_t + 1))
  6:   \theta_t = -(u_t + 1) (\theta + (1 + \epsilon) \ln(u_t +1))

  8: which can be reduced to a first order system,

 10:   u_t      = v
 11:   v_t      = c^2 u_{xx} - \tilde\gamma^2 u - (\gamma^2 / \xi)(\theta + ln(v + 1)))
 12:   \theta_t = -(v + 1) (\theta + (1 + \epsilon) \ln(v+1))
 13: */

 15:  #include <petscdm.h>
 16:  #include <petscdmda.h>
 17:  #include <petscts.h>

 19: typedef struct {
 20:   PetscScalar u,v, th;
 21: } Field;

 23: typedef struct _User *User;
 24: struct _User {
 25:   PetscReal epsilon;    /* inverse of seismic ratio, B-A / A */
 26:   PetscReal gamma;      /* wave frequency for interblock coupling */
 27:   PetscReal gammaTilde; /* wave frequency for coupling to plate */
 28:   PetscReal xi;         /* interblock spring constant */
 29:   PetscReal c;          /* wavespeed */
 30: };

 32: static PetscErrorCode FormRHSFunction(TS ts, PetscReal t, Vec U, Vec F, void *ctx)
 33: {
 34:   User              user = (User) ctx;
 35:   DM                dm, cdm;
 36:   DMDALocalInfo     info;
 37:   Vec               C;
 38:   Field             *f;
 39:   const Field       *u;
 40:   const PetscScalar *x;
 41:   PetscInt          i;
 42:   PetscErrorCode    ierr;

 45:   TSGetDM(ts, &dm);
 46:   DMGetCoordinateDM(dm, &cdm);
 47:   DMGetCoordinatesLocal(dm, &C);
 48:   DMDAGetLocalInfo(dm, &info);
 49:   DMDAVecGetArrayRead(dm,  U, (void*)&u);
 50:   DMDAVecGetArray(dm,  F, &f);
 51:   DMDAVecGetArrayRead(cdm, C, (void*)&x);
 52:   for (i = info.xs; i < info.xs+info.xm; ++i) {
 53:     const PetscScalar hx = i+1 == info.xs+info.xm ? x[i] - x[i-1] : x[i+1] - x[i];

 55:     f[i].u  =  hx*(u[i].v);
 56:     f[i].v  = -hx*(PetscSqr(user->gammaTilde)*u[i].u + (PetscSqr(user->gamma) / user->xi)*(u[i].th + log(u[i].v + 1)));
 57:     f[i].th = -hx*(u[i].v + 1)*(u[i].th + (1 + user->epsilon)*log(u[i].v + 1));
 58:   }
 59:   DMDAVecRestoreArrayRead(dm,  U, (void*)&u);
 60:   DMDAVecRestoreArray(dm,  F, &f);
 61:   DMDAVecRestoreArrayRead(cdm, C, (void*)&x);
 62:   return(0);
 63: }

 65: static PetscErrorCode FormIFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx)
 66: {
 67:   User           user = (User) ctx;
 68:   DM             dm, cdm;
 69:   DMDALocalInfo  info;
 70:   Vec            Uloc, C;
 71:   Field         *u, *udot, *f;
 72:   PetscScalar   *x;
 73:   PetscInt       i;

 77:   TSGetDM(ts, &dm);
 78:   DMDAGetLocalInfo(dm, &info);
 79:   DMGetCoordinateDM(dm, &cdm);
 80:   DMGetCoordinatesLocal(dm, &C);
 81:   DMGetLocalVector(dm, &Uloc);
 82:   DMGlobalToLocalBegin(dm, U, INSERT_VALUES, Uloc);
 83:   DMGlobalToLocalEnd(dm, U, INSERT_VALUES, Uloc);
 84:   DMDAVecGetArrayRead(dm,  Uloc, &u);
 85:   DMDAVecGetArrayRead(dm,  Udot, &udot);
 86:   DMDAVecGetArray(dm,  F,    &f);
 87:   DMDAVecGetArrayRead(cdm, C,    &x);
 88:   for (i = info.xs; i < info.xs+info.xm; ++i) {
 89:     if (i == 0) {
 90:       const PetscScalar hx = x[i+1] - x[i];
 91:       f[i].u  = hx * udot[i].u;
 92:       f[i].v  = hx * udot[i].v - PetscSqr(user->c) * (u[i+1].u - u[i].u) / hx;
 93:       f[i].th = hx * udot[i].th;
 94:     } else if (i == info.mx-1) {
 95:       const PetscScalar hx = x[i] - x[i-1];
 96:       f[i].u  = hx * udot[i].u;
 97:       f[i].v  = hx * udot[i].v - PetscSqr(user->c) * (u[i-1].u - u[i].u) / hx;
 98:       f[i].th = hx * udot[i].th;
 99:     } else {
100:       const PetscScalar hx = x[i+1] - x[i];
101:       f[i].u  = hx * udot[i].u;
102:       f[i].v  = hx * udot[i].v - PetscSqr(user->c) * (u[i-1].u - 2.*u[i].u + u[i+1].u) / hx;
103:       f[i].th = hx * udot[i].th;
104:     }
105:   }
106:   DMDAVecRestoreArrayRead(dm,  Uloc, &u);
107:   DMDAVecRestoreArrayRead(dm,  Udot, &udot);
108:   DMDAVecRestoreArray(dm,  F,    &f);
109:   DMDAVecRestoreArrayRead(cdm, C,    &x);
110:   DMRestoreLocalVector(dm, &Uloc);
111:   return(0);
112: }

114: /* IJacobian - Compute IJacobian = dF/dU + a dF/dUdot */
115: PetscErrorCode FormIJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat J, Mat Jpre, void *ctx)
116: {
117:   User           user = (User) ctx;
118:   DM             dm, cdm;
119:   DMDALocalInfo  info;
120:   Vec            C;
121:   Field         *u, *udot;
122:   PetscScalar   *x;
123:   PetscInt       i;

127:   TSGetDM(ts, &dm);
128:   DMDAGetLocalInfo(dm, &info);
129:   DMGetCoordinateDM(dm, &cdm);
130:   DMGetCoordinatesLocal(dm, &C);
131:   DMDAVecGetArrayRead(dm,  U,    &u);
132:   DMDAVecGetArrayRead(dm,  Udot, &udot);
133:   DMDAVecGetArrayRead(cdm, C,    &x);
134:   for (i = info.xs; i < info.xs+info.xm; ++i) {
135:     if (i == 0) {
136:       const PetscScalar hx            = x[i+1] - x[i];
137:       const PetscInt    row           = i, col[] = {i,i+1};
138:       const PetscScalar dxx0          = PetscSqr(user->c)/hx,dxxR = -PetscSqr(user->c)/hx;
139:       const PetscScalar vals[3][2][3] = {{{a*hx,     0,0},{0,0,   0}},
140:                                          {{0,a*hx+dxx0,0},{0,dxxR,0}},
141:                                          {{0,0,     a*hx},{0,0,   0}}};

143:       MatSetValuesBlocked(Jpre, 1, &row, 2, col, &vals[0][0][0], INSERT_VALUES);
144:     } else if (i == info.mx-1) {
145:       const PetscScalar hx            = x[i+1] - x[i];
146:       const PetscInt    row           = i, col[] = {i-1,i};
147:       const PetscScalar dxxL          = -PetscSqr(user->c)/hx, dxx0 = PetscSqr(user->c)/hx;
148:       const PetscScalar vals[3][2][3] = {{{0,0,   0},{a*hx,     0,0}},
149:                                          {{0,dxxL,0},{0,a*hx+dxx0,0}},
150:                                          {{0,0,   0},{0,0,     a*hx}}};

152:       MatSetValuesBlocked(Jpre, 1, &row, 2, col, &vals[0][0][0], INSERT_VALUES);
153:     } else {
154:       const PetscScalar hx            = x[i+1] - x[i];
155:       const PetscInt    row           = i, col[] = {i-1,i,i+1};
156:       const PetscScalar dxxL          = -PetscSqr(user->c)/hx, dxx0 = 2.*PetscSqr(user->c)/hx,dxxR = -PetscSqr(user->c)/hx;
157:       const PetscScalar vals[3][3][3] = {{{0,0,   0},{a*hx,     0,0},{0,0,   0}},
158:                                          {{0,dxxL,0},{0,a*hx+dxx0,0},{0,dxxR,0}},
159:                                          {{0,0,   0},{0,0,     a*hx},{0,0,   0}}};

161:       MatSetValuesBlocked(Jpre, 1, &row, 3, col, &vals[0][0][0], INSERT_VALUES);
162:     }
163:   }
164:   DMDAVecRestoreArrayRead(dm,  U,    &u);
165:   DMDAVecRestoreArrayRead(dm,  Udot, &udot);
166:   DMDAVecRestoreArrayRead(cdm, C,    &x);
167:   MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY);
168:   MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY);
169:   if (J != Jpre) {
170:     MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
171:     MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
172:   }
173:   return(0);
174: }

176: PetscErrorCode FormInitialSolution(TS ts, Vec U, void *ctx)
177: {
178:   /* User            user = (User) ctx; */
179:   DM              dm, cdm;
180:   DMDALocalInfo   info;
181:   Vec             C;
182:   Field          *u;
183:   PetscScalar    *x;
184:   const PetscReal sigma = 1.0;
185:   PetscInt        i;
186:   PetscErrorCode  ierr;

189:   TSGetDM(ts, &dm);
190:   DMGetCoordinateDM(dm, &cdm);
191:   DMGetCoordinatesLocal(dm, &C);
192:   DMDAGetLocalInfo(dm, &info);
193:   DMDAVecGetArray(dm,  U, &u);
194:   DMDAVecGetArrayRead(cdm, C, &x);
195:   for (i = info.xs; i < info.xs+info.xm; ++i) {
196:     u[i].u  = 1.5 * PetscExpScalar(-PetscSqr(x[i] - 10)/PetscSqr(sigma));
197:     u[i].v  = 0.0;
198:     u[i].th = 0.0;
199:   }
200:   DMDAVecRestoreArray(dm,  U, &u);
201:   DMDAVecRestoreArrayRead(cdm, C, &x);
202:   return(0);
203: }

205: int main(int argc, char **argv)
206: {
207:   DM                dm;
208:   TS                ts;
209:   Vec               X;
210:   Mat               J;
211:   PetscInt          steps, mx;
212:   PetscReal         ftime, hx, dt;
213:   TSConvergedReason reason;
214:   struct _User      user;
215:   PetscErrorCode    ierr;

217:   PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
218:   DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, 11, 3, 1, NULL, &dm);
219:   DMSetFromOptions(dm);
220:   DMSetUp(dm);
221:   DMDASetUniformCoordinates(dm, 0.0, 20.0, 0.0, 0.0, 0.0, 0.0);
222:   DMCreateGlobalVector(dm, &X);

224:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Dynamic Friction Options", "");
225:   {
226:     user.epsilon    = 0.1;
227:     user.gamma      = 0.5;
228:     user.gammaTilde = 0.5;
229:     user.xi         = 0.5;
230:     user.c          = 0.5;
231:     PetscOptionsReal("-epsilon", "Inverse of seismic ratio", "", user.epsilon, &user.epsilon, NULL);
232:     PetscOptionsReal("-gamma", "Wave frequency for interblock coupling", "", user.gamma, &user.gamma, NULL);
233:     PetscOptionsReal("-gamma_tilde", "Wave frequency for plate coupling", "", user.gammaTilde, &user.gammaTilde, NULL);
234:     PetscOptionsReal("-xi", "Interblock spring constant", "", user.xi, &user.xi, NULL);
235:     PetscOptionsReal("-c", "Wavespeed", "", user.c, &user.c, NULL);
236:   }
237:   PetscOptionsEnd();

239:   TSCreate(PETSC_COMM_WORLD, &ts);
240:   TSSetDM(ts, dm);
241:   TSSetRHSFunction(ts, NULL, FormRHSFunction, &user);
242:   TSSetIFunction(ts, NULL, FormIFunction, &user);
243:   DMSetMatType(dm, MATAIJ);
244:   DMCreateMatrix(dm, &J);
245:   TSSetIJacobian(ts, J, J, FormIJacobian, &user);

247:   ftime = 800.0;
248:   TSSetMaxTime(ts,ftime);
249:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
250:   FormInitialSolution(ts, X, &user);
251:   TSSetSolution(ts, X);
252:   VecGetSize(X, &mx);
253:   hx   = 20.0/(PetscReal)(mx-1);
254:   dt   = 0.4 * PetscSqr(hx) / PetscSqr(user.c); /* Diffusive stability limit */
255:   TSSetTimeStep(ts,dt);
256:   TSSetFromOptions(ts);

258:   TSSolve(ts, X);
259:   TSGetSolveTime(ts, &ftime);
260:   TSGetStepNumber(ts, &steps);
261:   TSGetConvergedReason(ts, &reason);
262:   PetscPrintf(PETSC_COMM_WORLD, "%s at time %g after %D steps\n", TSConvergedReasons[reason], (double)ftime, steps);

264:   MatDestroy(&J);
265:   VecDestroy(&X);
266:   TSDestroy(&ts);
267:   DMDestroy(&dm);
268:   PetscFinalize();
269:   return ierr;
270: }

272: /*TEST

274:     build:
275:       requires: !single  !complex c99

277:     test:
278:       TODO: broken, was not nightly tested, SNES solve eventually fails, -snes_test_jacobian indicates Jacobian is wrong, but even -snes_mf_operator fails

280: TEST*/