Actual source code: ex34.c
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;
44: TSGetDM(ts, &dm);
45: DMGetCoordinateDM(dm, &cdm);
46: DMGetCoordinatesLocal(dm, &C);
47: DMDAGetLocalInfo(dm, &info);
48: DMDAVecGetArrayRead(dm, U, (void*)&u);
49: DMDAVecGetArray(dm, F, &f);
50: DMDAVecGetArrayRead(cdm, C, (void*)&x);
51: for (i = info.xs; i < info.xs+info.xm; ++i) {
52: const PetscScalar hx = i+1 == info.xs+info.xm ? x[i] - x[i-1] : x[i+1] - x[i];
54: f[i].u = hx*(u[i].v);
55: f[i].v = -hx*(PetscSqr(user->gammaTilde)*u[i].u + (PetscSqr(user->gamma) / user->xi)*(u[i].th + PetscLogScalar(u[i].v + 1)));
56: f[i].th = -hx*(u[i].v + 1)*(u[i].th + (1 + user->epsilon)*PetscLogScalar(u[i].v + 1));
57: }
58: DMDAVecRestoreArrayRead(dm, U, (void*)&u);
59: DMDAVecRestoreArray(dm, F, &f);
60: DMDAVecRestoreArrayRead(cdm, C, (void*)&x);
61: return 0;
62: }
64: static PetscErrorCode FormIFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx)
65: {
66: User user = (User) ctx;
67: DM dm, cdm;
68: DMDALocalInfo info;
69: Vec Uloc, C;
70: Field *u, *udot, *f;
71: PetscScalar *x;
72: PetscInt i;
75: TSGetDM(ts, &dm);
76: DMDAGetLocalInfo(dm, &info);
77: DMGetCoordinateDM(dm, &cdm);
78: DMGetCoordinatesLocal(dm, &C);
79: DMGetLocalVector(dm, &Uloc);
80: DMGlobalToLocalBegin(dm, U, INSERT_VALUES, Uloc);
81: DMGlobalToLocalEnd(dm, U, INSERT_VALUES, Uloc);
82: DMDAVecGetArrayRead(dm, Uloc, &u);
83: DMDAVecGetArrayRead(dm, Udot, &udot);
84: DMDAVecGetArray(dm, F, &f);
85: DMDAVecGetArrayRead(cdm, C, &x);
86: for (i = info.xs; i < info.xs+info.xm; ++i) {
87: if (i == 0) {
88: const PetscScalar hx = x[i+1] - x[i];
89: f[i].u = hx * udot[i].u;
90: f[i].v = hx * udot[i].v - PetscSqr(user->c) * (u[i+1].u - u[i].u) / hx;
91: f[i].th = hx * udot[i].th;
92: } else if (i == info.mx-1) {
93: const PetscScalar hx = x[i] - x[i-1];
94: f[i].u = hx * udot[i].u;
95: f[i].v = hx * udot[i].v - PetscSqr(user->c) * (u[i-1].u - u[i].u) / hx;
96: f[i].th = hx * udot[i].th;
97: } else {
98: const PetscScalar hx = x[i+1] - x[i];
99: f[i].u = hx * udot[i].u;
100: f[i].v = hx * udot[i].v - PetscSqr(user->c) * (u[i-1].u - 2.*u[i].u + u[i+1].u) / hx;
101: f[i].th = hx * udot[i].th;
102: }
103: }
104: DMDAVecRestoreArrayRead(dm, Uloc, &u);
105: DMDAVecRestoreArrayRead(dm, Udot, &udot);
106: DMDAVecRestoreArray(dm, F, &f);
107: DMDAVecRestoreArrayRead(cdm, C, &x);
108: DMRestoreLocalVector(dm, &Uloc);
109: return 0;
110: }
112: /* IJacobian - Compute IJacobian = dF/dU + a dF/dUdot */
113: PetscErrorCode FormIJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat J, Mat Jpre, void *ctx)
114: {
115: User user = (User) ctx;
116: DM dm, cdm;
117: DMDALocalInfo info;
118: Vec C;
119: Field *u, *udot;
120: PetscScalar *x;
121: PetscInt i;
124: TSGetDM(ts, &dm);
125: DMDAGetLocalInfo(dm, &info);
126: DMGetCoordinateDM(dm, &cdm);
127: DMGetCoordinatesLocal(dm, &C);
128: DMDAVecGetArrayRead(dm, U, &u);
129: DMDAVecGetArrayRead(dm, Udot, &udot);
130: DMDAVecGetArrayRead(cdm, C, &x);
131: for (i = info.xs; i < info.xs+info.xm; ++i) {
132: if (i == 0) {
133: const PetscScalar hx = x[i+1] - x[i];
134: const PetscInt row = i, col[] = {i,i+1};
135: const PetscScalar dxx0 = PetscSqr(user->c)/hx,dxxR = -PetscSqr(user->c)/hx;
136: const PetscScalar vals[3][2][3] = {{{a*hx, 0,0},{0,0, 0}},
137: {{0,a*hx+dxx0,0},{0,dxxR,0}},
138: {{0,0, a*hx},{0,0, 0}}};
140: MatSetValuesBlocked(Jpre, 1, &row, 2, col, &vals[0][0][0], INSERT_VALUES);
141: } else if (i == info.mx-1) {
142: const PetscScalar hx = x[i+1] - x[i];
143: const PetscInt row = i, col[] = {i-1,i};
144: const PetscScalar dxxL = -PetscSqr(user->c)/hx, dxx0 = PetscSqr(user->c)/hx;
145: const PetscScalar vals[3][2][3] = {{{0,0, 0},{a*hx, 0,0}},
146: {{0,dxxL,0},{0,a*hx+dxx0,0}},
147: {{0,0, 0},{0,0, a*hx}}};
149: MatSetValuesBlocked(Jpre, 1, &row, 2, col, &vals[0][0][0], INSERT_VALUES);
150: } else {
151: const PetscScalar hx = x[i+1] - x[i];
152: const PetscInt row = i, col[] = {i-1,i,i+1};
153: const PetscScalar dxxL = -PetscSqr(user->c)/hx, dxx0 = 2.*PetscSqr(user->c)/hx,dxxR = -PetscSqr(user->c)/hx;
154: const PetscScalar vals[3][3][3] = {{{0,0, 0},{a*hx, 0,0},{0,0, 0}},
155: {{0,dxxL,0},{0,a*hx+dxx0,0},{0,dxxR,0}},
156: {{0,0, 0},{0,0, a*hx},{0,0, 0}}};
158: MatSetValuesBlocked(Jpre, 1, &row, 3, col, &vals[0][0][0], INSERT_VALUES);
159: }
160: }
161: DMDAVecRestoreArrayRead(dm, U, &u);
162: DMDAVecRestoreArrayRead(dm, Udot, &udot);
163: DMDAVecRestoreArrayRead(cdm, C, &x);
164: MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY);
165: MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY);
166: if (J != Jpre) {
167: MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
168: MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
169: }
170: return 0;
171: }
173: PetscErrorCode FormInitialSolution(TS ts, Vec U, void *ctx)
174: {
175: /* User user = (User) ctx; */
176: DM dm, cdm;
177: DMDALocalInfo info;
178: Vec C;
179: Field *u;
180: PetscScalar *x;
181: const PetscReal sigma = 1.0;
182: PetscInt i;
185: TSGetDM(ts, &dm);
186: DMGetCoordinateDM(dm, &cdm);
187: DMGetCoordinatesLocal(dm, &C);
188: DMDAGetLocalInfo(dm, &info);
189: DMDAVecGetArray(dm, U, &u);
190: DMDAVecGetArrayRead(cdm, C, &x);
191: for (i = info.xs; i < info.xs+info.xm; ++i) {
192: u[i].u = 1.5 * PetscExpScalar(-PetscSqr(x[i] - 10)/PetscSqr(sigma));
193: u[i].v = 0.0;
194: u[i].th = 0.0;
195: }
196: DMDAVecRestoreArray(dm, U, &u);
197: DMDAVecRestoreArrayRead(cdm, C, &x);
198: return 0;
199: }
201: int main(int argc, char **argv)
202: {
203: DM dm;
204: TS ts;
205: Vec X;
206: Mat J;
207: PetscInt steps, mx;
208: PetscReal ftime, hx, dt;
209: TSConvergedReason reason;
210: struct _User user;
211: PetscErrorCode ierr;
213: PetscInitialize(&argc, &argv, NULL,help);
214: DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, 11, 3, 1, NULL, &dm);
215: DMSetFromOptions(dm);
216: DMSetUp(dm);
217: DMDASetUniformCoordinates(dm, 0.0, 20.0, 0.0, 0.0, 0.0, 0.0);
218: DMCreateGlobalVector(dm, &X);
220: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Dynamic Friction Options", "");
221: {
222: user.epsilon = 0.1;
223: user.gamma = 0.5;
224: user.gammaTilde = 0.5;
225: user.xi = 0.5;
226: user.c = 0.5;
227: PetscOptionsReal("-epsilon", "Inverse of seismic ratio", "", user.epsilon, &user.epsilon, NULL);
228: PetscOptionsReal("-gamma", "Wave frequency for interblock coupling", "", user.gamma, &user.gamma, NULL);
229: PetscOptionsReal("-gamma_tilde", "Wave frequency for plate coupling", "", user.gammaTilde, &user.gammaTilde, NULL);
230: PetscOptionsReal("-xi", "Interblock spring constant", "", user.xi, &user.xi, NULL);
231: PetscOptionsReal("-c", "Wavespeed", "", user.c, &user.c, NULL);
232: }
233: PetscOptionsEnd();
235: TSCreate(PETSC_COMM_WORLD, &ts);
236: TSSetDM(ts, dm);
237: TSSetRHSFunction(ts, NULL, FormRHSFunction, &user);
238: TSSetIFunction(ts, NULL, FormIFunction, &user);
239: DMSetMatType(dm, MATAIJ);
240: DMCreateMatrix(dm, &J);
241: TSSetIJacobian(ts, J, J, FormIJacobian, &user);
243: ftime = 800.0;
244: TSSetMaxTime(ts,ftime);
245: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
246: FormInitialSolution(ts, X, &user);
247: TSSetSolution(ts, X);
248: VecGetSize(X, &mx);
249: hx = 20.0/(PetscReal)(mx-1);
250: dt = 0.4 * PetscSqr(hx) / PetscSqr(user.c); /* Diffusive stability limit */
251: TSSetTimeStep(ts,dt);
252: TSSetFromOptions(ts);
254: TSSolve(ts, X);
255: TSGetSolveTime(ts, &ftime);
256: TSGetStepNumber(ts, &steps);
257: TSGetConvergedReason(ts, &reason);
258: PetscPrintf(PETSC_COMM_WORLD, "%s at time %g after %D steps\n", TSConvergedReasons[reason], (double)ftime, steps);
260: MatDestroy(&J);
261: VecDestroy(&X);
262: TSDestroy(&ts);
263: DMDestroy(&dm);
264: PetscFinalize();
265: return 0;
266: }
268: /*TEST
270: build:
271: requires: !single !complex
273: test:
274: TODO: broken, was not nightly tested, SNES solve eventually fails, -snes_test_jacobian indicates Jacobian is wrong, but even -snes_mf_operator fails
276: TEST*/