1 /* ------------------------------------------------------------------------
2
3 Solid Fuel Ignition (SFI) problem. This problem is modeled by the
4 partial differential equation
5
6 -Laplacian(u) - lambda * exp(u) = 0, 0 < x,y,z < 1,
7
8 with boundary conditions
9
10 u = 0 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1
11
12 A finite difference approximation with the usual 7-point stencil
13 is used to discretize the boundary value problem to obtain a
14 nonlinear system of equations. The problem is solved in a 3D
15 rectangular domain, using distributed arrays (DAs) to partition
16 the parallel grid.
17
18 ------------------------------------------------------------------------- */
19
20 #include "Bratu3D.h"
21
FormInitGuess(DM da,Vec X,Params * p)22 PetscErrorCode FormInitGuess(DM da, Vec X, Params *p)
23 {
24 PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
25 PetscReal lambda,temp1,hx,hy,hz,tempk,tempj;
26 PetscScalar ***x;
27
28 PetscFunctionBegin;
29 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));
30 lambda = p->lambda_;
31 hx = 1.0/(PetscReal)(Mx-1);
32 hy = 1.0/(PetscReal)(My-1);
33 hz = 1.0/(PetscReal)(Mz-1);
34 temp1 = lambda/(lambda + 1.0);
35
36 /*
37 Get a pointer to vector data.
38
39 - For default PETSc vectors, VecGetArray() returns a pointer to
40 the data array. Otherwise, the routine is implementation
41 dependent.
42
43 - You MUST call VecRestoreArray() when you no longer need access
44 to the array.
45 */
46 PetscCall(DMDAVecGetArray(da,X,&x));
47
48 /*
49 Get local grid boundaries (for 3-dimensional DMDA):
50
51 - xs, ys, zs: starting grid indices (no ghost points)
52
53 - xm, ym, zm: widths of local grid (no ghost points)
54 */
55 PetscCall(DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm));
56
57 /*
58 Compute initial guess over the locally owned part of the grid
59 */
60 for (k=zs; k<zs+zm; k++) {
61 tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
62 for (j=ys; j<ys+ym; j++) {
63 tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
64 for (i=xs; i<xs+xm; i++) {
65 if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
66 /* boundary conditions are all zero Dirichlet */
67 x[k][j][i] = 0.0;
68 } else {
69 x[k][j][i] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
70 }
71 }
72 }
73 }
74
75 /*
76 Restore vector
77 */
78 PetscCall(DMDAVecRestoreArray(da,X,&x));
79 PetscFunctionReturn(PETSC_SUCCESS);
80 }
81
FormFunction(DM da,Vec X,Vec F,Params * p)82 PetscErrorCode FormFunction(DM da, Vec X, Vec F, Params *p)
83 {
84 PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
85 PetscReal two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
86 PetscScalar u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
87 Vec localX;
88
89 PetscFunctionBegin;
90 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));
91 lambda = p->lambda_;
92 hx = 1.0/(PetscReal)(Mx-1);
93 hy = 1.0/(PetscReal)(My-1);
94 hz = 1.0/(PetscReal)(Mz-1);
95 sc = hx*hy*hz*lambda;
96 hxhzdhy = hx*hz/hy;
97 hyhzdhx = hy*hz/hx;
98 hxhydhz = hx*hy/hz;
99
100 PetscCall(DMGetLocalVector(da,&localX));
101
102 /*
103 Scatter ghost points to local vector,using the 2-step process
104 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). By placing code
105 between these two statements, computations can be done while
106 messages are in transition.
107 */
108 PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX));
109 PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX));
110
111 /*
112 Get pointers to vector data.
113 */
114 PetscCall(DMDAVecGetArray(da,localX,&x));
115 PetscCall(DMDAVecGetArray(da,F,&f));
116
117 /*
118 Get local grid boundaries.
119 */
120 PetscCall(DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm));
121
122 /*
123 Compute function over the locally owned part of the grid.
124 */
125 for (k=zs; k<zs+zm; k++) {
126 for (j=ys; j<ys+ym; j++) {
127 for (i=xs; i<xs+xm; i++) {
128 if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
129 /* boundary points */
130 f[k][j][i] = x[k][j][i] - 0.0;
131 } else {
132 /* interior grid points */
133 u = x[k][j][i];
134 u_east = x[k][j][i+1];
135 u_west = x[k][j][i-1];
136 u_north = x[k][j+1][i];
137 u_south = x[k][j-1][i];
138 u_up = x[k+1][j][i];
139 u_down = x[k-1][j][i];
140 u_xx = (-u_east + two*u - u_west)*hyhzdhx;
141 u_yy = (-u_north + two*u - u_south)*hxhzdhy;
142 u_zz = (-u_up + two*u - u_down)*hxhydhz;
143 f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
144 }
145 }
146 }
147 }
148
149 /*
150 Restore vectors.
151 */
152 PetscCall(DMDAVecRestoreArray(da,F,&f));
153 PetscCall(DMDAVecRestoreArray(da,localX,&x));
154 PetscCall(DMRestoreLocalVector(da,&localX));
155 PetscCall(PetscLogFlops(11.0*ym*xm));
156 PetscFunctionReturn(PETSC_SUCCESS);
157 }
158
FormJacobian(DM da,Vec X,Mat J,Params * p)159 PetscErrorCode FormJacobian(DM da, Vec X, Mat J, Params *p)
160 {
161 PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
162 PetscReal lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
163 PetscScalar v[7],***x;
164 MatStencil col[7],row;
165 Vec localX;
166
167 PetscFunctionBegin;
168 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));
169 lambda = p->lambda_;
170 hx = 1.0/(PetscReal)(Mx-1);
171 hy = 1.0/(PetscReal)(My-1);
172 hz = 1.0/(PetscReal)(Mz-1);
173 sc = hx*hy*hz*lambda;
174 hxhzdhy = hx*hz/hy;
175 hyhzdhx = hy*hz/hx;
176 hxhydhz = hx*hy/hz;
177
178 PetscCall(DMGetLocalVector(da,&localX));
179
180 /*
181 Scatter ghost points to local vector, using the 2-step process
182 DMGlobalToLocalBegin(), DMGlobalToLocalEnd(). By placing code
183 between these two statements, computations can be done while
184 messages are in transition.
185 */
186 PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX));
187 PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX));
188
189 /*
190 Get pointer to vector data.
191 */
192 PetscCall(DMDAVecGetArray(da,localX,&x));
193
194 /*
195 Get local grid boundaries.
196 */
197 PetscCall(DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm));
198
199 /*
200 Compute entries for the locally owned part of the Jacobian.
201
202 - Currently, all PETSc parallel matrix formats are partitioned by
203 contiguous chunks of rows across the processors.
204
205 - Each processor needs to insert only elements that it owns
206 locally (but any non-local elements will be sent to the
207 appropriate processor during matrix assembly).
208
209 - Here, we set all entries for a particular row at once.
210
211 - We can set matrix entries either using either
212 MatSetValuesLocal() or MatSetValues(), as discussed above.
213 */
214 for (k=zs; k<zs+zm; k++) {
215 for (j=ys; j<ys+ym; j++) {
216 for (i=xs; i<xs+xm; i++) {
217 row.k = k; row.j = j; row.i = i;
218 /* boundary points */
219 if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
220 v[0] = 1.0;
221 PetscCall(MatSetValuesStencil(J,1,&row,1,&row,v,INSERT_VALUES));
222 } else {
223 /* interior grid points */
224 v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j; col[0].i = i;
225 v[1] = -hxhzdhy; col[1].k=k; col[1].j=j-1;col[1].i = i;
226 v[2] = -hyhzdhx; col[2].k=k; col[2].j=j; col[2].i = i-1;
227 v[3] = 2.0*(hyhzdhx+hxhzdhy+hxhydhz)-sc*PetscExpScalar(x[k][j][i]);col[3].k=row.k;col[3].j=row.j;col[3].i = row.i;
228 v[4] = -hyhzdhx; col[4].k=k; col[4].j=j; col[4].i = i+1;
229 v[5] = -hxhzdhy; col[5].k=k; col[5].j=j+1;col[5].i = i;
230 v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j; col[6].i = i;
231 PetscCall(MatSetValuesStencil(J,1,&row,7,col,v,INSERT_VALUES));
232 }
233 }
234 }
235 }
236 PetscCall(DMDAVecRestoreArray(da,localX,&x));
237 PetscCall(DMRestoreLocalVector(da,&localX));
238
239 /*
240 Assemble matrix, using the 2-step process: MatAssemblyBegin(),
241 MatAssemblyEnd().
242 */
243 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY));
244 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY));
245
246 /*
247 Tell the matrix we will never add a new nonzero location to the
248 matrix. If we do, it will generate an error.
249 */
250 PetscCall(MatSetOption(J,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
251 PetscFunctionReturn(PETSC_SUCCESS);
252 }
253