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 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 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 } 158 159 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