1 static char help[] = "Surface processes in geophysics.\n\n"; 2 3 #include <petscsnes.h> 4 #include <petscdm.h> 5 #include <petscdmda.h> 6 7 /* 8 User-defined application context - contains data needed by the 9 application-provided call-back routines, FormJacobianLocal() and 10 FormFunctionLocal(). 11 */ 12 typedef struct { 13 PetscReal D; /* The diffusion coefficient */ 14 PetscReal K; /* The advection coefficient */ 15 PetscInt m; /* Exponent for A */ 16 } AppCtx; 17 18 /* 19 User-defined routines 20 */ 21 extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*); 22 extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,AppCtx*); 23 24 int main(int argc,char **argv) 25 { 26 SNES snes; /* nonlinear solver */ 27 AppCtx user; /* user-defined work context */ 28 PetscInt its; /* iterations for convergence */ 29 PetscErrorCode ierr; 30 DM da; 31 32 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 33 Initialize program 34 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 35 36 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 37 38 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 39 Initialize problem parameters 40 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 41 ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "", "Surface Process Problem Options", "SNES");PetscCall(ierr); 42 user.D = 1.0; 43 PetscCall(PetscOptionsReal("-D", "The diffusion coefficient D", __FILE__, user.D, &user.D, NULL)); 44 user.K = 1.0; 45 PetscCall(PetscOptionsReal("-K", "The advection coefficient K", __FILE__, user.K, &user.K, NULL)); 46 user.m = 1; 47 PetscCall(PetscOptionsInt("-m", "The exponent for A", __FILE__, user.m, &user.m, NULL)); 48 ierr = PetscOptionsEnd();PetscCall(ierr); 49 50 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 51 Create distributed array (DMDA) to manage parallel grid and vectors 52 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 53 PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da)); 54 PetscCall(DMSetFromOptions(da)); 55 PetscCall(DMSetUp(da)); 56 PetscCall(DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0)); 57 PetscCall(DMSetApplicationContext(da,&user)); 58 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 59 PetscCall(SNESSetDM(snes, da)); 60 61 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 62 Set local function evaluation routine 63 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 64 PetscCall(DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user)); 65 66 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 67 Customize solver; set runtime options 68 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 69 PetscCall(SNESSetFromOptions(snes)); 70 71 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 72 Solve nonlinear system 73 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 74 PetscCall(SNESSolve(snes,0,0)); 75 PetscCall(SNESGetIterationNumber(snes,&its)); 76 77 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 78 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 79 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its)); 80 81 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 82 Free work space. All PETSc objects should be destroyed when they 83 are no longer needed. 84 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 85 86 PetscCall(SNESDestroy(&snes)); 87 PetscCall(DMDestroy(&da)); 88 89 PetscCall(PetscFinalize()); 90 return 0; 91 } 92 93 PetscScalar funcU(DMDACoor2d *coords) 94 { 95 return coords->x + coords->y; 96 } 97 98 PetscScalar funcA(PetscScalar z, AppCtx *user) 99 { 100 PetscScalar v = 1.0; 101 PetscInt i; 102 103 for (i = 0; i < user->m; ++i) v *= z; 104 return v; 105 } 106 107 PetscScalar funcADer(PetscScalar z, AppCtx *user) 108 { 109 PetscScalar v = 1.0; 110 PetscInt i; 111 112 for (i = 0; i < user->m-1; ++i) v *= z; 113 return (PetscScalar)user->m*v; 114 } 115 116 /* 117 FormFunctionLocal - Evaluates nonlinear function, F(x). 118 */ 119 PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user) 120 { 121 DM coordDA; 122 Vec coordinates; 123 DMDACoor2d **coords; 124 PetscScalar u, ux, uy, uxx, uyy; 125 PetscReal D, K, hx, hy, hxdhy, hydhx; 126 PetscInt i,j; 127 128 PetscFunctionBeginUser; 129 D = user->D; 130 K = user->K; 131 hx = 1.0/(PetscReal)(info->mx-1); 132 hy = 1.0/(PetscReal)(info->my-1); 133 hxdhy = hx/hy; 134 hydhx = hy/hx; 135 /* 136 Compute function over the locally owned part of the grid 137 */ 138 PetscCall(DMGetCoordinateDM(info->da, &coordDA)); 139 PetscCall(DMGetCoordinates(info->da, &coordinates)); 140 PetscCall(DMDAVecGetArray(coordDA, coordinates, &coords)); 141 for (j=info->ys; j<info->ys+info->ym; j++) { 142 for (i=info->xs; i<info->xs+info->xm; i++) { 143 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) f[j][i] = x[j][i]; 144 else { 145 u = x[j][i]; 146 ux = (x[j][i+1] - x[j][i])/hx; 147 uy = (x[j+1][i] - x[j][i])/hy; 148 uxx = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx; 149 uyy = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy; 150 f[j][i] = D*(uxx + uyy) - (K*funcA(x[j][i], user)*PetscSqrtScalar(ux*ux + uy*uy) + funcU(&coords[j][i]))*hx*hy; 151 PetscCheck(!PetscIsInfOrNanScalar(f[j][i]),PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", (double)PetscRealPart(f[j][i])); 152 } 153 } 154 } 155 PetscCall(DMDAVecRestoreArray(coordDA, coordinates, &coords)); 156 PetscCall(PetscLogFlops(11.0*info->ym*info->xm)); 157 PetscFunctionReturn(0); 158 } 159 160 /* 161 FormJacobianLocal - Evaluates Jacobian matrix. 162 */ 163 PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user) 164 { 165 MatStencil col[5], row; 166 PetscScalar D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy; 167 PetscReal normGradZ; 168 PetscInt i, j,k; 169 170 PetscFunctionBeginUser; 171 D = user->D; 172 K = user->K; 173 hx = 1.0/(PetscReal)(info->mx-1); 174 hy = 1.0/(PetscReal)(info->my-1); 175 hxdhy = hx/hy; 176 hydhx = hy/hx; 177 178 /* 179 Compute entries for the locally owned part of the Jacobian. 180 - Currently, all PETSc parallel matrix formats are partitioned by 181 contiguous chunks of rows across the processors. 182 - Each processor needs to insert only elements that it owns 183 locally (but any non-local elements will be sent to the 184 appropriate processor during matrix assembly). 185 - Here, we set all entries for a particular row at once. 186 - We can set matrix entries either using either 187 MatSetValuesLocal() or MatSetValues(), as discussed above. 188 */ 189 for (j=info->ys; j<info->ys+info->ym; j++) { 190 for (i=info->xs; i<info->xs+info->xm; i++) { 191 row.j = j; row.i = i; 192 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { 193 /* boundary points */ 194 v[0] = 1.0; 195 PetscCall(MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES)); 196 } else { 197 /* interior grid points */ 198 ux = (x[j][i+1] - x[j][i])/hx; 199 uy = (x[j+1][i] - x[j][i])/hy; 200 normGradZ = PetscRealPart(PetscSqrtScalar(ux*ux + uy*uy)); 201 if (normGradZ < 1.0e-8) normGradZ = 1.0e-8; 202 A = funcA(x[j][i], user); 203 204 v[0] = -D*hxdhy; col[0].j = j - 1; col[0].i = i; 205 v[1] = -D*hydhx; col[1].j = j; col[1].i = i-1; 206 v[2] = D*2.0*(hydhx + hxdhy) + K*(funcADer(x[j][i], user)*normGradZ - A/normGradZ)*hx*hy; col[2].j = row.j; col[2].i = row.i; 207 v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ); col[3].j = j; col[3].i = i+1; 208 v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ); col[4].j = j + 1; col[4].i = i; 209 for (k = 0; k < 5; ++k) { 210 PetscCheck(!PetscIsInfOrNanScalar(v[k]),PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", (double)PetscRealPart(v[k])); 211 } 212 PetscCall(MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES)); 213 } 214 } 215 } 216 217 /* 218 Assemble matrix, using the 2-step process: 219 MatAssemblyBegin(), MatAssemblyEnd(). 220 */ 221 PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY)); 222 PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY)); 223 /* 224 Tell the matrix we will never add a new nonzero location to the 225 matrix. If we do, it will generate an error. 226 */ 227 PetscCall(MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE)); 228 PetscFunctionReturn(0); 229 } 230 231 /*TEST 232 233 test: 234 args: -snes_view -snes_monitor_short -da_refine 1 -pc_type mg -ksp_type fgmres -pc_mg_type full -mg_levels_ksp_chebyshev_esteig 0.5,1.1 235 236 test: 237 suffix: ew_1 238 args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 1 239 requires: !single 240 241 test: 242 suffix: ew_2 243 args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 2 244 245 test: 246 suffix: ew_3 247 args: -snes_monitor_short -ksp_converged_reason -da_grid_x 20 -da_grid_y 20 -snes_ksp_ew -snes_ksp_ew_version 3 248 requires: !single 249 250 test: 251 suffix: fm_rise_2 252 args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 1 -snes_ngmres_restart_fm_rise 253 requires: !single 254 255 test: 256 suffix: fm_rise_4 257 args: -K 3 -m 1 -D 0.2 -snes_monitor_short -snes_type ngmres -snes_npc_side right -npc_snes_type newtonls -npc_snes_linesearch_type basic -snes_ngmres_restart_it 2 -snes_ngmres_restart_fm_rise -snes_rtol 1.e-2 -snes_max_it 5 258 259 TEST*/ 260