1c4762a1bSJed Brown 2c4762a1bSJed Brown static char help[] ="Nonlinear Radiative Transport PDE with multigrid in 2d.\n\ 3c4762a1bSJed Brown Uses 2-dimensional distributed arrays.\n\ 4c4762a1bSJed Brown A 2-dim simplified Radiative Transport test problem is used, with analytic Jacobian. \n\ 5c4762a1bSJed Brown \n\ 6c4762a1bSJed Brown Solves the linear systems via multilevel methods \n\ 7c4762a1bSJed Brown \n\ 8c4762a1bSJed Brown The command line\n\ 9c4762a1bSJed Brown options are:\n\ 10c4762a1bSJed Brown -tleft <tl>, where <tl> indicates the left Diriclet BC \n\ 11c4762a1bSJed Brown -tright <tr>, where <tr> indicates the right Diriclet BC \n\ 12c4762a1bSJed Brown -beta <beta>, where <beta> indicates the exponent in T \n\n"; 13c4762a1bSJed Brown 14c4762a1bSJed Brown /* 15c4762a1bSJed Brown 16c4762a1bSJed Brown This example models the partial differential equation 17c4762a1bSJed Brown 18c4762a1bSJed Brown - Div(alpha* T^beta (GRAD T)) = 0. 19c4762a1bSJed Brown 20c4762a1bSJed Brown where beta = 2.5 and alpha = 1.0 21c4762a1bSJed Brown 22c4762a1bSJed Brown BC: T_left = 1.0, T_right = 0.1, dT/dn_top = dTdn_bottom = 0. 23c4762a1bSJed Brown 24c4762a1bSJed Brown in the unit square, which is uniformly discretized in each of x and 25c4762a1bSJed Brown y in this simple encoding. The degrees of freedom are cell centered. 26c4762a1bSJed Brown 27c4762a1bSJed Brown A finite volume approximation with the usual 5-point stencil 28c4762a1bSJed Brown is used to discretize the boundary value problem to obtain a 29c4762a1bSJed Brown nonlinear system of equations. 30c4762a1bSJed Brown 31c4762a1bSJed Brown This code was contributed by David Keyes 32c4762a1bSJed Brown 33c4762a1bSJed Brown */ 34c4762a1bSJed Brown 35c4762a1bSJed Brown #include <petscsnes.h> 36c4762a1bSJed Brown #include <petscdm.h> 37c4762a1bSJed Brown #include <petscdmda.h> 38c4762a1bSJed Brown 39c4762a1bSJed Brown /* User-defined application context */ 40c4762a1bSJed Brown 41c4762a1bSJed Brown typedef struct { 42c4762a1bSJed Brown PetscReal tleft,tright; /* Dirichlet boundary conditions */ 43c4762a1bSJed Brown PetscReal beta,bm1,coef; /* nonlinear diffusivity parameterizations */ 44c4762a1bSJed Brown } AppCtx; 45c4762a1bSJed Brown 46c4762a1bSJed Brown #define POWFLOP 5 /* assume a pow() takes five flops */ 47c4762a1bSJed Brown 48c4762a1bSJed Brown extern PetscErrorCode FormInitialGuess(SNES,Vec,void*); 49c4762a1bSJed Brown extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*); 50c4762a1bSJed Brown extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*); 51c4762a1bSJed Brown 52c4762a1bSJed Brown int main(int argc,char **argv) 53c4762a1bSJed Brown { 54c4762a1bSJed Brown SNES snes; 55c4762a1bSJed Brown AppCtx user; 56c4762a1bSJed Brown PetscInt its,lits; 57c4762a1bSJed Brown PetscReal litspit; 58c4762a1bSJed Brown DM da; 59c4762a1bSJed Brown 60*327415f7SBarry Smith PetscFunctionBeginUser; 619566063dSJacob Faibussowitsch PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 62c4762a1bSJed Brown 63c4762a1bSJed Brown /* set problem parameters */ 64c4762a1bSJed Brown user.tleft = 1.0; 65c4762a1bSJed Brown user.tright = 0.1; 66c4762a1bSJed Brown user.beta = 2.5; 679566063dSJacob Faibussowitsch PetscCall(PetscOptionsGetReal(NULL,NULL,"-tleft",&user.tleft,NULL)); 689566063dSJacob Faibussowitsch PetscCall(PetscOptionsGetReal(NULL,NULL,"-tright",&user.tright,NULL)); 699566063dSJacob Faibussowitsch PetscCall(PetscOptionsGetReal(NULL,NULL,"-beta",&user.beta,NULL)); 70c4762a1bSJed Brown user.bm1 = user.beta - 1.0; 71c4762a1bSJed Brown user.coef = user.beta/2.0; 72c4762a1bSJed Brown 73c4762a1bSJed Brown /* 74c4762a1bSJed Brown Create the multilevel DM data structure 75c4762a1bSJed Brown */ 769566063dSJacob Faibussowitsch PetscCall(SNESCreate(PETSC_COMM_WORLD,&snes)); 77c4762a1bSJed Brown 78c4762a1bSJed Brown /* 79c4762a1bSJed Brown Set the DMDA (grid structure) for the grids. 80c4762a1bSJed Brown */ 819566063dSJacob Faibussowitsch PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da)); 829566063dSJacob Faibussowitsch PetscCall(DMSetFromOptions(da)); 839566063dSJacob Faibussowitsch PetscCall(DMSetUp(da)); 849566063dSJacob Faibussowitsch PetscCall(DMSetApplicationContext(da,&user)); 859566063dSJacob Faibussowitsch PetscCall(SNESSetDM(snes,(DM)da)); 86c4762a1bSJed Brown 87c4762a1bSJed Brown /* 88c4762a1bSJed Brown Create the nonlinear solver, and tell it the functions to use 89c4762a1bSJed Brown */ 909566063dSJacob Faibussowitsch PetscCall(SNESSetFunction(snes,NULL,FormFunction,&user)); 919566063dSJacob Faibussowitsch PetscCall(SNESSetJacobian(snes,NULL,NULL,FormJacobian,&user)); 929566063dSJacob Faibussowitsch PetscCall(SNESSetFromOptions(snes)); 939566063dSJacob Faibussowitsch PetscCall(SNESSetComputeInitialGuess(snes,FormInitialGuess,NULL)); 94c4762a1bSJed Brown 959566063dSJacob Faibussowitsch PetscCall(SNESSolve(snes,NULL,NULL)); 969566063dSJacob Faibussowitsch PetscCall(SNESGetIterationNumber(snes,&its)); 979566063dSJacob Faibussowitsch PetscCall(SNESGetLinearSolveIterations(snes,&lits)); 98c4762a1bSJed Brown litspit = ((PetscReal)lits)/((PetscReal)its); 9963a3b9bcSJacob Faibussowitsch PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %" PetscInt_FMT "\n",its)); 10063a3b9bcSJacob Faibussowitsch PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %" PetscInt_FMT "\n",lits)); 1019566063dSJacob Faibussowitsch PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",(double)litspit)); 102c4762a1bSJed Brown 1039566063dSJacob Faibussowitsch PetscCall(DMDestroy(&da)); 1049566063dSJacob Faibussowitsch PetscCall(SNESDestroy(&snes)); 1059566063dSJacob Faibussowitsch PetscCall(PetscFinalize()); 106b122ec5aSJacob Faibussowitsch return 0; 107c4762a1bSJed Brown } 108c4762a1bSJed Brown /* -------------------- Form initial approximation ----------------- */ 109c4762a1bSJed Brown PetscErrorCode FormInitialGuess(SNES snes,Vec X,void *ctx) 110c4762a1bSJed Brown { 111c4762a1bSJed Brown AppCtx *user; 112c4762a1bSJed Brown PetscInt i,j,xs,ys,xm,ym; 113c4762a1bSJed Brown PetscReal tleft; 114c4762a1bSJed Brown PetscScalar **x; 115c4762a1bSJed Brown DM da; 116c4762a1bSJed Brown 117c4762a1bSJed Brown PetscFunctionBeginUser; 1189566063dSJacob Faibussowitsch PetscCall(SNESGetDM(snes,&da)); 1199566063dSJacob Faibussowitsch PetscCall(DMGetApplicationContext(da,&user)); 120c4762a1bSJed Brown tleft = user->tleft; 121c4762a1bSJed Brown /* Get ghost points */ 1229566063dSJacob Faibussowitsch PetscCall(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 1239566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,X,&x)); 124c4762a1bSJed Brown 125c4762a1bSJed Brown /* Compute initial guess */ 126c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 127c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 128c4762a1bSJed Brown x[j][i] = tleft; 129c4762a1bSJed Brown } 130c4762a1bSJed Brown } 1319566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,X,&x)); 132c4762a1bSJed Brown PetscFunctionReturn(0); 133c4762a1bSJed Brown } 134c4762a1bSJed Brown /* -------------------- Evaluate Function F(x) --------------------- */ 135c4762a1bSJed Brown PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr) 136c4762a1bSJed Brown { 137c4762a1bSJed Brown AppCtx *user = (AppCtx*)ptr; 138c4762a1bSJed Brown PetscInt i,j,mx,my,xs,ys,xm,ym; 139c4762a1bSJed Brown PetscScalar zero = 0.0,one = 1.0; 140c4762a1bSJed Brown PetscScalar hx,hy,hxdhy,hydhx; 141c4762a1bSJed Brown PetscScalar t0,tn,ts,te,tw,an,as,ae,aw,dn,ds,de,dw,fn = 0.0,fs = 0.0,fe =0.0,fw = 0.0; 142c4762a1bSJed Brown PetscScalar tleft,tright,beta; 143c4762a1bSJed Brown PetscScalar **x,**f; 144c4762a1bSJed Brown Vec localX; 145c4762a1bSJed Brown DM da; 146c4762a1bSJed Brown 147c4762a1bSJed Brown PetscFunctionBeginUser; 1489566063dSJacob Faibussowitsch PetscCall(SNESGetDM(snes,&da)); 1499566063dSJacob Faibussowitsch PetscCall(DMGetLocalVector(da,&localX)); 1509566063dSJacob Faibussowitsch PetscCall(DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0)); 151c4762a1bSJed Brown hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1); 152c4762a1bSJed Brown hxdhy = hx/hy; hydhx = hy/hx; 153c4762a1bSJed Brown tleft = user->tleft; tright = user->tright; 154c4762a1bSJed Brown beta = user->beta; 155c4762a1bSJed Brown 156c4762a1bSJed Brown /* Get ghost points */ 1579566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX)); 1589566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX)); 1599566063dSJacob Faibussowitsch PetscCall(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 1609566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,localX,&x)); 1619566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,F,&f)); 162c4762a1bSJed Brown 163c4762a1bSJed Brown /* Evaluate function */ 164c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 165c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 166c4762a1bSJed Brown t0 = x[j][i]; 167c4762a1bSJed Brown 168c4762a1bSJed Brown if (i > 0 && i < mx-1 && j > 0 && j < my-1) { 169c4762a1bSJed Brown 170c4762a1bSJed Brown /* general interior volume */ 171c4762a1bSJed Brown 172c4762a1bSJed Brown tw = x[j][i-1]; 173c4762a1bSJed Brown aw = 0.5*(t0 + tw); 174c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 175c4762a1bSJed Brown fw = dw*(t0 - tw); 176c4762a1bSJed Brown 177c4762a1bSJed Brown te = x[j][i+1]; 178c4762a1bSJed Brown ae = 0.5*(t0 + te); 179c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 180c4762a1bSJed Brown fe = de*(te - t0); 181c4762a1bSJed Brown 182c4762a1bSJed Brown ts = x[j-1][i]; 183c4762a1bSJed Brown as = 0.5*(t0 + ts); 184c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 185c4762a1bSJed Brown fs = ds*(t0 - ts); 186c4762a1bSJed Brown 187c4762a1bSJed Brown tn = x[j+1][i]; 188c4762a1bSJed Brown an = 0.5*(t0 + tn); 189c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 190c4762a1bSJed Brown fn = dn*(tn - t0); 191c4762a1bSJed Brown 192c4762a1bSJed Brown } else if (i == 0) { 193c4762a1bSJed Brown 194c4762a1bSJed Brown /* left-hand boundary */ 195c4762a1bSJed Brown tw = tleft; 196c4762a1bSJed Brown aw = 0.5*(t0 + tw); 197c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 198c4762a1bSJed Brown fw = dw*(t0 - tw); 199c4762a1bSJed Brown 200c4762a1bSJed Brown te = x[j][i+1]; 201c4762a1bSJed Brown ae = 0.5*(t0 + te); 202c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 203c4762a1bSJed Brown fe = de*(te - t0); 204c4762a1bSJed Brown 205c4762a1bSJed Brown if (j > 0) { 206c4762a1bSJed Brown ts = x[j-1][i]; 207c4762a1bSJed Brown as = 0.5*(t0 + ts); 208c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 209c4762a1bSJed Brown fs = ds*(t0 - ts); 210c4762a1bSJed Brown } else fs = zero; 211c4762a1bSJed Brown 212c4762a1bSJed Brown if (j < my-1) { 213c4762a1bSJed Brown tn = x[j+1][i]; 214c4762a1bSJed Brown an = 0.5*(t0 + tn); 215c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 216c4762a1bSJed Brown fn = dn*(tn - t0); 217c4762a1bSJed Brown } else fn = zero; 218c4762a1bSJed Brown 219c4762a1bSJed Brown } else if (i == mx-1) { 220c4762a1bSJed Brown 221c4762a1bSJed Brown /* right-hand boundary */ 222c4762a1bSJed Brown tw = x[j][i-1]; 223c4762a1bSJed Brown aw = 0.5*(t0 + tw); 224c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 225c4762a1bSJed Brown fw = dw*(t0 - tw); 226c4762a1bSJed Brown 227c4762a1bSJed Brown te = tright; 228c4762a1bSJed Brown ae = 0.5*(t0 + te); 229c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 230c4762a1bSJed Brown fe = de*(te - t0); 231c4762a1bSJed Brown 232c4762a1bSJed Brown if (j > 0) { 233c4762a1bSJed Brown ts = x[j-1][i]; 234c4762a1bSJed Brown as = 0.5*(t0 + ts); 235c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 236c4762a1bSJed Brown fs = ds*(t0 - ts); 237c4762a1bSJed Brown } else fs = zero; 238c4762a1bSJed Brown 239c4762a1bSJed Brown if (j < my-1) { 240c4762a1bSJed Brown tn = x[j+1][i]; 241c4762a1bSJed Brown an = 0.5*(t0 + tn); 242c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 243c4762a1bSJed Brown fn = dn*(tn - t0); 244c4762a1bSJed Brown } else fn = zero; 245c4762a1bSJed Brown 246c4762a1bSJed Brown } else if (j == 0) { 247c4762a1bSJed Brown 248c4762a1bSJed Brown /* bottom boundary,and i <> 0 or mx-1 */ 249c4762a1bSJed Brown tw = x[j][i-1]; 250c4762a1bSJed Brown aw = 0.5*(t0 + tw); 251c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 252c4762a1bSJed Brown fw = dw*(t0 - tw); 253c4762a1bSJed Brown 254c4762a1bSJed Brown te = x[j][i+1]; 255c4762a1bSJed Brown ae = 0.5*(t0 + te); 256c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 257c4762a1bSJed Brown fe = de*(te - t0); 258c4762a1bSJed Brown 259c4762a1bSJed Brown fs = zero; 260c4762a1bSJed Brown 261c4762a1bSJed Brown tn = x[j+1][i]; 262c4762a1bSJed Brown an = 0.5*(t0 + tn); 263c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 264c4762a1bSJed Brown fn = dn*(tn - t0); 265c4762a1bSJed Brown 266c4762a1bSJed Brown } else if (j == my-1) { 267c4762a1bSJed Brown 268c4762a1bSJed Brown /* top boundary,and i <> 0 or mx-1 */ 269c4762a1bSJed Brown tw = x[j][i-1]; 270c4762a1bSJed Brown aw = 0.5*(t0 + tw); 271c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 272c4762a1bSJed Brown fw = dw*(t0 - tw); 273c4762a1bSJed Brown 274c4762a1bSJed Brown te = x[j][i+1]; 275c4762a1bSJed Brown ae = 0.5*(t0 + te); 276c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 277c4762a1bSJed Brown fe = de*(te - t0); 278c4762a1bSJed Brown 279c4762a1bSJed Brown ts = x[j-1][i]; 280c4762a1bSJed Brown as = 0.5*(t0 + ts); 281c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 282c4762a1bSJed Brown fs = ds*(t0 - ts); 283c4762a1bSJed Brown 284c4762a1bSJed Brown fn = zero; 285c4762a1bSJed Brown 286c4762a1bSJed Brown } 287c4762a1bSJed Brown 288c4762a1bSJed Brown f[j][i] = -hydhx*(fe-fw) - hxdhy*(fn-fs); 289c4762a1bSJed Brown 290c4762a1bSJed Brown } 291c4762a1bSJed Brown } 2929566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,localX,&x)); 2939566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,F,&f)); 2949566063dSJacob Faibussowitsch PetscCall(DMRestoreLocalVector(da,&localX)); 2959566063dSJacob Faibussowitsch PetscCall(PetscLogFlops((22.0 + 4.0*POWFLOP)*ym*xm)); 296c4762a1bSJed Brown PetscFunctionReturn(0); 297c4762a1bSJed Brown } 298c4762a1bSJed Brown /* -------------------- Evaluate Jacobian F(x) --------------------- */ 299c4762a1bSJed Brown PetscErrorCode FormJacobian(SNES snes,Vec X,Mat jac,Mat B,void *ptr) 300c4762a1bSJed Brown { 301c4762a1bSJed Brown AppCtx *user = (AppCtx*)ptr; 302c4762a1bSJed Brown PetscInt i,j,mx,my,xs,ys,xm,ym; 303c4762a1bSJed Brown PetscScalar one = 1.0,hx,hy,hxdhy,hydhx,t0,tn,ts,te,tw; 304c4762a1bSJed Brown PetscScalar dn,ds,de,dw,an,as,ae,aw,bn,bs,be,bw,gn,gs,ge,gw; 305c4762a1bSJed Brown PetscScalar tleft,tright,beta,bm1,coef; 306c4762a1bSJed Brown PetscScalar v[5],**x; 307c4762a1bSJed Brown Vec localX; 308c4762a1bSJed Brown MatStencil col[5],row; 309c4762a1bSJed Brown DM da; 310c4762a1bSJed Brown 311c4762a1bSJed Brown PetscFunctionBeginUser; 3129566063dSJacob Faibussowitsch PetscCall(SNESGetDM(snes,&da)); 3139566063dSJacob Faibussowitsch PetscCall(DMGetLocalVector(da,&localX)); 3149566063dSJacob Faibussowitsch PetscCall(DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0)); 315c4762a1bSJed Brown hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1); 316c4762a1bSJed Brown hxdhy = hx/hy; hydhx = hy/hx; 317c4762a1bSJed Brown tleft = user->tleft; tright = user->tright; 318c4762a1bSJed Brown beta = user->beta; bm1 = user->bm1; coef = user->coef; 319c4762a1bSJed Brown 320c4762a1bSJed Brown /* Get ghost points */ 3219566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX)); 3229566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX)); 3239566063dSJacob Faibussowitsch PetscCall(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 3249566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,localX,&x)); 325c4762a1bSJed Brown 326c4762a1bSJed Brown /* Evaluate Jacobian of function */ 327c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 328c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 329c4762a1bSJed Brown t0 = x[j][i]; 330c4762a1bSJed Brown 331c4762a1bSJed Brown if (i > 0 && i < mx-1 && j > 0 && j < my-1) { 332c4762a1bSJed Brown 333c4762a1bSJed Brown /* general interior volume */ 334c4762a1bSJed Brown 335c4762a1bSJed Brown tw = x[j][i-1]; 336c4762a1bSJed Brown aw = 0.5*(t0 + tw); 337c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 338c4762a1bSJed Brown /* dw = bw * aw */ 339c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 340c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 341c4762a1bSJed Brown 342c4762a1bSJed Brown te = x[j][i+1]; 343c4762a1bSJed Brown ae = 0.5*(t0 + te); 344c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 345c4762a1bSJed Brown /* de = be * ae; */ 346c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 347c4762a1bSJed Brown ge = coef*be*(te - t0); 348c4762a1bSJed Brown 349c4762a1bSJed Brown ts = x[j-1][i]; 350c4762a1bSJed Brown as = 0.5*(t0 + ts); 351c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 352c4762a1bSJed Brown /* ds = bs * as; */ 353c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 354c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 355c4762a1bSJed Brown 356c4762a1bSJed Brown tn = x[j+1][i]; 357c4762a1bSJed Brown an = 0.5*(t0 + tn); 358c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 359c4762a1bSJed Brown /* dn = bn * an; */ 360c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 361c4762a1bSJed Brown gn = coef*bn*(tn - t0); 362c4762a1bSJed Brown 363c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 364c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 365c4762a1bSJed Brown v[2] = hxdhy*(ds + dn + gs - gn) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 366c4762a1bSJed Brown v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1; 367c4762a1bSJed Brown v[4] = -hxdhy*(dn + gn); col[4].j = j+1; col[4].i = i; 3689566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,5,col,v,INSERT_VALUES)); 369c4762a1bSJed Brown 370c4762a1bSJed Brown } else if (i == 0) { 371c4762a1bSJed Brown 372c4762a1bSJed Brown /* left-hand boundary */ 373c4762a1bSJed Brown tw = tleft; 374c4762a1bSJed Brown aw = 0.5*(t0 + tw); 375c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 376c4762a1bSJed Brown /* dw = bw * aw */ 377c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 378c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 379c4762a1bSJed Brown 380c4762a1bSJed Brown te = x[j][i + 1]; 381c4762a1bSJed Brown ae = 0.5*(t0 + te); 382c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 383c4762a1bSJed Brown /* de = be * ae; */ 384c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 385c4762a1bSJed Brown ge = coef*be*(te - t0); 386c4762a1bSJed Brown 387c4762a1bSJed Brown /* left-hand bottom boundary */ 388c4762a1bSJed Brown if (j == 0) { 389c4762a1bSJed Brown 390c4762a1bSJed Brown tn = x[j+1][i]; 391c4762a1bSJed Brown an = 0.5*(t0 + tn); 392c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 393c4762a1bSJed Brown /* dn = bn * an; */ 394c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 395c4762a1bSJed Brown gn = coef*bn*(tn - t0); 396c4762a1bSJed Brown 397c4762a1bSJed Brown v[0] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[0].j = row.j = j; col[0].i = row.i = i; 398c4762a1bSJed Brown v[1] = -hydhx*(de + ge); col[1].j = j; col[1].i = i+1; 399c4762a1bSJed Brown v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i; 4009566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 401c4762a1bSJed Brown 402c4762a1bSJed Brown /* left-hand interior boundary */ 403c4762a1bSJed Brown } else if (j < my-1) { 404c4762a1bSJed Brown 405c4762a1bSJed Brown ts = x[j-1][i]; 406c4762a1bSJed Brown as = 0.5*(t0 + ts); 407c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 408c4762a1bSJed Brown /* ds = bs * as; */ 409c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 410c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 411c4762a1bSJed Brown 412c4762a1bSJed Brown tn = x[j+1][i]; 413c4762a1bSJed Brown an = 0.5*(t0 + tn); 414c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 415c4762a1bSJed Brown /* dn = bn * an; */ 416c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 417c4762a1bSJed Brown gn = coef*bn*(tn - t0); 418c4762a1bSJed Brown 419c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 420c4762a1bSJed Brown v[1] = hxdhy*(ds + dn + gs - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 421c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 422c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 4239566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 424c4762a1bSJed Brown /* left-hand top boundary */ 425c4762a1bSJed Brown } else { 426c4762a1bSJed Brown 427c4762a1bSJed Brown ts = x[j-1][i]; 428c4762a1bSJed Brown as = 0.5*(t0 + ts); 429c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 430c4762a1bSJed Brown /* ds = bs * as; */ 431c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 432c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 433c4762a1bSJed Brown 434c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 435c4762a1bSJed Brown v[1] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 436c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 4379566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 438c4762a1bSJed Brown } 439c4762a1bSJed Brown 440c4762a1bSJed Brown } else if (i == mx-1) { 441c4762a1bSJed Brown 442c4762a1bSJed Brown /* right-hand boundary */ 443c4762a1bSJed Brown tw = x[j][i-1]; 444c4762a1bSJed Brown aw = 0.5*(t0 + tw); 445c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 446c4762a1bSJed Brown /* dw = bw * aw */ 447c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 448c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 449c4762a1bSJed Brown 450c4762a1bSJed Brown te = tright; 451c4762a1bSJed Brown ae = 0.5*(t0 + te); 452c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 453c4762a1bSJed Brown /* de = be * ae; */ 454c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 455c4762a1bSJed Brown ge = coef*be*(te - t0); 456c4762a1bSJed Brown 457c4762a1bSJed Brown /* right-hand bottom boundary */ 458c4762a1bSJed Brown if (j == 0) { 459c4762a1bSJed Brown 460c4762a1bSJed Brown tn = x[j+1][i]; 461c4762a1bSJed Brown an = 0.5*(t0 + tn); 462c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 463c4762a1bSJed Brown /* dn = bn * an; */ 464c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 465c4762a1bSJed Brown gn = coef*bn*(tn - t0); 466c4762a1bSJed Brown 467c4762a1bSJed Brown v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1; 468c4762a1bSJed Brown v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 469c4762a1bSJed Brown v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i; 4709566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 471c4762a1bSJed Brown 472c4762a1bSJed Brown /* right-hand interior boundary */ 473c4762a1bSJed Brown } else if (j < my-1) { 474c4762a1bSJed Brown 475c4762a1bSJed Brown ts = x[j-1][i]; 476c4762a1bSJed Brown as = 0.5*(t0 + ts); 477c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 478c4762a1bSJed Brown /* ds = bs * as; */ 479c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 480c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 481c4762a1bSJed Brown 482c4762a1bSJed Brown tn = x[j+1][i]; 483c4762a1bSJed Brown an = 0.5*(t0 + tn); 484c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 485c4762a1bSJed Brown /* dn = bn * an; */ 486c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 487c4762a1bSJed Brown gn = coef*bn*(tn - t0); 488c4762a1bSJed Brown 489c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 490c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 491c4762a1bSJed Brown v[2] = hxdhy*(ds + dn + gs - gn) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 492c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 4939566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 494c4762a1bSJed Brown /* right-hand top boundary */ 495c4762a1bSJed Brown } else { 496c4762a1bSJed Brown 497c4762a1bSJed Brown ts = x[j-1][i]; 498c4762a1bSJed Brown as = 0.5*(t0 + ts); 499c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 500c4762a1bSJed Brown /* ds = bs * as; */ 501c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 502c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 503c4762a1bSJed Brown 504c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 505c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 506c4762a1bSJed Brown v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 5079566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 508c4762a1bSJed Brown } 509c4762a1bSJed Brown 510c4762a1bSJed Brown /* bottom boundary,and i <> 0 or mx-1 */ 511c4762a1bSJed Brown } else if (j == 0) { 512c4762a1bSJed Brown 513c4762a1bSJed Brown tw = x[j][i-1]; 514c4762a1bSJed Brown aw = 0.5*(t0 + tw); 515c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 516c4762a1bSJed Brown /* dw = bw * aw */ 517c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 518c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 519c4762a1bSJed Brown 520c4762a1bSJed Brown te = x[j][i+1]; 521c4762a1bSJed Brown ae = 0.5*(t0 + te); 522c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 523c4762a1bSJed Brown /* de = be * ae; */ 524c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 525c4762a1bSJed Brown ge = coef*be*(te - t0); 526c4762a1bSJed Brown 527c4762a1bSJed Brown tn = x[j+1][i]; 528c4762a1bSJed Brown an = 0.5*(t0 + tn); 529c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 530c4762a1bSJed Brown /* dn = bn * an; */ 531c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 532c4762a1bSJed Brown gn = coef*bn*(tn - t0); 533c4762a1bSJed Brown 534c4762a1bSJed Brown v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1; 535c4762a1bSJed Brown v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 536c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 537c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 5389566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 539c4762a1bSJed Brown 540c4762a1bSJed Brown /* top boundary,and i <> 0 or mx-1 */ 541c4762a1bSJed Brown } else if (j == my-1) { 542c4762a1bSJed Brown 543c4762a1bSJed Brown tw = x[j][i-1]; 544c4762a1bSJed Brown aw = 0.5*(t0 + tw); 545c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 546c4762a1bSJed Brown /* dw = bw * aw */ 547c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 548c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 549c4762a1bSJed Brown 550c4762a1bSJed Brown te = x[j][i+1]; 551c4762a1bSJed Brown ae = 0.5*(t0 + te); 552c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 553c4762a1bSJed Brown /* de = be * ae; */ 554c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 555c4762a1bSJed Brown ge = coef*be*(te - t0); 556c4762a1bSJed Brown 557c4762a1bSJed Brown ts = x[j-1][i]; 558c4762a1bSJed Brown as = 0.5*(t0 + ts); 559c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 560c4762a1bSJed Brown /* ds = bs * as; */ 561c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 562c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 563c4762a1bSJed Brown 564c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 565c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 566c4762a1bSJed Brown v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 567c4762a1bSJed Brown v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1; 5689566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 569c4762a1bSJed Brown 570c4762a1bSJed Brown } 571c4762a1bSJed Brown } 572c4762a1bSJed Brown } 5739566063dSJacob Faibussowitsch PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 5749566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,localX,&x)); 5759566063dSJacob Faibussowitsch PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 5769566063dSJacob Faibussowitsch PetscCall(DMRestoreLocalVector(da,&localX)); 577c4762a1bSJed Brown if (jac != B) { 5789566063dSJacob Faibussowitsch PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY)); 5799566063dSJacob Faibussowitsch PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY)); 580c4762a1bSJed Brown } 581c4762a1bSJed Brown 5829566063dSJacob Faibussowitsch PetscCall(PetscLogFlops((41.0 + 8.0*POWFLOP)*xm*ym)); 583c4762a1bSJed Brown PetscFunctionReturn(0); 584c4762a1bSJed Brown } 585c4762a1bSJed Brown 586c4762a1bSJed Brown /*TEST 587c4762a1bSJed Brown 588c4762a1bSJed Brown test: 58941ba4c6cSHeeho Park suffix: 1 590c4762a1bSJed Brown args: -pc_type mg -ksp_type fgmres -da_refine 2 -pc_mg_galerkin pmat -snes_view 591c4762a1bSJed Brown requires: !single 592c4762a1bSJed Brown 59341ba4c6cSHeeho Park test: 59441ba4c6cSHeeho Park suffix: 2 59541ba4c6cSHeeho Park args: -pc_type mg -ksp_type fgmres -da_refine 2 -pc_mg_galerkin pmat -snes_view -snes_type newtontrdc 59641ba4c6cSHeeho Park requires: !single 59741ba4c6cSHeeho Park 598c4762a1bSJed Brown TEST*/ 599