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 609566063dSJacob Faibussowitsch PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 61c4762a1bSJed Brown 62c4762a1bSJed Brown /* set problem parameters */ 63c4762a1bSJed Brown user.tleft = 1.0; 64c4762a1bSJed Brown user.tright = 0.1; 65c4762a1bSJed Brown user.beta = 2.5; 669566063dSJacob Faibussowitsch PetscCall(PetscOptionsGetReal(NULL,NULL,"-tleft",&user.tleft,NULL)); 679566063dSJacob Faibussowitsch PetscCall(PetscOptionsGetReal(NULL,NULL,"-tright",&user.tright,NULL)); 689566063dSJacob Faibussowitsch PetscCall(PetscOptionsGetReal(NULL,NULL,"-beta",&user.beta,NULL)); 69c4762a1bSJed Brown user.bm1 = user.beta - 1.0; 70c4762a1bSJed Brown user.coef = user.beta/2.0; 71c4762a1bSJed Brown 72c4762a1bSJed Brown /* 73c4762a1bSJed Brown Create the multilevel DM data structure 74c4762a1bSJed Brown */ 759566063dSJacob Faibussowitsch PetscCall(SNESCreate(PETSC_COMM_WORLD,&snes)); 76c4762a1bSJed Brown 77c4762a1bSJed Brown /* 78c4762a1bSJed Brown Set the DMDA (grid structure) for the grids. 79c4762a1bSJed Brown */ 809566063dSJacob 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)); 819566063dSJacob Faibussowitsch PetscCall(DMSetFromOptions(da)); 829566063dSJacob Faibussowitsch PetscCall(DMSetUp(da)); 839566063dSJacob Faibussowitsch PetscCall(DMSetApplicationContext(da,&user)); 849566063dSJacob Faibussowitsch PetscCall(SNESSetDM(snes,(DM)da)); 85c4762a1bSJed Brown 86c4762a1bSJed Brown /* 87c4762a1bSJed Brown Create the nonlinear solver, and tell it the functions to use 88c4762a1bSJed Brown */ 899566063dSJacob Faibussowitsch PetscCall(SNESSetFunction(snes,NULL,FormFunction,&user)); 909566063dSJacob Faibussowitsch PetscCall(SNESSetJacobian(snes,NULL,NULL,FormJacobian,&user)); 919566063dSJacob Faibussowitsch PetscCall(SNESSetFromOptions(snes)); 929566063dSJacob Faibussowitsch PetscCall(SNESSetComputeInitialGuess(snes,FormInitialGuess,NULL)); 93c4762a1bSJed Brown 949566063dSJacob Faibussowitsch PetscCall(SNESSolve(snes,NULL,NULL)); 959566063dSJacob Faibussowitsch PetscCall(SNESGetIterationNumber(snes,&its)); 969566063dSJacob Faibussowitsch PetscCall(SNESGetLinearSolveIterations(snes,&lits)); 97c4762a1bSJed Brown litspit = ((PetscReal)lits)/((PetscReal)its); 98*63a3b9bcSJacob Faibussowitsch PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %" PetscInt_FMT "\n",its)); 99*63a3b9bcSJacob Faibussowitsch PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %" PetscInt_FMT "\n",lits)); 1009566063dSJacob Faibussowitsch PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",(double)litspit)); 101c4762a1bSJed Brown 1029566063dSJacob Faibussowitsch PetscCall(DMDestroy(&da)); 1039566063dSJacob Faibussowitsch PetscCall(SNESDestroy(&snes)); 1049566063dSJacob Faibussowitsch PetscCall(PetscFinalize()); 105b122ec5aSJacob Faibussowitsch return 0; 106c4762a1bSJed Brown } 107c4762a1bSJed Brown /* -------------------- Form initial approximation ----------------- */ 108c4762a1bSJed Brown PetscErrorCode FormInitialGuess(SNES snes,Vec X,void *ctx) 109c4762a1bSJed Brown { 110c4762a1bSJed Brown AppCtx *user; 111c4762a1bSJed Brown PetscInt i,j,xs,ys,xm,ym; 112c4762a1bSJed Brown PetscReal tleft; 113c4762a1bSJed Brown PetscScalar **x; 114c4762a1bSJed Brown DM da; 115c4762a1bSJed Brown 116c4762a1bSJed Brown PetscFunctionBeginUser; 1179566063dSJacob Faibussowitsch PetscCall(SNESGetDM(snes,&da)); 1189566063dSJacob Faibussowitsch PetscCall(DMGetApplicationContext(da,&user)); 119c4762a1bSJed Brown tleft = user->tleft; 120c4762a1bSJed Brown /* Get ghost points */ 1219566063dSJacob Faibussowitsch PetscCall(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 1229566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,X,&x)); 123c4762a1bSJed Brown 124c4762a1bSJed Brown /* Compute initial guess */ 125c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 126c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 127c4762a1bSJed Brown x[j][i] = tleft; 128c4762a1bSJed Brown } 129c4762a1bSJed Brown } 1309566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,X,&x)); 131c4762a1bSJed Brown PetscFunctionReturn(0); 132c4762a1bSJed Brown } 133c4762a1bSJed Brown /* -------------------- Evaluate Function F(x) --------------------- */ 134c4762a1bSJed Brown PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr) 135c4762a1bSJed Brown { 136c4762a1bSJed Brown AppCtx *user = (AppCtx*)ptr; 137c4762a1bSJed Brown PetscInt i,j,mx,my,xs,ys,xm,ym; 138c4762a1bSJed Brown PetscScalar zero = 0.0,one = 1.0; 139c4762a1bSJed Brown PetscScalar hx,hy,hxdhy,hydhx; 140c4762a1bSJed 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; 141c4762a1bSJed Brown PetscScalar tleft,tright,beta; 142c4762a1bSJed Brown PetscScalar **x,**f; 143c4762a1bSJed Brown Vec localX; 144c4762a1bSJed Brown DM da; 145c4762a1bSJed Brown 146c4762a1bSJed Brown PetscFunctionBeginUser; 1479566063dSJacob Faibussowitsch PetscCall(SNESGetDM(snes,&da)); 1489566063dSJacob Faibussowitsch PetscCall(DMGetLocalVector(da,&localX)); 1499566063dSJacob Faibussowitsch PetscCall(DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0)); 150c4762a1bSJed Brown hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1); 151c4762a1bSJed Brown hxdhy = hx/hy; hydhx = hy/hx; 152c4762a1bSJed Brown tleft = user->tleft; tright = user->tright; 153c4762a1bSJed Brown beta = user->beta; 154c4762a1bSJed Brown 155c4762a1bSJed Brown /* Get ghost points */ 1569566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX)); 1579566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX)); 1589566063dSJacob Faibussowitsch PetscCall(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 1599566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,localX,&x)); 1609566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,F,&f)); 161c4762a1bSJed Brown 162c4762a1bSJed Brown /* Evaluate function */ 163c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 164c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 165c4762a1bSJed Brown t0 = x[j][i]; 166c4762a1bSJed Brown 167c4762a1bSJed Brown if (i > 0 && i < mx-1 && j > 0 && j < my-1) { 168c4762a1bSJed Brown 169c4762a1bSJed Brown /* general interior volume */ 170c4762a1bSJed Brown 171c4762a1bSJed Brown tw = x[j][i-1]; 172c4762a1bSJed Brown aw = 0.5*(t0 + tw); 173c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 174c4762a1bSJed Brown fw = dw*(t0 - tw); 175c4762a1bSJed Brown 176c4762a1bSJed Brown te = x[j][i+1]; 177c4762a1bSJed Brown ae = 0.5*(t0 + te); 178c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 179c4762a1bSJed Brown fe = de*(te - t0); 180c4762a1bSJed Brown 181c4762a1bSJed Brown ts = x[j-1][i]; 182c4762a1bSJed Brown as = 0.5*(t0 + ts); 183c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 184c4762a1bSJed Brown fs = ds*(t0 - ts); 185c4762a1bSJed Brown 186c4762a1bSJed Brown tn = x[j+1][i]; 187c4762a1bSJed Brown an = 0.5*(t0 + tn); 188c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 189c4762a1bSJed Brown fn = dn*(tn - t0); 190c4762a1bSJed Brown 191c4762a1bSJed Brown } else if (i == 0) { 192c4762a1bSJed Brown 193c4762a1bSJed Brown /* left-hand boundary */ 194c4762a1bSJed Brown tw = tleft; 195c4762a1bSJed Brown aw = 0.5*(t0 + tw); 196c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 197c4762a1bSJed Brown fw = dw*(t0 - tw); 198c4762a1bSJed Brown 199c4762a1bSJed Brown te = x[j][i+1]; 200c4762a1bSJed Brown ae = 0.5*(t0 + te); 201c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 202c4762a1bSJed Brown fe = de*(te - t0); 203c4762a1bSJed Brown 204c4762a1bSJed Brown if (j > 0) { 205c4762a1bSJed Brown ts = x[j-1][i]; 206c4762a1bSJed Brown as = 0.5*(t0 + ts); 207c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 208c4762a1bSJed Brown fs = ds*(t0 - ts); 209c4762a1bSJed Brown } else fs = zero; 210c4762a1bSJed Brown 211c4762a1bSJed Brown if (j < my-1) { 212c4762a1bSJed Brown tn = x[j+1][i]; 213c4762a1bSJed Brown an = 0.5*(t0 + tn); 214c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 215c4762a1bSJed Brown fn = dn*(tn - t0); 216c4762a1bSJed Brown } else fn = zero; 217c4762a1bSJed Brown 218c4762a1bSJed Brown } else if (i == mx-1) { 219c4762a1bSJed Brown 220c4762a1bSJed Brown /* right-hand boundary */ 221c4762a1bSJed Brown tw = x[j][i-1]; 222c4762a1bSJed Brown aw = 0.5*(t0 + tw); 223c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 224c4762a1bSJed Brown fw = dw*(t0 - tw); 225c4762a1bSJed Brown 226c4762a1bSJed Brown te = tright; 227c4762a1bSJed Brown ae = 0.5*(t0 + te); 228c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 229c4762a1bSJed Brown fe = de*(te - t0); 230c4762a1bSJed Brown 231c4762a1bSJed Brown if (j > 0) { 232c4762a1bSJed Brown ts = x[j-1][i]; 233c4762a1bSJed Brown as = 0.5*(t0 + ts); 234c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 235c4762a1bSJed Brown fs = ds*(t0 - ts); 236c4762a1bSJed Brown } else fs = zero; 237c4762a1bSJed Brown 238c4762a1bSJed Brown if (j < my-1) { 239c4762a1bSJed Brown tn = x[j+1][i]; 240c4762a1bSJed Brown an = 0.5*(t0 + tn); 241c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 242c4762a1bSJed Brown fn = dn*(tn - t0); 243c4762a1bSJed Brown } else fn = zero; 244c4762a1bSJed Brown 245c4762a1bSJed Brown } else if (j == 0) { 246c4762a1bSJed Brown 247c4762a1bSJed Brown /* bottom boundary,and i <> 0 or mx-1 */ 248c4762a1bSJed Brown tw = x[j][i-1]; 249c4762a1bSJed Brown aw = 0.5*(t0 + tw); 250c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 251c4762a1bSJed Brown fw = dw*(t0 - tw); 252c4762a1bSJed Brown 253c4762a1bSJed Brown te = x[j][i+1]; 254c4762a1bSJed Brown ae = 0.5*(t0 + te); 255c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 256c4762a1bSJed Brown fe = de*(te - t0); 257c4762a1bSJed Brown 258c4762a1bSJed Brown fs = zero; 259c4762a1bSJed Brown 260c4762a1bSJed Brown tn = x[j+1][i]; 261c4762a1bSJed Brown an = 0.5*(t0 + tn); 262c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 263c4762a1bSJed Brown fn = dn*(tn - t0); 264c4762a1bSJed Brown 265c4762a1bSJed Brown } else if (j == my-1) { 266c4762a1bSJed Brown 267c4762a1bSJed Brown /* top boundary,and i <> 0 or mx-1 */ 268c4762a1bSJed Brown tw = x[j][i-1]; 269c4762a1bSJed Brown aw = 0.5*(t0 + tw); 270c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 271c4762a1bSJed Brown fw = dw*(t0 - tw); 272c4762a1bSJed Brown 273c4762a1bSJed Brown te = x[j][i+1]; 274c4762a1bSJed Brown ae = 0.5*(t0 + te); 275c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 276c4762a1bSJed Brown fe = de*(te - t0); 277c4762a1bSJed Brown 278c4762a1bSJed Brown ts = x[j-1][i]; 279c4762a1bSJed Brown as = 0.5*(t0 + ts); 280c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 281c4762a1bSJed Brown fs = ds*(t0 - ts); 282c4762a1bSJed Brown 283c4762a1bSJed Brown fn = zero; 284c4762a1bSJed Brown 285c4762a1bSJed Brown } 286c4762a1bSJed Brown 287c4762a1bSJed Brown f[j][i] = -hydhx*(fe-fw) - hxdhy*(fn-fs); 288c4762a1bSJed Brown 289c4762a1bSJed Brown } 290c4762a1bSJed Brown } 2919566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,localX,&x)); 2929566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,F,&f)); 2939566063dSJacob Faibussowitsch PetscCall(DMRestoreLocalVector(da,&localX)); 2949566063dSJacob Faibussowitsch PetscCall(PetscLogFlops((22.0 + 4.0*POWFLOP)*ym*xm)); 295c4762a1bSJed Brown PetscFunctionReturn(0); 296c4762a1bSJed Brown } 297c4762a1bSJed Brown /* -------------------- Evaluate Jacobian F(x) --------------------- */ 298c4762a1bSJed Brown PetscErrorCode FormJacobian(SNES snes,Vec X,Mat jac,Mat B,void *ptr) 299c4762a1bSJed Brown { 300c4762a1bSJed Brown AppCtx *user = (AppCtx*)ptr; 301c4762a1bSJed Brown PetscInt i,j,mx,my,xs,ys,xm,ym; 302c4762a1bSJed Brown PetscScalar one = 1.0,hx,hy,hxdhy,hydhx,t0,tn,ts,te,tw; 303c4762a1bSJed Brown PetscScalar dn,ds,de,dw,an,as,ae,aw,bn,bs,be,bw,gn,gs,ge,gw; 304c4762a1bSJed Brown PetscScalar tleft,tright,beta,bm1,coef; 305c4762a1bSJed Brown PetscScalar v[5],**x; 306c4762a1bSJed Brown Vec localX; 307c4762a1bSJed Brown MatStencil col[5],row; 308c4762a1bSJed Brown DM da; 309c4762a1bSJed Brown 310c4762a1bSJed Brown PetscFunctionBeginUser; 3119566063dSJacob Faibussowitsch PetscCall(SNESGetDM(snes,&da)); 3129566063dSJacob Faibussowitsch PetscCall(DMGetLocalVector(da,&localX)); 3139566063dSJacob Faibussowitsch PetscCall(DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0)); 314c4762a1bSJed Brown hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1); 315c4762a1bSJed Brown hxdhy = hx/hy; hydhx = hy/hx; 316c4762a1bSJed Brown tleft = user->tleft; tright = user->tright; 317c4762a1bSJed Brown beta = user->beta; bm1 = user->bm1; coef = user->coef; 318c4762a1bSJed Brown 319c4762a1bSJed Brown /* Get ghost points */ 3209566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX)); 3219566063dSJacob Faibussowitsch PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX)); 3229566063dSJacob Faibussowitsch PetscCall(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 3239566063dSJacob Faibussowitsch PetscCall(DMDAVecGetArray(da,localX,&x)); 324c4762a1bSJed Brown 325c4762a1bSJed Brown /* Evaluate Jacobian of function */ 326c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 327c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 328c4762a1bSJed Brown t0 = x[j][i]; 329c4762a1bSJed Brown 330c4762a1bSJed Brown if (i > 0 && i < mx-1 && j > 0 && j < my-1) { 331c4762a1bSJed Brown 332c4762a1bSJed Brown /* general interior volume */ 333c4762a1bSJed Brown 334c4762a1bSJed Brown tw = x[j][i-1]; 335c4762a1bSJed Brown aw = 0.5*(t0 + tw); 336c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 337c4762a1bSJed Brown /* dw = bw * aw */ 338c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 339c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 340c4762a1bSJed Brown 341c4762a1bSJed Brown te = x[j][i+1]; 342c4762a1bSJed Brown ae = 0.5*(t0 + te); 343c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 344c4762a1bSJed Brown /* de = be * ae; */ 345c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 346c4762a1bSJed Brown ge = coef*be*(te - t0); 347c4762a1bSJed Brown 348c4762a1bSJed Brown ts = x[j-1][i]; 349c4762a1bSJed Brown as = 0.5*(t0 + ts); 350c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 351c4762a1bSJed Brown /* ds = bs * as; */ 352c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 353c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 354c4762a1bSJed Brown 355c4762a1bSJed Brown tn = x[j+1][i]; 356c4762a1bSJed Brown an = 0.5*(t0 + tn); 357c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 358c4762a1bSJed Brown /* dn = bn * an; */ 359c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 360c4762a1bSJed Brown gn = coef*bn*(tn - t0); 361c4762a1bSJed Brown 362c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 363c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 364c4762a1bSJed 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; 365c4762a1bSJed Brown v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1; 366c4762a1bSJed Brown v[4] = -hxdhy*(dn + gn); col[4].j = j+1; col[4].i = i; 3679566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,5,col,v,INSERT_VALUES)); 368c4762a1bSJed Brown 369c4762a1bSJed Brown } else if (i == 0) { 370c4762a1bSJed Brown 371c4762a1bSJed Brown /* left-hand boundary */ 372c4762a1bSJed Brown tw = tleft; 373c4762a1bSJed Brown aw = 0.5*(t0 + tw); 374c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 375c4762a1bSJed Brown /* dw = bw * aw */ 376c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 377c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 378c4762a1bSJed Brown 379c4762a1bSJed Brown te = x[j][i + 1]; 380c4762a1bSJed Brown ae = 0.5*(t0 + te); 381c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 382c4762a1bSJed Brown /* de = be * ae; */ 383c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 384c4762a1bSJed Brown ge = coef*be*(te - t0); 385c4762a1bSJed Brown 386c4762a1bSJed Brown /* left-hand bottom boundary */ 387c4762a1bSJed Brown if (j == 0) { 388c4762a1bSJed Brown 389c4762a1bSJed Brown tn = x[j+1][i]; 390c4762a1bSJed Brown an = 0.5*(t0 + tn); 391c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 392c4762a1bSJed Brown /* dn = bn * an; */ 393c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 394c4762a1bSJed Brown gn = coef*bn*(tn - t0); 395c4762a1bSJed Brown 396c4762a1bSJed Brown v[0] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[0].j = row.j = j; col[0].i = row.i = i; 397c4762a1bSJed Brown v[1] = -hydhx*(de + ge); col[1].j = j; col[1].i = i+1; 398c4762a1bSJed Brown v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i; 3999566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 400c4762a1bSJed Brown 401c4762a1bSJed Brown /* left-hand interior boundary */ 402c4762a1bSJed Brown } else if (j < my-1) { 403c4762a1bSJed Brown 404c4762a1bSJed Brown ts = x[j-1][i]; 405c4762a1bSJed Brown as = 0.5*(t0 + ts); 406c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 407c4762a1bSJed Brown /* ds = bs * as; */ 408c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 409c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 410c4762a1bSJed Brown 411c4762a1bSJed Brown tn = x[j+1][i]; 412c4762a1bSJed Brown an = 0.5*(t0 + tn); 413c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 414c4762a1bSJed Brown /* dn = bn * an; */ 415c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 416c4762a1bSJed Brown gn = coef*bn*(tn - t0); 417c4762a1bSJed Brown 418c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 419c4762a1bSJed 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; 420c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 421c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 4229566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 423c4762a1bSJed Brown /* left-hand top boundary */ 424c4762a1bSJed Brown } else { 425c4762a1bSJed Brown 426c4762a1bSJed Brown ts = x[j-1][i]; 427c4762a1bSJed Brown as = 0.5*(t0 + ts); 428c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 429c4762a1bSJed Brown /* ds = bs * as; */ 430c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 431c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 432c4762a1bSJed Brown 433c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 434c4762a1bSJed Brown v[1] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 435c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 4369566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 437c4762a1bSJed Brown } 438c4762a1bSJed Brown 439c4762a1bSJed Brown } else if (i == mx-1) { 440c4762a1bSJed Brown 441c4762a1bSJed Brown /* right-hand boundary */ 442c4762a1bSJed Brown tw = x[j][i-1]; 443c4762a1bSJed Brown aw = 0.5*(t0 + tw); 444c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 445c4762a1bSJed Brown /* dw = bw * aw */ 446c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 447c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 448c4762a1bSJed Brown 449c4762a1bSJed Brown te = tright; 450c4762a1bSJed Brown ae = 0.5*(t0 + te); 451c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 452c4762a1bSJed Brown /* de = be * ae; */ 453c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 454c4762a1bSJed Brown ge = coef*be*(te - t0); 455c4762a1bSJed Brown 456c4762a1bSJed Brown /* right-hand bottom boundary */ 457c4762a1bSJed Brown if (j == 0) { 458c4762a1bSJed Brown 459c4762a1bSJed Brown tn = x[j+1][i]; 460c4762a1bSJed Brown an = 0.5*(t0 + tn); 461c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 462c4762a1bSJed Brown /* dn = bn * an; */ 463c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 464c4762a1bSJed Brown gn = coef*bn*(tn - t0); 465c4762a1bSJed Brown 466c4762a1bSJed Brown v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1; 467c4762a1bSJed Brown v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 468c4762a1bSJed Brown v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i; 4699566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 470c4762a1bSJed Brown 471c4762a1bSJed Brown /* right-hand interior boundary */ 472c4762a1bSJed Brown } else if (j < my-1) { 473c4762a1bSJed Brown 474c4762a1bSJed Brown ts = x[j-1][i]; 475c4762a1bSJed Brown as = 0.5*(t0 + ts); 476c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 477c4762a1bSJed Brown /* ds = bs * as; */ 478c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 479c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 480c4762a1bSJed Brown 481c4762a1bSJed Brown tn = x[j+1][i]; 482c4762a1bSJed Brown an = 0.5*(t0 + tn); 483c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 484c4762a1bSJed Brown /* dn = bn * an; */ 485c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 486c4762a1bSJed Brown gn = coef*bn*(tn - t0); 487c4762a1bSJed Brown 488c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 489c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 490c4762a1bSJed 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; 491c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 4929566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 493c4762a1bSJed Brown /* right-hand top boundary */ 494c4762a1bSJed Brown } else { 495c4762a1bSJed Brown 496c4762a1bSJed Brown ts = x[j-1][i]; 497c4762a1bSJed Brown as = 0.5*(t0 + ts); 498c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 499c4762a1bSJed Brown /* ds = bs * as; */ 500c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 501c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 502c4762a1bSJed Brown 503c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 504c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 505c4762a1bSJed Brown v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 5069566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 507c4762a1bSJed Brown } 508c4762a1bSJed Brown 509c4762a1bSJed Brown /* bottom boundary,and i <> 0 or mx-1 */ 510c4762a1bSJed Brown } else if (j == 0) { 511c4762a1bSJed Brown 512c4762a1bSJed Brown tw = x[j][i-1]; 513c4762a1bSJed Brown aw = 0.5*(t0 + tw); 514c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 515c4762a1bSJed Brown /* dw = bw * aw */ 516c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 517c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 518c4762a1bSJed Brown 519c4762a1bSJed Brown te = x[j][i+1]; 520c4762a1bSJed Brown ae = 0.5*(t0 + te); 521c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 522c4762a1bSJed Brown /* de = be * ae; */ 523c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 524c4762a1bSJed Brown ge = coef*be*(te - t0); 525c4762a1bSJed Brown 526c4762a1bSJed Brown tn = x[j+1][i]; 527c4762a1bSJed Brown an = 0.5*(t0 + tn); 528c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 529c4762a1bSJed Brown /* dn = bn * an; */ 530c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 531c4762a1bSJed Brown gn = coef*bn*(tn - t0); 532c4762a1bSJed Brown 533c4762a1bSJed Brown v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1; 534c4762a1bSJed Brown v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 535c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 536c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 5379566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 538c4762a1bSJed Brown 539c4762a1bSJed Brown /* top boundary,and i <> 0 or mx-1 */ 540c4762a1bSJed Brown } else if (j == my-1) { 541c4762a1bSJed Brown 542c4762a1bSJed Brown tw = x[j][i-1]; 543c4762a1bSJed Brown aw = 0.5*(t0 + tw); 544c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 545c4762a1bSJed Brown /* dw = bw * aw */ 546c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 547c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 548c4762a1bSJed Brown 549c4762a1bSJed Brown te = x[j][i+1]; 550c4762a1bSJed Brown ae = 0.5*(t0 + te); 551c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 552c4762a1bSJed Brown /* de = be * ae; */ 553c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 554c4762a1bSJed Brown ge = coef*be*(te - t0); 555c4762a1bSJed Brown 556c4762a1bSJed Brown ts = x[j-1][i]; 557c4762a1bSJed Brown as = 0.5*(t0 + ts); 558c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 559c4762a1bSJed Brown /* ds = bs * as; */ 560c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 561c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 562c4762a1bSJed Brown 563c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 564c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 565c4762a1bSJed Brown v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 566c4762a1bSJed Brown v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1; 5679566063dSJacob Faibussowitsch PetscCall(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 568c4762a1bSJed Brown 569c4762a1bSJed Brown } 570c4762a1bSJed Brown } 571c4762a1bSJed Brown } 5729566063dSJacob Faibussowitsch PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 5739566063dSJacob Faibussowitsch PetscCall(DMDAVecRestoreArray(da,localX,&x)); 5749566063dSJacob Faibussowitsch PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 5759566063dSJacob Faibussowitsch PetscCall(DMRestoreLocalVector(da,&localX)); 576c4762a1bSJed Brown if (jac != B) { 5779566063dSJacob Faibussowitsch PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY)); 5789566063dSJacob Faibussowitsch PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY)); 579c4762a1bSJed Brown } 580c4762a1bSJed Brown 5819566063dSJacob Faibussowitsch PetscCall(PetscLogFlops((41.0 + 8.0*POWFLOP)*xm*ym)); 582c4762a1bSJed Brown PetscFunctionReturn(0); 583c4762a1bSJed Brown } 584c4762a1bSJed Brown 585c4762a1bSJed Brown /*TEST 586c4762a1bSJed Brown 587c4762a1bSJed Brown test: 58841ba4c6cSHeeho Park suffix: 1 589c4762a1bSJed Brown args: -pc_type mg -ksp_type fgmres -da_refine 2 -pc_mg_galerkin pmat -snes_view 590c4762a1bSJed Brown requires: !single 591c4762a1bSJed Brown 59241ba4c6cSHeeho Park test: 59341ba4c6cSHeeho Park suffix: 2 59441ba4c6cSHeeho Park args: -pc_type mg -ksp_type fgmres -da_refine 2 -pc_mg_galerkin pmat -snes_view -snes_type newtontrdc 59541ba4c6cSHeeho Park requires: !single 59641ba4c6cSHeeho Park 597c4762a1bSJed Brown TEST*/ 598