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 /*T 15c4762a1bSJed Brown Concepts: SNES^solving a system of nonlinear equations 16c4762a1bSJed Brown Concepts: DMDA^using distributed arrays 17c4762a1bSJed Brown Concepts: multigrid; 18c4762a1bSJed Brown Processors: n 19c4762a1bSJed Brown T*/ 20c4762a1bSJed Brown 21c4762a1bSJed Brown /* 22c4762a1bSJed Brown 23c4762a1bSJed Brown This example models the partial differential equation 24c4762a1bSJed Brown 25c4762a1bSJed Brown - Div(alpha* T^beta (GRAD T)) = 0. 26c4762a1bSJed Brown 27c4762a1bSJed Brown where beta = 2.5 and alpha = 1.0 28c4762a1bSJed Brown 29c4762a1bSJed Brown BC: T_left = 1.0, T_right = 0.1, dT/dn_top = dTdn_bottom = 0. 30c4762a1bSJed Brown 31c4762a1bSJed Brown in the unit square, which is uniformly discretized in each of x and 32c4762a1bSJed Brown y in this simple encoding. The degrees of freedom are cell centered. 33c4762a1bSJed Brown 34c4762a1bSJed Brown A finite volume approximation with the usual 5-point stencil 35c4762a1bSJed Brown is used to discretize the boundary value problem to obtain a 36c4762a1bSJed Brown nonlinear system of equations. 37c4762a1bSJed Brown 38c4762a1bSJed Brown This code was contributed by David Keyes 39c4762a1bSJed Brown 40c4762a1bSJed Brown */ 41c4762a1bSJed Brown 42c4762a1bSJed Brown #include <petscsnes.h> 43c4762a1bSJed Brown #include <petscdm.h> 44c4762a1bSJed Brown #include <petscdmda.h> 45c4762a1bSJed Brown 46c4762a1bSJed Brown /* User-defined application context */ 47c4762a1bSJed Brown 48c4762a1bSJed Brown typedef struct { 49c4762a1bSJed Brown PetscReal tleft,tright; /* Dirichlet boundary conditions */ 50c4762a1bSJed Brown PetscReal beta,bm1,coef; /* nonlinear diffusivity parameterizations */ 51c4762a1bSJed Brown } AppCtx; 52c4762a1bSJed Brown 53c4762a1bSJed Brown #define POWFLOP 5 /* assume a pow() takes five flops */ 54c4762a1bSJed Brown 55c4762a1bSJed Brown extern PetscErrorCode FormInitialGuess(SNES,Vec,void*); 56c4762a1bSJed Brown extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*); 57c4762a1bSJed Brown extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*); 58c4762a1bSJed Brown 59c4762a1bSJed Brown int main(int argc,char **argv) 60c4762a1bSJed Brown { 61c4762a1bSJed Brown SNES snes; 62c4762a1bSJed Brown AppCtx user; 63c4762a1bSJed Brown PetscInt its,lits; 64c4762a1bSJed Brown PetscReal litspit; 65c4762a1bSJed Brown DM da; 66c4762a1bSJed Brown 67*b122ec5aSJacob Faibussowitsch CHKERRQ(PetscInitialize(&argc,&argv,NULL,help)); 68c4762a1bSJed Brown 69c4762a1bSJed Brown /* set problem parameters */ 70c4762a1bSJed Brown user.tleft = 1.0; 71c4762a1bSJed Brown user.tright = 0.1; 72c4762a1bSJed Brown user.beta = 2.5; 735f80ce2aSJacob Faibussowitsch CHKERRQ(PetscOptionsGetReal(NULL,NULL,"-tleft",&user.tleft,NULL)); 745f80ce2aSJacob Faibussowitsch CHKERRQ(PetscOptionsGetReal(NULL,NULL,"-tright",&user.tright,NULL)); 755f80ce2aSJacob Faibussowitsch CHKERRQ(PetscOptionsGetReal(NULL,NULL,"-beta",&user.beta,NULL)); 76c4762a1bSJed Brown user.bm1 = user.beta - 1.0; 77c4762a1bSJed Brown user.coef = user.beta/2.0; 78c4762a1bSJed Brown 79c4762a1bSJed Brown /* 80c4762a1bSJed Brown Create the multilevel DM data structure 81c4762a1bSJed Brown */ 825f80ce2aSJacob Faibussowitsch CHKERRQ(SNESCreate(PETSC_COMM_WORLD,&snes)); 83c4762a1bSJed Brown 84c4762a1bSJed Brown /* 85c4762a1bSJed Brown Set the DMDA (grid structure) for the grids. 86c4762a1bSJed Brown */ 875f80ce2aSJacob Faibussowitsch CHKERRQ(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da)); 885f80ce2aSJacob Faibussowitsch CHKERRQ(DMSetFromOptions(da)); 895f80ce2aSJacob Faibussowitsch CHKERRQ(DMSetUp(da)); 905f80ce2aSJacob Faibussowitsch CHKERRQ(DMSetApplicationContext(da,&user)); 915f80ce2aSJacob Faibussowitsch CHKERRQ(SNESSetDM(snes,(DM)da)); 92c4762a1bSJed Brown 93c4762a1bSJed Brown /* 94c4762a1bSJed Brown Create the nonlinear solver, and tell it the functions to use 95c4762a1bSJed Brown */ 965f80ce2aSJacob Faibussowitsch CHKERRQ(SNESSetFunction(snes,NULL,FormFunction,&user)); 975f80ce2aSJacob Faibussowitsch CHKERRQ(SNESSetJacobian(snes,NULL,NULL,FormJacobian,&user)); 985f80ce2aSJacob Faibussowitsch CHKERRQ(SNESSetFromOptions(snes)); 995f80ce2aSJacob Faibussowitsch CHKERRQ(SNESSetComputeInitialGuess(snes,FormInitialGuess,NULL)); 100c4762a1bSJed Brown 1015f80ce2aSJacob Faibussowitsch CHKERRQ(SNESSolve(snes,NULL,NULL)); 1025f80ce2aSJacob Faibussowitsch CHKERRQ(SNESGetIterationNumber(snes,&its)); 1035f80ce2aSJacob Faibussowitsch CHKERRQ(SNESGetLinearSolveIterations(snes,&lits)); 104c4762a1bSJed Brown litspit = ((PetscReal)lits)/((PetscReal)its); 1055f80ce2aSJacob Faibussowitsch CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its)); 1065f80ce2aSJacob Faibussowitsch CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %D\n",lits)); 1075f80ce2aSJacob Faibussowitsch CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",(double)litspit)); 108c4762a1bSJed Brown 1095f80ce2aSJacob Faibussowitsch CHKERRQ(DMDestroy(&da)); 1105f80ce2aSJacob Faibussowitsch CHKERRQ(SNESDestroy(&snes)); 111*b122ec5aSJacob Faibussowitsch CHKERRQ(PetscFinalize()); 112*b122ec5aSJacob Faibussowitsch return 0; 113c4762a1bSJed Brown } 114c4762a1bSJed Brown /* -------------------- Form initial approximation ----------------- */ 115c4762a1bSJed Brown PetscErrorCode FormInitialGuess(SNES snes,Vec X,void *ctx) 116c4762a1bSJed Brown { 117c4762a1bSJed Brown AppCtx *user; 118c4762a1bSJed Brown PetscInt i,j,xs,ys,xm,ym; 119c4762a1bSJed Brown PetscReal tleft; 120c4762a1bSJed Brown PetscScalar **x; 121c4762a1bSJed Brown DM da; 122c4762a1bSJed Brown 123c4762a1bSJed Brown PetscFunctionBeginUser; 1245f80ce2aSJacob Faibussowitsch CHKERRQ(SNESGetDM(snes,&da)); 1255f80ce2aSJacob Faibussowitsch CHKERRQ(DMGetApplicationContext(da,&user)); 126c4762a1bSJed Brown tleft = user->tleft; 127c4762a1bSJed Brown /* Get ghost points */ 1285f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 1295f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecGetArray(da,X,&x)); 130c4762a1bSJed Brown 131c4762a1bSJed Brown /* Compute initial guess */ 132c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 133c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 134c4762a1bSJed Brown x[j][i] = tleft; 135c4762a1bSJed Brown } 136c4762a1bSJed Brown } 1375f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecRestoreArray(da,X,&x)); 138c4762a1bSJed Brown PetscFunctionReturn(0); 139c4762a1bSJed Brown } 140c4762a1bSJed Brown /* -------------------- Evaluate Function F(x) --------------------- */ 141c4762a1bSJed Brown PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr) 142c4762a1bSJed Brown { 143c4762a1bSJed Brown AppCtx *user = (AppCtx*)ptr; 144c4762a1bSJed Brown PetscInt i,j,mx,my,xs,ys,xm,ym; 145c4762a1bSJed Brown PetscScalar zero = 0.0,one = 1.0; 146c4762a1bSJed Brown PetscScalar hx,hy,hxdhy,hydhx; 147c4762a1bSJed 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; 148c4762a1bSJed Brown PetscScalar tleft,tright,beta; 149c4762a1bSJed Brown PetscScalar **x,**f; 150c4762a1bSJed Brown Vec localX; 151c4762a1bSJed Brown DM da; 152c4762a1bSJed Brown 153c4762a1bSJed Brown PetscFunctionBeginUser; 1545f80ce2aSJacob Faibussowitsch CHKERRQ(SNESGetDM(snes,&da)); 1555f80ce2aSJacob Faibussowitsch CHKERRQ(DMGetLocalVector(da,&localX)); 1565f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0)); 157c4762a1bSJed Brown hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1); 158c4762a1bSJed Brown hxdhy = hx/hy; hydhx = hy/hx; 159c4762a1bSJed Brown tleft = user->tleft; tright = user->tright; 160c4762a1bSJed Brown beta = user->beta; 161c4762a1bSJed Brown 162c4762a1bSJed Brown /* Get ghost points */ 1635f80ce2aSJacob Faibussowitsch CHKERRQ(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX)); 1645f80ce2aSJacob Faibussowitsch CHKERRQ(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX)); 1655f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 1665f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecGetArray(da,localX,&x)); 1675f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecGetArray(da,F,&f)); 168c4762a1bSJed Brown 169c4762a1bSJed Brown /* Evaluate function */ 170c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 171c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 172c4762a1bSJed Brown t0 = x[j][i]; 173c4762a1bSJed Brown 174c4762a1bSJed Brown if (i > 0 && i < mx-1 && j > 0 && j < my-1) { 175c4762a1bSJed Brown 176c4762a1bSJed Brown /* general interior volume */ 177c4762a1bSJed Brown 178c4762a1bSJed Brown tw = x[j][i-1]; 179c4762a1bSJed Brown aw = 0.5*(t0 + tw); 180c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 181c4762a1bSJed Brown fw = dw*(t0 - tw); 182c4762a1bSJed Brown 183c4762a1bSJed Brown te = x[j][i+1]; 184c4762a1bSJed Brown ae = 0.5*(t0 + te); 185c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 186c4762a1bSJed Brown fe = de*(te - t0); 187c4762a1bSJed Brown 188c4762a1bSJed Brown ts = x[j-1][i]; 189c4762a1bSJed Brown as = 0.5*(t0 + ts); 190c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 191c4762a1bSJed Brown fs = ds*(t0 - ts); 192c4762a1bSJed Brown 193c4762a1bSJed Brown tn = x[j+1][i]; 194c4762a1bSJed Brown an = 0.5*(t0 + tn); 195c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 196c4762a1bSJed Brown fn = dn*(tn - t0); 197c4762a1bSJed Brown 198c4762a1bSJed Brown } else if (i == 0) { 199c4762a1bSJed Brown 200c4762a1bSJed Brown /* left-hand boundary */ 201c4762a1bSJed Brown tw = tleft; 202c4762a1bSJed Brown aw = 0.5*(t0 + tw); 203c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 204c4762a1bSJed Brown fw = dw*(t0 - tw); 205c4762a1bSJed Brown 206c4762a1bSJed Brown te = x[j][i+1]; 207c4762a1bSJed Brown ae = 0.5*(t0 + te); 208c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 209c4762a1bSJed Brown fe = de*(te - t0); 210c4762a1bSJed Brown 211c4762a1bSJed Brown if (j > 0) { 212c4762a1bSJed Brown ts = x[j-1][i]; 213c4762a1bSJed Brown as = 0.5*(t0 + ts); 214c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 215c4762a1bSJed Brown fs = ds*(t0 - ts); 216c4762a1bSJed Brown } else fs = zero; 217c4762a1bSJed Brown 218c4762a1bSJed Brown if (j < my-1) { 219c4762a1bSJed Brown tn = x[j+1][i]; 220c4762a1bSJed Brown an = 0.5*(t0 + tn); 221c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 222c4762a1bSJed Brown fn = dn*(tn - t0); 223c4762a1bSJed Brown } else fn = zero; 224c4762a1bSJed Brown 225c4762a1bSJed Brown } else if (i == mx-1) { 226c4762a1bSJed Brown 227c4762a1bSJed Brown /* right-hand boundary */ 228c4762a1bSJed Brown tw = x[j][i-1]; 229c4762a1bSJed Brown aw = 0.5*(t0 + tw); 230c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 231c4762a1bSJed Brown fw = dw*(t0 - tw); 232c4762a1bSJed Brown 233c4762a1bSJed Brown te = tright; 234c4762a1bSJed Brown ae = 0.5*(t0 + te); 235c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 236c4762a1bSJed Brown fe = de*(te - t0); 237c4762a1bSJed Brown 238c4762a1bSJed Brown if (j > 0) { 239c4762a1bSJed Brown ts = x[j-1][i]; 240c4762a1bSJed Brown as = 0.5*(t0 + ts); 241c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 242c4762a1bSJed Brown fs = ds*(t0 - ts); 243c4762a1bSJed Brown } else fs = zero; 244c4762a1bSJed Brown 245c4762a1bSJed Brown if (j < my-1) { 246c4762a1bSJed Brown tn = x[j+1][i]; 247c4762a1bSJed Brown an = 0.5*(t0 + tn); 248c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 249c4762a1bSJed Brown fn = dn*(tn - t0); 250c4762a1bSJed Brown } else fn = zero; 251c4762a1bSJed Brown 252c4762a1bSJed Brown } else if (j == 0) { 253c4762a1bSJed Brown 254c4762a1bSJed Brown /* bottom boundary,and i <> 0 or mx-1 */ 255c4762a1bSJed Brown tw = x[j][i-1]; 256c4762a1bSJed Brown aw = 0.5*(t0 + tw); 257c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 258c4762a1bSJed Brown fw = dw*(t0 - tw); 259c4762a1bSJed Brown 260c4762a1bSJed Brown te = x[j][i+1]; 261c4762a1bSJed Brown ae = 0.5*(t0 + te); 262c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 263c4762a1bSJed Brown fe = de*(te - t0); 264c4762a1bSJed Brown 265c4762a1bSJed Brown fs = zero; 266c4762a1bSJed Brown 267c4762a1bSJed Brown tn = x[j+1][i]; 268c4762a1bSJed Brown an = 0.5*(t0 + tn); 269c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 270c4762a1bSJed Brown fn = dn*(tn - t0); 271c4762a1bSJed Brown 272c4762a1bSJed Brown } else if (j == my-1) { 273c4762a1bSJed Brown 274c4762a1bSJed Brown /* top boundary,and i <> 0 or mx-1 */ 275c4762a1bSJed Brown tw = x[j][i-1]; 276c4762a1bSJed Brown aw = 0.5*(t0 + tw); 277c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 278c4762a1bSJed Brown fw = dw*(t0 - tw); 279c4762a1bSJed Brown 280c4762a1bSJed Brown te = x[j][i+1]; 281c4762a1bSJed Brown ae = 0.5*(t0 + te); 282c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 283c4762a1bSJed Brown fe = de*(te - t0); 284c4762a1bSJed Brown 285c4762a1bSJed Brown ts = x[j-1][i]; 286c4762a1bSJed Brown as = 0.5*(t0 + ts); 287c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 288c4762a1bSJed Brown fs = ds*(t0 - ts); 289c4762a1bSJed Brown 290c4762a1bSJed Brown fn = zero; 291c4762a1bSJed Brown 292c4762a1bSJed Brown } 293c4762a1bSJed Brown 294c4762a1bSJed Brown f[j][i] = -hydhx*(fe-fw) - hxdhy*(fn-fs); 295c4762a1bSJed Brown 296c4762a1bSJed Brown } 297c4762a1bSJed Brown } 2985f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecRestoreArray(da,localX,&x)); 2995f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecRestoreArray(da,F,&f)); 3005f80ce2aSJacob Faibussowitsch CHKERRQ(DMRestoreLocalVector(da,&localX)); 3015f80ce2aSJacob Faibussowitsch CHKERRQ(PetscLogFlops((22.0 + 4.0*POWFLOP)*ym*xm)); 302c4762a1bSJed Brown PetscFunctionReturn(0); 303c4762a1bSJed Brown } 304c4762a1bSJed Brown /* -------------------- Evaluate Jacobian F(x) --------------------- */ 305c4762a1bSJed Brown PetscErrorCode FormJacobian(SNES snes,Vec X,Mat jac,Mat B,void *ptr) 306c4762a1bSJed Brown { 307c4762a1bSJed Brown AppCtx *user = (AppCtx*)ptr; 308c4762a1bSJed Brown PetscInt i,j,mx,my,xs,ys,xm,ym; 309c4762a1bSJed Brown PetscScalar one = 1.0,hx,hy,hxdhy,hydhx,t0,tn,ts,te,tw; 310c4762a1bSJed Brown PetscScalar dn,ds,de,dw,an,as,ae,aw,bn,bs,be,bw,gn,gs,ge,gw; 311c4762a1bSJed Brown PetscScalar tleft,tright,beta,bm1,coef; 312c4762a1bSJed Brown PetscScalar v[5],**x; 313c4762a1bSJed Brown Vec localX; 314c4762a1bSJed Brown MatStencil col[5],row; 315c4762a1bSJed Brown DM da; 316c4762a1bSJed Brown 317c4762a1bSJed Brown PetscFunctionBeginUser; 3185f80ce2aSJacob Faibussowitsch CHKERRQ(SNESGetDM(snes,&da)); 3195f80ce2aSJacob Faibussowitsch CHKERRQ(DMGetLocalVector(da,&localX)); 3205f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0)); 321c4762a1bSJed Brown hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1); 322c4762a1bSJed Brown hxdhy = hx/hy; hydhx = hy/hx; 323c4762a1bSJed Brown tleft = user->tleft; tright = user->tright; 324c4762a1bSJed Brown beta = user->beta; bm1 = user->bm1; coef = user->coef; 325c4762a1bSJed Brown 326c4762a1bSJed Brown /* Get ghost points */ 3275f80ce2aSJacob Faibussowitsch CHKERRQ(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX)); 3285f80ce2aSJacob Faibussowitsch CHKERRQ(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX)); 3295f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0)); 3305f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecGetArray(da,localX,&x)); 331c4762a1bSJed Brown 332c4762a1bSJed Brown /* Evaluate Jacobian of function */ 333c4762a1bSJed Brown for (j=ys; j<ys+ym; j++) { 334c4762a1bSJed Brown for (i=xs; i<xs+xm; i++) { 335c4762a1bSJed Brown t0 = x[j][i]; 336c4762a1bSJed Brown 337c4762a1bSJed Brown if (i > 0 && i < mx-1 && j > 0 && j < my-1) { 338c4762a1bSJed Brown 339c4762a1bSJed Brown /* general interior volume */ 340c4762a1bSJed Brown 341c4762a1bSJed Brown tw = x[j][i-1]; 342c4762a1bSJed Brown aw = 0.5*(t0 + tw); 343c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 344c4762a1bSJed Brown /* dw = bw * aw */ 345c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 346c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 347c4762a1bSJed Brown 348c4762a1bSJed Brown te = x[j][i+1]; 349c4762a1bSJed Brown ae = 0.5*(t0 + te); 350c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 351c4762a1bSJed Brown /* de = be * ae; */ 352c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 353c4762a1bSJed Brown ge = coef*be*(te - t0); 354c4762a1bSJed Brown 355c4762a1bSJed Brown ts = x[j-1][i]; 356c4762a1bSJed Brown as = 0.5*(t0 + ts); 357c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 358c4762a1bSJed Brown /* ds = bs * as; */ 359c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 360c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 361c4762a1bSJed Brown 362c4762a1bSJed Brown tn = x[j+1][i]; 363c4762a1bSJed Brown an = 0.5*(t0 + tn); 364c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 365c4762a1bSJed Brown /* dn = bn * an; */ 366c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 367c4762a1bSJed Brown gn = coef*bn*(tn - t0); 368c4762a1bSJed Brown 369c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 370c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 371c4762a1bSJed 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; 372c4762a1bSJed Brown v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1; 373c4762a1bSJed Brown v[4] = -hxdhy*(dn + gn); col[4].j = j+1; col[4].i = i; 3745f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,5,col,v,INSERT_VALUES)); 375c4762a1bSJed Brown 376c4762a1bSJed Brown } else if (i == 0) { 377c4762a1bSJed Brown 378c4762a1bSJed Brown /* left-hand boundary */ 379c4762a1bSJed Brown tw = tleft; 380c4762a1bSJed Brown aw = 0.5*(t0 + tw); 381c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 382c4762a1bSJed Brown /* dw = bw * aw */ 383c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 384c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 385c4762a1bSJed Brown 386c4762a1bSJed Brown te = x[j][i + 1]; 387c4762a1bSJed Brown ae = 0.5*(t0 + te); 388c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 389c4762a1bSJed Brown /* de = be * ae; */ 390c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 391c4762a1bSJed Brown ge = coef*be*(te - t0); 392c4762a1bSJed Brown 393c4762a1bSJed Brown /* left-hand bottom boundary */ 394c4762a1bSJed Brown if (j == 0) { 395c4762a1bSJed Brown 396c4762a1bSJed Brown tn = x[j+1][i]; 397c4762a1bSJed Brown an = 0.5*(t0 + tn); 398c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 399c4762a1bSJed Brown /* dn = bn * an; */ 400c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 401c4762a1bSJed Brown gn = coef*bn*(tn - t0); 402c4762a1bSJed Brown 403c4762a1bSJed Brown v[0] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[0].j = row.j = j; col[0].i = row.i = i; 404c4762a1bSJed Brown v[1] = -hydhx*(de + ge); col[1].j = j; col[1].i = i+1; 405c4762a1bSJed Brown v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i; 4065f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 407c4762a1bSJed Brown 408c4762a1bSJed Brown /* left-hand interior boundary */ 409c4762a1bSJed Brown } else if (j < my-1) { 410c4762a1bSJed Brown 411c4762a1bSJed Brown ts = x[j-1][i]; 412c4762a1bSJed Brown as = 0.5*(t0 + ts); 413c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 414c4762a1bSJed Brown /* ds = bs * as; */ 415c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 416c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 417c4762a1bSJed Brown 418c4762a1bSJed Brown tn = x[j+1][i]; 419c4762a1bSJed Brown an = 0.5*(t0 + tn); 420c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 421c4762a1bSJed Brown /* dn = bn * an; */ 422c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 423c4762a1bSJed Brown gn = coef*bn*(tn - t0); 424c4762a1bSJed Brown 425c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 426c4762a1bSJed 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; 427c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 428c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 4295f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 430c4762a1bSJed Brown /* left-hand top boundary */ 431c4762a1bSJed Brown } else { 432c4762a1bSJed Brown 433c4762a1bSJed Brown ts = x[j-1][i]; 434c4762a1bSJed Brown as = 0.5*(t0 + ts); 435c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 436c4762a1bSJed Brown /* ds = bs * as; */ 437c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 438c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 439c4762a1bSJed Brown 440c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 441c4762a1bSJed Brown v[1] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 442c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 4435f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 444c4762a1bSJed Brown } 445c4762a1bSJed Brown 446c4762a1bSJed Brown } else if (i == mx-1) { 447c4762a1bSJed Brown 448c4762a1bSJed Brown /* right-hand boundary */ 449c4762a1bSJed Brown tw = x[j][i-1]; 450c4762a1bSJed Brown aw = 0.5*(t0 + tw); 451c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 452c4762a1bSJed Brown /* dw = bw * aw */ 453c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 454c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 455c4762a1bSJed Brown 456c4762a1bSJed Brown te = tright; 457c4762a1bSJed Brown ae = 0.5*(t0 + te); 458c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 459c4762a1bSJed Brown /* de = be * ae; */ 460c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 461c4762a1bSJed Brown ge = coef*be*(te - t0); 462c4762a1bSJed Brown 463c4762a1bSJed Brown /* right-hand bottom boundary */ 464c4762a1bSJed Brown if (j == 0) { 465c4762a1bSJed Brown 466c4762a1bSJed Brown tn = x[j+1][i]; 467c4762a1bSJed Brown an = 0.5*(t0 + tn); 468c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 469c4762a1bSJed Brown /* dn = bn * an; */ 470c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 471c4762a1bSJed Brown gn = coef*bn*(tn - t0); 472c4762a1bSJed Brown 473c4762a1bSJed Brown v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1; 474c4762a1bSJed Brown v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 475c4762a1bSJed Brown v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i; 4765f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 477c4762a1bSJed Brown 478c4762a1bSJed Brown /* right-hand interior boundary */ 479c4762a1bSJed Brown } else if (j < my-1) { 480c4762a1bSJed Brown 481c4762a1bSJed Brown ts = x[j-1][i]; 482c4762a1bSJed Brown as = 0.5*(t0 + ts); 483c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 484c4762a1bSJed Brown /* ds = bs * as; */ 485c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 486c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 487c4762a1bSJed Brown 488c4762a1bSJed Brown tn = x[j+1][i]; 489c4762a1bSJed Brown an = 0.5*(t0 + tn); 490c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 491c4762a1bSJed Brown /* dn = bn * an; */ 492c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 493c4762a1bSJed Brown gn = coef*bn*(tn - t0); 494c4762a1bSJed Brown 495c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 496c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 497c4762a1bSJed 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; 498c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 4995f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 500c4762a1bSJed Brown /* right-hand top boundary */ 501c4762a1bSJed Brown } else { 502c4762a1bSJed Brown 503c4762a1bSJed Brown ts = x[j-1][i]; 504c4762a1bSJed Brown as = 0.5*(t0 + ts); 505c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 506c4762a1bSJed Brown /* ds = bs * as; */ 507c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 508c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 509c4762a1bSJed Brown 510c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 511c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 512c4762a1bSJed Brown v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 5135f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,3,col,v,INSERT_VALUES)); 514c4762a1bSJed Brown } 515c4762a1bSJed Brown 516c4762a1bSJed Brown /* bottom boundary,and i <> 0 or mx-1 */ 517c4762a1bSJed Brown } else if (j == 0) { 518c4762a1bSJed Brown 519c4762a1bSJed Brown tw = x[j][i-1]; 520c4762a1bSJed Brown aw = 0.5*(t0 + tw); 521c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 522c4762a1bSJed Brown /* dw = bw * aw */ 523c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 524c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 525c4762a1bSJed Brown 526c4762a1bSJed Brown te = x[j][i+1]; 527c4762a1bSJed Brown ae = 0.5*(t0 + te); 528c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 529c4762a1bSJed Brown /* de = be * ae; */ 530c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 531c4762a1bSJed Brown ge = coef*be*(te - t0); 532c4762a1bSJed Brown 533c4762a1bSJed Brown tn = x[j+1][i]; 534c4762a1bSJed Brown an = 0.5*(t0 + tn); 535c4762a1bSJed Brown bn = PetscPowScalar(an,bm1); 536c4762a1bSJed Brown /* dn = bn * an; */ 537c4762a1bSJed Brown dn = PetscPowScalar(an,beta); 538c4762a1bSJed Brown gn = coef*bn*(tn - t0); 539c4762a1bSJed Brown 540c4762a1bSJed Brown v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1; 541c4762a1bSJed Brown v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i; 542c4762a1bSJed Brown v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1; 543c4762a1bSJed Brown v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i; 5445f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 545c4762a1bSJed Brown 546c4762a1bSJed Brown /* top boundary,and i <> 0 or mx-1 */ 547c4762a1bSJed Brown } else if (j == my-1) { 548c4762a1bSJed Brown 549c4762a1bSJed Brown tw = x[j][i-1]; 550c4762a1bSJed Brown aw = 0.5*(t0 + tw); 551c4762a1bSJed Brown bw = PetscPowScalar(aw,bm1); 552c4762a1bSJed Brown /* dw = bw * aw */ 553c4762a1bSJed Brown dw = PetscPowScalar(aw,beta); 554c4762a1bSJed Brown gw = coef*bw*(t0 - tw); 555c4762a1bSJed Brown 556c4762a1bSJed Brown te = x[j][i+1]; 557c4762a1bSJed Brown ae = 0.5*(t0 + te); 558c4762a1bSJed Brown be = PetscPowScalar(ae,bm1); 559c4762a1bSJed Brown /* de = be * ae; */ 560c4762a1bSJed Brown de = PetscPowScalar(ae,beta); 561c4762a1bSJed Brown ge = coef*be*(te - t0); 562c4762a1bSJed Brown 563c4762a1bSJed Brown ts = x[j-1][i]; 564c4762a1bSJed Brown as = 0.5*(t0 + ts); 565c4762a1bSJed Brown bs = PetscPowScalar(as,bm1); 566c4762a1bSJed Brown /* ds = bs * as; */ 567c4762a1bSJed Brown ds = PetscPowScalar(as,beta); 568c4762a1bSJed Brown gs = coef*bs*(t0 - ts); 569c4762a1bSJed Brown 570c4762a1bSJed Brown v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i; 571c4762a1bSJed Brown v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1; 572c4762a1bSJed Brown v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i; 573c4762a1bSJed Brown v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1; 5745f80ce2aSJacob Faibussowitsch CHKERRQ(MatSetValuesStencil(B,1,&row,4,col,v,INSERT_VALUES)); 575c4762a1bSJed Brown 576c4762a1bSJed Brown } 577c4762a1bSJed Brown } 578c4762a1bSJed Brown } 5795f80ce2aSJacob Faibussowitsch CHKERRQ(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 5805f80ce2aSJacob Faibussowitsch CHKERRQ(DMDAVecRestoreArray(da,localX,&x)); 5815f80ce2aSJacob Faibussowitsch CHKERRQ(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 5825f80ce2aSJacob Faibussowitsch CHKERRQ(DMRestoreLocalVector(da,&localX)); 583c4762a1bSJed Brown if (jac != B) { 5845f80ce2aSJacob Faibussowitsch CHKERRQ(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY)); 5855f80ce2aSJacob Faibussowitsch CHKERRQ(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY)); 586c4762a1bSJed Brown } 587c4762a1bSJed Brown 5885f80ce2aSJacob Faibussowitsch CHKERRQ(PetscLogFlops((41.0 + 8.0*POWFLOP)*xm*ym)); 589c4762a1bSJed Brown PetscFunctionReturn(0); 590c4762a1bSJed Brown } 591c4762a1bSJed Brown 592c4762a1bSJed Brown /*TEST 593c4762a1bSJed Brown 594c4762a1bSJed Brown test: 59541ba4c6cSHeeho Park suffix: 1 596c4762a1bSJed Brown args: -pc_type mg -ksp_type fgmres -da_refine 2 -pc_mg_galerkin pmat -snes_view 597c4762a1bSJed Brown requires: !single 598c4762a1bSJed Brown 59941ba4c6cSHeeho Park test: 60041ba4c6cSHeeho Park suffix: 2 60141ba4c6cSHeeho Park args: -pc_type mg -ksp_type fgmres -da_refine 2 -pc_mg_galerkin pmat -snes_view -snes_type newtontrdc 60241ba4c6cSHeeho Park requires: !single 60341ba4c6cSHeeho Park 604c4762a1bSJed Brown TEST*/ 605