1 static char help[] = "Solves the constant-coefficient 1D heat equation \n\ 2 with an Implicit Runge-Kutta method using MatKAIJ. \n\ 3 \n\ 4 du d^2 u \n\ 5 -- = a ----- ; 0 <= x <= 1; \n\ 6 dt dx^2 \n\ 7 \n\ 8 with periodic boundary conditions \n\ 9 \n\ 10 2nd order central discretization in space: \n\ 11 \n\ 12 [ d^2 u ] u_{i+1} - 2u_i + u_{i-1} \n\ 13 [ ----- ] = ------------------------ \n\ 14 [ dx^2 ]i h^2 \n\ 15 \n\ 16 i = grid index; h = x_{i+1}-x_i (Uniform) \n\ 17 0 <= i < n h = 1.0/n \n\ 18 \n\ 19 Thus, \n\ 20 \n\ 21 du \n\ 22 -- = Ju; J = (a/h^2) tridiagonal(1,-2,1)_n \n\ 23 dt \n\ 24 \n\ 25 This example is a TS version of the KSP ex74.c tutorial. \n"; 26 27 #include <petscts.h> 28 29 typedef enum { 30 PHYSICS_DIFFUSION, 31 PHYSICS_ADVECTION 32 } PhysicsType; 33 const char *const PhysicsTypes[] = {"DIFFUSION","ADVECTION","PhysicsType","PHYSICS_",NULL}; 34 35 typedef struct Context { 36 PetscReal a; /* diffusion coefficient */ 37 PetscReal xmin,xmax; /* domain bounds */ 38 PetscInt imax; /* number of grid points */ 39 PhysicsType physics_type; 40 } UserContext; 41 42 static PetscErrorCode ExactSolution(Vec,void*,PetscReal); 43 static PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*); 44 45 int main(int argc, char **argv) 46 { 47 TS ts; 48 Mat A; 49 Vec u,uex; 50 UserContext ctxt; 51 PetscReal err,ftime; 52 PetscErrorCode ierr; 53 54 CHKERRQ(PetscInitialize(&argc,&argv,(char*)0,help)); 55 56 /* default value */ 57 ctxt.a = 0.1; 58 ctxt.xmin = 0.0; 59 ctxt.xmax = 1.0; 60 ctxt.imax = 40; 61 ctxt.physics_type = PHYSICS_DIFFUSION; 62 63 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"IRK options","");CHKERRQ(ierr); 64 CHKERRQ(PetscOptionsReal("-a","diffusion coefficient","<1.0>",ctxt.a,&ctxt.a,NULL)); 65 CHKERRQ(PetscOptionsInt ("-imax","grid size","<20>",ctxt.imax,&ctxt.imax,NULL)); 66 CHKERRQ(PetscOptionsReal("-xmin","xmin","<0.0>",ctxt.xmin,&ctxt.xmin,NULL)); 67 CHKERRQ(PetscOptionsReal("-xmax","xmax","<1.0>",ctxt.xmax,&ctxt.xmax,NULL)); 68 CHKERRQ(PetscOptionsEnum("-physics_type","Type of process to discretize","",PhysicsTypes,(PetscEnum)ctxt.physics_type,(PetscEnum*)&ctxt.physics_type,NULL)); 69 ierr = PetscOptionsEnd();CHKERRQ(ierr); 70 71 /* allocate and initialize solution vector and exact solution */ 72 CHKERRQ(VecCreate(PETSC_COMM_WORLD,&u)); 73 CHKERRQ(VecSetSizes(u,PETSC_DECIDE,ctxt.imax)); 74 CHKERRQ(VecSetFromOptions(u)); 75 CHKERRQ(VecDuplicate(u,&uex)); 76 /* initial solution */ 77 CHKERRQ(ExactSolution(u,&ctxt,0.0)); 78 79 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A)); 80 CHKERRQ(MatSetType(A,MATAIJ)); 81 CHKERRQ(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,ctxt.imax,ctxt.imax)); 82 CHKERRQ(MatSetUp(A)); 83 84 /* Create and set options for TS */ 85 CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts)); 86 CHKERRQ(TSSetProblemType(ts,TS_LINEAR)); 87 CHKERRQ(TSSetTimeStep(ts,0.125)); 88 CHKERRQ(TSSetSolution(ts,u)); 89 CHKERRQ(TSSetMaxSteps(ts,10)); 90 CHKERRQ(TSSetMaxTime(ts,1.0)); 91 CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 92 CHKERRQ(TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&ctxt)); 93 CHKERRQ(RHSJacobian(ts,0,u,A,A,&ctxt)); 94 CHKERRQ(TSSetRHSJacobian(ts,A,A,TSComputeRHSJacobianConstant,&ctxt)); 95 CHKERRQ(TSSetFromOptions(ts)); 96 CHKERRQ(TSSolve(ts,u)); 97 98 CHKERRQ(TSGetSolveTime(ts,&ftime)); 99 /* exact solution */ 100 CHKERRQ(ExactSolution(uex,&ctxt,ftime)); 101 102 /* Calculate error in final solution */ 103 CHKERRQ(VecAYPX(uex,-1.0,u)); 104 CHKERRQ(VecNorm(uex,NORM_2,&err)); 105 err = PetscSqrtReal(err*err/((PetscReal)ctxt.imax)); 106 CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"L2 norm of the numerical error = %g (time=%g)\n",(double)err,(double)ftime)); 107 108 /* Free up memory */ 109 CHKERRQ(TSDestroy(&ts)); 110 CHKERRQ(MatDestroy(&A)); 111 CHKERRQ(VecDestroy(&uex)); 112 CHKERRQ(VecDestroy(&u)); 113 CHKERRQ(PetscFinalize()); 114 return 0; 115 } 116 117 PetscErrorCode ExactSolution(Vec u,void *c,PetscReal t) 118 { 119 UserContext *ctxt = (UserContext*) c; 120 PetscInt i,is,ie; 121 PetscScalar *uarr; 122 PetscReal x,dx,a=ctxt->a,pi=PETSC_PI; 123 124 PetscFunctionBegin; 125 dx = (ctxt->xmax - ctxt->xmin)/((PetscReal) ctxt->imax); 126 CHKERRQ(VecGetOwnershipRange(u,&is,&ie)); 127 CHKERRQ(VecGetArray(u,&uarr)); 128 for (i=is; i<ie; i++) { 129 x = i * dx; 130 switch (ctxt->physics_type) { 131 case PHYSICS_DIFFUSION: 132 uarr[i-is] = PetscExpScalar(-4.0*pi*pi*a*t)*PetscSinScalar(2*pi*x); 133 break; 134 case PHYSICS_ADVECTION: 135 uarr[i-is] = PetscSinScalar(2*pi*(x - a*t)); 136 break; 137 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for physics type %s",PhysicsTypes[ctxt->physics_type]); 138 } 139 } 140 CHKERRQ(VecRestoreArray(u,&uarr)); 141 PetscFunctionReturn(0); 142 } 143 144 static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat J,Mat Jpre,void *ctx) 145 { 146 UserContext *user = (UserContext*) ctx; 147 PetscInt matis,matie,i; 148 PetscReal dx,dx2; 149 150 PetscFunctionBegin; 151 dx = (user->xmax - user->xmin)/((PetscReal)user->imax); dx2 = dx*dx; 152 CHKERRQ(MatGetOwnershipRange(J,&matis,&matie)); 153 for (i=matis; i<matie; i++) { 154 PetscScalar values[3]; 155 PetscInt col[3]; 156 switch (user->physics_type) { 157 case PHYSICS_DIFFUSION: 158 values[0] = user->a*1.0/dx2; 159 values[1] = -user->a*2.0/dx2; 160 values[2] = user->a*1.0/dx2; 161 break; 162 case PHYSICS_ADVECTION: 163 values[0] = user->a*.5/dx; 164 values[1] = 0.; 165 values[2] = -user->a*.5/dx; 166 break; 167 default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for physics type %s",PhysicsTypes[user->physics_type]); 168 } 169 /* periodic boundaries */ 170 if (i == 0) { 171 col[0] = user->imax-1; 172 col[1] = i; 173 col[2] = i+1; 174 } else if (i == user->imax-1) { 175 col[0] = i-1; 176 col[1] = i; 177 col[2] = 0; 178 } else { 179 col[0] = i-1; 180 col[1] = i; 181 col[2] = i+1; 182 } 183 CHKERRQ(MatSetValues(J,1,&i,3,col,values,INSERT_VALUES)); 184 } 185 CHKERRQ(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 186 CHKERRQ(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 187 PetscFunctionReturn(0); 188 } 189 190 /*TEST 191 192 test: 193 requires: double 194 suffix: 1 195 nsize: {{1 2}} 196 args: -ts_max_steps 5 -ts_monitor -ksp_monitor_short -pc_type pbjacobi -ksp_atol 1e-6 -ts_type irk -ts_irk_nstages 2 197 198 test: 199 requires: double 200 suffix: 2 201 args: -ts_max_steps 5 -ts_monitor -ksp_monitor_short -pc_type pbjacobi -ksp_atol 1e-6 -ts_type irk -ts_irk_nstages 3 202 203 testset: 204 requires: hpddm 205 args: -ts_max_steps 5 -ts_monitor -ksp_monitor_short -pc_type pbjacobi -ksp_atol 1e-4 -ts_type irk -ts_irk_nstages 3 -ksp_view_final_residual -ksp_hpddm_type gcrodr -ksp_type hpddm -ksp_hpddm_precision {{single double}shared output} 206 test: 207 suffix: 3 208 requires: double 209 test: 210 suffix: 3_single 211 requires: single 212 TEST*/ 213