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 TS ts; 47 Mat A; 48 Vec u, uex; 49 UserContext ctxt; 50 PetscReal err, ftime; 51 52 PetscFunctionBeginUser; 53 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 54 /* default value */ 55 ctxt.a = 0.1; 56 ctxt.xmin = 0.0; 57 ctxt.xmax = 1.0; 58 ctxt.imax = 40; 59 ctxt.physics_type = PHYSICS_DIFFUSION; 60 61 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "IRK options", ""); 62 PetscCall(PetscOptionsReal("-a", "diffusion coefficient", "<1.0>", ctxt.a, &ctxt.a, NULL)); 63 PetscCall(PetscOptionsInt("-imax", "grid size", "<20>", ctxt.imax, &ctxt.imax, NULL)); 64 PetscCall(PetscOptionsReal("-xmin", "xmin", "<0.0>", ctxt.xmin, &ctxt.xmin, NULL)); 65 PetscCall(PetscOptionsReal("-xmax", "xmax", "<1.0>", ctxt.xmax, &ctxt.xmax, NULL)); 66 PetscCall(PetscOptionsEnum("-physics_type", "Type of process to discretize", "", PhysicsTypes, (PetscEnum)ctxt.physics_type, (PetscEnum *)&ctxt.physics_type, NULL)); 67 PetscOptionsEnd(); 68 69 /* allocate and initialize solution vector and exact solution */ 70 PetscCall(VecCreate(PETSC_COMM_WORLD, &u)); 71 PetscCall(VecSetSizes(u, PETSC_DECIDE, ctxt.imax)); 72 PetscCall(VecSetFromOptions(u)); 73 PetscCall(VecDuplicate(u, &uex)); 74 /* initial solution */ 75 PetscCall(ExactSolution(u, &ctxt, 0.0)); 76 77 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 78 PetscCall(MatSetType(A, MATAIJ)); 79 PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, ctxt.imax, ctxt.imax)); 80 PetscCall(MatSetUp(A)); 81 82 /* Create and set options for TS */ 83 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 84 PetscCall(TSSetProblemType(ts, TS_LINEAR)); 85 PetscCall(TSSetTimeStep(ts, 0.125)); 86 PetscCall(TSSetSolution(ts, u)); 87 PetscCall(TSSetMaxSteps(ts, 10)); 88 PetscCall(TSSetMaxTime(ts, 1.0)); 89 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 90 PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &ctxt)); 91 PetscCall(RHSJacobian(ts, 0, u, A, A, &ctxt)); 92 PetscCall(TSSetRHSJacobian(ts, A, A, TSComputeRHSJacobianConstant, &ctxt)); 93 PetscCall(TSSetFromOptions(ts)); 94 PetscCall(TSSolve(ts, u)); 95 96 PetscCall(TSGetSolveTime(ts, &ftime)); 97 /* exact solution */ 98 PetscCall(ExactSolution(uex, &ctxt, ftime)); 99 100 /* Calculate error in final solution */ 101 PetscCall(VecAYPX(uex, -1.0, u)); 102 PetscCall(VecNorm(uex, NORM_2, &err)); 103 err = PetscSqrtReal(err * err / ((PetscReal)ctxt.imax)); 104 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "L2 norm of the numerical error = %g (time=%g)\n", (double)err, (double)ftime)); 105 106 /* Free up memory */ 107 PetscCall(TSDestroy(&ts)); 108 PetscCall(MatDestroy(&A)); 109 PetscCall(VecDestroy(&uex)); 110 PetscCall(VecDestroy(&u)); 111 PetscCall(PetscFinalize()); 112 return 0; 113 } 114 115 PetscErrorCode ExactSolution(Vec u, void *c, PetscReal t) { 116 UserContext *ctxt = (UserContext *)c; 117 PetscInt i, is, ie; 118 PetscScalar *uarr; 119 PetscReal x, dx, a = ctxt->a, pi = PETSC_PI; 120 121 PetscFunctionBeginUser; 122 dx = (ctxt->xmax - ctxt->xmin) / ((PetscReal)ctxt->imax); 123 PetscCall(VecGetOwnershipRange(u, &is, &ie)); 124 PetscCall(VecGetArray(u, &uarr)); 125 for (i = is; i < ie; i++) { 126 x = i * dx; 127 switch (ctxt->physics_type) { 128 case PHYSICS_DIFFUSION: uarr[i - is] = PetscExpScalar(-4.0 * pi * pi * a * t) * PetscSinScalar(2 * pi * x); break; 129 case PHYSICS_ADVECTION: uarr[i - is] = PetscSinScalar(2 * pi * (x - a * t)); break; 130 default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for physics type %s", PhysicsTypes[ctxt->physics_type]); 131 } 132 } 133 PetscCall(VecRestoreArray(u, &uarr)); 134 PetscFunctionReturn(0); 135 } 136 137 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat J, Mat Jpre, void *ctx) { 138 UserContext *user = (UserContext *)ctx; 139 PetscInt matis, matie, i; 140 PetscReal dx, dx2; 141 142 PetscFunctionBeginUser; 143 dx = (user->xmax - user->xmin) / ((PetscReal)user->imax); 144 dx2 = dx * dx; 145 PetscCall(MatGetOwnershipRange(J, &matis, &matie)); 146 for (i = matis; i < matie; i++) { 147 PetscScalar values[3]; 148 PetscInt col[3]; 149 switch (user->physics_type) { 150 case PHYSICS_DIFFUSION: 151 values[0] = user->a * 1.0 / dx2; 152 values[1] = -user->a * 2.0 / dx2; 153 values[2] = user->a * 1.0 / dx2; 154 break; 155 case PHYSICS_ADVECTION: 156 values[0] = user->a * .5 / dx; 157 values[1] = 0.; 158 values[2] = -user->a * .5 / dx; 159 break; 160 default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for physics type %s", PhysicsTypes[user->physics_type]); 161 } 162 /* periodic boundaries */ 163 if (i == 0) { 164 col[0] = user->imax - 1; 165 col[1] = i; 166 col[2] = i + 1; 167 } else if (i == user->imax - 1) { 168 col[0] = i - 1; 169 col[1] = i; 170 col[2] = 0; 171 } else { 172 col[0] = i - 1; 173 col[1] = i; 174 col[2] = i + 1; 175 } 176 PetscCall(MatSetValues(J, 1, &i, 3, col, values, INSERT_VALUES)); 177 } 178 PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); 179 PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); 180 PetscFunctionReturn(0); 181 } 182 183 /*TEST 184 185 test: 186 requires: double 187 suffix: 1 188 nsize: {{1 2}} 189 args: -ts_max_steps 5 -ts_monitor -ksp_monitor_short -pc_type pbjacobi -ksp_atol 1e-6 -ts_type irk -ts_irk_nstages 2 190 191 test: 192 requires: double 193 suffix: 2 194 args: -ts_max_steps 5 -ts_monitor -ksp_monitor_short -pc_type pbjacobi -ksp_atol 1e-6 -ts_type irk -ts_irk_nstages 3 195 196 testset: 197 requires: hpddm 198 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 199 test: 200 suffix: 3 201 requires: double 202 args: -ksp_hpddm_precision {{single double}shared output} 203 test: 204 suffix: 3_single 205 requires: single 206 args: -ksp_hpddm_precision {{single double}shared output} 207 test: 208 suffix: 3___float128 209 requires: __float128 210 output_file: output/ex74_3.out 211 args: -ksp_hpddm_precision {{double quadruple}shared output} 212 TEST*/ 213