1 static char help[] ="Solves the time dependent Allen-Cahn equation with IMEX methods"; 2 3 /* 4 * allen_cahn.c 5 * 6 * Created on: Jun 8, 2012 7 * Author: Hong Zhang 8 */ 9 10 #include <petscts.h> 11 12 /* 13 * application context 14 */ 15 typedef struct { 16 PetscReal param; /* parameter */ 17 PetscReal xleft,xright; /* range in x-direction */ 18 PetscInt mx; /* Discretization in x-direction */ 19 }AppCtx; 20 21 22 static PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*); 23 static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*); 24 static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void *ctx); 25 static PetscErrorCode FormInitialSolution(TS,Vec,void*); 26 27 28 int main(int argc, char **argv) 29 { 30 TS ts; 31 Vec x; /*solution vector*/ 32 Mat A; /*Jacobian*/ 33 PetscInt steps,mx; 34 PetscErrorCode ierr; 35 PetscReal ftime; 36 AppCtx user; /* user-defined work context */ 37 38 ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr; 39 40 /* Initialize user application context */ 41 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Allen-Cahn equation",""); 42 user.param = 9e-4; 43 user.xleft = -1.; 44 user.xright = 2.; 45 user.mx = 400; 46 ierr = PetscOptionsReal("-eps","parameter","",user.param,&user.param,NULL);CHKERRQ(ierr); 47 ierr = PetscOptionsEnd();CHKERRQ(ierr); 48 49 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 50 Set runtime options 51 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 52 /* 53 * ierr = PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr); 54 */ 55 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 56 Create necessary matrix and vectors, solve same ODE on every process 57 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 58 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 59 ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,user.mx,user.mx);CHKERRQ(ierr); 60 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 61 ierr = MatSetUp(A);CHKERRQ(ierr); 62 ierr = MatCreateVecs(A,&x,NULL);CHKERRQ(ierr); 63 64 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 65 Create time stepping solver context 66 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 67 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 68 ierr = TSSetType(ts,TSEIMEX);CHKERRQ(ierr); 69 ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr); 70 ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);CHKERRQ(ierr); 71 ierr = TSSetIJacobian(ts,A,A,FormIJacobian,&user);CHKERRQ(ierr); 72 ftime = 22; 73 ierr = TSSetMaxTime(ts,ftime);CHKERRQ(ierr); 74 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 75 76 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 77 Set initial conditions 78 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 79 ierr = FormInitialSolution(ts,x,&user);CHKERRQ(ierr); 80 ierr = TSSetSolution(ts,x);CHKERRQ(ierr); 81 ierr = VecGetSize(x,&mx);CHKERRQ(ierr); 82 83 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 84 Set runtime options 85 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 86 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 87 88 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 89 Solve nonlinear system 90 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 91 ierr = TSSolve(ts,x);CHKERRQ(ierr); 92 ierr = TSGetTime(ts,&ftime);CHKERRQ(ierr); 93 ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr); 94 ierr = PetscPrintf(PETSC_COMM_WORLD,"eps %g, steps %D, ftime %g\n",(double)user.param,steps,(double)ftime);CHKERRQ(ierr); 95 /* ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);*/ 96 97 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 98 Free work space. 99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 100 ierr = MatDestroy(&A);CHKERRQ(ierr); 101 ierr = VecDestroy(&x);CHKERRQ(ierr); 102 ierr = TSDestroy(&ts);CHKERRQ(ierr); 103 ierr = PetscFinalize(); 104 return ierr; 105 } 106 107 108 static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr) 109 { 110 PetscErrorCode ierr; 111 AppCtx *user = (AppCtx*)ptr; 112 PetscScalar *f; 113 const PetscScalar *x; 114 PetscInt i,mx; 115 PetscReal hx,eps; 116 117 PetscFunctionBegin; 118 mx = user->mx; 119 eps = user->param; 120 hx = (user->xright-user->xleft)/(mx-1); 121 ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr); 122 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 123 f[0] = 2.*eps*(x[1]-x[0])/(hx*hx); /*boundary*/ 124 for (i=1;i<mx-1;i++) { 125 f[i]= eps*(x[i+1]-2.*x[i]+x[i-1])/(hx*hx); 126 } 127 f[mx-1] = 2.*eps*(x[mx-2]- x[mx-1])/(hx*hx); /*boundary*/ 128 ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr); 129 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 130 PetscFunctionReturn(0); 131 } 132 133 134 static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ptr) 135 { 136 PetscErrorCode ierr; 137 AppCtx *user = (AppCtx*)ptr; 138 PetscScalar *f; 139 const PetscScalar *x,*xdot; 140 PetscInt i,mx; 141 142 PetscFunctionBegin; 143 mx = user->mx; 144 ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr); 145 ierr = VecGetArrayRead(Xdot,&xdot);CHKERRQ(ierr); 146 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 147 148 for (i=0;i<mx;i++) { 149 f[i]= xdot[i] - x[i]*(1.-x[i]*x[i]); 150 } 151 152 ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr); 153 ierr = VecRestoreArrayRead(Xdot,&xdot);CHKERRQ(ierr); 154 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 155 PetscFunctionReturn(0); 156 } 157 158 159 static PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U, Vec Udot, PetscReal a, Mat J,Mat Jpre,void *ctx) 160 { 161 PetscErrorCode ierr; 162 AppCtx *user = (AppCtx *)ctx; 163 PetscScalar v; 164 const PetscScalar *x; 165 PetscInt i,col; 166 167 PetscFunctionBegin; 168 ierr = VecGetArrayRead(U,&x);CHKERRQ(ierr); 169 for (i=0; i < user->mx; i++) { 170 v = a - 1. + 3.*x[i]*x[i]; 171 col = i; 172 ierr = MatSetValues(J,1,&i,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr); 173 } 174 ierr = VecRestoreArrayRead(U,&x);CHKERRQ(ierr); 175 176 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 177 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 178 if (J != Jpre) { 179 ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 180 ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 181 } 182 /* MatView(J,PETSC_VIEWER_STDOUT_WORLD);*/ 183 PetscFunctionReturn(0); 184 } 185 186 187 static PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ctx) 188 { 189 AppCtx *user = (AppCtx*)ctx; 190 PetscInt i; 191 PetscScalar *x; 192 PetscReal hx,x_map; 193 PetscErrorCode ierr; 194 195 PetscFunctionBegin; 196 hx = (user->xright-user->xleft)/(PetscReal)(user->mx-1); 197 ierr = VecGetArray(U,&x);CHKERRQ(ierr); 198 for (i=0;i<user->mx;i++) { 199 x_map = user->xleft + i*hx; 200 if (x_map >= 0.7065) { 201 x[i] = PetscTanhReal((x_map-0.8)/(2.*PetscSqrtReal(user->param))); 202 } else if (x_map >= 0.4865) { 203 x[i] = PetscTanhReal((0.613-x_map)/(2.*PetscSqrtReal(user->param))); 204 } else if (x_map >= 0.28) { 205 x[i] = PetscTanhReal((x_map-0.36)/(2.*PetscSqrtReal(user->param))); 206 } else if (x_map >= -0.7) { 207 x[i] = PetscTanhReal((0.2-x_map)/(2.*PetscSqrtReal(user->param))); 208 } else if (x_map >= -1) { 209 x[i] = PetscTanhReal((x_map+0.9)/(2.*PetscSqrtReal(user->param))); 210 } 211 } 212 ierr = VecRestoreArray(U,&x);CHKERRQ(ierr); 213 PetscFunctionReturn(0); 214 } 215 216 /*TEST 217 218 test: 219 args: -ts_rtol 1e-04 -ts_dt 0.025 -pc_type lu -ksp_error_if_not_converged TRUE -ts_type eimex -ts_adapt_type none -ts_eimex_order_adapt -ts_eimex_max_rows 7 -ts_monitor_draw_solution 220 requires: x 221 timeoutfactor: 3 222 223 TEST*/ 224