11   To visualize the solution, configure with petsc4py, pip install pyvista, and use
13     -potential_view pyvista  -view_pyvista_warp 1.
17     -snes_convergence_estimate -convest_num_refine 2 -convest_monitor -convest_error_view pyvista
21     -snes_vi_monitor_residual pyvista -snes_vi_monitor_active pyvista
25   -snes_vi_monitor -snes_converged_reason -convest_monitor
57   const PetscReal r_0    = par->r_0;  in obstacle_ball()
59   const PetscReal psi_0  = PetscSqrtReal(1. - PetscSqr(r_0));  in obstacle_ball()
60   const PetscReal dpsi_0 = -r_0 / psi_0;  in obstacle_ball()
64   if (r < r_0) u[0] = PetscSqrtReal(1.0 - PetscSqr(r));  in obstacle_ball()
65   else u[0] = psi_0 + dpsi_0 * (r - r_0);  in obstacle_ball()
72   const PetscReal r_free = par->r_free;  in exactSol_ball()
73   const PetscReal A      = par->A;  in exactSol_ball()
74   const PetscReal B      = par->B;  in exactSol_ball()
80   else u[0] = -A * PetscLogReal(r) + B;  in exactSol_ball()
98   options->obsType = OBSTACLE_BALL;  in ProcessOptions()
102 …tscCall(PetscOptionsEList("-obs_type", "Type of obstacle", "ex34.c", obstacleTypes, NUM_OBSTACLE_T…  in ProcessOptions()
103   options->obsType = (ObstacleType)obs;  in ProcessOptions()
115   PetscCall(PetscBagGetData(ctx->bag, &p));  in SetupParameters()
116   PetscCall(PetscBagSetName(ctx->bag, "par", "Obstacle Parameters"));  in SetupParameters()
117   bag = ctx->bag;  in SetupParameters()
118   PetscCall(PetscBagRegisterReal(bag, &p->r_0, 0.9, "r_0", "Ball radius, m"));  in SetupParameters()
119 …PetscCall(PetscBagRegisterReal(bag, &p->r_free, 0.697965148223374, "r_free", "Ball free boundary r…  in SetupParameters()
120 …PetscCall(PetscBagRegisterReal(bag, &p->A, 0.680259411891719, "A", "Logarithmic coefficient in exa…  in SetupParameters()
121 …PetscCall(PetscBagRegisterReal(bag, &p->B, 0.471519893402112, "B", "Constant coefficient in exact …  in SetupParameters()
128     PetscCall(PetscOptionsCreateViewer(comm, NULL, NULL, "-param_view", &viewer, &format, &flg));  in SetupParameters()
147   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));  in CreateMesh()
166   PetscCall(PetscBagGetData(user->bag, &param));  in SetupPrimalProblem()
167   switch (user->obsType) {  in SetupPrimalProblem()
175 …alid obstacle type: %s (%d)", obstacleTypes[PetscMin(user->obsType, NUM_OBSTACLE_TYPES)], user->ob…  in SetupPrimalProblem()
177   PetscCall(PetscBagGetData(user->bag, &ctx));  in SetupPrimalProblem()
185     constants[0] = param->r_0;    // Ball radius  in SetupPrimalProblem()
186     constants[1] = param->r_free; // Radius of the free boundary for the ball obstacle  in SetupPrimalProblem()
187     constants[2] = param->A;      // Logarithmic coefficient in exact ball solution  in SetupPrimalProblem()
188     constants[3] = param->B;      // Constant coefficient in exact ball solution  in SetupPrimalProblem()
209   PetscCall(PetscFECreateByCell(PETSC_COMM_SELF, dim, 1, ct, name ? prefix : NULL, -1, &fe));  in SetupFE()
228   AppCtx user; /* User-defined work context */  in main()
250   PetscCall(VecViewFromOptions(u, NULL, "-potential_view"));  in main()
263     args: -dm_plex_box_lower -2.,-2. -dm_plex_box_upper 2.,2. -dm_plex_box_faces 20,20 \
264           -potential_petscspace_degree 1 \
265           -snes_type vinewtonrsls -snes_vi_zero_tolerance 1.0e-12 \
266           -ksp_type preonly -pc_type lu
272       args: -dmsnes_check
278       args: -snes_convergence_estimate -convest_num_refine 2
284       args: -r_0 0.4
290       args: -dm_plex_simplex 0 -snes_convergence_estimate -convest_num_refine 2