Thank you very much for your reply. I'm a bit confused if I use what you recommend: - snes_fd -pc_type lu means that I explicitly construct the Jacobian matrix using the finite difference method, construct the precondition matrix using the completely LU decomposition, and solve the step size \ delta x with the GMRES method (default).
In fact, what I want to use is to approximate the vector product of a matrix with finite difference, so that the explicit construction of Jacobian matrices can be avoided. If so, should I use MatrixFreeMethod? How should I set it up? If I want to set up precondition, what do I need to add? In addition, I want to output variables in each nolinear step. What should I add code to make SNES step by step? There may be many problems, but they bother me very much. I am looking forward to your reply. Thanks, Yingjie Matthew Knepley <[email protected]> 于2018年9月6日周四 下午10:34写道： > On Thu, Sep 6, 2018 at 4:47 AM Yingjie Wu <[email protected]> wrote: > >> Dear Petsc developer: >> Hi, >> Thank you for your previous help. >> I recently modeled on PETSc's SNES example and wrote a computer program >> myself. This program is mainly for solving nonlinear equations of thermal >> hydraulics. >> >> ∇·（λ∇T） - ∇_y（ρ*Cp*u） - T_source = 0 >> >> w*ρ*u = ρg - ∇_y（P） >> >> ∇·（ 1/w * ∇P ） = - ∇（ ρg / w ） >> >> Where P, T and u are variables, the distribution represents pressure, >> temperature and velocity. The rest are nonlinear physical parameters and >> constants. >> >> Because the program is very preliminary, so I use - snes_mf so that I can >> save the part of writing to calculate the Jacobian matrix. >> >> After compiling and passing, I found that the residual function had not >> dropped to a small enough level, but the program stopped, as follows: >> >> Setting Up: -snes_mf -snes_monitor -draw_pause 10 -snes_view >> >> > First, do not use -snes_mf. It is not for testing, but for sophisticated > use. The first option you > might try is > > -snes_fd -pc_type lu > > That uses a full Jacobian and LU factorization for a direct solve. Always > run the solve using > > -snes_view -snes_converged_reason -snes_monitor -ksp_converged_reason > -ksp_monitor_true_residual > > When that gets too expensive, you can try > > -snes_fd_color -snes_fd_color_use_mat -mat_coloring_type greedy > > but that requires you to preallocate the Jacobian matrix correctly. > > Thanks, > > Matt > >> 0 SNES Function norm 3.724996516631e+09 >> >> 1 SNES Function norm 2.194322909557e+09 >> >> 2 SNES Function norm 1.352051559826e+09 >> >> 3 SNES Function norm 1.522311916217e+08 >> >> SNES Object: 1 MPI processes >> >> type: newtonls >> >> maximum iterations=50, maximum function evaluations=10000 >> >> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 >> >> total number of linear solver iterations=1298 >> >> total number of function evaluations=11679 >> >> norm schedule ALWAYS >> >> SNESLineSearch Object: 1 MPI processes >> >> type: bt >> >> interpolation: cubic >> >> alpha=1.000000e-04 >> >> maxstep=1.000000e+08, minlambda=1.000000e-12 >> >> tolerances: relative=1.000000e-08, absolute=1.000000e-15, >> lambda=1.000000e-08 >> >> maximum iterations=40 >> >> KSP Object: 1 MPI processes >> >> type: gmres >> >> restart=30, using Classical (unmodified) Gram-Schmidt >> Orthogonalization with no iterative refinement >> >> happy breakdown tolerance 1e-30 >> >> maximum iterations=10000, initial guess is zero >> >> tolerances: relative=1e-05, absolute=1e-50, divergence=10000. >> >> left preconditioning >> >> using PRECONDITIONED norm type for convergence test >> >> PC Object: 1 MPI processes >> >> type: none >> >> linear system matrix = precond matrix: >> >> Mat Object: 1 MPI processes >> >> type: mffd >> >> rows=300, cols=300 >> >> Matrix-free approximation: >> >> err=1.49012e-08 (relative error in function evaluation) >> >> Using wp compute h routine >> >> Does not compute normU >> >> I would like to know why the residual function can not continue to >> decline, and why the program will stop before convergence. >> I do not know much about the convergence criteria and convergence rules >> of PETSc for solving nonlinear equations. I hope I can get your help. >> I'm looking forward to your reply~ >> >> Thanks, >> Yingjie >> > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener > > https://www.cse.buffalo.edu/~knepley/ > <http://www.cse.buffalo.edu/~knepley/> >
