​Hi, Thanks for your answers.
I just figured out the issues which are mainly due to the ill-conditioning of my matrix. I found the conditional number blows up when the beam is discretized into large number of elements. Now, I am using the 1D bar model to solve the same problem. The good news is the solution is always accurate and stable even I discretized into 10 million elements. When I run the model with both iterative solver(CG+BJACOBI/ASM) and direct solver(SUPER_LU) in parallelization, I got the following results: Mesh size: 1 million unknowns Processes 1 2 4 6 8 10 12 16 20 CG+BJ 0.36 0.22 0.15 0.12 0.11 0.1 0.096 0.097 0.099 CG+ASM 0.47 0.46 0.267 0.2 0.17 0.15 0.145 0.16 0.15 SUPER_LU_DIST 4.73 5.4 4.69 4.58 4.38 4.2 4.27 4.28 4.38 It seems the CG+BJ works correctly, i.e. time decreases fast with a few more processes and reach stable with many more cores. However, I have some concerns about CG+ASM and SUPER_LU_DIST. The time of both two methods goes up when I use two processes compared with uniprocess. The tendency is more obvious when I use larger mesh size. I especially doubt the results of SUPER_LU_DIST in parallelism since the overall expedition is very small which is not expected. The runtime option I use for ASM pc and SUPER_LU_DIST solver is shown as below: ASM preconditioner: -pc_type asm -pc_asm_type basic SUPER_LU_DIST solver: -ksp_type preonly -pc_type lu -pc_factor_mat_solver_package superlu_dist I use same mpiexec -n np ./xxxx for all solvers. Am I using them correctly? If so, is there anyway to speed up the computation further, especially for SUPER_LU_DIST? Thank you very much! Bests, Jinlei On Mon, Aug 1, 2016 at 2:10 PM, Matthew Knepley <[email protected]> wrote: > On Mon, Aug 1, 2016 at 12:52 PM, Jinlei Shen <[email protected]> wrote: > >> Hi Barry, >> >> Thanks for your reply. >> >> Firstly, as you suggested, I checked my program under valgrind. The >> results for both sequential and parallel cases showed there are no memory >> errors detected. >> >> Second, I coded a sequential program without using PETSC to generate the >> global matrix of small mesh for the same problem. I then checked the matrix >> both from petsc(sequential and parallel) and serial code, and they are same. >> The way I assembled the global matrix in parallel is first distributing >> the nodes and elements into processes, then I loop with elements on the >> calling process to put the element stiffness into the global. Since the >> nodes and elements in cantilever beam are numbered successively, the >> connectivity is simple. I didn't use any partition tools to optimize mesh. >> It's also easy to determine the preallocation d_nnz and o_nnz since each >> node only connects the left and right nodes except for beginning and end, >> the maximum nonzeros in each row is 6. The MatSetValue process is shown as >> follows: >> do iEL = idElStart, idElEnd >> g_EL = (/2*iEL-1-1,2*iEL-1,2*iEL+1-1,2*iEL+2-1/) >> call MatSetValues(SG,4,g_EL,4,g_El,SE,ADD_VALUES,ierr) >> end do >> where idElStart and idElEnd are the global number of first element and >> end element that the process owns, g_EL is the global index for DOF in >> element iEL, SE is the element stiffness which is same for all elements. >> From above assembling, most of the elements are assembled within own >> process while there are few elements crossing two processes. >> >> The BC for my problem(cantilever under end point load) is to fix the >> first two DOF, so I called the MatZeroRowsColumns to set the first two >> rows and columns into zero with diagonal equal to one, without changing the >> RHS. >> >> Now some new issues show up : >> >> I run with -ksp_monitor_true_residual and -ksp_converged_reason, the >> monitor showed two different residues, one is the residue I can >> set(preconditioned, unpreconditioned, natural), the other is called true >> residue. >> ​​ >> I initially thought the true residue is same as unpreconditioned based on >> definition. But it seems not true. Is it the norm of the residue (b-Ax) >> between computed RHS and true RHS? But, how to understand >> unprecondition residue since its definition is b-Ax as well? >> > > It is the unpreconditioned residual. You must be misinterpreting. And we > could determine exactly if you sent the output with the suggested options. > > >> Can I set the true residue as my converging criteria? >> > > Use right preconditioning. > > >> I found the accuracy of large mesh in my problem didn't necessary depend >> on the tolerance I set, either preconditioned or unpreconditioned, >> sometimes, it showed converged while the solution is not correct. But the >> true residue looks reflecting the true convergence very well, if the true >> residue is diverging, no matter what the first residue says, the results >> are bad! >> > > Yes, your preconditioner looks singular. Note that BJACOBI has an inner > solver, and by default the is GMRES/ILU(0). I think > ILU(0) is really ill-conditioned for your problem. > > >> For the preconditioner concerns, actually, I used BJACOBI before I sent >> the first email, since the JACOBI or PBJACOBI didn't even converge when the >> size was large. >> But BJACOBI also didn't perform well in the paralleliztion for large mesh >> as posed in my last email, while it's fine for small size (below 10k >> elements) >> >> Yesterday, I tried the ASM with CG using the runtime option: -pc_type >> asm -pc_asm_type basic -sub_pc_type lu (default is ilu). >> For 15k elements mesh, I am now able to get the correct answer with 1-3, >> 6 and more processes, using either -sub_pc_type lu or ilu. >> > > Yes, LU works for your subdomain solver. > > >> Based on all the results I have got, it shows the results varies a lot >> with different PC and seems ASM is better for large problem. >> > > Its not ASM so much as an LU subsolver that is better. > > >> But what is the major factor to produce such difference between different >> PCs, since it's not just the issue of computational efficiency, but also >> the accuracy. >> Also, I noticed for large mesh, the solution is unstable with small >> number of processes, for the 15k case, the solution is not correct with 4 >> and 5 processes, however, the solution becomes always correct with more >> than 6 processes. For the 50k mesh case, more processes are required to >> show the stability. >> > > Yes, partitioning is very important here. Since you do not have a good > partition, you can get these wild variations. > > Thanks, > > Matt > > >> What do you think about this? Anything wrong? >> Since the iterative solver in parallel is first computed locally(if this >> is correct), can it be possible that there are 'good' and 'bad' locals when >> dividing the global matrix, and the result from 'bad' local will >> contaminate the global results. But with more processes, such risk is >> reduced. >> >> It is highly appreciated if you could give me some instruction for above >> questions. >> >> Thank you very much. >> >> Bests, >> Jinlei >> >> >> On Fri, Jul 29, 2016 at 2:09 PM, Barry Smith <[email protected]> wrote: >> >>> >>> First run under valgrind all the cases to make sure there is not some >>> use of uninitialized data or overwriting of data. Go to >>> http://www.mcs.anl.gov/petsc follow the link to FAQ and search for >>> valgrind (the web server seems to be broken at the moment). >>> >>> Second it is possible that your code the assembles the matrices and >>> vectors is not correctly assembling it for either the sequential or >>> parallel case. Hence a different number of processes could be generating a >>> different linear system hence inconsistent results. How are you handling >>> the parallelism? How do you know the matrix generated in parallel is >>> identically to that sequentially? >>> >>> Simple preconditioners such as pbjacobi will converge slower and slower >>> with more elements. >>> >>> Note that you should run with -ksp_monitor_true_residual and >>> -ksp_converged_reason to make sure that the iterative solver is even >>> converging. By default PETSc KSP solvers do not stop with a big error >>> message if they do not converge so you need make sure they are always >>> converging. >>> >>> Barry >>> >>> >>> >>> > On Jul 29, 2016, at 11:46 AM, Jinlei Shen <[email protected]> wrote: >>> > >>> > Dear PETSC developers, >>> > >>> > Thank you for developing such a powerful tool for scientific >>> computations. >>> > >>> > I'm currently trying to run a simple cantilever beam FEM to test the >>> scalability of PETSC on multi-processors. I also want to verify whether >>> iterative solver or direct solver is more efficient for parallel large FEM >>> problem. >>> > >>> > Problem description, An Euler elementary cantilever beam with point >>> load at the end along -y direction. Each node has 2 DOF (deflection and >>> rotation)). MPIBAIJ is used with bs = 2, dnnz and onnz are determined based >>> on the connectivity. Loop with elements in each processor to assemble the >>> global matrix with same element stiffness matrix. The boundary condition is >>> set using call MatZeroRowsColumns(SG,2,g_BC,one,PETSC_NULL_OBJECT,PETSC_ >>> NULL_OBJECT,ierr); >>> > >>> > Based on what I have done, I find the computations work well, i.e the >>> results are correct compared with theoretical solution, for small mesh size >>> (small than 5000 elements) using both solvers with different numbers of >>> processes. >>> > >>> > However, there are several confusing issues when I increase the mesh >>> size to 10000 and more elements with iterative solve(CG + PCBJACOBI) >>> > >>> > 1. For 10k elements, I can get accurate solution using iterative >>> solver with uni-processor(i.e. only one process). However, when I use 2-8 >>> processes, it tells the linear solver converged with different iterations, >>> but, the results are all different for different processes and erroneous. >>> The wired thing is when I use >9 processes, the results are correct again. >>> I am really confused by this. Could you explain me why? If my >>> parallelization is not correct, why it works for small cases? And I check >>> the global matrix and RHS vector and didn't see any mallocs during the >>> process. >>> > >>> > 2. For 30k elements, if I use one process, it says: Linear solve did >>> not converge due to DIVERGED_INDEFINITE_PC. Does this commonly happen for >>> large sparse matrix? If so, is there any stable solver or pc for large >>> problem? >>> > >>> > >>> > For parallel computing using direct solver(SUPERLU_DIST + PCLU), I can >>> only get accuracy when the number of elements are below 5000. There must be >>> something wrong. The way I use the superlu_dist solver is first convert >>> MatType to AIJ, then call PCFactorSetMatSolverPackage, and change the PC to >>> PCLU. Do I miss anything else to run SUPER_LU correctly? >>> > >>> > >>> > I also use SUPER_LU and iterative solver(CG+PCBJACOBI) to solve the >>> sequential version of the same problem. The results shows that iterative >>> solver works well for <50k elements, while SUPER_LU only gets right >>> solution below 5k elements. Can I say iterative solver is better than >>> SUPER_LU for large problem? How can I improve the solver to copy with very >>> large problem, such as million by million? Another thing is it's still >>> doubtable of performance of SUPER_LU. >>> > >>> > For the inaccuracy issue, do you think it may be due to the memory? >>> However, there is no memory error showing during the execution. >>> > >>> > I really appreciate someone could resolve those puzzles above for me. >>> My goal is to replace the current SUPER_LU solver in my parallel CPFEM >>> main program with the iterative solver using PETSC. >>> > >>> > >>> > Please let me if you would like to see my code in detail. >>> > >>> > Thank you very much. >>> > >>> > Bests, >>> > Jinlei >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> >>> >> > > > -- > 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 >
