On Tue, Aug 9, 2016 at 9:52 AM, Jinlei Shen <[email protected]> wrote: > Hi Barry, > > Thanks for your answer. > > But logically for large problem, we are always expecting to see paralleled > program perform better with regard to both speed and memory since each of > the multi-processes independently deal with its own submatrix, especially > for iterative solver, which is revealed by CG+BJ. > I just don't understand, in the computing with CG+ASM and SUPER_LU, why > the two-process is most inefficient among these cases. If this is due to > the communication cost compared with uni-process, why the speed goes down > for triple and more processes. I'm new to parallelism, could you speculate > any possible reason for such situation? >
As Barry noted, there are two reasons that you get slowdown: 1) Worse performance of existing algorithm This comes from things like communication. This is usually a small contributor to slowdown. 2) Different parallel algorithm This is what is causing your slowdown most likely. Matt > Great thanks > > > > On Fri, Aug 5, 2016 at 10:09 PM, Barry Smith <[email protected]> wrote: > >> >> > On Aug 5, 2016, at 5:58 PM, Jinlei Shen <[email protected]> wrote: >> > >> > ​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. >> >> This is actually not surprising at all but since the mantra is >> "parallelism will always make things faster" it can confuse people. When >> run with one process the ASM and SuperLU_DIST utilize essentially >> sequential algorithms, when run with two processes they "switch" to >> parallel algorithms which simply are not as good as the essentially >> sequential algorithm that is obtained with one process hence they run >> slower. This is just life, there really isn't something one can do about it >> except to perhaps use a poorer quality algorithm on one process so that two >> processes look better but the goal of PETSc is not to make parallelism to >> look good but to provide efficient solvers (as best we can) for one and >> multiple processes. >> >> Barry >> >> >> >> >> > 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,o >> ne,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 >> > >> >> > -- 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
