Thanks Martin ! I never considered about Debug or optimized mode before. Cmake result says I'm using Debug mode.
Some more information: The computaiton is done in deal.ii 9.4.0 oracle virtualBox, with 1 mpi process in qtcreator, and CPU is intel 10600kf. I didn't change the CMakeLists and just copy from examples, so I think by default it's debug mode. Best, Wayne 在2022年10月19日星期三 UTC+8 19:40:01<Martin Kronbichler> 写道： > Dear Wayne, > > I am a bit surprised by your numbers and find them rather high, at least > with the chosen problem sizes. I would expect the matrix-free solver to run > in less than a second for 111,000 unknowns on typical computers, not almost > 10 seconds. I need to honestly say that I do not have a good explanation at > this point. I did not write this tutorial program, but I know more or less > what should happen. Let me ask a basic question first: Did you record the > timings with release mode? The numbers would make more sense if they are > based on the debug mode. > > Best, > Martin > > > On 19.10.22 12:08, 'yy.wayne' via deal.II User Group wrote: > > Thanks for your reply Peter, > > The matrix-free run is basic same as in step-75 except I substitute coarse > grid solver. For fe_degree=6 without GMG and fe_degree in each level > decrease by 1 for pMG, the solve_system() function runtime is 24.1s. It's > decomposed to *MatrixFree MG operators construction*(1.36s), MatrixFree > MG transfers(2.73s), KLU coarse grid solver(5.7s), *setting > smoother_data and compute_inverse_diagonal for level matrices*(3.4s) CG > iteration(9.8s). > > The two bold texts cost a lot more(133s and 62s, respectively) in > matrix-based multigrid case. I noticed just as in step-16, the finest level > matrix is assembled twice(one for system_matrix and one for > mg_matrices[maxlevel]) so assembling time cost more. > > Best, > Wayne > > 在2022年10月19日星期三 UTC+8 17:10:27<peterr...@gmail.com> 写道： > >> Hi Wayne, >> >> your numbers make totally sense. Don't forget that you are running for >> high order: degree=6! The number of non-zeroes per element-stiffness matrix >> is ((degree + 1)^dim)^2 and the cost of computing the element stiffness >> matrix is even ((degree + 1)^dim)^3 if I am not mistaken (3 nested loop: i, >> j and q). Higher orders are definitely made for matrix-free algorithms! >> >> Out of curiosity: how large is the setup cost of MG in the case of the >> matrix-free run? As a comment: don't be surprised that the setup costs are >> relatively high compared to the solution process: you are probably setting >> up a new Triangulation-, DoFHander-, MatrixFree-, ... -object per level. In >> many simulations, you can reuse these objects, since you don't perform AMR >> every time step. >> >> Peter >> >> On Wednesday, 19 October 2022 at 10:38:34 UTC+2 yy.wayne wrote: >> >>> Hello everyone, >>> >>> I modified step-75 a little bit and try to test it's runtime. However >>> the result is kind of inexplainable from my point of view, especially on >>> *disproportionate >>> assemble time and solve time*. Here are some changes: >>> 1. a matrix-based version of step75 is contructed to compare with >>> matrix-free one. >>> 2. no mesh refinement and no GMG, and fe_degree is constant across all >>> cells within every cycle. Fe_degree adds one after each cycle. I make this >>> setting to compare runtime due to fe_degree. >>> 3. a direct solver on coareset grid. I think it won't affect runtime >>> since coarest grid never change >>> >>> For final cycle it has fe_degree=6 and DoFs=111,361. >>> For matrix-based method, overall runtime is 301s where setup system(84s) >>> and solve system(214s) take up most. In step-75 solve system actually did >>> both multigrid matrices assembling, smoother construction, and CG solving. >>> Runtime of this case is shown: >>> [image: matrix-based.png] >>> On each level I print time assembling level matrix. *The solve system >>> is mostly decomposed to MG matrices assembling(83.9+33.6+...=133s), >>> smoother set up(65s), coarse grid solve(6s) and CG solve(2.56).* My >>> doubt is why actual CG solve only takes 2.56 out of 301 seconds for this >>> problem? The time spent on assembling and smoother construction account too >>> much that they seems a burden. >>> >>> For matrix-free method however, runtime is much smaller without >>> assembling matrices. Besides, CG solve cost more because of more >>> computation required by matrix-free I guess. But *smoother construction >>> time reduces significantly* as well is out of my expectation. >>> [image: matrix-free.png] >>> >>> Matrix-free framework saves assembling time but it seems too efficient >>> to be real. The text in bold are my main confusion. May someone share some >>> experience on matrix-free and multigrid methods' time consumption？ >>> >>> Best, >>> Wayne >>> >>> -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+un...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/58dae75e-644e-49d8-bee2-e212c5184e1cn%40googlegroups.com > > <https://groups.google.com/d/msgid/dealii/58dae75e-644e-49d8-bee2-e212c5184e1cn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. 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